Managing understory light to maintain the coexistence of forest tree species with different shade

COMMUNAUTE FRANCAISE DE BELGIQUEACADEMIE UNIVERSITAIRE WALLONIE-EUROPE

UNIVERSITE DE LIEGE - GEMBLOUX AGRO-BIO TECH

Managing understory light to maintainthe coexistence of forest tree species

with dierent shade tolerances

Gauthier LIGOT

Essai preacutesenteacute en vue de lrsquoobtention du gradede docteur en sciences agronomiques et ingeacutenierie biologique

Promoteur Prof Philippe LEJEUNE

Gauthier LIGOT

Gauthier LIGOT (2014) Managing understory light to maintain the coexis-tence of forest tree species with dierent shade tolerances (PhD Thesis) Uni-versiteacute de Liegravege ndash Gembloux Agro-Bio Tech 112 p 24 tabl 25 g

S U M M A R Y

Similar to the management of the other environmental resources forestmanagement has been questioned and more sustainable practices of forestmanagement are being sought New close-to-nature practices aim to favornatural processes over human interventions Particularly continuous-coverforestry has the goal of relying on natural regeneration and maintainingirregular stand structure and tree species mixture However maintainingmixture of species with dierent shade tolerances appears arduous withsuch a silvicultural system Successfully managing irregular and mixedforests relying on natural processes requires a strong knowledge of theecology of natural regeneration In particular strong knowledge is requiredto predict the result of the interspecic competition in the understorydepending upon light availability The amount of radiation transmitted tothe understory is indeed a critical factor determining regeneration dynam-ics It determines at least in part regeneration composition because ofinterspecic dierences of growth and survival under shade Moreover ourquantitative understanding of understory light in uneven-aged and mixedstands remains incomplete A better quantitative understanding of under-story light is needed to provide quantitative guidelines for the managementof understory light in uneven-aged and mixed stands and hence for themanagement of natural regeneration The purpose of this thesis is to de-termine how close-to-nature forest management can maintain mixtures ofspecies with contrasting shade tolerances I consider ecological conditionswith good water and nutrient supplies In these conditions partially closedcanopy limits the amount of light that reaches the understory and light isthe major factor driving regeneration composition Consequently I studythe dynamics of natural regeneration with regards to light availability aswell as the interception of light by the canopy of heterogeneous standsStudying the regeneration ecology of two species with contrasting shadetolerances (Fagus sylvatica L and Quercus petraea (Matt) Liebl) I ndthat the shade-tolerant species outgrow the less shade-tolerant speciesin all light conditions Even though the control of understory light withcontinuous-cover silviculture is required to sustain the growth of lessshade-tolerant regenerations it might not be sucient to maintain thecoexistence of species with contrasting shade tolerances In order to exam-ine the eects of canopy structure and composition on understory lightavailability I use a model of light interception by heterogeneous canopiesafter synthesizing and discussing the approaches reported in the literatureThe model predicts satisfactorily measures of transmitted light even thoughit is a relatively simple radiative transfer model I next explore how various

silvicultural treatments can be manipulated to provide favorable understorylight conditions for natural regeneration These silvicultural strategiescorrespond to selective thinnings of ve dierent types eg harvestingpreferentially small trees large trees or trees of shade-tolerant species orcreating circular gaps The results underline that creating favorable under-story light conditions for natural regeneration can be achieved with variousregeneration treatments However the adequate reduction of stand densitydepends upon the chosen silvicultural strategies In particular creatinggaps of about 500 m2 provides adequate light for small regeneration clumpsHarvesting preferentially small and trees of shade-tolerant species are alsoappropriate but required higher harvest intensity Harvesting preferentiallylarge trees slightly increases understory light and promotes more shade-tolerant species than less shade-tolerant species In order to maintain thecoexistence of species with contrasting shade tolerances forest managermust control understory light and in some cases manually suppress the re-generation of the shade-tolerant species The outcome of this study providesforesters with the necessary tools to evaluate how silvicultural treatmentscan be manipulated to create or maintain favorable light conditions for theregeneration of species of dierent shade tolerances Guidelines are addi-tionally proposed for forest managers wanting to maintain the coexistenceof species with contrasting shade tolerances

Gauthier LIGOT (2014) Gestion de lrsquoeacuteclairement dans le sous-bois pourmaintenir la coexistence drsquoessences forestiegraveres sciaphiles et semi-heacuteliophiles(Thegravese de doctorat en anglais) Universiteacute de Liegravege ndash Gembloux Agro-BioTech 112 p 24 tabl 25 g

R Eacute S U M Eacute

Tout comme la gestion des autres ressources environnementales la gestiondes forecircts a eacuteteacute remise en question et de nouvelles pratiques dites plusdurables et plus proches de la nature sont rechercheacutees Ces derniegraveresminimisent les interventions humaines et preacutefegraverent utiliser les processusnaturels Bien souvent cela se traduit par le maintien de forecircts irreacuteguliegravereset meacutelangeacutees avec un couvert continu et en utilisant la reacutegeacuteneacuterationnaturelle Lrsquoune des principales diculteacutes est de pouvoir maintenir unmeacutelange drsquoespegraveces sciaphiles et semi-heacuteliophiles crsquoest-agrave-dire des espegravecesavec dieacuterents niveaux de toleacuterance agrave lrsquoombre Reacuteussir agrave maintenir untel meacutelange avec une gestion proche de la nature demande une bonneconnaissance de lrsquoeacutecologie de la reacutegeacuteneacuteration naturelle notamment ande pouvoir preacutedire lrsquoissue de la compeacutetition interspeacutecique en fonction dela quantiteacute de lumiegravere disponible dans le sous-bois La lumiegravere disponiblepour la reacutegeacuteneacuteration deacutetermine au moins en partie la future compositionde la reacutegeacuteneacuteration puisque les espegraveces en meacutelange ont dieacuterents niveaux detoleacuterance agrave lrsquoombre et que leur croissance et survie diegraverent en fonction de laquantiteacute de lumiegravere disponible Cependant il est dicile de preacutedire la quan-titeacute de lumiegravere disponible pour la reacutegeacuteneacuteration en peuplements irreacutegulierset meacutelangeacutes Le but de cette thegravese de doctorat est de deacuteterminer commentune gestion proche de la nature peut maintenir un meacutelange drsquoessencesforestiegraveres avec dieacuterents niveaux de toleacuterance agrave lrsquoombre Jrsquoeacutetudie cetteprobleacutematique pour des conditions eacutecologiques avec de bons apports en eauet en nutriments Dans ces conditions la lumiegravere est le facteur preacutedominantde la composition de la reacutegeacuteneacuteration car seul une fraction de la lumiegraveredisponible au-dessus de la canopeacutee est transmise jusqursquoagrave la reacutegeacuteneacuterationdans le sous-bois Jrsquoeacutetudie donc le deacuteveloppement de la reacutegeacuteneacuteration na-turelle en fonction de la lumiegravere disponible ainsi que lrsquointerception de lalumiegravere par la canopeacutee de peuplements heacuteteacuterogegravenes Lrsquoeacutetude de lrsquoeacutecologiede la reacutegeacuteneacuteration de deux espegraveces avec des niveaux de toleacuterance agrave lrsquoombrecontrasteacutes (Fagus sylvatica L et Quercus petraea (Matt) Liebl) montreque lrsquoespegravece sciaphile grandit plus vigoureusement que lrsquoespegravece semi-heacuteliophile dans toutes les conditions drsquoeacuteclairement Bien que le controcirclede la lumiegravere transmise agrave la reacutegeacuteneacuteration soit neacutecessaire pour promouvoirla croissance de la reacutegeacuteneacuteration de lrsquoespegravece semi-heacuteliophile ce controcircleest dans certains cas insusant pour maintenir la coexistence drsquoespegravecessciaphiles et semi-heacuteliophiles Dans le but drsquoexaminer la disponibiliteacute de lalumiegravere dans le sous-bois en fonction de la structure et de la compositionde forecircts irreacuteguliegraveres jrsquoutilise un modegravele drsquointerception de la lumiegravere par

la canopeacutee apregraves avoir syntheacutetiseacute et discuteacute les dieacuterentes approches demodeacutelisations proposeacutees dans la litteacuterature Ce modegravele preacutedit de maniegraveresatisfaisante les mesures de lrsquoeacuteclairement disponible dans le sous-bois bienque ce soit un modegravele relativement simple Jrsquoexplore lrsquoeet de dieacuterentesstrateacutegies sylvicoles visant agrave controcircler lrsquoeacuteclairement disponible pour lareacutegeacuteneacuteration Ces strateacutegies correspondent agrave des eacuteclaircies seacutelectives dedieacuterentes natures preacutelevant par exemple plutocirct les gros arbres les petitsarbres les arbres des espegraveces les plus toleacuterantes agrave lrsquoombre ou formant destroueacutees circulaires Les reacutesultats soulignent qursquoil est possible drsquoapportersusamment de lumiegravere pour la reacutegeacuteneacuteration drsquoespegraveces semi-heacuteliophilesavec des strateacutegies sylvicoles tregraves varieacutees Il convient neacuteanmoins drsquoajusterlrsquointensiteacute des eacuteclaircies en fonction de la strateacutegie sylvicole choisie Enparticulier lrsquoouverture de troueacutees de 500 m2 apporte susamment de lu-miegravere pour de petits groupes de reacutegeacuteneacuteration Les eacuteclaircies qui preacutelegraveventpreacutefeacuterentiellement les petits arbres et les arbres des espegraveces toleacuterantesagrave lrsquoombre permettent eacutegalement drsquoapporter susamment drsquoeacuteclairementpour la reacutegeacuteneacuteration mais demandent une intensiteacute drsquoeacuteclaircie plus forteLes coupes qui preacutelegravevent preacutefeacuterentiellement les gros arbres nrsquoaugmententque faiblement lrsquoeacuteclairement disponible pour la reacutegeacuteneacuteration et favorisentainsi la reacutegeacuteneacuteration des espegraveces toleacuterantes agrave lrsquoombre An de maintenir lacoexistence de certaines espegraveces sciaphiles et semi-heacuteliophiles le gestion-naire forestier doit controcircler lrsquoeacuteclairement disponible pour la reacutegeacuteneacuterationet dans certains cas reacuteduire manuellement la compeacutetition exerceacutee par lareacutegeacuteneacuteration des espegraveces toleacuterantes agrave lrsquoombre Cette eacutetude propose un outilpermettant de manipuler dieacuterentes strateacutegies sylvicoles pour produire desconditions drsquoeacuteclairement favorables agrave la coexistence drsquoespegraveces sciaphiles etsemi-heacuteliophiles Des recommandations sylvicoles sont en outre proposeacuteespour les gestionnaires forestiers soucieux de maintenir la coexistencedrsquoespegraveces sciaphiles et semi-heacuteliophiles

Copyright Aux termes de la loi belge du 30 juin 1994 sur le droit drsquoauteur etles droits voisins seul lrsquoauteur a le droit de reproduire partiellement ou com-plegravetement cet ouvrage de quelque faccedilon et forme que ce soit ou drsquoen autoriserla reproduction partielle ou complegravete de quelque maniegravere et sous quelqueforme que ce soit Toute photocopie ou reproduction sous autre forme estdonc faite en violation de la dite loi et des modications ulteacuterieures

No one can whistle a symphony It takes a whole orchestra to play it

HE Luccock

R E M E R C I E M E N T S

Lrsquoouvrage que vous vous apprecirctez agrave ouvrir feuilleter ou lire selon votreambition et votre courage se veut ecirctre lrsquoaboutissement drsquoune thegravese dedoctorat Mais en reacutealiteacute crsquoest bien plus que cela Crsquoest lrsquoeacutetude drsquoun sujetque jrsquoai trouveacute passionnant avec agrave la fois de reacuteelles implications pratiquespour les gestionnaires forestiers et drsquointeacuteressants questionnements scien-tiques Ce sont de nombreuses et agreacuteables journeacutees passeacutees dans deshecirctraies-checircnaies ardennaises (on peut dicilement espeacuterer mieux commelaboratoire) pour prendre des mesures varieacutees dans un vaste dispositifexpeacuterimental Ce sont de multiples voyages agrave lrsquoeacutetranger (France AllemagneSloveacutenie Canada) avec toujours un merveilleux accueil de tregraves agreacuteablesrencontres et drsquoinnombrables deacutecouvertes en tous genres Et crsquoest uneformation enrichissante qui mrsquoa permis drsquoapprofondir mes compeacutetences enprogrammation statistiques reacutedaction eacutecologie et sylviculture

Pour avoir eu la chance de vivre cette expeacuterience qui a si bien reacutepondu agrave mesattentes je remercie chaleureusement lrsquoensemble des personnes y ayantcontribueacute Bien que je sois le seul auteur de ce document il est eacutevident quesans leur aide et leurs encouragements cet ouvrage nrsquoaurait jamais pu voirle jour

Merci agrave Philippe Lejeune et Hugues Claessens de mrsquoavoir oert lesressources neacutecessaires pour lrsquoeacutelaboration de ce projet avec lrsquoappui nancierde lrsquoAccord-Cadre de recherches et de vulgarisation forestiegravere de ma boursedrsquoaspirant du Fond de la Recherche Scientique (FRS - FNRS) des boursesde voyages du Bureau International de la Jeunesse et de lrsquoUniversiteacute de Liegravegeet de la bourse drsquoexcellence du WBI Merci eacutegalement agrave Daniel Portetellepour son coup de pouce et le suivi de ces deux derniegraveres bourses Merci aussiagrave Jacques Rondeux pour mrsquoavoir initialement proposeacute ce projet Jrsquoespegravereavoir appliqueacute au mieux vos divers enseignements

Merci encore une fois agrave Philippe Lejeune et Hugues Claessens pour avoirassumeacute le rocircle de promoteur et mrsquoavoir accordeacute votre conance mecircmevis-agrave-vis de certaines de mes ideacutees parfois loufoques Avec les autres mem-bres du comiteacute de thegravese Yves Brostaux Philippe Balandier et Gilles Colinetvotre encadrement mrsquoa permis drsquoorienter mes travaux dans la bonne voie

Jrsquoai beaucoup appreacutecieacute le travail collaboratif pour la reacutedaction des dif-feacuterents articles scientiques et de vulgarisation associeacutee agrave ce projet HuguesClaessens tu auras apporteacute une touche sylvicole toujours tregraves inteacuteressante

Mon travail a ainsi gardeacute une dimension pratique pour le gestionnaireforestier qui mrsquoa particuliegraverement motiveacute Philippe Balandier tu as su mefaire proter de ta grande connaissance de lrsquoeacutecologie de la reacutegeacuteneacuteration etavec Andreacute Marquier de votre expertise pour la mesure de lrsquoeacuteclairementdans le sous-bois Sans votre aide et ce degraves le deacutebut du projet je nrsquoaurais passu eacutetudier la reacutegeacuteneacuteration en fonction de lrsquoeacuteclairement comme je lrsquoai faitles reacutesultats auraient eacuteteacute diciles agrave valoriser dans des revues scientiqueset je nrsquoaurais vraisemblablement pas pu terminer cette thegravese endeacuteans lesdeacutelais de ma bourse du FNRS Benoicirct Courbaud ton expertise pour lamodeacutelisation de lrsquointerception de la lumiegravere par la canopeacutee mrsquoa eacutegalementfait gagner beaucoup de temps Tu as rapidement embarqueacute dans monprojet de revue de la litteacuterature avec de preacutecieuses propositions pour larendre la plus inteacuteressante possible Tes relectures rapides et suggestionsont grandement ameacutelioreacute la qualiteacute des deux derniers manuscrits DanielKneeshaw outre de mrsquoavoir si bien accueilli dans ton laboratoire ton œilparticuliegraverement aiguiseacute pour mettre en avant les messages clefs drsquoun textesans srsquoencombrer de lrsquoinutile ont certainement permis la publication tregravesrapide des deux derniers articles scientiques Merci de mrsquoavoir partageacute cesavoir-faire Jrsquoespegravere signer drsquoautres futurs papiers avec toi Adeline Fay-olle merci pour ton aide lorsque je deacutebutais la reacutedaction de mes premiersreacutesultats Tu as su me montrer comment mieux structurer mes ideacutees touten me proposant la lecture de dieacuterents articles qui font maintenant partiedes principales reacutefeacuterences de cette thegravese Mathieu Jonard merci pour tesdieacuterentes remarques lors de la reacutedaction du dernier article et surtout pourles brainstormings Louvano-Gembloutois Jrsquoespegravere que de tels eacutechanges sereacutepeacuteteront Il a eacuteteacute tregraves inteacuteressant de confronter ta vision de modeacutelisationplutocirct orienteacutee sur les processus eacutecophysiologiques avec la vision gem-bloutoise de tradition plutocirct empirique Franccedilois Lehaire merci pour tonaide lors la vulgarisation de mes reacutesultats

Le travail de modeacutelisation a eacutegalement eacuteteacute particuliegraverement agreacuteable MerciFranccedilois de Coligny de mrsquoavoir initieacute au langage de programmation Java etde mrsquoavoir si bien eacutepauleacute pour impleacutementer mon modegravele dans la plateformeCapsis Il a eacuteteacute tregraves preacutecieux de pouvoir gracircce agrave toi et agrave tout le travail investidans Capsis impleacutementer mes modegraveles rapidement et sans grandes con-naissances informatiques Benoicirct Courbaud tu avais vu juste en creacuteant unelibrairie de calcul du bilan radiatif Lrsquoinvestissement consacreacute pour creacuteer unmodule de calcul geacuteneacuterique en valait vraiment la peine Merci encore agrave vousdeux ainsi qursquoagrave Mathieu Jonard Nicolas Donegraves et Philippe Balandier pourles reacuteunions et eacutechanges tregraves constructifs Crsquoeacutetait passionnant de deacutevelopperdes outils avec dieacuterentes perspectives drsquoutilisation

Le travail sur le terrain eacutetait la partie la plus ressourccedilante de ce travail Merciagrave tous les acolytes de terrain pour ces si agreacuteables journeacutees Je pense pourcommencer agrave Benoicirct Mackels et Julien Goijen pour les preacutecieuses reacuteexionsque lrsquoon a eu sur le terrain et pour votre aide pour la gestion des sorties

de terrain et de la paperasse Benoicirct Mackels tu auras eacuteteacute particuliegraverementecace pour le traitement des photographies heacutemispheacuteriques Pour mon-sieur tout le monde il est sans doute impensable de passer des journeacuteesentiegraveres agrave quatre pattes au milieu de semis parfois pleins de tiques parfoissous la pluie voire sur la neige et parfois mecircme agrave partir quatre heuresdu matin Avec lrsquoaide de toute lrsquoeacutequipe preacutesente et passeacutee vous lrsquoavez faitavec le sourire et mesureacute entre autres 5090 arbres 58 218 semis et pris817 photographies heacutemispheacuteriques Crsquoest eacutenorme Merci agrave Seacutebastien De-laitte Reacutegine Borremans Taziaux Sophie Edwin Dufays Freacutedeacuteric HenrotayCleacutemence Teugels Quentin Nachtergaele Thomas Baijot Alain MonseurAdrien Schot Ceacutedric Geerts Coralie Mengal Amauri Andreacute et FranccediloisLehaire

Les meacuterites relatifs au dispositif expeacuterimental reviennent surtout agrave Lau-rence Delahaye qui lrsquoa mis en place et agrave Matthieu Alderweireld qui lrsquoatemporairement pris en main Merci en particulier agrave ce dernier pour sontravail meacutethodique qui mrsquoa permis de prendre la relegraveve facilement et drsquoavoirtoujours pris le temps de reacutepondre agrave mes questions Tu retrouveras dans lecontexte de cette eacutetude des eacuteleacutements que tu avais deacutejagrave mentionneacutes dans tesrapports et synthegraveses Merci eacutegalement aux ingeacutenieurs de cantonnement etaux agents forestiers avec qui nous avons collaboreacute lors de lrsquoinstallation etdu suivi du dispositif expeacuterimental

Face agrave certaines diculteacutes meacutethodiques jrsquoai eacutegalement toujours pu comptersur diverses aides exteacuterieures Merci agrave Benoicirct Jourez et Ceacuteline Vaianopoulospour avoir mis agrave ma disposition votre savoir et le mateacuteriel neacutecessaire pouranalyser les cernes minuscules de semis au DEMNA Yves Brostaux et MarcMazerolle votre aide a eacuteteacute tregraves preacutecieuse pour lrsquoutilisation des modegravelesmixtes

La qualiteacute de ce document nrsquoaurait pas non plus eu son pareil sans lesreacutevisions attentives des rapporteurs Philippe Balandier et Yves Brostaux lesrelectures de Philippe Lejeune Hugues Claessens et Aitor Ameztegui ni lacorrection de lrsquoanglais eectueacutee par agrave William FJ Parsons

Lrsquoambiance au bureau eacutetait eacutegalement au top que ce soit agrave Gembloux ouagrave Montreacuteal Merci agrave tous pour vos dieacuterents conseils aviseacutes et encourage-ments les tartes agrave 10h les parties de belotte les parties drsquoeacutechec les verresen terrasse et tout le reste Gracircce agrave vous on garde toujours le sourire auboulot

Last but not least merci aux proches et amis pour votre soutien durantces cinq anneacutees Quand le travail srsquoenlise et que les reacutesultats traicircnent agravemontrer le bout de leur nez il est si preacutecieux de pouvoir se coner rireet srsquoeacutevader dans les bois sur les rochers sous terre ou en montagne ensi bonne compagnie Vous avez contribueacute agrave maintenir en moi un eacutequilibre

propice agrave la production drsquoun travail de qualiteacute

P U B L I C AT I O N S

Some ideas and gures have appeared previously in the following publica-tions

1 Alderweireld M Ligot G Latte N Claessens H 2010 Le checircneen forecirct ardennaise un atout agrave preacuteserver Forecirct Wallonne 10910-24handle 2268 79321

2 Ligot G Balandier P Fayolle A Lejeune P Claessens H 2013Height competition between Quercus petraea and Fagus sylvaticanatural regeneration in mixed and uneven-aged stands For EcolManage 304391-398 handle 2268151307

3 Ligot G Balandier P Mackels B Lehaire F Claessens H 2014Suivi scientique de vingt-sept reacutegeacuteneacuterations naturelles de checircnesessile et de hecirctre en Ardenne retour drsquoexpeacuterience Forecirct Wallonne1283-13 handle 2268151800

4 Ligot G Balandier P Courbaud B Claessens H 2014 Forestradiative transfer models which approach for which applicationCan J For Res 44385-397 handle 2268163600

5 Ligot G Balandier P Coubraud B Jonard M Kneeshaw DClaessens H 2014 Managing understory light to maintain a mixtureof species with dierent shade tolerance For Ecol Manage 327189-200 handle 2268163600

With the exception of the general introduction and the general discussion allchapters are the result of a collaborative work with the authors mentionedabove Chapter 2 is a modied translation of paper number 1 Chapter 3 isa slightly modied transcription of paper number 2 The literature reviewin Section 41 is a transcription of paper number 4 Section 42 contains el-ements of paper number 5 Chapter 5 is a slightly modied transcription ofthe same paper number 5

C O N T E N T S

1 general introduction 1

2 study area and species 721 Ecological conditions 722 Reduction of oak population 923 Why maintain oak 10

231 Biodiversity 10232 Resilience 10233 Productivity 11234 Wood quality 12235 Climate change 12

24 Forest management 13

3 regeneration height growth 1531 Methods 18

311 Study sites 18312 Regeneration height growth 19313 Understory light conditions 21314 Statistical analyses 21

32 Results 22321 Regeneration characteristics 22322 Height growth models 23323 Diuse and direct radiation 24324 Analyzing site eect 24

33 Discussion 25331 Height growth ranking 25332 Competition 27333 Direct radiation 27334 Between-site variation 28

34 Conclusion 28

4 model of light interception 3141 Literature review 32

411 Classication of FRTMs 34412 Input variables 40413 Model applications and output variables 44414 Model evaluation 46415 Model sensitivity 48416 Discussion 52

42 Implementing a radiative transfer model 57421 Crown geometry 57422 Crown radius 58

xviii contents

423 Tree Height 59424 Height to the base of the crown 59425 Crown openness and leaf area density 59426 Model evaluation 65

5 managing understory light 6951 Methods 70

511 Study sites 70512 Light model settings 71513 Cutting scenarios 71514 Statistical analyses 72

52 Results 77521 Tree inventory 77522 Cutting scenarios 77523 Simulation 77

53 Discussion 80531 Mean light response 80532 Optimum cutting scenario 83

6 general discussion 8561 Maintaining species diversity 8562 Silvicultural recommandations 8763 Study limitations and perspectives 8864 Conclusion 94

bibliography 95

L I S T O F F I G U R E S

Figure 11 Examples of mixed forests 4Figure 21 Locations of the 27 sites in the study area 8Figure 22 Soil conditions in which oaks and beech are found 9Figure 23 Frequency histogram of oaks and beech 11Figure 31 Plot layout in a site 18Figure 32 Model of the height growth of oak and beech 25Figure 41 Chart ow of forest radiative models 33Figure 42 3D plant mock-up 39Figure 43 Overview of the end-uses of FRTMs 53Figure 44 Geometric models of tree crown 58Figure 45 Measurements required to estimate LAD 63Figure 46 Predictions versus measures of PACL 67Figure 47 Cumulative distributions of predictions and mea-

sures of PACL 68Figure 51 Structure of the studied stands 73Figure 52 Simulated plot layout 74Figure 53 Mean increase of PACL by cutting type and intensity 79Figure 54 Post-harvest understory light and cutting intensity 81Figure 55 Post-harvest understory light and target basal area 82Figure 61 Post-harvest proportion of microsites favorable to

less shade-tolerant species 87Figure 62 Availability of direct radiation at varying slopes and

canopy heights 91Figure 63 Light microsites in a canopy gap 93

L I S T O F TA B L E S

Table 31 Shade tolerance of oak and beech 17Table 32 Main characteristics of the study sites 20Table 33 Main characteristics of the measured regenerations 23Table 34 Parameters of the model of regeneration growth 24Table 41 Classication of FRTM modeling approaches 36Table 42 Examples of 3D-geometric crown models 37Table 43 Reported values of leaf area density 42Table 44 Reported values of crown openness 45Table 45 Summary of the published evaluations of FRTMs 49Table 46 FRTM sensitivity to calibration parameters 51Table 47 Synthesis of FRTM advantages and drawbacks 56Table 48 Parameters of the model of crown radius 60Table 49 Parameters of the model of tree height 60Table 410 Parameters of the model of the height to the base

of the crown 61Table 411 Parameters of the power model of the height to the

base of the crown 61Table 412 Parameters of the polynomial model of LAD 64Table 51 Description of the 5 cutting types 75Table 52 Stand structure and composition in the studied sites 78Table 53 Parameters of the model of post-harvest PACL 79

A C R O N Y M S

1D One-dimensional

3D Three-dimensional

dbh Diameter at Breast Height (13 m)

DIFF Percentage of Diuse Above Canopy Light

DIR Percentage of Direct Above Canopy Light

LAD Leaf Area Density

LAI Leaf Area Index

PACL Percentage of Above Canopy Light

PAR Photosynthetically Active Radiation

PE Porous Envelope

RMSE Root Mean Square Error

TM Turbid Medium

1G E N E R A L I N T R O D U C T I O N

Come forth into the light of things Letnature be your teacher

William Wordsworth

Like the management of other environmental resources forest manage-ment has been questioned and more sustainable practices of forest man-agement are being sought The management of even-aged pure stands withclearcutting has been particularly debated because clearcuts can incur long-lasting environmental damage such as soil mass movement stream siltationwindthrow and biodiversity loss (Keenan and Kimmins 1993) The goalof new forest management practices is to be adaptive and close-to-naturewhile sustaining biodiversity and ecosystem services Forest managers mustconsider the constantly changing and growing needs of society take intoaccount climate change and evaluate of the eects of past managementstrategies Attempts are being made to reproduce the structure of old-growthforests in which trees of dierent sizes and species coexist in the hope of pre-serving ecosystem values and functions (Touzet 1996) Natural processessuch as natural regeneration are being favored over human interventionswith the aim of preserving ecosystem services and reducing managementcosts More particularly continuous-cover forestry is being favored Such sil-vicultural techniques have the goal of relying on natural regeneration whilemaintaining irregular stand structure and tree species mixture (Pommeren-ing and Murphy 2004 Bruciamacchie and de Turckheim 2005 Schuumltz et al2012)

Successfully managing irregular and mixed forests by relying upon nat-ural processes requires comprehensive knowledge of the ecology of natu-

2 general introduction

ral regeneration Continuous-cover forestry systems mimic the dynamicsof forests without anthropogenic perturbation and where large-scale dis-turbances are rare The dynamics of such forests are dominated by smallcanopy openings which originate following the death of single or multi-ple canopy trees These small-scale disturbances create a mosaic of patchesin which vegetation continuously changes through time and space Regen-eration of dierent tree species can establish within canopy openings de-pending upon the size of the openings Regeneration of late-successionalspecies can colonize small gaps that result for example from the death ofa single tree Regeneration of mid-successional species can colonize gaps ofmoderate size that originate following the death of a small cluster of treesRegeneration of early-successional species can establish in large gaps thatoriginate for example from windthrow Once the canopy of early- or mid-successional species closes understory conditions evolve in favor of mid- orlate-successional species respectively (Finegan 1984 Rameau 1999) Envi-ronmental conditions in partially shaded understories contrast with thosethat have been observed in clearcut areas Tree retention creates microcli-mates with limited light availability reduced air movement and modiedwater and nutrient cycling (Messier et al 1999) Because species responddierently to these particular conditions management of the forest canopycan be used in theory to manipulate the microclimate and hence controlunderstory development and composition (Lieers et al 1999) Understand-ing regeneration ecology is therefore a requirement for predicting ecosystemdynamics and manipulating them

The amount of radiation transmitted to the understory is a critical factordetermining regeneration dynamics wherever nutrient and water availabil-ity satises regeneration requirements Solar radiation drives plant photo-synthesis and the exchange of mass and energy between soil vegetationand the atmosphere As a consequence the quantity and the spectrum oflight that is intercepted by the regeneration greatly aects its survival andgrowth (Lieers et al 1999) as well as stem branch leaf and root morphol-ogy (Balandier et al 2006a Galen et al 2007 Niinemets 2010) In temper-ate and boreal forests that are managed with a continuous-cover forestrysystem due to radiation interception by overstory trees light availability inthe understory is often the predominant limiting resource for regenerationand consequently drives regeneration dynamics The amount of transmit-ted radiation determines at least in part regeneration composition becauseof interspecic dierences in growth and survival under shade ie interspe-cic dierences in shade tolerance Shade-intolerant species are capable ofinvading open areas while shade-tolerant species establish under a closedcanopy

Our quantitative understanding of understory light environments inuneven-aged and mixed stands remains incomplete Due to the complex-ity of multilayered and mixed canopies understory light conditions varygreatly in time and space (Pukkala et al 1991) Measuring and predictinglight is complicated under complex canopies (Lieers et al 1999) Assessing

general introduction 3

understory light requires repeated measurements and specic equipmentIn contrast to the situation in even-aged stands understory light in uneven-aged and mixed stands is poorly predicted by stand density (Lochhead andComeau 2012) Understory light also depends upon the vertical and hori-zontal distribution of gaps and biomass elements Consequently new toolsneed to be developed and validated to predict understory light availabilityand improve our understanding of the dynamics of heterogeneous forests

A better quantitative understanding of understory light is required to pro-vide guidelines for the management of understory light regimes in uneven-aged and mixed stands Forest managers indeed lack quantitative instruc-tions for controlling understory light levels with partial cutting and therebycontrol regeneration growth and survival Using continuous-cover forestrysystems partial cutting reduces the density and modies the structure of thevegetation that absorbs incoming light By maintaining a closed canopy orby opening gaps forest managers can theoretically create distinct regenera-tion niches (Grubb 1977) that promote shade-tolerant species or less shade-tolerant species respectively Even though these key principles have longbeen described important questions remain regarding their practical imple-mentation How a canopy that is favorable to the regeneration of shade-tolerant species can be distinguished from a canopy that is favorable to theregeneration of less shade-tolerant species What are the stand characteris-tics that should be considered apart from stand density to predict understorylight Close-to-nature silviculture can create microclimates that are favor-able for the coexistence of species with dierent shade tolerances but thisrequires further scientic investigation

As a matter of fact while forest managers maintain complex stand struc-ture with continuous-cover silviculture they often face diculties or evenfail to maintain some desired species mixtures (Schuumltz 1999) Problematicsituations occur mostly with mixtures of species with contrasting shadetolerances (Figure 11) Such diculties have been reported worldwide forexample with the regeneration of valuable and less shade-tolerant speciesin tree-fall gaps in African rain forests (Hall 2008 Doucet et al 2009) theregeneration of yellow birch (Betula alleghaniensis Britton) or sugar maple(Acer saccharum Marsh) after partial cutting in stands with respectivelybalsam r (Abies balsamea (L) Mill) or American beech (Fagus grandifoliaEhrh) in the province of Quebec (Canada) (Delagrange et al 2004 Preacutevostet al 2010) or the regeneration of admixed less shade-tolerant species inEuropean beech (Fagus sylvatica L) forests (von Luumlpke and Hauskeller-Bullerjahn 1999 Petriţan et al 2007 Van Couwenberghe et al 2013Petriţan et al 2014)

The purpose of this thesis is to determine how close-to-nature forest man-agement can maintain mixtures of species with contrasting shade tolerancesI consider ecological conditions in which light is presumably the major factordriving regeneration composition and hence I study the ecology of mixedregeneration with respect to light availability the interception of light by ir-

(a) oak-beech in the Belgian Ardennes (b) oak-pine in Orleanrsquos forest

(c) maple-beech in Quebec

Figure 11 Examples of mixed forests with species of contrasting shade tolerances

regular and mixed canopies and how forest management aects understorylight and regeneration dynamics

I examine the mixture of sessile oak (Quercus petraea (Matt) Liebl) andEuropean beech (Fagus sylvatica L) in the Belgian Ardennes (Chapter 2) Themixture of oak and beech is of considerable economic importance in Euro-pean temperate forests and makes an interesting ecological model for study-ing the coexistence of species with contrasting shade tolerances Indeed thetwo species are often mixed together and they have contrasting shade tol-erances Beech is a late-successional species that is very shade-tolerant Incontrast oak is a mid-successional species that is less shade-tolerant Conse-quently the mixture of oak and beech naturally evolves towards pure beechforest ie the climax forest

First I study the ecology of advance regeneration of the two species Istudy competition between these two species along a gradient of light avail-ability (Chapter 3) Because both species have contrasting shade tolerancesI expect that the shade-tolerant species dominates regeneration in low-lightenvironments while the opposite situation occurs in high-light environ-ments In low-light environments the growth of the less shade-tolerantspecies is low and the mortality risk is high (Ellenberg 1974 Pedersen1998) whereas in high-light environments the less shade-tolerant speciescan outgrow the shade-tolerant species (Huston 1979 Smith and Huston1989 Kobe et al 1995) According to this theory adequately managing un-derstory light allows regeneration composition to be controlled Howeverit hardly explains why forest managers have diculties in maintainingthe mixture of the two species In modeling competition between the twospecies I test whether there is a rank reversal between the height growth

rates of both species in high-light environments or in low-light environ-ments and I seek after the understory light conditions that are favorable forthe coexistence of both species

Second I attempt to better understand and model light interception byirregular and mixed forest canopies (Chapter 4) Measuring the amount ofradiation that is intercepted by the diverse components of a forest canopyis very tedious and time-consuming especially in heterogeneous forests (Li-eers et al 1999) Therefore I investigate how a model of light intercep-tion can advantageously replace light measurements Since several model-ing approaches have already been proposed I synthesize their advantagesand drawbacks and I identify which approaches are the most appropriateto which application Then I implement one of these approaches in a simu-lation model with the goal of exploring understory dynamics regarding thedensity structure and composition of heterogeneous canopies Once imple-mented I validate this approach with eld measurements of understory lightavailability

Third the implemented model of light interception provides an excellentopportunity for exploring how canopies can be manipulated to maintain mix-tures of species with dierent shade tolerances (Chapter 5) I use the modelto explore how modications to stand density structure and compositioncan aect understory light availability With continuous-cover forestry sys-tems sylvicultural operations mimic small-scale perturbations with group-and single-tree selection cuttings Cutting aggregated groups of trees openscanopy gaps substantially increases understory light (Coates et al 2003Beaudet et al 2011) and is often recommended for promoting the regen-eration of less shade-tolerant species (von Luumlpke 1998 Bruciamacchie andde Turckheim 2005) Yet other strategies that harvest scattered trees canalso create microsites with sucient light availability for less shade-tolerantspecies I quantify the understory light conditions following the applicationof 5 selection cutting systems and I identify how these systems can be ma-nipulated to optimize the understory area favorable for either shade-tolerantspecies or less shade-tolerant species This work yields new insights intothe interception of light by heterogeneous canopies and provides quantita-tive guidelines for maintaining mixtures of species with contrasting shadetolerances

2S T U D Y A R E A A N D S P E C I E S

Keep close to Naturersquos heart andbreak clear away once in awhile andclimb a mountain or spend a week inthe woods Wash your spirit clean

John Muir

In the Belgian Ardennes the mixture of sessile oak (Quercus petraea(Matt) Liebl) and European beech (Fagus sylvatica L) is of considerableimportance as it covers most broadleaf forests While increasing attentionis nowadays being paid to the maintainance of species diversity in forestsoak populations are decreasing in this region Oak regeneration diminisheswhereas beech regeneration invades the understory

21 ecological conditions

The Belgian Ardennes (50degN 5degE Figure 21) is an ecoregion that is char-acterized by rather homogeneous soil and climate conditions and is fairlyrepresentative of medio-European acidophilous beech forests (CORINE clas-sication 41111) For the period of 1971 to 2000 mean annual rainfall var-ied between 933 mm yearminus1 and 1357 mm yearminus1 and precipitation was welldistributed throughout the year Mean annual temperature ranges between74 C and 90 C1 Dominant soils are well drained brown acidic soils (WRB

1 These values were computed by spatial interpolation of climatic data (Tanguy Dejaegere2014 Pers Comm)

8 study area and species

Belgium

France

Luxembourg

Germany

Belgian Ardennes

0 10050 Km

Figure 21 Locations of the 27 sites in the study area

soil classication) of variable depth which have developed on Hercynianoligotrophic schist and sandstone substrates

In the Belgian Ardennes sessile oak (Quercus petraea (Matt) Liebl) andpedunculate oak (Quercus robur L) are both indigenous species that are fre-quently mixed with European beech (Fagus sylvatica L) According to theregional forest inventory that does not distinguish pedunculate oak and ses-sile oak (Lecomte et al 2003) pure and mixed stands with beech and oakscover almost three-quarters (71 ) of the broadleaf forests These stands havevaried structures ranging from secondary oak forests to late-successionalbeech forest

In the Belgian Ardennes oaks and beech have similar requirements re-garding soil conditions and most sites are suitable for both species withfew exceptions They both thrive in acidic soil conditions with good wa-ter supplies Nevertheless oak thrives better at elevations lower than 500 mabove sea level Sessile oak also thrives better than beech on dry south-facingslopes and pedunculate oak thrives better than beech in valley bottoms (wet-ter and richer soil conditions) The data that is collected by the regional for-est inventory highlights well that oaks and beech are found in similar soilconditions (Figure 22) but the abundance of oaks decreases as elevation in-creases and oaks are more abundant than beech on well-exposed slopes andvalley bottoms

For the purposes of this study 27 sites were selected in public forestswhere European beech and sessile oak grow well (Figure 21) Sites at high el-evation valley bottoms and steep-sloping sites were avoided The elevationof the sites ranged between 244 m and 514 m above sea level The averageslope was about 9 with a maximum of 36 The soil depth ranged between

22 reduction of oak population 9

15 cm and 110 cm with an average of 47 cm No pedunculate oak was foundin the sites Because of the homogeneity of the substrates and topographicpositions water and nutrient supplies were assumed to be similar amongsites The ground ora was indeed homogeneous among sites The domi-nant herbaceous species were Luzula luzuloides (Lam) Dandy amp Willm Vac-cinium myrtillus L Deschampsia exuosa (L) Trin Dryopteris carthusiana(Villar) HP Fuchs and Pteridium aquilinum (L) Kuhn

number of plotsHigh

Fagus sylvaticaQuercus sp

soil moisture

HumidAcidic Alkaline

soil pH

Acidic Alkaline

Figure 22 Soil conditions in which oaks (sessile oak and pedunculate oak) andbeech are found in the Belgian Ardennes Soil conditions were in-ferred from Ecoore indexes (Bartoli et al 2000) computed from theoristic surveys gathered by the regional forest inventory of Wallonia(2596 plots)

22 reduction of oak population

The area that is covered by oak is decreasing According to data that werecompiled by the regional forest inventory there is a shortage of oak treeswith diameters less than 60 cm which clearly indicated that oak regenera-tion has been decient (Figure 23) Several factors contribute to the decreasein oak abundance The evolution of social and economic conditions the con-trasted shade tolerances of the two species and the pressure exerted by wildgame are the main contributing factors

Until the end of the 19th century oak was preferred over beech when thestrength hardness resistance and tannins of oak wood were needed for theconstruction of ships timber-framed buildings furniture weapons plowsand for leather tanning However the evolution of social and economic con-ditions led foresters to stop investing in oak regeneration The demand foroak wood has decreased and coppicing of oak was abandoned and replacedby the planting of fast-growing species Harvests in broadleaf stands werelimited and oak stands gradually evolved from coppices with standard towell-stocked high forests (Lemaire 2001)

In the absence of natural and human perturbation oak regeneration israpidly suppressed by beech regeneration Under closed canopies beechis indeed a strong competitor and a very shade-tolerant species Beechseedlings usually establish before other less shade-tolerant species andbefore canopy opening Once light availability increases less shade-tolerantspecies start to develop but beech rapidly suppresses them This commonobservation has been reported many times since the beginning of the 20th

century (Poskin 1934) Oak the less shade-tolerant species has persistedin mixtures with beech mainly because of its longevity and through humanintervention Yet nowadays the natural succession of mixed stands that arecomposed of beech and oak toward pure beech stands is clearly observed

Finally red deer (Cervus elaphus L) and roe deer (Capreolus capreolus L)preferentially browse oak saplings over beech saplings The browsing pres-sure exerted by wild game depends mainly upon the density of game pop-ulations and environment carrying capacity In the Belgian Ardennes car-rying capacity is limited due to the acidic soils but game populations haveincreased remarkably over the last decades Wildlife pressure on regenera-tion has become dramatically important in some places ruining the eortsof forest managers to renew their stands and obliging them to fence largeareas in the hope of promoting oak regeneration (Licoppe 2005)

23 why maintain oak

231 Biodiversity

As a general rule the coexistence of several tree species promotes forestbiodiversity since dierent sets of organisms are associated with dierenttree species Moreover oak is known to have a large set of associated or-ganisms (Branquart and De Keersmaeker 2010) with some ldquocharismaticrdquospecies such as woodpeckers (Picidae) In contrast beech tends to suppressthe admixed tree species and consequently reduce ecosystem diversity

232 Resilience

Mixed stands are more resilient and recover faster than pure stands becauseof interspecic dierences in the sensitivity of individual species to bioticand abiotic stressors The risk of major degradation is therefore weaker inmixed stands than in pure stands Additionally trees seem to be less aectedby pest damage in mixed stands than in pure stands (Jactel et al 2005) Asa case in point beech stands are known to be very sensitive to wind stormsand drought Indeed beech has a supercial root system that is very sensitiveto wind storms Beech stands were among the most aected stands after thewind storm of 1999 in France (Bock et al 2005) Furthermore the strikingdecay of beech trees that is partly attributable to an outbreak of ambrosiabeetles (Trypodendron domesticum L and Trypodendron signatum FabriciusScolytidae) in the beginning of the current century in the Belgian Ardennes

23 why maintain oak 11

Quercus sp

Fagus sylvatica

Girth classes (cm)

shortage of small oak trees

Number of trees

Figure 23 The data of the regional forest inventory of Wallonia indicates a shortageof oak (Sessile oak and pedunculate oak) trees with girth of less than60 cm which underlines the deciency of oak regeneration

(Henin et al 2003) has highlighted the sensitivity of beech stands to pestsand pathogens

233 Productivity

Biomass productivity can be greater in mixed stands than in pure stands be-cause of niche complementarity and positive interspecic interactions (Hec-tor et al 1999) According to Pretzsch et al (2013a) mixtures of oak andbeech have an average biomass production that is 30 greater than that ofpure stands of oak or beech Oak and beech have contrasting strategies foraboveground and belowground resource foraging Due to the complementar-ity of their strategies the proportion of captured resources can be higher inmixed stands than in pure stands Moreover several facilitation interactionsbetween oak and beech have been reported such as greater levels of atmo-spheric deposition (Andreacute et al 2008) higher nutrient contents of leaf litter

faster litter decomposition (Jonard et al 2008) and greater mycorrhizal di-versity (Tyler 1992) Recent studies have even shown that beech trees areless sensitive to drought if they grow in mixed stands with oak (Pretzschet al 2013b Moumllder and Leuschner 2014)

234 Wood quality

Oak trees in the high forests of the Belgian Ardennes produce valuable woodfor furniture (Plak 1987 Gruselle 2002) Although the quality of oak woodin the Belgian Ardennes has a poor reputation this problem mostly has orig-inated from past management practices in oak stands (oak coppicing) Withthe exception of sites at high elevations the ecological conditions in the Bel-gian Ardennes and presumably the continuous-cover forestry managementof mixtures of oak and beech are suitable for producing wood of high qual-ity

235 Climate change

According to the last report of the IPCC (IPCC Working group I 2013) cli-mate change is unequivocal human intervention is clear and continuedgreenhouse gas emissions are likely to cause further climate change By theend of the 21st century in the Belgian Ardennes according to Laurent et al(2009) and based on IPCCrsquos scenario A1B (IPCC 2007) mean annual tem-perature is predicted to increase by about 3 C Precipitation is supposed toincrease during winter (+18 ) and decrease during summer (minus15 ) withmore severe drought episodes Even if the extent of climate change is ques-tionable scientists agree on the temperature and precipitation trends for thiscentury

Such climate changes will likely aect forest ecosystems in various waysEven though most of them are still unpredictable (eg species adaptationscommunity dynamics pest outbreaks) scientists have agreed that summerdrought will probably be one of the major drivers of ecosystem change inWestern Europe The increase in temperatures implies an increase in evapo-transpiration with an increasing demand for water resources Competitionfor water resources is likely to increase and trees will suer from periodicwater shortages depending upon site conditions and species ecology

Summer drought is already a key factor that contributes to the annual vari-ability of tree growth as has been highlighted in numerous dendrochrono-logical studies (Scharnweber et al 2011) From that perspective oak seemsbetter adapted than beech The ecological niche of oak with respect to meanannual temperatures (73 C to 13 C) extends into warmer regions more thanthat of beech (5 C to 12 C) (Piedallu et al 2009) Oak has a deeper and moreecient root system a lower vulnerability to cavitation and is less drought-sensitive than beech (Breacuteda et al 1993 Backes and Leuschner 2000 Garciacutea-Plazaola and Becerril 2000 Cavin et al 2013 Mette et al 2013)

24 forest management 13

Furthermore recent studies have shown that oak competitiveness mightincrease with climate change In France the height growth of beech hasrecently declined whereas the height growth of oak has substantially in-creased (Bontemps et al 2012) A similar trend has been observed in Cen-tral Europe (Mette et al 2013) In the latter study researchers even estimatedclimatic conditions under which oak could become more competitive thanbeech They estimated that rank reversal would occur with mean annualtemperatures of 11 C to 12 C and annual precipitation of 500 mm to 530 mm(with 230 mm during the growing period)

Therefore there is serious evidence that beech will suer from climatechange to a greater degree than oak However the decline of beech in mixedstands will probably be mitigated by positive interspecic interactionsBeech decline in the Belgian Ardennes will likely be observed later thanin surrounding areas because the Belgian Ardennes has a relatively coolerand wetter climate than the surrounding areas Nevertheless the forecasted3 C increase in mean annual temperature endangers beech trees by the endof the 21st century especially in the most xeric conditions as has alreadyobserved on south-facing slopes

24 forest management

With the gradual degradation of the market for small oak timber during the20th century broadleaf forests of the Belgian Ardennes have been managedwith continuous-cover forestry systems to convert oak coppices and oak cop-pices with standards progressively to high forests Forest managers have usu-ally maintained high forest stocking of adult trees (Lemaire 2001) therebypromoting beech regeneration Nevertheless during the last decade the out-break of ambrosia beetles and the induced beech decay (Henin et al 2003)has opened the canopy of some of these forests providing opportunities forthe regeneration of less shade-tolerant species

Currently the management of these forests aims to maintain irregular andmixed stands that rely upon the establishment of natural regeneration undera partially closed canopy Despite the diculties of maintaining the coexis-tence of beech and oak continuous-cover and close-to-nature silviculture isconsidered to better fulll the needs of todayrsquos society than the other silvi-cultural systems (Touzet 1996) because it is considered to preserve ecosys-tem values and services (multiple-use management) to oer greater man-agement exibility (de Turckheim 2006) and to reduce biotic and abiotichazards in the context of climate change (Pretzsch et al 2013a)

3C O M P E T I T I O N B E T W E E N T W O S P E C I E S W I T HC O N T R A S T I N G S H A D E T O L E R A N C E S

You will nd something more in woodsthan in books Trees and stones willteach you that which you can neverlearn from masters

Saint Bernard

The management of mixed stands with continuous-cover forestry systemshas been increasingly promoted to improve forest biodiversity resiliencysustainability and ecosystem services (Schuumltz 1997) However this ap-proach relies upon the natural regeneration (Pommerening and Murphy2004) of species that can have contrasting shade tolerances

Light availability in the understory determines competitive outcomesbetween species with dierent shade tolerances light availability can becontrolled by forest managers through adequate control of canopy closureMaintaining a closed canopy promotes regeneration of shade-tolerantspecies whereas opening canopy gaps promotes the regeneration of lessshade-tolerant species According to Kobe et al (1995) light-demandingspecies are characterized by fast growth allowing them to outcompeteneighboring trees in high-light environments whereas shade-tolerantspecies are characterized by slow growth and low mortality which allowstheir persistence in low-light environments

However these assumptions can be questioned as they hardly explain whyforest managers rarely succeed in promoting sessile oak (Quercus petraea(Matt) Liebl) regeneration beneath canopies that also contain European

16 regeneration height growth

beech (Fagus sylvatica L) in Europe (von Luumlpke and Hauskeller-Bullerjahn1999)

The regeneration of oak and beech has been intensively studied in Euro-pean forests In particular many studies have detailed the shade tolerance ofboth species (Table 31) Beech juveniles have greater abilities to survive andgrow in shade than oak juveniles They have greater morphological plastic-ity which can presumably enable them to maintain a positive carbon balancein low-light environments Oak juveniles have greater light requirementsthan beech juveniles (Collet et al 1997 Emborg 1998 Collet et al 2001Collet and Chenost 2006 Stancioiu and OrsquoHara 2006 Balandier et al 2007Petriţan et al 2007 2009 Wagner et al 2010) According to the denition ofshade tolerance that was proposed by Kobe et al (1995) and from greenhouseexperiments (Dreyer et al 2005) in high-light understories the most light-demanding species oak is expected to outgrow the shade-tolerant beech

Little information has been published concerning the in situ dynamics ofadvanced and well-established natural regeneration of the two species inmixed stands Indeed both species have mostly been studied separately atthe seedling stage and under controlled conditions Our understanding ofinterspecic competition is therefore largely inferred by extrapolating in-formation on the autoecology of the two species (Table 31) Consequentlyscientic investigation is required to better explain the diculties that arefaced by forest managers who want to maintain the coexistence of oak andbeech

Additionally modeling the growth of natural regeneration has raised twomethodological issues First it requires assessing a relevant indicator of un-derstory light conditions which depend upon the interception of diuse anddirect radiation by trees The percentage of transmitted diuse radiation hasoften been considered to represent accurately the percentage of total trans-mitted radiation (Petriţan et al 2007 2009) Nevertheless direct radiationcarries more energy than does diuse radiation but direct radiation that istransmitted under the canopy is limited in time and space (sunecks) due tocanopy irregularities and constant change of sunlight direction (Bonhomme1993) Second in situ experiments cannot control all the dierent factors thatinuence sapling growth The growth of beech and oak regeneration is ex-pected to vary from site to site due to both biotic and abiotic factors In par-ticular dierent herbaceous species are known to compete with the saplingsfor supplies of nutrients water and light (Collet and Frochot 1996 Coll et al2003 2004 Wagner et al 2010) or to produce allelochemicals (Timbal et al1990 Dolling 1996 Jaderlund et al 1996) Local variations in climate andsoil (Turbang 1954) are additional factors that could inuence regenerationdevelopment

Within this context the growth of natural oak and beech regenerationwas monitored and modeled to test that

bull The less shade-tolerant oak grows faster in high-light environmentsthan the shade-tolerant beech

Table 31 Literature review of the shade tolerance of sessile oak and European beech The columns titled beech and oak provide indications regarding the variableof interest and development stage (if specied) for beech and oak respectively

variable of interest development stage beech oak references

Transmittance at light compensationpoint

1st-year seedling very low very low Turbang (1954) Welander and Ottosson (1998) Chaar and Colin (1999)Nicolini et al (2000)

Young seedling 2ndash5 10 Madsen and Larsen (1997) Le Duc and Havill (1998) von Luumlpkeand Hauskeller-Bullerjahn (1999) Emborg et al (2000) Collet et al(2001)Collet and Chenost (2006) Petriţan et al (2007)

Transmittance at saturating growth young seedling 10 20 Dineur (1951) Emborg (1998) von Luumlpke (1998) Stancioiu and OrsquoHara(2006b)

old seedling (gt10 years) 20 30 Jarret (2004) Petriţan et al (2009)Morphological plasticity to dierentlight conditions

high low Farque et al (2001) Collet and Frochot (1996) Stancioiu and OrsquoHara(2006b) Wagner et al (2010)

Sensitivity to ground vegetation com-petition

medium low Newbold et al (1981) Collet and Frochot (1996) Coll et al (2004) Loumlfand Welander (2004) Wagner et al (2010)

bull Regeneration growth is reduced by interspecic competition betweensaplings

bull Regeneration growth responds better to the availability of diuse ra-diation than to the availability of direct radiation

bull Regeneration growth varies from site to site and this ldquosite eectrdquo iscorrelated with the local climate and soil conditions

31 methods

311 Study sites

We selected 23 sites within the study area (Figure 21 and ) The sites hadwell-established regeneration (10ndash300 cm high) that spanned a wide range ofstand structures and compositions in mixed stands of the Belgian Ardennesforests In spring 2007 regeneration areas (100ndash6500 m2) were fenced o toprotect them from browsing by wildlife Inside each fence we sampled thesaplings within 5ndash31 square plots of 4 m2 (total of 242 plots) The plots werelaid out every 4 m following a square grid (Figure 31) Inside the fences andwithin 20 m outside the fences we measured and mapped every tree with adiameter at breast height (dbh) greater than 13 cm

square grid

Figure 31 Plot layout in a site Experimental plots were laid out following North-South and West-East transects inside a 2-m tall fence

We performed a soil and humus description (Jabiol et al 1995) as well asoristic surveys (Braun-Blanquet method) in order to compute levels of thesupply of nutrients and water at every site (Bartoli et al 2000) Similarly toEllenbergrsquos method every species indicates a range of nutrient and water

31 methods 19

conditions and site values correspond to a weighted average of the indexesof found species The variation of soil richness between the sites appearedlimited with index values ranging between 08 and 2 on a scale of 0 (very acidsoils) to 6 (calcareous soil) The local variations of climate between sites werealso assessed using a regional climate model and computing approximately30 indexes of temperature precipitation and evapotranspiration (Tychon2000) They corresponded to averages standard deviations minimums andmaximums computed either per season or per year

Studied stands had complex vertical and horizontal structures and in-cluded a wide range of dbh and height classes Stand composition wasalso diverse varying from monospecic beech stands to stands almost com-pletely dominated by oak (Table 32) Other species (mainly Carpinus betulusL Betula pendula Roth Betula pubescens Ehrh Acer pseudoplatanus L andAcer pseudoplatanus L) accounted for up to 20 of stand compositionThe percentage of above canopy light measured in the understory (PACL)ranged between 1 and 61 for plots dominated by oak and between 2 and 43 for plots dominated by beech This encompassed a wide gradientranging from a close canopy to a canopy with a gap size varying up toapproximately 1200 m2 (area without overtopping crown)

312 Regeneration height growth

In this study we monitored sapling height growth between 2009 and 2011 In2009 and 2011 we measured sapling height using a telescopic meter stick tothe nearest centimeter of the 3 tallest saplings of oak and beech in each plotSaplings measured in 2009 were not tagged and therefore the saplings mea-sured in 2011 could have been dierent The mean annual height incrementin site i and plot j (iHi js ) was computed for each species s (Equation 31)

iHi js =H11i js minusH09i js

2 (31)

where H09i js and H11i js are respectively the average height of the threetallest saplings of species s in site i and plot j measured during year 2009and 2011 iHi js therefore corresponds to the annual height growth of oak orbeech saplings two years after the installation of fences

We counted the sapling in every 4 m2 plot for every species in 2007 and2012 In 2009 the sapling density was computed as the average of these twocounts

Up to ve dierent species (beech oak with mainly Carpinus betulus LBetula sp Acer pseudoplatanus L and Coryllus avellana L) were found tocoexist in the plots In order to take into account the eects of the poten-tial competition between species we identied the species dominance iewhether H11i js was the greatest for the species s in plot ij

In 2011 we selected ve representative saplings of oak and beech withineach site inside the fences but outside the 4 m2 plots to determine sapling

Table 32 Main characteristics of the study sites The number of sites and the number of plots per site (n) are given in the two rst columns Thestructure and composition of the study stands is shown by the minimum and maximum tree diameter (dbh) the average basal area and theaverage proportion of oak Regeneration is characterized by the minimum and maximum height age and total sapling density The last columncontains the minimum and maximum of the percentage of above canopy light (PACL) The table is sorted by average PACL

overstory oak saplings beech saplings all saplings light

Site n dbh basal area oak basal area height age height age density PACLcm m2 haminus1 cm year cm year mminus2

17 6 9 - 74 25 80 26 - 39 4 - 8 49 - 127 4 - 12 10 ndash 36 6 - 1022 18 12 - 78 16 74 105 - 209 7 - 12 6 ndash 13 3 - 1425 20 13 - 81 22 0 28 - 248 5 - 16 3 ndash 110 2 - 2512 10 13 - 81 22 68 16 - 171 5 - 12 39 - 220 5 - 10 12 ndash 39 5 - 2315 31 6 - 72 23 80 18 - 58 3 - 6 29 - 145 5 - 13 3 ndash 25 1 - 2619 12 8 - 84 15 0 176 - 252 9 - 14 4 ndash 52 2 - 1326 6 7 - 80 14 6 133 - 265 7 - 12 4 ndash 14 2 - 433 7 7 - 66 18 17 23 - 80 3 - 6 42 - 210 4 - 21 21 ndash 94 10 - 192 6 6 - 74 17 25 73 - 186 6 - 17 155 - 245 10 - 15 5 ndash 19 8 -23

10 9 6 - 60 23 85 123 - 249 12 - 13 10 ndash 29 10 - 2229 15 7 - 67 20 51 25 - 204 4 - 12 105 - 264 6 - 17 10 ndash 43 10 - 218 11 6 - 63 19 89 76 - 243 1 - 13 6 ndash 69 9 - 27

20 5 7 - 92 19 37 159 - 231 11 - 18 14 ndash 19 10 - 274 7 6 - 74 25 73 168 - 255 13 - 18 4 ndash 95 13 - 20

14 7 7 - 73 20 41 74 - 134 7 - 17 174 - 274 10 - 19 5 ndash 30 16 - 2224 11 6 - 55 11 93 166 - 273 10 - 15 17 - 75 10 - 3428 18 14 - 65 10 6 122 - 246 9 - 12 6 ndash 15 14 - 3223 15 6 - 77 21 58 80 - 245 7 - 13 196 - 277 7 - 11 4 ndash 28 7 - 2913 2 7 - 73 14 51 21 - 111 7 - 14 203 - 248 12 - 17 8 ndash 45 12 - 131 3 6 - 67 11 28 13 - 43 3 - 5 99 - 152 4 - 11 25 ndash 67 20 - 26

18 5 6 - 80 7 19 47 - 234 8 - 14 208 - 272 9 - 14 3 ndash 12 4 - 3511 9 7 - 68 14 91 165 - 236 11 - 17 7 ndash 13 42 -459 8 7 - 50 11 95 175 - 2403 12 - 13 3 ndash 53 14 - 61

31 methods 21

age Sapling age was determined by counting the number of bud scars andgrowth rings (Collet et al 1997) The rings were counted on stem sections ata height of 5 cm using a binocular microscope The sections were carefullysanded beforehand with sandpaper with a grit designation of up to 2000

313 Understory light conditions

To estimate light availability just above the saplings hemispherical pho-tographs were taken before sunrise during mid-summer 2010 or 2011 abovethe regeneration at the center of the plot The photographs were used tocompute three indexes of light availability for the whole growing season(from 1st April to 31st October) the percentage of total above canopy light(PACL) the percentage of diuse above canopy light (DIFF) and the percent-age of direct above canopy light (DIR) Photographs were thresholded withPiafPhotem software (Adam et al 2006) and light was calculated with GLAsoftware (Frazer et al 1999) Additional details are provided in

We validated our PACL estimates by comparing them with measuresof the Photosynthetically Active Radiation (PAR) carried out with sensors(Solem SA Palaiseau France) in ve sites during one day in July 2010 Therelationship between the estimates and the measures was highly signicant(r = 091 P lt 0001 n = 70) with a slope not signicantly dierent from 1

314 Statistical analyses

We modeled the height growth of saplings (iH ) in relation to the initialheight (H ) understory light (PACL) and species dominance (SDOM) Sim-ilarly to other studies (Pacala et al 1994 Kunstler et al 2005 Stancioiuand OrsquoHara 2006 Petriţan et al 2007 Wagner et al 2010) height growthof saplings (iH ) was modeled with a nonlinear saturated relationship withPACL which meant that growth increased at an increasing rate with PACLup to a certain point (inection point) and then saturated progressively(asymptote) We attempted to add additional explanatory variables such asregeneration age and sapling density Nevertheless adding these latter vari-ables did not improve signicantly the models () We used mixed modelsto take into account that the observed growth depended upon a randomsite factor and a set of explanatory variables (H PACL and SDOM) Sitecharacteristics were not included in the model as xed factors because wedid not sample the sites across a gradient of environmental conditions Thesites were thus considered as random repetitions of the experiment withinthe Belgian Ardennes The mixed modeling approach enabled to quantifyand explain the between-site variation Based on Akaikersquos InformationCriterion (AIC) and residual dispersal () we selected the logistic model

among others For beech (Equation 32) it was a function of both the initialheight (Hi j ) and the percentage of above canopy light (PACL) For oak theselected model (Equation 33) took additionally into account the speciesdominance (SDOM) ie whether or not oak saplings dominated saplings ofother species

iHi j = (α j + b middotradicHi j ) middot

11 + exp (1 minus PACLi j

c )+ ϵi j (32)

cSDOM)+ ϵi j (33)

α j sim dN (0θα )ϵi j sim dN (0θϵ )

We further tested whether adding the percentage of transmitted directradiation improved signicantly models containing the percentage of trans-mitted diuse radiation We replaced PACL in the model with a linear com-bination of the percentage of above direct (DIR) and diuse light (DIFF)e middotDIR+ (1ndashe ) middotDIFF The null hypothesis was that direct light would not in-uence height growth if the diuse light was already taken into account iee = 0 According to the ratio between diuse and direct radiation measuredby the meteorological institute of Belgium the mean annual proportion ofdirect radiation e equals 046 above canopy

Finally we computed the best linear unbiased estimates of the random fac-tor α (BLUPα ) and tested the Pearsonrsquos correlations between these estimatesand indexes of nutrient and water supply as well as microclimatic indexes

All of the statistical analyses were performed within the R environment(R Core Team 2013) with a signicance level of 005 Nonlinear mixed mod-els were adjusted with the nlme package (Pinheiro et al 2011) using therestricted maximum likelihood approach

32 results

321 Regeneration characteristics

Details of the studied regeneration for every site are given in Table 32 andaverage characteristics are given in Table 33 Regeneration density stronglyvaried across sites from 0 to 110 saplings mminus2 Species composition alsovaried across sites The proportion of other admixed species was large insome plots (max 98 ) but exceeded 50 in only 28 plots

32 results 23

On average beech saplings had higher initial height and height incrementthan oak saplings Harvested saplings of the two species were 11 years old inaverage but the studied regenerations were clearly uneven-aged Moreoverin plots with a mixture of beech and oak oak saplings were on average 15years younger (two-way mixed ANOVA F = 58 P lt 0001)

Negative height increment occurred (n = 18) because the three tallestmeasured saplings were not necessary the same for the two measurementsSaplings measured the rst time were not tagged Before the second mea-surement some measured saplings could have died and be no longer amongthe three tallest saplings

The Pearsonrsquos correlations between PACL and the initial height of oak andbeech saplings were respectively 0387 (P lt 0001) and 0042 (P = 0608) Atthe beginning of the study high oak regenerations were thus mostly foundin plots with higher light levels

Overtopped and overtopping oak regenerations occurred in 104 and 70plots respectively Overtopped and overtopping beech regenerations oc-curred in 120 and 29 plots respectively In half of the plots with overtoppedoak regeneration oak saplings represented the major proportion of the totalsapling count By contrast overtopped regeneration of beech involved onlya few individuals

Table 33 Main characteristics of the measured regenerations Average (minimumand maximum) sapling height height increment and age for oak beechand other species encountered in the plots The last column indicates thenumber of subplots for which the species dominates the regeneration

species n height in2009

heightincrement

age in 2009 dominantrege

cm cm year

Beech 149 153 (23277) 26 (-962) 10 (421) 120Oak 174 125 (13273) 16 (-1052) 10 (119) 70Other 93 118 (7285) 20 (-6684) 51

322 Height growth models

The modeling of height growth for the two species showed that beechsaplings grew on average faster than oak saplings whatever the light condi-tions (Figure 32) For the two species as PACL increased growth increasedfollowing a sigmoid curve and then reached a horizontal asymptote Thisasymptote increased with sapling initial height For instance in high-lightconditions the height increment of small beech saplings (Hi j = 50 cm) wasfound to be approximately 20 cm whereas the height increment of tallerbeech saplings (Hi j = 300 cm) was up to 50 cm Between saplings of oak andbeech of similar height the beech saplings had a greater height incrementthan the oak saplings

Moreover beech saplings reached their asymptotic growth at lower lightlevels than oak saplings Overtopping beeches overtopping oaks and over-topped oaks reached 90 of their asymptotic growth at respectively 12 20 and 29 of above canopy light Indeed the inection point of the mod-els denoted by parameter c in Equation 32 and Equation 33 varied signi-cantly between models (Table 34)

The good dispersal of residuals indicated no evidence of model bias How-ever residual scatterplots indicated a substantial residual variation () thatwas greater in the model for beech (θϵ = 105 cm) than for oak (θϵ = 68 cm)The between-site variation θα was about 7 cm in both models

Table 34 Parameter estimates (condence intervals with α level of 005) of the se-lected models presented in Equation 32 and Equation 33 b is the param-eters of the asymptotic height growth and c is the inection point Inthe model for oak there were two estimates for c (denoted by cSDOM inEquation 33) one for overtopping regeneration and one for overtoppedregeneration θα and θϵ are respectively the standard deviation associ-ated to the random factor (between-site variation) and the residual error(within-site variation)

species b c c θα θϵ

(overtopping) (overtopped)

Oak 2059(16422476)

6058(34688648)

10257(646914046)

7255 6759

Beech 2431(20352828)

3964(23785550)

7261 10491

323 Diuse and direct radiation

We tested whether adding the percentage of transmitted direct radiation(DIR) into a model already including the percentage of transmitted diuseradiation (DIFF) improved the prediction of height increment by replacingPACL in Equation 32 and Equation 33 with e middot DIR + (1 minus e ) middot DIFF Thenull hypothesis was accepted for beech (e = 0300 P = 0640) which meansthat DIR did not inuence signicantly the height growth of beech regener-ation At the opposite the null hypothesis was rejected for oak (e = 1001P = 0005) This indicated that the height growth of oak responded mainlyto DIR The same conclusion would have been obtained by adjusting modelsincluding only the overtopping saplings

324 Analyzing site eect

For the oak saplings the ldquosite eectrdquo estimated using BLUPα was positivelycorrelated with soil richness (r = 0562 P = 0015) and mean annual temper-ature (r = 0638 P = 0004) The site eect was negatively correlated withaltitude (r = minus0631 P = 0005) and mean annual precipitation (r = minus0689

33 discussion 25

a Initial height = 50 cm b Initial height = 150 cm

c Initial height = 300 cm

Figure 32 Model of the height growth of oak and beech saplings in mixed forestsin the Belgium Ardennes Beech showed a higher growth rate under alllight conditions The presence of taller saplings of beech reduced thegrowth of the neighboring oak saplings (overtopped oak saplings)

P = 0002) In addition altitude was inversely correlated with mean temper-ature (r = minus0522 P = 0026) but not signicantly with mean precipitation

For beech saplings the ldquosite eectrdquo was only positively correlated withsoil richness (r = 0553 P = 0001)

33 discussion

Our large in situ sampling of beech and oak regenerations enabled us toadjust mixed nonlinear models of height growth according to initial heightlight availability and species dominance (Equation 32 and Equation 33) Wefurther used the adjusted models to ascertain (i) the height growth of thetwo studied species under dierent light conditions (ii) the eects of speciesdominance (iii) the inuence of direct radiation (iv) the between-site varia-tions (v) and silvicultural implications

331 Height growth ranking

The ecological theory of forest succession postulates that under high-lightlevels light-demanding species outcompete shade-tolerant species Accord-ing to Kobe et al (1995) a high capacity to survive under low-light levels isoset by lower growth rate under high-light levels Light demanding species

would thus allocate preferentially resources to height growth and hence riskdying from light starvation (Messier et al 1999)

Our ndings indicated well that oak saplings have greater light require-ments than beech saplings We found that the beech and oak saplings neededmore than 10 and 20 of above canopy light (PACL) respectively to ex-hibit more than 90 of the maximum height growth (Figure 32) In accor-dance with previous studies (Farque et al 2001 Stancioiu and OrsquoHara 2006Petriţan et al 2007 2009) we found that under higher levels of PACL anyincrease in PACL induced little variation in height growth (asymptote) Nev-ertheless our ndings indicated that oak saplings the less shade-tolerantspecies generally exhibited a lower height increment than beech saplingseven under high-light conditions (PACL gt 20 Figure 32)

This observation is partly in contradiction with the denition of shadetolerance proposed by Kobe et al (1995) but similar observations have al-ready been reported with other species (Walters and Reich 1996 Kunstleret al 2005) It highlights the strong ability of beech to survive in deep shade(Wagner et al 2010) and lead us to infer that oak saplings have an insignif-icant chance of survival under beech saplings The lower height growth ofoak means that in mixed clumps of oak and beech oak saplings are natu-rally suppressed Nevertheless the height growth might be traded o withadaptations to low nutrient and water supply (Kobe et al 1995 Walters andReich 1996 Beaudet and Messier 1998 Collet et al 2001 Wagner et al2010) or herbaceous competition (Walters and Reich 1996 Coll et al 20032004)

In this study we focused on the variations of saplings height growth withlight availability and we admit that the response of diameter growth andmortality rate could have led to dierent conclusions Nevertheless heightgrowth has been shown to be a good proxy for sapling mortality (Kobe et al1995 Walters and Reich 1996 Kunstler et al 2005 Petriţan et al 2007)

Beech saplings were on average taller and older at the beginning of theexperiment which gave them a competitive advantage over oak saplingsDue to their shade-tolerant nature and the higher frequency of seed produc-tion by adult trees beech saplings often pre-exist in the understory beforethe canopy opening (Wagner et al 2010) They maintain large seedling pop-ulations in the understory while waiting for more suitable light conditionsConsequently beech saplings are often established before oak saplings How-ever the small age dierences between the oak and beech saplings in thisstudy are unlikely to be responsible for the dierences in height growth In-deed we found that sapling age did not appear as a signicant explanatoryvariable in height growth models This result is in agreement with the nd-ings of Collet et al (2001) and partly in agreement with those of Emborg(1998)

Growth ranking might depend upon tree ontogeny and size (Delagrangeet al 2004 Niinemets 2006 Balandier et al 2007) and availability of nu-trient and water (Kobe et al 1995 Walters and Reich 1996) Our resultsmight therefore be limited to the studied ontogenetic stage characterized by

33 discussion 27

saplings with a height of less than 300 cm and within the conditions of theBelgian Ardennes

Moreover we ensured strict protection of the studied saplings from her-bivorous browsing As deer prefer browsing oak over beech (Gill 1992) oakregeneration is more severely damaged than beech regeneration and thedominance of beech is intensied by ungulate pressure

332 Competition

Overtopping saplings of beech (and hornbeam) signicantly reduced theheight growth of overtopped oak saplings This shifted leftward the inec-tion point from 10 to 6 of above canopy light Such a reduction was ex-pected because PACL was measured above the regeneration and overtoppedspecies receive only the PACL that was not intercepted by overtopping re-generations Overtopped beeches were not signicantly aected The levelsof transmitted radiation in plots with overtopped beeches were probably toohigh (average PACL of 15 ) to model the eect of interspecic competitionon the growth of beech saplings In such conditions (PACL gt 10 ) a smalldecrease in transmitted radiation does not really aect beech growth (Ta-ble 34 and Figure 32) Moreover diameter growth may be more aectedby competition than height growth (Collet and Chenost 2006 Preacutevosto andBalandier 2007)

333 Direct radiation

We tested whether the height growth of oak and beech saplings was sen-sitive to direct radiation Our results suggested that stem elongation of oaksaplings was promoted by direct radiation in contrast with the height growthof beech saplings This result conrmed the higher light requirement of oaksaplings In addition beech growth was sensitive to light change when PACLwas less than 10 In these conditions gaps are generally very small andthe periods with transmitted direct radiation are very short (Chazdon andPearcy 1991) This stresses the importance of using total PAR radiation tomodel the growth of less shade-tolerant species Diaci (2002) and Diaci et al(2007) demonstrated the relative importance of diuse and direct radiationon regeneration success of Norway spruce beech and pedunculate oak inSlovenia In particular they reported the successful development of beechunder diuse canopy openings something that is in accordance with ourresults On the other hand sites with higher levels of direct radiation mightalso be drier (Diaci et al 2007) We studied solely the eect of light supplywhile in another study changes in light conditions were shown to inducechanges in microclimatic and soil variables (Aussenac 2000)

334 Between-site variation

In this study we showed that between-site variations was substantial (θα asymp72 cm) and in the same order of magnitude that the within-site error (θϵ =67 cm and 105 cm for oak and beech respectively) We attempted to explainthis variation with both biotic and abiotic characteristics of the sites

Soil richness was the only signicantly correlated variable for bothspecies Both species are known to require similar levels of nutrient avail-ability (Piedallu et al 2009) and the investigated range of soil richnesswas small between the sites and it was computed from a oristic surveyThese variations might hence denote complex interactions between canopycomposition canopy closure and ground vegetation

In contrast with beech saplings the height growth of oak saplings re-sponded positively to mean annual temperature and negatively to mean an-nual precipitation Oak has higher mean annual temperature requirementsand its optimum temperature is about 11 C in Western Europe (Piedalluet al 2009) Rainfall is abundant throughout the study area and should notaect negatively sapling growth in the absence of soil waterlogging How-ever abundant rainfall implies greater cloud cover and precipitation that arenegatively correlated with temperature Sites with abundant rainfall couldthen be characterized by higher cloud cover and lower temperatures whichmight negatively aect oak growth within the study area Taken togetherthese climatic considerations underlined the sub-montane trend of the cli-mate of the Ardennes that is less convenient for oak than for beech regener-ation even in high-light environments Possible additional explanations forwithin- and between-site variations may lie in genetic variation incidenceof disease canopy history unmeasured soil and microclimatic conditions

34 conclusion

We sampled in situ advanced regenerations within the whole range of con-ditions encountered in beech and oak forests managed with a continuous-cover forestry system in the Belgian Ardennes Transmittance ranged from1 to 60 under heterogeneous canopies Transmittance below 3 istypical under closed canopy (Emborg 1998) whereas after canopy releasethe level of transmittance might increase up to 15 (Collet et al 2001) 30 (Pacala et al 1994) or even beyond 60 according to our data We observedthat beech saplings naturally outgrow oak saplings Beech saplings reachedan optimum growth at 10 of above-canopy light whereas oak saplingsneeded twice as much light In addition our sapling age analysis high-lighted that beech saplings were usually established before oak saplingsAfter canopy opening these pre-existing beeches derived greater benetfrom the increase of light availability than younger and smaller oaks Inthese conditions oaks are rapidly suppressed and mixed stands of oakand beech evolve naturally toward pure beech stands The two specieshave mainly coexisted because beech naturally regenerates under well-

34 conclusion 29

established oak stands where oak has previously been favored by selectivethinning coppicing and plantations (Claessens et al 2010) The reversesituation is unlikely to occur naturally without frequent disturbances

4M O D E L O F L I G H T I N T E R C E P T I O N B YH E T E R O G E N E O U S C A N O P Y

The sun is new each day

Heraclitus

Radiation is fundamental in forest ecology Besides being the main vari-able explaining regeneration growth (Chapter 3) radiation drives plant pho-tosynthesis and exchanges of mass and energy between soil vegetation andthe atmosphere As a consequence the amount of energy and the spectrumof the radiation that is intercepted by trees have been widely studied as itgreatly aects the gross primary production of forests (Duursma and Maumlkelauml2007 Tian et al 2010) forest dynamics and competition between species(Pacala et al 1996) individual tree growth (Lieers et al 1999 Balandieret al 2007) and tree morphogenesis (Balandier et al 2006a Galen et al2007 Niinemets 2010)

Measuring the amount of radiation and photosynthetically active radia-tion (PAR) in particular which is intercepted by the diverse components ofa forest canopy is tedious and time-consuming Compared with PAR mea-surements in agricultural crops and due to the complexity of multilayeredforest canopy the spatial and temporal variability of transmitted light be-neath the forest canopy is substantial Vegetation beneath a closed canopyindeed benets from sunecks or very brief increases in transmitted irradi-ance (Messier et al 1999) Measurements must then be repeated at numerouspoints and for rather long periods of time to capture this variability More-over measuring transmitted PAR at various canopy heights is almost impos-sible without installing a crane (Mariscal et al 2004) Faced with these di-culties and given the cost of such measurements modeling radiative transfer

32 model of light interception

appears essential for supplementing eld measurements and for a greater un-derstanding of how radiation is partitioned among the components of forestecosystems

To explore how light regimes under complex canopies can be manipulatedwith silvicultural practices that could maintain the coexistence of specieswith contrasting shade tolerances (Chapter 5) the modeling approaches thathave been proposed in the literature are rstly synthesized and discussed(Section 41) Second one of these approaches was implemented to exploreunderstory light conditions regarding forest structure and composition inuneven-aged mixed stands (Section 42)

41 literature review

Solar radiation and the attenuation of light through plant canopy were rstmodeled with physical laws by analogy of the Beerrsquos law in homogeneousmedium Consequently they were rstly limited to homogeneous crops butwere rapidly adapted to forest ecosystems using more complex laws Thegeneral functioning of these latter models have already been presented inseveral literature reviews (Sinoquet et al 1993 Brunner 1998 Lieers et al1999) and have changed little since then Briey they share a common struc-ture that can be divided into three submodels (Figure 41) Firstly most mod-els start by computing above canopy light both in magnitude and angulardistribution using standard astronomical laws (ldquoabove canopy light modelrdquo)Secondly the interception of light through the canopy (ldquoradiative transfermodelrdquo) is computed It depends mainly upon the geometric structure of thecanopy and the mathematical formulation used to describe the fractions oflight that are intercepted absorbed and transmitted by canopy componentsThirdly a light reection model can optionally be used (ldquoscattering modelrdquo)to describe more precisely complex light trajectories within the canopy

Even though most forest radiative transfer models (FRTMs) share a com-mon general framework they have special features that rely on dierent as-sumptions and they are used to predict dierent output variables aggregatedor not in time and space according to the objectives of the model The costsof specic eld measurements to calibrate the model the increasing interestin complex forests composed of trees of dierent species and sizes and thevariety of study purposes have indeed stimulated modelers to adapt FRTMsto their needs Most of these adaptations concerned the radiative transfermodel one of the submodels depicted in Figure 41 which is the main topicof this review For example contrasted approaches have been used to modelthe distribution of foliage within the canopy Some authors have used verydetailed three-dimensional (3D) mock-ups of the canopy which require in-tensive eld measurements whereas others describe the canopy as a singlehorizontal layer The improvements brought to above canopy light modelsare very limited as only two standard algorithms (uniform overcast sky orstandard overcast sky) have been used among all o the papers that we re-viewed Moreover the use of one of them does not really aect model perfor-

41 literature review 33

Output variables

- Understory irradiance- Understory transmittance- Energy absorbed by trees

Forest radiative models

Above canopy light modelHow much light is available above canopyHow is it distributed between ray directions

Radiative transfer modelHow is light attenuated through the canopy How is the canopy geometry described

Scattering modelHow is light reflected by canopy components

Input variables

- Calibration parameters- StandTree measurements- Tree mapping

Figure 41 Chart ow of forest radiative models indicating the three submodels

mance (Brunner 1998) ie model ability to predict the measurements witha low level of error and bias Similarly the improvements brought to the scat-tering model aect model performance less than the improvements broughtto FRTMs Scattering depends upon the optical properties of leaves woodand soil and the considered radiation wavelength Radiation scattering isespecially low in PAR and in ultraviolet radiation (400ndash700 nm) (Sinoquetet al 1993 Parker 1997) The reectivity of a green leaf is approximately02 and this value is even lower for an entire crown because of multiplescattering (Brunner 1998 Landsberg and Sands 2010) Moreover scatter-ing models require large numbers of parameters (Kuusk 1993) and muchcomputation time (Ross 1981 Rey et al 2008) Consequently the use of ascattering model has often been neglected in forestry assuming that leavesand ground behave like black bodies within the PAR waveband (ie show-ing no transmittance and no reectance) (Sinoquet et al 1993) even thoughit might improve the precision of the prediction of transmitted irradiance(Mariscal et al 2004)

Given the variety of applications and newly developed modeling ap-proaches of FRTMs it would be of great help for modelers to know whichapproach enables them to predict the variable of their interest with a givenprecision a low bias and accepted calibration eorts Moreover havinginsight of the expected precision and bias associated with a modeling ap-proach is also precious information in assessing whether it would fulll thestudy objectives Similarly knowing beforehand to which parameters themodels are most sensitive and the order of magnitude of parameter valuescan speed up and improve the calibration work This would allow for eortto be invested in estimating precisely the sensitive parameters and usingsimplication assumptions for the less sensitive parameters

Unfortunately as far as forests are concerned the performance analysesand the sensitivity analysis of dierent modeling approaches have been re-ported separately and for very restricted sets of canopy conditions and studyobjectives The information is therefore scattered and no general guidelinehas been formulated to help forest modelers to choose which modeling ap-proach suits best his needs

We synthesized both the performance analyzes and the sensitivity anal-yses of radiation transfer models through forest canopies After classifyingthese approaches we attempted to quantify the expected uncertainty and ap-praise the calibration eorts associated with most combinations of modelingapproaches and model applications We provided order of magnitude esti-mates for the main calibration parameters and attempted to report how sen-sitive models are to these parameters Finally we attempted to identify themodeling approaches that best suit to the dierent applications of FRTMs

411 Classication of FRTMs

We identied four families of FRTMs that combine three approaches to de-scribe the geometry of forest canopy and two approaches to compute the

proportion of incident radiation intercepted by the canopy (Table 41) Be-low we briey describe and discuss each of these approaches details canbe found in previous articles (Sinoquet et al 1993 Cescatti 1997a Brunner1998 Lieers et al 1999)

4111 Canopy geometry

one-dimensional canopy The simplest approach for modeling thegeometry of a forest canopy is to assimilate it to a single horizontal layer ofvegetation without individualizing crowns or trees (one-dimensional (1D)model) Due to its simplicity this approach is particularly appropriate mod-eling a homogeneous canopy such as the one of pure even-aged stands Thisapproach is more challenging with heterogeneous stands as additional as-sumptions and parameters are required (Duursma and Maumlkelauml 2007 Kimet al 2011) to oset the simplicity of the canopy description

The model developed by Kim et al (2011) illustrates well this approachThis model requires calibrating for each species three extinction coecients(corresponding to the distribution of inclination angles of leaves branchesand stems) the one-sided area of leaves branches and stems the horizon-tal crown projection and tree density Some of these parameters might alsodepend upon ray directions (ie ray zenith angle and ray azimuthal angle)Furthermore the model assumes that branches and stems are randomly dis-tributed whereas the distribution of leaves depends upon a clumping fac-tor Simpler approaches with fewer variables and empirical parameters havebeen developed For instance Duursma and Maumlkelauml (2007) used a 1D modelwith four variables (leaf area crown surface area number of trees and ex-tinction coecient) and one empirical parameter

Another solution to modeling the distribution of leaves consist of subdi-viding the canopy into several homogeneous regions eg horizontal lay-ers on the condition that the vertical structure of the stand can be approx-imated Such as multilayer models can then predict understory light at dif-ferent canopy heights

Moreover due to the main hypothesis of considering continuous layer(s)of vegetation with the same properties for the whole forest stand we did notexpect the 1D model to predict accurately the spatial variation of irradiancebeneath the canopy The 1D model is rather utilized to predict the temporalvariation of irradiance (Kim et al 2011 Govind et al 2013)

3d crown models Alternatively 3D crown models (see 3D-TM and 3D-PE in Table 41) assimilate forest stands into a set of spatialized geometricshapes representing tree crowns and optionally trunks Many dierent geo-metric shapes have been used (Table 42) The simplest are quadratic surfacessuch as cylinder cone ellipsoid or paraboloid Such shapes have the advan-tages of requiring few parameters and allowing analytical computation ofthe interceptions between light rays and crowns In contrast nonquadraticshapes (eg combinations of degenerated surfaces) t well to real crowns butrequire numerous parameters and more complex numerical computations

Table 41 Classication of FRTM modeling approaches

frtm family abbreviation canopy transmittance main objectives

1D model 1D Stand canopy is composed of one or several hor-izontal layers

Turbid medium Ecophysiological processes at stand level

3D crown model with tur-bid medium

3D-TM Tree crowns are composed of one or a set of ge-ometric shapes

Turbid medium Forest growth and yield Dynamics of standstructure

3D crown model withporous envelope

3D-PE Tree crowns are composed of one or a set of ge-ometric shapes

Porous envelope Forest growth and yield Dynamics of standstructure

3D surface model 3D-S Trees are composed of surfaces representing theleaves branches and stems

Porous envelope or radia-tive transfer theory

Tree architecture ecophysiological processes attree level

Note FRTM forest radiative transfer model 1D one-dimensional 3D three-dimensional

Table 42 Examples of 3D-geometric crown models used in FRTMs Most authors used relatively simple quadratic shapes whereas few tested more complicatedshapes

qadratic shapes combination of qadratic shapes combination of nonqadratic shapes

No of parameters 3 ge 4 8-18References Pukkala et al (1993) Canham et al (1994) Koop

and Sterck (1994) Bartelink (1998b) Stadt and Li-eers (2000) Pinno et al (2001) Beaudet et al(2002) Courbaud et al (2003) Mariscal et al (2004)Beaudet et al (2011) Paquette et al (2008)

Gersonde et al (2004) Cescatti (1997a) Brunner (1998) Piboule (2001)Groot (2004) Piboule et al (2005) Da Silva et al(2011)

Many renements to 3D crown models have been described in the lit-erature and have been notably reviewed by Brunner (1998) For examplecrowns can be divided into dierent sections characterized by dierent leafdensities A combination of several shapes can be used to distinguish an illu-minated surface (eg upper half ellipsoid) from a shaded surface Similarlya special foliage envelope can be constructed within a crown for examplewith branches that have developed during the last 5 years Missing parame-ters are often estimated using allometric relationships to diameter at breastheight (Da Silva et al 2011) or relationships to species shade tolerance (Can-ham et al 1999 Beaudet et al 2011) Algorithms of crown reconstructionaccording to neighbor competition are also available (Piboule et al 2005)

In brief the recent improvements brought to 3D crown models attemptedto model crown geometry as realistically as possible taking into accountthat trees often lean and crown shapes often deviate from simple geometricforms Hence they required adjusting a greater set of parameters and someof them can hardly be measured in the eld and must be estimated withadditional models

Moreover on one hand the 3D crown model requires determining the po-sition and crown dimensions of every tree whereas the 1D model requiresonly estimating stand features On the other hand measuring crown dimen-sions is easier and more commonly performed than estimating foliage aggre-gation within the stand canopy Additionally taking explicitly into accountstand heterogeneity 3D crown models can predict the spatial variability oftransmitted light

3d surface models 3D surface models (3D-S) represent leavesbranches and stems as realistically as possible with surfaces or shells Thisleads to very detailed 3D mock-ups (Figure 42) with components that areusually assimilated into opaque envelopes (Section 4112) Due to thenumber of input parameters for these models they are used to representsingle trees (Sinoquet et al 2001) orchard trees (Da Silva et al 2008) oragroforestry systems (Dauzat and Eroy 1997 Leroy et al 2009) ratherthan entire forest stands Homogeneous forest stands could be obtained byreplicating one or a few model trees (Figure 42) but it seems unlikely to beable to gather all the necessary information to model every single tree ofone heterogeneous stand Hence we believe that the use of 3D-S models inforestry is nowadays limited to applications involving tree architecture andecophysiological processes

4112 Radiation attenuation

turbid medium The rst approach to computing the fraction of trans-mitted light through the canopy (τ ) consists of using an analogy to Beerrsquoslaw Beerrsquos law describes the attenuation of a monochromatic ray within aturbid medium ie a medium made up of small elements randomly scat-tered and presenting a homogeneous transparency (Brunner 1998) Canopyis assimilated to such a turbid medium and τ is computed as a function of

Figure 42 3D plant mock-up Lateral view of a digitalized scene with six 3- to 4-year-old beech seedlings (in grey) scattered every 50 cm from each othertogether with a systematic network of raspberry (in black) (Balandieret al 2009)

the density and the spatial distribution of canopy elements such as leavesand branches (Sinoquet et al 1993 Lieers et al 1999) The turbid mediumanalogy can be applied to an entire stand canopy a horizontal layer withina stand canopy a crown envelope or even a section of a crown This ap-proach relies on the assumption that canopies have the properties of sucha homogeneous medium Nevertheless stand canopies or tree crowns aremade up of various size elements often aggregated within crowns and ver-tices Therefore several correction coecients have been developed to adaptBeerrsquos law to forest canopies Briey the probability of beam interception(1 minus τ ) by canopy elements is a function of the canopy element density (leafarea density LAD (m2 mminus3) the path length of a ray through the canopy(l ) the extinction coecient (k) and the clumping factor (Ω) k and Ω de-pend upon canopy element inclination and spatial distribution respectively(Equation 41) Ω describes the aggregative pattern of branches and leaveswithin the canopy Many dierent mathematical expressions have been usedto adapt the Beerrsquos law models to 1D and 3D models but all somehow includethese three parameters Equation 41 is commonly used to compute τ for aray of zenith angle η and azimuthal angle γ with 3D crown models

τ (ηγ ) = exp(minusk middot Ω middot LAD middot l (ηγ )) (41)

The advantage of the turbid medium approach lies mainly in its mech-anistic formulation and the use of the leaf area because leaf area is a keyvariable in forest ecology (eg used to model photosynthesis and transpira-tion) However this approach often requires empirical estimation of k andΩ and leaf area measurements that remain both dicult to obtain and im-precise (Breda 2003) Moreover this is the only approach that applies if thecanopy geometry is described with a 1D model

porous envelope The second approach called porous envelope as-sumes that crowns or parts of crown are envelopes with one empirically

estimated parameter namely the crown openness (p Equation 42) which isthe probability of a ray being intercepted by the foliage This approach as-sumes that leaves do not transmit or reect light (like black bodies) Thisassumption can be more easily veried for coniferous species with darkfoliage than for broadleaved species with lighter foliage (Williams 1991)Therefore some authors have adjusted Equation 42 for the dierent radia-tion wavelength ranges (Goudriaan 1977) The variable p is independent ofray direction and path length (l ) (Canham et al 1994 Groot 2004 Da Silvaet al 2008 Boivin et al 2011) and is also dened as the fraction of sky visiblethrough a crown (Canham et al 1999)

τ (ηγ ) = p (42)

In comparison with the previous approach this one is less mechanistic butrequires fewer parameters (usually one per species) and is therefore easierto calibrate On the other hand this approach describes the attenuation ofradiation through crowns and not through stand canopy Therefore it cannotbe utilized with a 1D model

Other simplications of these submodels have also been proposed For ex-ample Koop and Sterck (1994) used an opaque crown model (p = 0) Otherauthors have simplied the turbid medium submodel by removing l Ω andLAD from Equation 41 In this way they obtained a ldquohit modelrdquo with a for-mulation (Equation 43) very close to Equation 42 with one empirical pa-rameter k which they called the extinction coecient (Canham et al 1994Koop and Sterck 1994 Boivin et al 2011)

τ (ηγ ) = exp (minusk ) (43)

412 Input variables

Dierent input data and calibration parameters are required depending uponthe chosen modeling approach These parameters are measured estimatedor adjusted by model inversion Below we give an overview of model re-quirements in terms of input data and summarize their denitions and esti-mation methods

4121 Stand and tree measurements

Among all FRTM inputs stand and tree measurements probably require themost workforce and consequently represent one of the major cost in utilizingFRTM As far as stand and tree measurements are concerned 1D modelsobviously require less eld data than 3D models and hence require lesseld work 1D models depend mainly upon foliage density and distribution(see Section 4122 Section 4123 and Section 4124) which does not requirecarrying out intensive tree inventory In most cases measuring stand densityis enough However 3D models often rely on an intensive inventory and

mapping of every tree within a plot For 3D crown models at least threeparameters are generally needed for each tree height crown base heightand crown radius (Table 42) Additional measurements such as crown radiimeasured in dierent directions height of maximum crown extension andshape coecients might be required to construct more complex shapes For3D surface models a geometric description of leaves branches and stemscan be obtained by vectorization (Fournier et al 1996) digitalization (Mouliaand Sinoquet 1993) or simulations of plant morphology (Leroy et al 2009)

4122 Density of canopy elements

The stand leaf area index (LAI m2 mminus2) is the total one-sided foliage areaper unit of soil surface LAI is the primary descriptor of plant canopy anda key variable in studying plant physiological processes (eg photosynthe-sis transpiration) In the eld stand LAI is directly assessed with litterfalltraps or vertical line intercept sampling coupled with measures of leaf incli-nation LAI can also be estimated indirectly with optical methods mainlyusing hemispherical photographs or LAI-2000 devices (LI-COR BiosciencesLincoln Nebraska USA) (Jonckheere et al 2004 Weiss et al 2004) Theselast two methods measure the gap fraction (ie the fraction of sky visiblefrom the measuring point) and use the turbid medium analogy to infer leafarea Optical approaches therefore rely on the same assumptions and param-eters as Equation 41 Moreover such methods give estimates of the eectiveLAI which includes the area of branches and trunks (Jonckheere et al 2004)Additionally reference values and allometric relationships are available inthe literature for the most common species

Measurements of leaf area for individual trees are very dicult to repli-cate for every tree in a stand even though individual values of leaf areaare necessary with 3D-TM Therefore tree leaf area is often estimated foreach species by the inversion of a turbid medium model (Courbaud et al2003) or by measuring leaf area density (LAD m2 mminus3) on a sample of trees(Stadt and Lieers 2000) Nevertheless as indicated by Nock et al (2008) in-tracrown leaf area decreases with tree age by up to 40 It might thereforebe preferred to use allometric relationships with for example tree diame-ter (Bartelink 1998a Gersonde et al 2004) tree height (Essery et al 2008)sapwood area (Gersonde et al 2004) or tapering equations (Kim et al 2011)

Moreover LAI is often used with a 1D model whereas LAD is usuallypreferred with 3D crown models LAD corresponds to the one-sided leaf areadivided by the canopy element modeled volume (Gersonde et al 2004) Thereported values of LAD used with 3D-TM models range from 03 m2 mminus3 to6 m2 mminus3 (Table 43) This variation is therefore substantial even for the samespecies This encourages improving and harmonizing the methods used toestimate LAD

Some simplications used to estimate foliage density might appear roughto some readers but they reect well the diculty of measuring it due totree size and heterogeneity its measure in forests is much more challengingthan in crops or orchards

Table 43 Reported values of leaf area density (LAD m2 mminus2) used in 3D crownmodels with the turbid medium analogy (3D-TM)

species lad references

not specied 186 Kuuluvainen and Pukkala (1991)

softwoodPinus ponderosa 003-036 Law et al (2001)Tsuga heterophylla 038 Mariscal et al (2004)Pseudotsuga menziesii 038 096 274

600Webb and Ungs (1993) Brunner (1998)Gersonde et al (2004) Mariscal et al(2004)

Picea abies 040 Courbaud et al (2003)Pinus contorta 139 Stadt and Lieers (2000)Picea glauca 180-188 Stadt and Lieers (2000)Abies balsamea 198 Stadt and Lieers (2000)not specied 200 Sprugel et al (2009)Pinus ponderosa 201 Gersonde et al (2004)Pinus lambertiana 256 Gersonde et al (2004)Abies concolor 336 Gersonde et al (2004)Calocedrus sp 451 Gersonde et al (2004)

hardwoodPopulus balsamifera 030 Stadt and Lieers (2000)Populus tremuloides 044 Stadt and Lieers (2000)Fagus sylvatica 066 Piboule (2001)not specied 050-100 Sprugel et al (2009)Betula pendula 079 Piboule (2001)Betula papyrifera 080 Stadt and Lieers (2000)Quercus kelloggii 132 Gersonde et al (2004)

4123 Extinction coecients

The extinction coecient k is a parameter of Equation 41 and is thereforeused whenever the radiation attenuation submodel corresponds to the turbidmedium approach It is usually a species-specic constant but it can alsobe computed as a function (the ldquoG-functionrdquo) which depends mainly uponthe orientation and inclination of leaves as well as on the ray zenith angle(η) The parameter k has been estimated by measuring leaf inclination andprojected leaf areas (Campbell and Norman 1998 Kim et al 2011) computedwith theoretical functions of leaf distribution (Govind et al 2013) or deducedfrom the relationship between transmittance and LAI measured at dierentcanopy heights (Landsberg and Sands 2010)

With 3D crown models most authors assume that leaf inclination followsa theoretical distribution that is either spherical withk = 05 (Cescatti 1997aBrunner 1998 Piboule 2001 Courbaud et al 2003) or ellipsoidal (Stadt and

Lieers 2000) With 1D models authors have sometimes preferred usingempirical estimates of k ranging between 02 and 06 (Jarvis and Leverenz1983 Pierce and Running 1988 Bartelink 1998b Aubin et al 2000)

4124 Clumping factors

The assumption of the random spatial distribution of canopy elements israrely satised (Sinoquet et al 2005 Da Silva et al 2008) especially with 1Dmodels because the spatial distribution of trees but also of canopy elementswithin trees is rarely completely random Moreover leaves are gatheredaround branches and branches are grouped around stems and sometimesgrouped in vertices Whenever the spatial distribution of canopy elementsis not known or approximated (eg stand map tree architecture) a clump-ing factor Ω is required in Equation 41 Indeed a canopy with regularlyspaced elements (Ω gt 1) transmits less light than a canopy with randomlyscattered elements (Ω = 1) By contrast a canopy with aggregated elementstransmits much more light (Ω lt 1) (Niinemets 2010)

There is a lack of reference values for the clumping factor and this mea-surement is therefore often estimated by model inversion Like the extinc-tion coecient the clumping factor is rarely measured because measuringit for adult trees is very labor intensive Consequently it is often assumedto be constant With 1D models Chen et al (1999) used values of the clump-ing factor of 05 and 07 for softwoods and hardwoods respectively Thesevalues were computed by measuring the canopy gap size distribution (Chenet al 1997) Kim et al (2011) estimated the clumping factor by harvestingpine shoots They observed that the clumping factor varied between 02 (up-per part of the canopy) and 09 (lower part of the canopy) while other stud-ies reported values for long-needled species ranging between 04 and 09(Theacutereacutezien et al 2007) In addition some studies have demonstrated a vari-ation in the clumping factor with stand density crown diameter and rayzenith angle (Wang and Jarvis 1990 Govind et al 2013) Because tree aggre-gation is already taken into account with 3D crown models the clumpingfactor in these models is usually assumed to be 1

4125 Crown openness

Crown openness (p) can be assessed by photographing isolated crowns (Can-ham et al 1994 1999 Beaudet and Messier 2002 Astrup and Larson 2006Paquette et al 2008 Beaudet et al 2011 Da Silva et al 2011) or by modelinversion (Groot 2004) Photographs can be taken using either sh-eye lens(Canham et al 1994 1999 Beaudet and Messier 2002 Astrup and Larson2006 Beaudet et al 2011) or classic lens (Da Silva et al 2011) In compar-ison with sh-eye lenses classic lenses allow smaller isolated parts of thecrown to be photographed Therefore the use of a classic lens makes it eas-ier to obtain a correct exposure even when sky conditions are not overcastSubject crowns need to be isolated with no overlapping neighboring crownsPhotographs are processed to compute the proportion of sky pixels (ie the

crown openness) Boivin et al (2011) presented an algorithm that identiesthe crown extent and argued that crown delimitation has a strong inuenceon porosity estimates Canham et al (1994) observed no variation in p withzenith angle and tree dimensions However Astrup and Larson (2006) ob-served that p varied to a limited extent in spruce stands with tree diameterand by regions Similar to the estimates of LAD standard methods are re-quired to uniformly estimate p taking into account the variability amongspecies and individuals

Crown openness (p) and LAD are two related parameters Indeed Da Silvaet al (2011) bridged the two approaches proposing a method to computek middot LAD from p The two approaches of modeling light attenuation throughcanopy namely the turbid medium and porous envelope approaches cantherefore be calibrated with eld measurements of p Even though it appliedonly to isolated trees the measurement of p is more convenient and lesslaborious than the measurement of LAD Moreover the reported variabilityof p seems lower than that of LAD with values ranging from 003 to 029 andan average around 01 (Table 44)

413 Model applications and output variables

Because FRTMs are most often used to model forest ecosystem function-ing they are usually coupled with many other models describing for exam-ple photosynthesis transpiration tree growth timber production carbonsequestration nutrient uptake or hydrological balance The applications ofFRTMs are therefore numerous but they can be seen for the sake of simplic-ity as either ecophysiological applications or stand-dynamics applications

ecophysiological applications Ecophysiological studies usesFRTMs coupled mainly with process-based models that embody our currentknowledge of the functioning of forest ecosystem Such holistic modelsinclude for instance equations describing the uxes of carbon water andenergy between soil vegetation and atmosphere (Govind et al 2013) Suchstudies aim at improving our understanding of forest ecosystem function-ing exploring forest productivity as a function of resource availability orat exploring how variation of forest structure and composition can aectecosystem functioning and dynamics Forest productivity standing forestbiomass nutrient uptake or hydrological balance as examples can thenbe predicted for particular environmental conditions and for forecastedmodications of these Within this context FRTMs are necessary to predictthe irradiance (W mminus2) and (or) the spectrum of the intercepted radiation atvarious scales from a global scale to a leaf scale

stand-dynamics applications The second group of studies pref-erentially uses empirical models They bring less concerns on ecosystemfunctioning and focus rather on the dendrometric data of interest for for-est managers They aim mainly at predicting the natural evolution of stand

Table 44 Reported values of crown openness used with 3D crown models (3D-PE)

species crown openness references

softwoodAbies alba 0034 Da Silva et al (2011)Abies amabilis 0060 Canham et al (1999)Tsuga heterophylla 0080 Canham et al (1999)Pinus sylvestris 0065 - 0110 Da Silva et al (2011)Abies lasiocarpa 0090 Canham et al (1999)Thuja plicata 0090 Canham et al (1999)Picea glauca 0109 0110 0130 Canham et al (1999) Astrup and Larson

(2006) Beaudet et al (2011)Abies balsamea 0111 Beaudet et al (2011)Pinus banksiana 0124 Beaudet et al (2011)Pinus contorta 0135 Canham et al (1999)Thuja occidentalis 0144 Beaudet et al (2011)Picea mariana 0070 - 0290 Groot (2004)

hardwoodFagus sylvatica 0048 Da Silva et al (2011)Fagus grandifolia 0050 Beaudet et al (2002)Malus sylvestris 0052 Da Silva et al (2011)Quercus petraea 0043 - 0073 Da Silva et al (2011)Betula papyrifera 0058 Canham et al (1999)Populus tremula 0082 Da Silva et al (2011)Sorbus torminalis 0049 - 0120 Da Silva et al (2011)Betula alleghaniensis 0097 (Beaudet et al 2002)Betula papyrifera 0101 Beaudet et al (2011)Acer saccharum 0108 Beaudet et al (2002)Populus balsamifera 0140 Canham et al (1999)Populus tremuloides 0163 0183 Astrup and Larson (2006) Beaudet et al

(2011)Betula alleghaniensis 0206 Canham et al (1999)Populus hybrid 0300 Paquette et al (2008)

structure and composition and (or) predicting the eect of overstory man-agement on understory light conditions (Courbaud et al 2001 Beaudet et al2002 Sprugel et al 2009 Beaudet et al 2011) Also their objective is the bestpossible prediction of forest growth and the outcome of intra and inter spe-cic competition Such models can more precisely predict forest dynamicsbut contrary to process-based models their uses are more strictly limited tothe conditions from where they were derived On the other hand using em-pirical models of tree growth allows focusing on light availability withoutcalibrating and programming all of the physiological processes in relationto tree growth This simplication has often been justied whenever lightcan be considered as the rst limiting factor of vegetation growth (eg treeregeneration under closed canopy) Within this context FRTMs are neededto predict tree irradiance ie the amount of energy absorbed by trees (Cour-baud et al 2003) the proportion of radiation transmitted (transmittance) tothe regeneration (Pacala et al 1996 Lieers et al 1999 Beaudet et al 2002Sprugel et al 2009 Beaudet et al 2011) the amount of light available forunderstory biodiversity (Balandier et al 2006a Barbier et al 2008) or thevertical gradient of transmittance within the canopy (Gersonde et al 2004Mariscal et al 2004) They are used mostly at plot or stand scales (from100 m2 to 1 ha) with a simulated period of at least 1 year

414 Model evaluation

Most authors evaluate their model by comparing estimates and measure-ments of irradiance or transmittance taking into account either total inci-dent light or only the incident diuse light (eg indirect site factor) Lightmeasurements are performed usually with hemispherical photographs andless frequently with light sensors Hemispherical photography is an indirectmethod with an associated level of error that can occasionally be substan-tial Moreover this approach uses a radiative model to assess irradiance andtransmittance Using hemispherical photography to evaluate FRTMs there-fore leads to a comparative evaluation of one radiative model with anotherIn addition FRTMs have been evaluated for their performance in predictingirradiance or transmittance at the ground level above the understory veg-etation or occasionally at dierent heights within a tree canopy (Mariscalet al 2004 Kim et al 2011) In the present study we compiled published in-formation on the performance of dierent models ie their ability to predictthe measurements with low levels of error and bias We considered all pub-lished light models that were used to predict radiative transfer through for-est canopies and for which the performance was evaluated In Table 45 wesummarized the reported performance of these models Unfortunately au-thors have used dierent approaches to assess model performance makingcomparison dicult They often adjusted linear models between estimatesand observations and hence assessed model precision using the coecientof determination (R2) or the root mean square error (RMSE) Model bias wasusually examined graphically but some authors have used the coecients of

the linear regression between measurements and estimates Moreover evensimilar indicators (eg R2) could not be compared without caution Whilemost authors compared estimates and measurements carried out at dierentperiods (Kim et al 2011 Govind et al 2013) or at dierent positions withinplots others compared average estimates and measurements between sitesof areas ranging from 900 m2 to 1600 m2 (Stadt and Lieers 2000) or the av-erage gap prole (Mariscal et al 2004) In addition others compared the sta-tistical distribution of transmittance estimates and measurements (Da Silvaet al 2011) Finally the numbers of plots and sites were also far from con-stant among model evaluations

Most authors found good agreement between measurements and esti-mates when averaged at the stand scale (Stadt and Lieers 2000 Mariscalet al 2004) In other words most models predicted transmitted light poorlyat a particular location (at sensor scale) beneath the canopy but ratherwell at the stand scale After a good calibration the relationship betweenmeasurements and predictions was found to be generally close to a 11relationship and hence without unacceptable bias in the point-to-pointcomparison Nevertheless large deviations were often observed betweenestimates and measurements of transmittance (often up to 20 of abovecanopy light) even for low-light levels Many authors argued that point-to-point variations beneath the forest canopy are rarely predicted withaccuracy because minor errors in tree position and crown dimensions canlead to dramatic changes in simulations of transmittance (Fournier et al1996 Groot 2004 Mariscal et al 2004 Da Silva et al 2011) On the otherhand site averages were better predicted (Stadt and Lieers 2000 Pinnoet al 2001 Mariscal et al 2004 Da Silva et al 2011) Similarly modelperformance increased with the length of the simulated period (eg 1 yearversus 1 hour) especially when direct radiation were taken into account(Brunner 1998 Groot 2004)

All of the dierent modeling approaches were reported to perform wellbut few authors compared the dierent approaches Kim et al (2011) foundthat their 1D model performed as well as 3D crown models when they tookinto account the aggregation of trees leaves and branches with appropri-ate clumping factors Similarly Balandier et al (2009) obtained very similarresults with a 1D model and a 3D surface model in a mixed understory of Eu-ropean beech (Fagus sylvatica L) and European red raspberry (Rubus idaeusL) (Figure 42) 3D-TM (eg MIXLIGHT) and 3D-PE (eg SORTIE-ND) ap-peared to exhibit a very similar performance although Canham et al (1994)found that a hit model (ie 3D-PE with p = 0) performed better than a 3D-TM These authors interpreted this result as an eect of foliage scatteringat the crown periphery especially for shade intolerant species Boivin et al(2011) used a 3D-PE model and obtained good results in plantations of hy-brid poplars with p = 0 whereas in the same study this parameter valueprovided the worst results in young boreal mixedwoods

Nevertheless we noted that the relative performance depended uponthe modeled description of canopy geometry (Table 45) The highest levels

of model performance were obtained with very detailed 3D-TM models(Cescatti 1997b Brunner 1998) These models used asymmetric crownsdescribed by a combination of nonquadratic shapes and modeled the radia-tive transfer using a turbid medium approach with k = 05 and Ω = 1 Inaddition Brunner (1998) restricted the foliage to shells within the crown butacknowledged that simplication of his canopy model would have alteredthe results only slightly Moreover he restricted his sample to a singleeven-aged coniferous stand with a large gradient of transmittance whichmade model calibration and validation easier The model of Cescatti (1997b)diered from the model developed by Brunner (1998) in its inclusion of analgorithm for scattering processes

Additionally model performance appears to be related to forest structure(Table 45) Model performance decreases from even-aged young stands tomultilayered and mixed mature stands This observation is well supportedby pairs of publications in which the same model has been applied to dier-ent forest structures For instance the model FOREST was shown to provideexcellent results in an 80-year-old spruce stand in Finland (Cescatti 1997b)whereas it provided only moderate results in a multilayered forest of pon-derosa pine in Oregon (Law et al 2001) Similarly using the model tRAYciBrunner (1998) successfully predicted the spatial distribution of the trans-mittance under a 20-year-old stand of Douglas r whereas Gersonde et al(2004) obtained a lower model performance under a mixed conifer forestMIXLIGHT successfully predicted point-to-point variation in transmittanceunder aspen-dominated stands aged from 1 to 30 years (Pinno et al 2001)but it was less successful in predicting the average values of transmittancein various even-aged boreal stands aged from 69 to 159 years (Stadt and Li-eers 2000) Finally Boivin et al (2011) observed the same trend betweenyoung boreal forests and hybrid poplar plantations and Koop and Sterck(1994) found that including measurement points located close to small treesreduced the R2 from 94 to 77

415 Model sensitivity

We attempted to identify which model parameter was reported to havestrong eect on FRTM performance As many studies actually lack a com-mon referenced method we classied the studied parameters into threequalitative levels according to their impact on FRTM predictions highmedium and low This classication was based mainly on the discussion bythe respective authors as part of their studies For example given the resultsof Gersonde et al (2004) LAD and crown radius were classied respectivelyin the low and high categories Indeed these authors observed that replacingindividual LAD with a species average did not reduce the model t On theother hand in the same study the same simplication applied to the crownradius reduced very signicantly model t (R2 was reduced from about 75 to 65 ) Next we counted the number of publications of each combinationof parameter and sensitivity level (Table 46) Unfortunately not all of the

Table 45 Summary of the published evaluations of FRTMs Models are classied by canopy model and typeof forest stand forest structure R2 with an symbol means that the validation was performed withpredictions and measurements averaged for each sites rather than by point-to-point comparisons

plantation even-aged pure stand uneven-aged or mixed stands

1d canopyno model nameGovind et al (2013)R2 = 093RMSE = 30 minus 70 micromol mminus2 sminus1

no model nameKim et al (2011)RMSE = 006 minus 135 micromol mminus2 sminus1

4C-A-RTMBertin et al (2011)good relationship (R2 = 092) withseedling growth

MIXLIGHT MIXLIGHT SORTIEPinno et al (2001) Stadt and Lieers (2000) Canham et al (1999)R2 = 092 R2 = 074 R2 = 086

3d crown with qadratic shapesSORTIE-ND SORTIE-ND SILVI-STARPaquette et al (2008) Boivin et al (2011) Koop and Sterck (1994)R2 = 092 R2 = 052 R2 = 077 ndash 094

SORTIE-ND SAMSARABoivin et al (2011) Courbaud et al (2003)R2 = 046 - 092 RMSE = 52

OLTREE amp SolTranMariscal et al (2004)R2 = 094

MAESTRO tRAYciWang and Jarvis (1990) Gersonde et al (2004)RMSE = 10 R2 = 080

TASStRAYci CORONABrunner (1998) Groot (2004)R2 = 097 R2 = 088

3d crown with nonqadratic shapestRAYci MmicroSLIMPiboule (2001) Da Silva et al (2011)RMSE = 2 ldquoin the range of model using

similar scales of descriptionrdquo

FOREST FORESTCescatti (1997b) Law et al (2001)R2 = 097 R2 = 062

3d surfaces of leaves branches and stemsAmapSim no model nameLeroy et al (2009) Fournier et al (1996)no statistical dierence in 34 sites RMSE asymp 10 ndash 15

RATPSinoquet et al (2001)RMSE = 60 minus 120 micromol mminus2 sminus1

parameters had been tested in similar conditions or with the same model asfar as forest stands are considered We therefore recognize that our analysisis incomplete but underlines well the common trends between dierentstudies

As a general rule we found that models appeared more sensitive to theparameters describing between-crown gaps than to those describing within-crown gaps or within-crown architecture In most studies a larger amountof light was transmitted between rather than through the crowns Indeedas shown by the estimates of crown openness in Table 44 only 5 to 30 of incident light passes through the crown The parameters describing thebetween-crown gap geometry were therefore of primary importance justi-fying the use of a hit model (3D-PE with p = 0) for certain types of standsNevertheless we found that authors often noted that FRTMs were more sen-sitive to other parameters such as tree clumping or leaf area in dense stands(Wang and Jarvis 1990 Boivin et al 2011)

Stand density and stand edges are not model calibration parameters butthey greatly aect transmitted light estimates (Bartelink 1998b Piboule2001) Moreover it is even possible that stand density modies model sen-sitivity to the inner-crown parameters In dense and homogeneous standsmost rays were found to intercept crowns whereas in low-density standsthe majority of transmitted radiation comes from canopy gaps Models arethus found to be less sensitive to inner-crown parameters with low-densitystands

4151 1D model

The main source of variability of 1D models was found in the areas coveredby crowns (Duursma and Maumlkelauml 2007) and leaves (Duursma and Maumlkelauml2007 Bertin et al 2011 Kim et al 2011) These parameters appeared tobe highly inuential in all the sensitivity analyses that studied their eectsThese estimates were further corrected with clumping factors that took intoaccount the aggregation of stems branches and (or) leaves The clumpingfactor or the spatial structure of trees or crowns therefore played an impor-tant role in the corresponding studies However model sensitivity to theseparameters decreased with stand density stand LAI and leaf inclination (Kimet al 2011)

Parameters of crown architecture played a secondary role Only a fewstudies reported that changes in values of branch area foliage inclinationand vertical distribution of leaves aected notably 1D model predictionsSimilarly crown shape and modeling stem interception had only a minoreect on model prediction

4152 3D crown model

3D crown models appeared highly sensitive to the crown radius in all of thesensitivity analyses that studied the inuence of this parameter (Canhamet al 1994 Cescatti 1997b Brunner 1998 Stadt and Lieers 2000 Piboule2001 Beaudet et al 2002) It even appeared that estimating the crown ra-dius using allometric relationships instead of measuring this parameter inthe eld individually for each tree signicantly decreased model precision

Table 46 FRTM sensitivity to calibration parameters For each parameter we counted the number of publications (n) analyzing its eect on modelpredictions According to the authorsrsquo conclusion we classied their results into three categories low medium or high impact The scorecorresponds to (high + 05 middot medium)n

parameter n low medium high score references

3d crown modelcrown radius 7 7 1 Beaudet and Messier (2002) Brunner (1998) Gersonde et al (2004) Piboule

(2001) Cescatti (1997b) Da Silva et al (2011) Stadt and Lieers (2000)crown shape 2 2 1 Brunner (1998) Piboule (2001)stand density 2 2 1 Bartelink (1998b) Essery et al (2008)stand edge 1 1 1 Piboule (2001)understory vegetation 1 1 1 Beaudet and Messier (2002)tree height 2 1 1 08 Beaudet and Messier (2002) Gersonde et al (2004)crown length 3 2 1 07 Piboule (2001) Stadt and Lieers (2000) Gersonde et al (2004)crown openness 2 1 1 05 Beaudet and Messier (2002) Boivin et al (2011)LAD 5 2 2 1 04 Bartelink (1998b) Brunner (1998) Gersonde et al (2004) Piboule (2001) Stadt

and Lieers (2000)foliage clustering within crowns 2 1 1 03 Bartelink (1998b) Cescatti (1997b)trunk interception 2 1 1 025 Brunner (1998) Fournier et al (1996)crown max-width height 1 1 0 Piboule (2001)foliage clustering around shoots 1 1 0 Bartelink (1998b)foliage inclination 1 1 0 Stadt and Lieers (2000)foliage as a sub-shell of crown 1 1 0 Gersonde et al (2004) Cescatti (1997b)

1d canopy modelleaf distribution 1 1 0 Wang and Jarvis (1990)crown surface 1 1 1 Duursma and Maumlkelauml (2007)leaf area 3 3 1 Kim et al (2011) Bertin et al (2011) Duursma and Maumlkelauml (2007)tree clumping 3 1 2 08 Kim et al (2011) Bertin et al (2011) Duursma and Maumlkelauml (2007)branch area 2 2 05 Kim et al (2011) Bertin et al (2011)foliage inclination 1 1 05 Kim et al (2011)vertical distribution of leaves 1 1 05 Kim et al (2011)stem area 2 1 1 03 Kim et al (2011) Bertin et al (2011)crown shape 1 1 0 Duursma and Maumlkelauml (2007)

(Piboule 2001 Da Silva et al 2011) Indeed crown dimensions largely de-pend upon neighboring competition and tree history which are two eectsusually not included in allometric relationships and that should be takeninto account (Piboule 2005)

Crown shape tree height and height to crown base seemed to have lessinuence (Brunner 1998 Da Silva et al 2011) FRTMs appeared highly sen-sitive to these parameters in less than 50 of the sensitivity analyses Forinstance Brunner (1998) tested two representations of crowns (with conesor asymmetric ellipsoids) and concluded that the two models gave similarresults Similarly the height of maximum crown extension is needed to de-ne the most complicated crown shapes and using such complex shape ledto only minor improvements (Piboule 2001)

The density of leaves and branches within crowns (expressed by LAD andcrown openness) moderately aected the estimates of transmitted light be-neath the forest canopy (Bartelink 1998b Brunner 1998 Lieers et al 1999Stadt and Lieers 2000) Interestingly reasonable changes in LAD aectedmodel predictions markedly in only one of the ve corresponding sensitivityanalyses (Bartelink 1998b Brunner 1998) It is worth noting that good esti-mates of LAD (3D-TM) or crown openness (3D-PE) require the correct delim-itation of crown volume Errors in computing the crown volume would leadto for example errors in calculating total leaf area Similarly LAD clump-ing factors and extinction coecients are strongly correlated (Equation 41Bartelink (1998b)) This nding therefore justies using xed values of LADper species

Foliage distribution clustering and inclination were studied to a slightlylesser extent but these parameters appeared to have a small eect on 3Dcrown model predictions (Wang and Jarvis 1990 Cescatti 1997b Bartelink1998b Stadt and Lieers 2000 Gersonde et al 2004) Foliage distributionlikely depends upon species For instance Cescatti (1997b) reported evidenceof the aggregation of spruce needles around vertices Nevertheless the in-uence of this aggregation on FRTM predictions appeared weak (Cescatti1997b Bartelink 1998b) probably because 3D models are used mostly forstands with rather open canopy where gaps between crowns are more im-portant than gaps within crowns Similarly modeling trunk interception wasreported without signicant eects in the two sensitivity analyses studyingthis parameter (Fournier et al 1996 Brunner 1998) With 3D crown modelusing the default values of k = 05 and Ω = 1 appeared therefore a reason-able simplication

416 Discussion

This review illustrates and provides an overview of the variety of approachesused to represent a forest canopy and to estimate radiation intercepted by

CanEweEmapEandEinventoryEeveryEtreeIsEtheEmodeledEstandEheterogeneous

TurbidEmediumLADEk Ω

PorousEenvelopep

SimulationsEoftheEforestEdynamicsE

EcologicalEstudiesEofforestEecosystemE

processes

3DEcrownEmodelHeightEcrownEbaseEheightcrownEradius

1DEmodelΩECrownEsurfaceETreeEdensity

Applications

Radiative transfer

Canopy geometry

DoEweEpreferEusingEtheELADEratherEthanEp

Figure 43 Overview of FRTMs according to their end-uses Most FRTMs includedin stand-dynamics models are 3D crown models whereas most FRTMsused for ecophysiological studies are 1D models LAD leaf area densityk extinction coecient Ω clumping factor p crown openness 1D onedimensional 3D three-dimensional

the canopy elements (Figure 43) Even though more thoroughgoing conclu-sions could likely have been formulated with benchmarking of a wide setof FRTMs using a common data set with dierent stand structures we wereable to highlight the specicity of forest canopy in comparison with manyagricultural crops and consequences in terms of modeling The recent stud-ies that we reviewed enabled us to quantify model uncertainty to identifysensitive parameters and to recommend the modeling approaches that bestsuit the dierent FRTM applications

4161 Model uncertainty

1D models accurately predict the temporal variations of irradiance (RMSEranged roughly between 30 micromol mminus2 sminus1 and 120 micromol mminus2 sminus1) within ho-mogeneous stands (Kim et al 2011 Govind et al 2013) The vertical gra-dient of transmitted light beneath the canopy can be predicted reasonablywell with multilayer models (Landsberg and Sands 2010) but the spatialvariation in irradiance in the understory is not predicted by 1D models

3D crown models accurately predict averaged measures of transmittedlight in a forest plot The prediction of transmittance at a particular location

beneath the canopy is clearly less accurate with errors often up to 20 oftransmittance (Cescatti 1997b Brunner 1998 Stadt and Lieers 2000) 3Dcrown models are capable of capturing a certain spatial variability of trans-mitted light but not with a resolution as precise as the one using light sensorsWithin forest dynamics models small errors in the spatial distribution of un-derstory light should be considered as being of minor importance comparedwith for example the prediction of the cumulated area of microsites favor-able to regeneration growth ie receiving an irradiance within the rangecorresponding to the needs of a given species

Moreover model uncertainty increases with the complexity of the canopyTransmittance beneath young plantation is better predicted than beneathuneven-aged and mixed stands Transmitted light under homogeneouscanopy is usually well predicted with every modeling approach On thecontrary transmitted light under heterogeneous canopy is supposed to behardly predicted with 1D models 3D crown model appeared so far the bestsolution to model the radiative transfer through such complex canopies

Model uncertainty also decreases with increasing length of the simulatedperiod especially if direct radiation is taken into account As already pointedout for forest productivity models (Landsberg and Sands 2010) predictingtransmitted radiation for a brief period (eg 30 minutes) requires very ac-curate radiation and canopy measurements Accurate monthly and yearlyaveraged predictions are however more easily obtained (Essery et al 2008Landsberg and Sands 2010) probably because of errors compensation

We found no clear evidence regarding the advantage of using the turbidmedium approach (3D-TM) versus the porous envelope approach (3D-PE)Both methods provided satisfactory results Besides if the crown opennessvaries with crown dimensions both method are somehow related becausek middot LAD can be deduced fromp (Da Silva et al 2011) If LAD andp are speciesconstant then for every tree independent of their size the porous envelopeapproach aects transmittance to every crown in the same way whereasit depends upon crown size and beam orientation with the turbid mediumapproach In this latter case model performance of both approaches likelydiers with the variability of crown dimensions

4162 Sensitive input parameters

Calibration eorts must focus primarily in the description of between-crown gaps or crown radius which are the most sensitive parameters ofFRTMs This result is perhaps not intuitive but probably reects that theforest canopy consist of deep crowns with dense foliage Therefore crownsintercept a large amount of light whatever their specic features As a resultthe proportion of transmitted light that is not intercepted by tree crownsie transmitted through gaps between crowns is fundamental

With 1D models the key calibration parameters are the crown surface and(or) the LAI which might further be corrected with extinction and clump-ing factors On the other hand 3D models require overall an accurate treemap and individual measurements of the crown radius especially in order

to characterize heterogeneous canopies Crown shape appeared of lesser im-portance than crown radius and we did not nd that it was worth usingcomplex crown shapes Furthermore standard values of the extinction coe-cient and clumping factors (k = 05 and Ω = 1 respectively) were often usedwith 3D crown model and frequently gave a good approximation Therefore3D models appear better suited for long simulation periods than 1D modelbecause 3D model usually do not imply predicting changes of extinction andclumping factors

4163 Applications

We identied the advantages and drawbacks of the FRTM modeling ap-proaches which allowed us to identify the approaches that best suit todierent potential applications of FRTM (Table 47) Overall the potentialapplications depend mainly upon how the canopy is modeled

1D models predict well the irradiance of canopy with a low number ofinput data and parameters They are sensitive to the parameters describingfoliage density and distribution (k and Ω respectively) They are ideally cou-pled with process-based of photosynthesis rate in order to explore forestproductivity carbon uptake or nutrient cycling at the stand or greater scaleThey are however limited to stands with one or two species and a relativelyhomogeneous (even-aged) structure Moreover the simulated forest shouldhave a stable structure or the simulated time period should be limited be-cause the calibration parameter depends strongly upon stand structure andcomposition In most cases 1D models hardly predict light conditions af-ter silvicultural operations such as partial harvests Silvicultural operationsoften modify not only stand height and density but also foliage featuresand distribution because some categories of trees are preferentially cut orbecause gaps are created Through time tree growth self-thinning and self-pruning additionally modify the spatial distribution of foliage In particularas trees become mature foliage tends to accumulate in fewer and biggercrowns Next as several regeneration cohorts develop foliage becomes ag-gregated in crowns of varied dimensions

3D crown models (3D-TM and 3D-PE) are better used in studies focusingon timber production and stand dynamics because in many cases those pro-cesses are generally not explicitly related to photosynthesis transpirationor nutrient cycling They accommodate to heterogeneous stand structureThey include explicitly stand spatial structure which enables studying theimpact of forest structure (eg testing dierent silvicultural scenarios) onforest production and yield This is an interesting feature with the generalincreasing interest devoted to uneven-aged shelterwood or close-to-naturesilviculture in many countries Moreover single tree based models such as3D crown models oer the best opportunity to analyze forest managementstrategies (Porte and Bartelink 2002) Indeed partial harvest modies the av-erage dimensions of trees and stand spatial structure The increase in trans-mitted light is therefore complex and does not depend only upon changesof stand density 3D crown models are sensitive to canopy spatial structure

Table 47 Synthesis of model advantages and drawbacks with suggested scale of uses forest structures and examples of applications

model scale of uses forest structure advantages disadvantages applications

1D model from stand to globalfrom hours to one year

even-aged stand withone or two species

low number of eld dataeasy to couple to stand leveldata and models (canopy gastransfers canopy cover LeafArea Index)

model parameters (foliagedistribution) are hardlymeasured in the eld lackof knowledge to model ad-equately changes of foliagedistribution parametersthrough time and afterthinning do not take ex-plicitly into account spatialstructure

net primary production car-bon uptake nutrient cyclingphotosynthesis rate

3D-M or 3D-PE from plot to standyears

even-aged or unven-aged stand pure andmixed stand

translate directly changes ofstand structure (tree densityspecies sizes spatial distribu-tion) into changes of canopyallow the calculation of ra-diation interception by eachtree allow the calculationof maps of irradiance undercanopy

require information on treelocation (obtained eitherfrom eld measures orfrom theoretical distribu-tions) require informationon crown characteristics(obtained either from eldmeasures or from allometricrelationships)

timber production un-derstory growth forestdynamics

3D-S from leaf to tree fromhours to years

isolated tree agro-forestry systemhomogeneous stand

allow the most precise mod-eling of radiation intercep-tion can be coupled to plantstructure-function models

require information onplant architecture (eithermeasured or modeled) highcomputing complexity limit-ing the number of simulatedtrees

tree physiology tree mor-phogenesis tree architecture

42 implementing a radiative transfer model 57

and hence require precise mapping and crown measuring Currently thecost of these measurements limits the size of the modeled stand but the useof airborne technologies is promising (Essery et al 2008)

3D surface models require acquiring large amounts of eld data to repro-duce tree architecture but they enable studying light capture at plant organto tree levels (Rey et al 2008) Whenever trees can realistically be duplicatedin a forest model 3D surface models oer good opportunity for studyingthe eects of tree architecture on tree physiological processes Future tech-nologies such as terrestrial LiDAR can also help in acquiring the eld datarequired to build 3D surface models for more complex stands

42 implementing a radiative transfer model

Exploring how forest managers can manipulate understory light requiresa model that is capable of predicting light interception by heterogeneouscanopies especially in uneven-aged forests that are composed of severalbroadleaved species and that takes directly into account the structure anddensity of the simulated stands According to our literature review the mostecient strategy for achieving this goal consists in utilizing a 3D crownmodel Crowns are best modeled with combinations of quadratic shapes toreproduce accurately the variability of crown dimensions and to computeanalytically (ie faster than with numerical computations) the interceptionof radiation by crowns The turbid medium approach is preferred over theporous envelope approach where we have hypothesized that this approachmight better predict how much radiation is intercepted by crowns of varioussizes

Such a model is implemented in the forest simulation platform Capsis(Dufour-Kowalski et al 2012) in a library named SamsaraLight The full de-scription of the functioning of this library is beyond the scope of this thesisA rst version of SamsaraLight was described by Courbaud et al (2003) andfurther documentation can be found on the Capsis website (Ligot et al 2013)

Hereafter I introduce how a heterogeneous canopy was modeled ie the3D reconstruction of a stand canopy with models of crown geometry (Sec-tion 421) crown dimensions (Section 422 Section 423 and Section 424)and how foliage features were characterized (Section 425) Models of crowndimensions and foliage density were adjusted with the data that were gath-ered in the 27 studied sites (Chapter 2) Next I report on an evaluation ofmodel predictions (Section 426)

421 Crown geometry

We modeled crown geometry with one or several sections of asymmetric el-lipsoids (Figure 44) The choice of one of these options depends mainly uponthe tree measurements that are available For example in the next chapterwe opted to model crowns with single asymmetric ellipsoids because we didnot measure the height to the largest crown cross-section or the 4 crownradii of every tree

The crown geometry is dened by 4 crown radii which are measuredalong the cardinal directions together with tree height and height to the baseof the crown These measurements enable us to compute the parameters ofthe equation of an ellipsoid or sections of an ellipsoid (Equation 44)

(x minus x0)2

(y minus y0)2

(z minus z0)2

c= 1 (44)

where (x0 y0 z0) are the coordinates of the ellipsoid center and a b andc are the semi-axes that are respectively oriented from West to East Southto North and from bottom to top

Furthermore to estimate missing measurements of crown dimensions andto develop an algorithm describing the evolution of crown dimensions weadjusted a set of allometric relationships for the six groups of species thatwere used in our simulation program In we additionally introduce howthe height to the largest crown extension can be estimated to dene crownshapes with upper and lower sections of dierent length (dierent cup andcdown in Figure 44)

(a) 1 ellipsoid

(b) 2 sections of ellipsoid

aeastawest

bnorth

bsouth

(c) 8 sections of ellipsoid

Figure 44 Geometric models of tree crown with the parameters of the ellipsoidequation (Equation 44)

422 Crown radius

Crown radii (CR) were best modeled with power function of tree diameter(dbh) in a manner similar to that used by Beaudet et al (2011) The modelwas adjusted with nonlinear least-squares methods (R Core Team 2013) Thepower function models of crown radius tted well the 6 groups of speciesRoot mean square error (RMSE) was less than 81 cm (Table 48) For compa-rable tree dbhs individuals of the shade-tolerant species (eg hornbeam andbeech) had wider crowns than individuals of the less shade-tolerant species(eg oak and birch)

423 Tree Height

Tree height was best modeled with Mitscherlichrsquos model of tree diameter(dbh) (Table 49) The model tted well every group of species and was ad-justed with nonlinear least-squares methods (R Core Team 2013) With theexception of coniferous trees root mean square error was less than 26 mHowever the models that we have presented should only be used withinthe range of observed dbh In particular we did not measure large conifer-ous trees and the validity of the model is doubtful for such trees

424 Height to the base of the crown

The height to the base of the crown (Hcb ) was estimated with the speciesaveraged ratio between crown length and tree length (Table 410) The useof a power model as was proposed by Beaudet et al (2011) did not sub-stantially improve the predictions and required the estimation of one addi-tional parameter for each species However the parameters of the adjust-ment of the power model were also reported (Table 411) because they canbe used to run simulations with another simulation program of stand dy-namics SORTIE-ND (Canham 2011) The parameter estimates underscoreour observations that shade-tolerant species have deeper crowns than lessshade-tolerant species (greater a estimate in Table 410)

425 Crown openness and leaf area density

In addition to information about crown geometry SamsaraLight requires theestimation of either crown openness or crown leaf area density (LAD) Wemeasured both parameters with photographs of isolated crowns in a man-ner similar to the method that was used to estimate crown openness (Can-ham et al 1999 Beaudet and Messier 2002 Astrup and Larson 2006) Thismethod is rapidly executed relative to previously reported methods that useleaf samples or leaf traps (Bartelink 1997 Jonard et al 2006) or vertical line-intersect sampling methods (Nock et al 2008) but it applies only to treeswith relatively isolated crowns

Table 48 Parameter estimates and their 95 condence intervals with α = 005 (CI) for the power function model between crown radius (CR) and treediameter (dbh) CR = a middot dbhb Also presented are the number of measured trees (n) the ranges of measured dbh the ranges of measured CRand the root mean square error (RMSE)

species n dbh CR a b RMSE

cm m Estimate CI Estimate CI m

Oak 314 24923 0577 0310 02400396 0698 06340764 0808Beech 475 24805 03104 0742 06790808 0516 04920541 0755Hornbeam 67 24420 0851 0854 06821054 0503 04250583 0632Birch 40 24497 0638 0536 04570621 0493 04440545 0266Other hardwoods 43 25198 0734 0960 06161436 0325 01440515 0576Other softwoods 45 24210 0625 0516 04410601 0509 04400579 0179

Table 49 Parameter estimates and their 95 condence intervals with α = 005 (CI) of Mitscherlichrsquos model between tree height and tree diameter (dbh)height =m middot (1minus exp(minus(dbhminus a)b) Also presented are the number of measured trees (n) the ranges of measured dbh the ranges of measuredtree height and the root mean square error (RMSE)

species n dbh height a b m RMSE

cm m Estimate CI Estimate CI Estimate CI m

Oak 706 24949 31358 -1629 -193-133 32733 29953551 31524 30383267 2565Beech 1271 24844 33395 -1835 -215-152 36298 33443915 36424 34883797 2626Hornbeam 175 24420 41258 -2441 -374-114 32776 14315125 32083 20434374 2522Birch 69 24497 36273 -0762 -144-008 19122 13172507 28617 24403284 1619Other hardwoods 73 25767 33293 -1134 -253026 50156 22607771 42830 27535813 2354Other softwoods 60 24210 31141 -1822 -476112 42926 -498613572 29273 -18467701 1207

Table 410 Parameter estimates and their 95 condence intervals with α = 005 (CI) of the model between the crown length (CL = H minus Hcb ) and treeheight (H ) CL = a middotH Also presented are the numbers of measured trees (n) the ranges of measured tree diameters (dbh) tree height andheight to the crown base (Hcb ) and the root mean square error of the crown length model

species n dbh Hcb height a RMSE

cm m m Estimate CI m

Oak 702 24949 04232 31358 0673 066069 4344Beech 1083 24844 01196 33390 0794 078080 3356Hornbeam 154 24420 02119 41258 0813 079083 1910Birch 65 24497 04183 36273 0669 063071 2691Other hardwoods 57 25767 02205 34293 0674 063072 3311Other softwoods 29 24207 0119 31126 0774 072082 0864

Table 411 Parameter estimates and their 95 condence intervals with α = 005 (CI) of the power model between the crown length (CL = H minusHcb ) andtree height (H ) CL = a middotH b Also presented are the numbers of measured trees (n) the ranges of measured tree diameter (dbh) tree heightand height to the crown base (Hcb ) and the root mean square error of the crown length model

species n dbh Hcb height a b RMSE

cm m m Estimate CI Estimate CI m

Oak 706 24949 04232 31358 1162 082150 0827 074092 4300Beech 1271 24844 01196 33390 1063 094118 0900 087094 3285Hornbeam 175 24420 02119 41258 1098 085135 0885 080097 1853Birch 69 24497 04183 36273 1298 088172 0719 061083 1952Other hardwoods 73 25767 02205 34293 0773 032122 0931 074112 3206Other softwoods 60 24210 0119 31126 0547 047063 1233 116130 0441

We took 112 photographs of isolated crowns of 21 oaks 13 beeches8 birches and 4 hornbeams The photographs were processed with Piaf-Photem (Adam et al 2006) to compute the gap fraction ie crown opennessAdditionally for every photographed crown we recorded 4 crown radiicrown base height and tree height

We computed the path length l (Equation 41) as the distance betweenthe intersections between the modeled crown ellipsoids and the photographdirection (Figure 45) Computing the intersections between an ellipsoid anda line requires solving a second-degree equation (Equation 45)

AL2 + B L+C = 0 (45)

A =cos2 (θ ) cos2 (α )

a2 +cos2 (θ ) sin2 (α )

b2 +sin2 (θ )

B = minus2 x1 cos(θ ) cos(α )

a2 minus2y1 cos(θ ) sin(α )

b2 minus2 z1 sin(θ )

b2 +z2

1c2 minus 1

where (x1 y1 z1) are the coordinates of the ellipsoid center in the samecoordinate system as the photograph direction The distance between theintersections ie the path length of light within the crown Figure 45 isgiven by the dierence between L solutions

Photograph direction was computed from the recorded photograph ele-vation angle and the estimated distance to the trunk The equation of thisdirection within a polar coordinate system where the origin corresponds tothe camera position is given in Equation 46

x = L cos(θ ) cos(α ) (46)y = L cos(θ ) sin(α )z = L sin(θ )

where L is the distance along the direction from the camera position θis the direction elevation angle and α is its azimuthal angle (Figure 45)Because the distance between the photographer and the tree trunk was notrecorded in the eld we estimated it by considering that the photographerwas 17 m tall and always aimed the camera at the mid-height of the targetedcrown The distance d is estimated as (Equation 47)

d =05 (H minusHcb ) +Hcb minus 17

tanθ (47)

crown radius crown radius

tree height

photographer height = 17 m

crown ellipsoid envelope

photograph direction

path length

crown base height

Figure 45 Illustration of the dierent measurements involved in the computationof crown LAD

where H is tree height Hcb is height to the base of the crown and θ is therecorded elevation angle (Figure 45)

Finally LAD values were estimated by inverting Beerrsquos law (Equation 41)with the common assumption of spherical distribution of leaves (k = 05)(Phattaralerphong et al 2006 Da Silva et al 2011) We could have usedk middot LAD instead of LAD Although this would have allowed us to assumethat the distribution of leaves was not spherical it would not have allowedus to compare LAD values with other published work

We nally modeled the LAD estimates for beech and oak We obtained thebest ts with a polynomial function of dbh that was adjusted according toordinary least-squares methods (R Core Team 2013) For the other specieswe did not collect enough data to model LAD as a function of dbh Neverthe-less Courbaud et al (2003) mentioned that SamsaraLight sensitivity to leafarea density was low between 03 m2 mminus3 and 09 m2 mminus3 We assumed LADto be 06 m2 mminus3 for all other species as 06 corresponded to the LAD averageof all measured trees Trunks were modeled as cylinders of dbh diameter andcrown base height and do not transmit light

Estimates of crown LAD varied noticeably from tree to tree and even fromphotograph to photograph of the same tree Foliage biomass is usually as-sumed to depend upon sapwood area (pipe model) (Shinozaki et al 1964)and hence also upon tree dbh However tree dbh explained only 48 and30 of LAD variability for oak and beech trees respectively (Table 412)LAD decreased with tree dbh and more so for beech than for oak Addition-ally LAD stopped decreasing for beech at around 50 cm dbh and then startedto increase gently Our LAD estimates matched previously reported valuesof leaf area for beech and oak (Bartelink 1997 Jonard et al 2006) and were in

Table 412 Parameter estimates and their 95 condence intervals (CI) of the polynomial model between crown leaf area density (LAD) and tree diameter(dbh) LAD = a+b middot (dbh middot π )+ c middot (dbh middot π )2 Also presented are tree number (nt ) photograph number (np) ranges of measured dbh (in cm)ranges of estimated LAD (in m2 mminus3) and the model root mean square error (RMSE) We assumed LAD to be 06 m2 mminus3 for all other species

species nt np dbh LAD a b c RMSE

Estimate CI Estimate CI Estimate CIcm m2 mminus3 middot10minus2 middot10minus2 middot10minus5 middot10minus5 m2 mminus3

Beech 13 71 76710 023238 1720 14501990 -188 -241-135 627 421833 0326Oak 21 112 51719 018225 1207 09721441 104 -147-061 309 134485 0292Hornbeam 4 23 76722 029084 0521 04680574 0125Birch 8 42 127344 042090 0595 05620628 0107

the range of reported LAD values for broadleaved species (Stadt and Lieers2000 Piboule 2001 Gersonde et al 2004 Sprugel et al 2009)

A rst version of SamsaraLight was initially validated in one heterogeneousstand of Norway spruce (Picea abies (L) H Karst) (Courbaud et al 2003)Nevertheless we further evaluated model predictions in mixed broadleafforests Additionally we compared the predictions of SamsaraLight with thepredictions of another radiative transfer model ()

4261 Method

In mid-July 2010 we took 307 hemispherical photographs in 19 sites in het-erogeneous forests of oak and beech The photographs were taken just be-fore sunrise and above the regeneration layer of the plots that had beeninstalled every 4 m following a square grid The number of photographs persite therefore depended upon the area of each site and ranged between 6 and39 We then computed the percentage of above canopy light (PACLphoto) thatis transmitted through the canopy between 1st April and 31st October 2012

To predict understory light with SamsaraLight we measured and mappedevery tree with a circumference greater than 40 cm We measured the cir-cumference at breast height (13 m) total height and height to the base ofthe crown for each tree On 13 sites we also measured at least 4 crown radiifor every tree The inventoried plots are the same as those that were used inChapter 3 and had an oval shape of variable area because they surroundedfenced areas in which advanced regeneration has been studied Trees weremeasured if they were located at a distance of less than 20 m from the fenceDue to local abundance of the understory we additionally measured andmapped smaller trees near the points where hemispherical photographswere taken Two dierent measurement protocols were applied because of alack of time and resources In 10 sites we measured and mapped every treewith a circumference that was greater than 74 cm and 20 cm which wererespectively located less than 7 m or less than 15 m from the points wherehemispherical photographs were taken In the 9 other sites we measuredtrees with a circumference that was greater than 20 cm and which werelocated less than 7 m from the points where hemispherical photographswere taken Plot area ranged from 2070 m2 to 10 540 m2 with an average of4340 m2

We compared the hemispherical photograph light estimates (PACLphoto)with SamsaraLight predictions (PACLmodel) that were computed for the sameperiod and at the same locations We adjusted linear models with the ordi-nary least-squares method between PACLmodel and PACLphoto Next we com-

puted the condence intervals (α = 005) of model coecients to estimatethe deviation of the modeled relationship from a 1 1 relationship Using aprotocol similar to Da Silva et al (2011) we also compared the cumulativedistribution function (CDF) of PACLphoto and PACLmodel for every site Wecomputed a Kolmogorov-Smirnov statistic (K-S test) to quantify and test thedistance between the two CDFs against the null hypothesis that the samplesare drawn from the same population

4262 Results and discussion

There was a good linear relationship between the modeled PACLmodel andthe measured PACLphoto (R2 = 68 ) although our model tended to overesti-mate PACLphoto (intercept signicantly greater than 0 and the slope not sig-nicantly dierent from 1) The model predicted better PACL values whenaveraged at the site level (R2 = 87 with intercept not signicantly dierentfrom 0 and the slope slightly signicantly greater than 1) (Figure 46)

Removing small trees from the dataset signicantly altered the relation-ship between PACLmodel and PACLphoto For example removing every treewith a circumference smaller than 20 cm reduced R2 to 65 while removingevery tree with a circumference smaller than 40 cm reduced the R2 to 58

According to K-S tests the distributions of PACLmodel and PACLphoto dif-fered signicantly (P lt 005) from one another for 7 of the 19 plots (Fig-ure 47) Nevertheless the dierences were noteworthy for only 5 plots inwhich PACLmodel clearly overestimated PACLphoto These plots were charac-terized by an abundance of small beech and hornbeam trees that coveredthe regeneration layer where PACLphoto measurements were taken Yet evenin these cases the variation between the distributions of PACLmodel andPACLphoto was less than 15

Overall our model captured the variability of PACL independently ofstand structure The agreement between PACLphoto and PACLmodel was sat-isfactory and within the range of previously reported studies (Law et al2001 Boivin et al 2011) For some plots PACLmodel slightly overestimatedPACLphoto Such over-estimation mostly occurred in the presence of denseunderstory trees (Beaudet et al 2011) The predictions that were made bythe PACLmodel could be aected by these understory trees because somehad a circumference smaller than our inventory circumference threshold orhad a crown that was not correctly modeled by sections of ellipsoids More-over the precision of PACLphoto estimates was poorer in the presence of suchdense understories Nevertheless the bias was of limited magnitude

4263 Conclusion

After synthesizing and discussing the approaches that have been reported inthe literature we implemented a mechanistic and relatively simple radiativemodel Compared to other forest radiative models (Cescatti 1997b Brunner1998 Courbaud et al 2003 Gersonde et al 2004) we utilized a model with

a R2 = 68 b R

2 = 87

Figure 46 Relationships between predicted percentages of above canopy light(PACLmodel) and the percentages of above canopy light estimated fromhemispherical photographs (PACLphoto) point-to-point comparison ofall PACLmodel and PACLphoto (a) and comparison of the PACLmodel andPACLphoto averaged by site (b) The dotted lines show the 11 relation-ships whereas the full lines correspond to the linear least-squares re-gressions

a low number of parameters that did not require calibration by model inver-sion

The model captured well the variability of PACL in stands with varieddensity structure and composition ranging from early-successional oakforests to late-successional beech forests Therefore we have condencein the modelrsquos robustness for exploring how the understory light regimecan be aected by overstory density overstory structure overstory com-position and topography However caution should be exercised regardingthe exactitude of single model predictions especially where understory isabundant

Figure 47 Cumulative distributions of modeled (dashed lines) and measured (solidlines) percentages of above canopy light (PACL) The number of mea-surements and predicted PACL values (n) K-S test statistics (D) and as-sociated P-values (P) are also reported for each plot Our model capturedthe variability of PACL except in sites with an abundant understory Theplots were ordered by decreasing oak proportions showing no eect ofstand composition on model performance

5M A N A G I N G U N D E R S T O R Y L I G H T

Nature never hurries atom by atomlittle by little she achieves her workThe lesson one learns from yachting orplanting is the manners of Nature pa-tience with the delays of wind and sundelays of the seasons bad weather ex-cess or lack of water

Ralph Waldo Emerson

As understory light is the main driver of regeneration growth (Chapter 3)controlling understory light is a key factor in regenerating mixed stands(Lieers et al 1999) The control of understory light with partial cuttingrequires properly modifying stand structure and composition in additionto solely managing stand density To date this question of how changesin stand structure and composition aect understory light has rarely beenaddressed especially for heterogeneous broadleaf forests Only a few eldexperiments have successfully dened levels of canopy openness that aresuitable for the regeneration of mixed species (von Luumlpke 1998 Preacutevost andPothier 2003) and simulation studies have been limited to particular ecosys-tems Cutting groups of spatially aggregated trees or creating gaps has beenreported to drastically increase light availability for the regeneration in bo-real mixedwoods (Coates et al 2003 Beaudet et al 2011) even-aged west-ern hemlock or Douglas-r forests (Sprugel et al 2009) or in uneven-agedspruce forests (Courbaud et al 2001 Lafond et al 2013) Additionally cut-ting understory poles and trees with branches immediately above the regen-eration or cutting from below in some way has often been recommended

70 managing understory light

for shelterwood systems These poles and trees unless they are removedcompete strongly with regeneration for nutrients water and light resources(Nyland 1996) Moreover removing shade-tolerant species presumably in-creases understory light more eectively than removing trees randomly be-cause shade-tolerant species usually have wider deeper and denser crownsthan less shade-tolerant species (Coates et al 2003 Beaudet et al 2011)

In this chapter the radiative transfer model that was established in Chap-ter 4 is used to explore how silvicultural regeneration treatments that modifystand structure and composition can aect understory light and what is thebest treatment to promote the regeneration of mixed species given the lightrequirements of two species with contrasting shade tolerances (Chapter 3)In particular the aims are

bull To compare dierent cutting scenarios by hypothesizing that at simi-lar levels of harvest intensity gap creation cutting from below remov-ing shade-tolerant species (species-specic cutting) cutting randomlyand cutting from above respectively induced high to low responses intransmitted light (H1)

bull To test whether our rst hypothesis is general or depends upon initialstand structure (H2)

bull To identify the combinations of cutting scenarios that maximize theunderstory area receiving 10ndash20 (levels favorable to regeneration ofshade-tolerant species) or 20ndash40 (levels favorable to regeneration ofmid-tolerant species) and above 40 (little light limitation for mostregeneration) of above canopy light

51 methods

511 Study sites

In the Belgian Ardennes we selected 27 sites with varying stand structuresand compositions and with established regeneration of oak and (or) beech(Chapter 2) These studied stands characterized the diversity of forest struc-tures that can be found during forest succession from early-successional oakforests to late-successional pure beech forests (Figure 51)

Every tree with a circumference greater than 40 cm was mapped and mea-sured We measured the circumference at breast height total height andheight to the base of the crown for each tree On 13 sites we also measuredat least 4 crown radii for every tree Besides oak and beech our data set con-tained 7 hornbeam (Carpinus betulus L) 4 small coniferous trees (Pseu-dotsuga menziessi (Mirb) Franco Picea abies (L) Karst and Pinus sylvestrisL) 2 birches (Betula pendula Roth Betula pubescens Ehrh) and 2 otherbroadleaved species (Acer pseudoplatanus L Acer platanoides L Sorbus au-cuparia L and Corylus avellana L)

The inventoried plots had an oval shape of variable area because theysurrounded fenced areas in which advanced regeneration has been studied

51 methods 71

(Chapter 3) Trees were measured if they were located at a distance of lessthan 20 m from the fence Plot area ranged from 2070 m2 to 10 540 m2 withan average of 4340 m2

512 Light model settings

We set SamsaraLight to sample 130 diuse and 81 direct ray directions foreach month of the growing period (from April to October) Ray directionsare sampled at regular increasing zenithal angles with a starting value of 10degand an angle step of 15deg For every direction parallel rays are cast at groundlevel in either cell centers or any other specied locations (virtual sensor)Samsaralight then identies the interceptions of light rays by tree crownsand computes radiation attenuation using Beerrsquos law (Equation 41)

SamsaraLight predicts transmitted light within a rectangular plot Sinceour inventory plots were not rectangular we developed an algorithm thatadded virtual trees in order to obtain a rectangular plot (Figure 52) For eachsite virtual trees were randomly drawn with replacement from the measuredtrees Their location outside the inventoried area was then randomly gener-ated This process was repeated until the basal area of the rectangular plotequaled the basal area of the inventoried plot The number of virtual treescreated in each plot ranged between 0 and 68 and the area over which theywere simulated represented on average 28 of the rectangular plot area Thedimensions and foliage density of the modeled crowns were measured andestimated as described in Section 425

SamsaraLight additionally required monthly meteorological records of to-tal and diuse irradiances in MJ mminus2 We computed such monthly averageddata from data recorded between 2007 and 2011 by the meteorological insti-tute of Belgium in Humain (50deg33primeN 5deg43primeE) Furthermore we set Samsara-Light to predict percentages of above canopy light (PACL) at 2 m above theforest oor at each intersection of a 7 times 7 rectangular grid (Figure 52) Wethus obtained 49 estimates of PACL for each simulation

513 Cutting scenarios

For the 27 inventoried stands we simulated 5 cutting types that reproduced5 silvicultural regeneration strategies commonly practiced in forests of theBelgian Ardennes namely cutting from above cutting from below gap cre-ation species-specic cutting and uniform cutting (Table 51) Cutting fromabove harvests the most valuable trees Typically the trees with a diametergreater than the exploitable diameter are cut ie these are diameter limitcuts In contrast cutting from below harvests small trees with low economicvalue Such a strategy is typically applied to promote the growth of domi-nant trees increase light for natural regeneration and mimics self-thinningCutting that creates gaps are especially used to increase light for a clump ofsaplings and promote regeneration Species-specic cutting has been prac-ticed recently because oak has become scarce Therefore foresters conserve

oak seed trees even if for example their diameter exceeds the exploitablediameter or if they are wounded Finally we simulated uniform cuttings inwhich trees were randomly harvested This scenario can be considered to bethe control treatment

The 5 algorithms of the 5 cutting types started computing scoret (Ta-ble 51) for every tree and then cut the trees by order of decreasing scoretuntil the harvest intensity level was reached scoret computed for cuttingsfrom below and from above were on average greater for narrow and largetrees respectively scoret included a random component that ensured thattree selection diered between simulations The weight given to this ran-dom contribution for the cuttings from above and from below was set to02 so that the distribution of the diameter of cut trees followed a realisticnormal distribution Gap creation scenarios harvested trees around a ran-dom location that must lie within the central part of the plots (Figure 52)Furthermore with cutting intensities greater or equal to 04 the gap radiuswas often greater than 20 m which corresponded to the buer distance be-tween the plot boundary and the central part of the plots (Figure 52) Insuch cases the gap shape became a truncated circle These algorithms arenow available in Capsis (Dufour-Kowalski et al 2012) for most individualtree growth models

The 5 cutting types were applied to the 27 stands with 4 dierent levels ofharvest intensity (10 20 40 and 60 of initial plot basal area) Since thealgorithms of every cutting type had stochastic components we repeatedthe simulation 10 times For each simulation 49 estimates of PACL werecomputed according to the grid introduced in Section 512 We thereforetested 20 cutting scenarios with 5427 simulations and 265 923 computationsof PACLmodel

In order to compare the dierent scenarios we computed the dierencesbetween the average of the 49 estimates of transmitted light before and afterharvesting (∆PACL) Then we adjusted a linear mixed model (Equation 51with lme4 R package (Bates et al 2013) to quantify the relationship between∆PACL and cutting intensity (Ii )

∆PACL = (bl + β jl ) Ii + ϵi jkl

β jl sim N (0θβ )ϵi jkl sim N (0θϵ )

With i j k l the indices corresponding to the cutting intensity plot thesimulation run and the cutting type respectively bl was the xed-eect pa-rameter which was estimated for each l cutting type β jl was a random-eectparameter varying between plot and cutting type Similarly to the residualterm β jl followed a centered normal distribution This model assumed that∆PACL was proportional to Ii and that the slope of this relationship (bl + β jl )

51 methods 73

Figure 51 Stand structure and composition of the 27 studied plots expressed astree frequency by diameter class The charts are sorted by decreasingproportion of oak Plot basal area is reported next to the plot id numbershowing no trend between plot basal area and plot composition Theasterisks next to plot id numbers denote the 9 plots where initial meanpercentage of above canopy light (PACL) was below 20

Buffer areawhere virtual trees

were randomly added

Inventory areawhere trees were

mapped and measured

Plot center part

Virtual light sensorwhere transmitted lightwas predicted

Figure 52 Three dimensional visualizations of the dierent zones within a plotwith and without trees In order to evaluate the cutting scenarios ourmodel was set to predict the percentage of above canopy light at 2 mabove forest ground and at every intersection of a 7 m times 7 m grid withinthe center part of the plots

Table 51 Description of the 5 cutting types With (xt yt ) the tree coordinates (xд yд) the random gap center coordinates that must be within the central part ofthe plot (ie within (xmin xmax ymin ymax ) dbht the diameter of tree t dbhmin and dbhmax the minimum and maximum of dbh u a random numbergenerated between 0 and 1

cutting type description scoret

Uniform cutting Random harvest of trees scoret sim u

Species-specic cutting Preferential harvest of beech and hornbeam (β = 2) then the other species (β = 1) and nallyoak (β = 0)

scoret = β +u

Cutting from below Preferential harvest of small trees scoret = 02u + 08 (1 minus dbht minusdbhmindbhmax+dbhmin+1 )

Cutting from above Preferential harvest of large trees scoret = 02u + 08 (1 minus dbhmax minusdbhtdbhmax+dbhmin+1 )

Gap creation Harvest of all trees around a gap center The location of the gap center was determined atrandom but must be within the central part of a plot (Figure 52)

scoret =radic(xt minus xд )2 + (yt minus yд )2

xд sim U[xmin xmax ]yд sim U[ymin ymax ]

varied with cutting type and initial site conditions The hypothesis H1 wastested computing the approximate condence intervals of bl These con-dence intervals were obtained from the likelihood prole of bl (Bates et al2013)

In order to further analyze how initial stand structure aected the re-sponse (H2) we tted ve additional models that included the eects of 5dierent stand structure parameters (denoted by P j in Equation 52) Theseparameters were stand basal area quadratic mean diameter basal area pro-portion of oak standard deviation of dbh Clark-Evans aggregation indexand basal area of trees with dbh smaller than 25 cm With the exception ofthe latter parameter they have commonly been used to describe stand den-sity and structure in similar studies (Sprugel et al 2009 Beaudet et al 2011Lafond et al 2013) These indices describe the stand density and structure be-fore harvest The Clark-Evans aggregation index (Equation 53) gives valuesgreater than 1 for regular tree distributions and lower than 1 for aggregatedtree distributions The basal area of small trees was added because poles andsmall trees were sometimes abundant in the understory and were expectedto capture a high proportion of transmitted radiation We tested the additionof the corresponding xed-eect parameter cl with the log likelihood ratiotest (Bates et al 2013)

∆PACL = (bl + cl middot P j + β jl ) middot Ii + ϵi jkl (52)

05radicAN

where r is the mean distance between trees and their nearest neighbor Athe plot area and N the number of trees within the plot

Next we created four classes of PACL These classes had PACL valuesranging between 0ndash10 10ndash20 20ndash40 and 40ndash100 They corre-sponded respectively to light levels that are unfavorable to natural regener-ation of tree species favorable to beech sapling growth favorable to beechand oak sapling growth and above light saturation point (Chapter 3)

Furthermore we computed the average frequency of the predictions byPACL classes and cutting intensity In order to provide a guide to forest man-agers we repeated these computations replacing the harvest intensity by theresulting post-harvest basal area We restricted these analyses to the 9 plotswhere the mean PACL before cutting was less than 20 ie where cuttingwas necessary to promote the natural regeneration of less shade-tolerantspecies

52 results 77

52 results

521 Tree inventory

According to the eld data stand composition and stand density varied con-siderably among study sites (Figure 51 and Table 52) The proportion of oakin the overstory ranged between 0 and 98 High proportions of oak oc-curred mostly in stands with high basal area (r = 0389 P = 0045) and lowquadratic mean diameter (r = minus0523 P = 0004) Additionally in some sitesthe distribution of tree diameters followed an inverted j-shaped curve whilein other sites it approximated a bell-shaped curve (Figure 51) Tree aggre-gation was greater in stands with complex vertical structure Clark-Evansaggregation index was indeed negatively correlated with the standard devi-ation of tree diameter (r = minus0500 P = 0008)

The dierent cutting scenarios harvested the same quantities of basal areabut caused very dierent modications to stand structure Firstly post-harvest density varied notably between cutting scenarios Cutting frombelow harvested the greatest number of trees while cutting from aboveharvested the fewest number of trees The other cutting scenarios harvestedan intermediate number of trees

Secondly harvests aected stand composition Species-specic cutting in-creased the proportion of oak trees Moreover because the understory wasmainly composed of shade-tolerant species (beech and hornbeam) cuttingfrom below also tended to increase the proportion of oak trees Cutting fromabove tended to harvest more oak trees than the other scenarios

Thirdly stand spatial structure was little aected by harvests except bygap creation Gap creation increased the aggregation of trees as indicated bya reduction in the Clark-Evan aggregation index Even at low harvest inten-sity large gaps were created and remaining trees were aggregated along gapperiphery For example removal of 10 and 20 stand basal area using gapharvesting led to an average opening of 475 m2 and 1182 m2 respectively

523 Simulation

The increase in understory light levels (∆PACL) varied signicantly betweenthe cutting scenarios as illustrated by Figure 53 and the results of the ad-justed model (Table 53) In agreement with our rst hypothesis (H1) thecutting types ordered by decreasing ∆PACL response were gap creation cut-ting from below species-specic cutting uniform cutting and cutting fromabove This hypothesis was veried by ordering the slopes of the relation-ship (bl ) between changes in PACL and cutting intensity for all the scenariosThe slope of this relationship was statistically dierent among cutting treat-ments except between cutting from below and species-specic cutting

Table 52 Stand structure and composition in the studied sites The presented parameters are density (N) basalarea (BA) quadratic mean diameter (Dg) the Clark-Evans aggregation index (CE) and the minimum(dbhmin) and maximum (dbhmax) of tree diameter Plots are ordered by increasing oak proportion

stand oak beech

Site N BA Dg CE BA Dg dbhmin dbhmax BA Dg dbhmin dbhmax

19 983 1494 4398 096 1494 4398 1273 843525 1272 2184 4675 105 2184 4675 1305 843527 353 782 5313 105 645 5297 1273 725728 514 747 4304 119 028 4742 4170 5252 719 4289 1273 649426 617 1460 5489 127 194 7576 7576 7576 1263 5362 1432 78303 1136 1810 4503 107 317 3942 2801 6016 1493 4657 1432 6557

18 467 752 4529 097 140 6232 5443 6430 606 4533 1273 79901 872 1115 4034 118 286 4433 2706 6525 790 3935 1273 71622 1139 1633 4273 097 435 4930 1623 5921 1195 4135 1273 7226

14 1245 2121 4657 128 670 6564 5443 8276 1451 4200 1273 697120 1439 1949 4152 104 697 7187 5570 9231 1252 3546 1273 805329 1270 2056 4541 120 1114 5542 4043 6812 942 3853 1273 652513 1338 1537 3825 109 869 6021 4615 7289 668 2870 1273 69715 2178 2051 3462 103 1195 5387 1783 7130 856 2567 1273 6812

12 1566 2265 4292 116 1361 5324 3947 8085 904 3474 1273 75764 2073 2416 3852 097 1670 5773 3820 7226 746 2572 1273 8403

22 2165 1531 3000 112 1107 2902 1369 4966 362 4336 1751 779921 1203 1954 4548 097 1471 7306 5761 9486 391 3151 1273 763923 1215 1631 4135 100 1241 4387 1464 7576 276 4531 1432 770315 1905 2469 4062 106 1980 5721 3215 7162 006 1305 1273 133717 1885 2689 4262 131 2227 5485 2451 7385 176 2913 1273 49346 1075 2079 4962 112 1738 6659 2897 8976 251 2771 1273 4902

10 1352 2165 4515 129 1929 4899 1655 5952 106 3041 2960 31198 2153 1906 3358 108 1731 4077 1655 6303 023 2135 1305 3056

24 1119 1180 3664 130 1085 4035 2005 550711 1146 1444 4005 100 1351 4822 1273 6685 023 1969 1751 21659 1225 1274 3640 125 1246 3754 1324 6971

52 results 79

Cutting type

Figure 53 Mean increase of transmitted light levels (∆PACL) by cutting scenarioand by intensity The adjusted mixed model indicated that the dier-ences between cutting types are signicant (Table 53) and accentuatedas cutting intensity increased Gap creation induced the greatest ∆PACLresponses

We found no evidence that the relationship between ∆PACL cutting typeand cutting intensity depended upon the initial stand structure All likeli-hood ratio tests indicated that adding any stand parameter P j in the model(Equation 52) did not signicantly improve it Within the conditions of oursampled study sites our rst hypothesis appeared rather general and inde-pendent of initial stand conditions Furthermore the between-site variabilityof ∆PACL response (θβ ranged from 0172 to 3870) was limited in compar-ison to the within-site variability (θϵ = 4150) ∆PACL response dependedmore likely upon the conditions of the immediate surroundings of the mea-surement point rather than on general stand structure

For the 9 plots where initial mean PACL was below 20 (Figure 51) weanalyzed the percentage of understory area receiving PACL ranging between

Table 53 Fixed-eect estimates bl of the adjusted model (Equation 41) with ap-proximate condence intervals with α = 005 (CI) and standard errorsOur model assumed that any removal of 1 of stand basal area inducedan increase in PACL of bl additionally θβ is the standard deviation of therandom eect and indicated the variability of this relationship betweenplots

cutting type bl θβ

Estimate CI

gap creation 0835 076090 1580cutting from below 0615 057067 2635species-specic cutting 0579 053063 3148uniform cutting 0459 043048 3870cutting from above 0349 030040 0172

0ndash10 10ndash20 20ndash40 or 40ndash100 Contrary to ∆PACL changes in per-centage of microsites above a given light level depended noticeably upon aninteraction between cutting type and harvest intensity (Figure 54) or post-harvest basal area (Figure 55)

As most plots received an average of more than 10 PACL before harvestthe proportion of understory area receiving less than 10 PACL decreasedwith harvest intensity (Figure 54a) The proportion of microsites receiving10ndash20 PACL also decreased rapidly with harvest intensity Nevertheless har-vesting only 10 of stand basal area did not signicantly reduce the propor-tion of these microsites except with gap creation (Figure 54b) A cuttingintensity of 10 with all cutting types but gap creation maintained basalarea around 15ndash20 m2 haminus1 (Figure 55)

The dierent cutting scenarios provided very dierent proportions ofmicrosites receiving 20ndash40 PACL which is the range of light conditionsthat promotes the less shade-tolerant oak (Figure 54c and Figure 55c)Gap creation maximized this proportion at 10 harvest intensity (targetbasal area 20ndash25 m2 haminus1) but at higher harvest intensities very little areawas in the 20ndash40 PACL range Cutting from below and species-specicharvesting maximized the proportion of microsite receiving 20ndash40 PACLat about 20 of harvest intensity (target basal area of 15ndash20 m2 haminus1) butthey provided more than 40 of the area in the 20ndash40 PACL range in all butthe most intense harvesting scenario Uniform cutting maximized the areareceiving 20ndash40 PACL at about 40 of harvest intensity (target basal areaof 10ndash15 m2 haminus1) whereas cutting from above provided about 40 of thearea in the 20ndash40 PACL range independently of harvest intensity

Cutting from above maintained a remarkably high proportion of mi-crosites with less than 20 PACL at all cutting intensities and only created alow proportion of microsites with more than 40 PACL (Figure 54d) In con-trast the proportion of microsites with more than 40 PACL was the greatestfor all cutting intensities with gap creation The dierence in microsite withgreater than 40 PACL between gap-harvesting and the other cutting typeswas particularly notable at harvest intensity of 20

53 discussion

531 Mean light response to the dierent cutting scenarios

The dierent cutting types led to dierent increases in mean PACL that wereordered according to our rst hypothesis (H1) independently of initial standstructure and composition (in contradiction with H2) On average harvest-ing 10 of stand basal area increased mean PACL by about 84 with gapcreation 62 with cutting from below 58 with species-specic cutting46 with uniform cutting and 35 with cutting from above (Table 53 andFigure 53)

Similar to the ndings of numerous studies (Canham et al 1994 Cescatti1997a Brunner 1998 Stadt and Lieers 2000 Beaudet and Messier 2002

10 20 40 60

10 20 40 60 10 20 40 60

10 20 40 60

beforeharvest

Figure 54 Frequency of microsites with percentage of above canopy light (PACL) ranging between 0ndash10 10ndash20 20ndash40 and 40ndash100 These frequencies were computed by harvest intensity in the 9 plots whereinitial mean PACL was below 20 The proportion of microsites with PACL of 0ndash10 (a) or 10ndash20 (b)was high prior to cutting (white bar on the left) This proportion decreased the most rapidly with gapcreation in contrast with cutting from above High proportions of microsites receiving 20ndash40 PACL (c)were obtained with 10 gap creation 20 cutting from below 20 species-specic cutting or 40 uniform cutting

5-10 10-15 15-20 20-25 5-10 10-15 15-20 20-25

5-10 10-15 15-20 20-25 5-10 10-15 15-20 20-250

Figure 55 Frequency of microsites by class of percentage of above canopy light (PACL) and post-harvest basalarea The frequencies were computed from the 9 plots where initial mean PACL was below 20 andnext averaged by classes of post-harvest basal area Cutting scenarios that maximized the under-story area receiving 10ndash20 PACL (b) reduced stand basal area to about 15ndash20 m2 haminus1 Cutting Fromabove only slightly aected the proportion of microsites with 20ndash40 PACL (c) High proportions ofmicrosites with 20ndash40 PACL were obtained with cutting that created gaps that reduced basal area to20ndash25 m2 haminus1 with cutting from below that reduced basal area to 15ndash20 m2 haminus1 or with uniformcutting and cutting from above that reduced basal area to 10ndash15 m2 haminus1

53 discussion 83

Beaudet et al 2011 Da Silva et al 2011) the main factor limiting under-story light was the absence of gaps between crowns Consequently at similarcutting intensities harvests that create gaps strongly increased understorylight Additionally we only considered immediate post-harvest conditionswhile the evolution of understory light several years after cutting may leadto increased or reduced dierences between treatments In particular theincrease in understory light due to the creation of large gaps would be ex-pected to last longer than the eects of the other cutting types since largeropenings would take longer to close (Sprugel et al 2009)

Another factor that strongly limits light availability for regeneration isthe presence of a sublayer of shade-tolerant species We already noticed thisinuence of a dense understory when evaluating the performance of ourlight model (Chapter 4) In addition our simulation conrmed that under-story trees might intercept a large proportion of light and that cutting frombelow can increase signicantly understory light levels and can therefore beessential to promote the regeneration of less shade-tolerant species

Preferentially harvesting shade-tolerant species ie species-speciccutting increased more transmitted light than harvesting trees randomlyTrees of shade-tolerant species intercept more light than trees of less shade-tolerant species since they have wider deeper and denser crowns (Table 48Table 410 and Table 412) Additionally shade-tolerant species are usuallymore abundant in the understory than less shade-tolerant species Species-specic cutting therefore tend to harvest a high proportion of poles andsmall trees similarly to the cutting from below

532 Optimum cutting scenario

The optimum cutting scenario within the context of this study maximizedthe understory area that is favorable to the natural regeneration of lessshade-tolerant species ie the area receiving 20ndash40 PACL Contrary tomean PACL the area receiving 20ndash40 PACL depended upon the interac-tions between cutting type and cutting intensity High proportions ofmicrosites with 20ndash40 PACL were obtained by either harvesting few treesor by harvesting more than 50 of stand basal area

Creating gaps appears particularly promising to promote small clumps ofoak regeneration with limited reduction of stand stocking Harvesting thefew trees located within and around these clumps largely increase the pro-portion of microsites with 20ndash40 PACL In our simulations the gaps thatmaximize this proportion of microsites are about 470 m2 in size which cor-roborates the recommendations by von Luumlpke (1998) and Bruciamacchie andde Turckheim (2005) as well as the observations of Rugani et al (2013) in oldgrowth beech forests These authors reported that oak regeneration was pos-sible in gaps of at least 500 m2 created by harvesting 4ndash5 mature trees (Bru-ciamacchie and de Turckheim 2005) Larger gaps increase the proportion ofmicrosites with more than 40 PACL and should likely be avoided during therst stages of regeneration development because such conditions are favor-able to the rapid development of competitive herbaceous species (Gaudioet al 2008 2011)

Cutting from below and cutting preferentially shade-tolerant species werethe best techniques to promote the recruitment of less shade-tolerant regen-eration especially if saplings were uniformly spread in the understory as ithappens after generalized masting For the studied stands the optimum har-vest intensity was about 20 which corresponded approximately to a targetbasal area of about 15ndash20 m2 haminus1

Randomly cutting trees requires a greater harvest intensity to maximizethe proportion of microsites with 20ndash40 PACL than gap creation cuttingfrom below and species-specic cutting We obtained an optimum numberof microsites with 20ndash40 PACL with a harvest intensity of 40 which corre-sponded to a target basal area of about 10ndash15 m2 haminus1 and agrees with theresults obtained by Balandier et al (2006b) in even-aged oak stands

Cutting from above maintained large understory areas receiving less than40 full light It maintained a more asymmetric right-skewed distributionof PACL (Beaudet et al 2011) than the other cuttings and hence a highproportion of microsites in shady conditions even after harvesting up to60 of stand basal area By preferentially eliminating large overstory oaksand maintaining low-light levels in the understory this treatment can beexpected to quickly lead to a successional transition to dominance by shade-tolerant species

In conclusion promoting less shade-tolerant species can be achieved withvarious regeneration treatments Forest managers should consider whetherthe seedlings of less shade-tolerant species are aggregated or uniformlyspread whether a small reduction in stand stocking is more appropriateand what is the desired composition of the dierent tree layers after harvestThe results from this study provide foresters with the necessary toolsto evaluate how silvicultural treatments can be manipulated to create ormaintain favorable conditions for the regeneration of species of dierentshade tolerances

6G E N E R A L D I S C U S S I O N

Science goes from question to questionbig questions and little tentative an-swers The questions as they age growever broader the answers are seen to bemore limited

George Wald

61 maintaining the mixture of species with contrastedshade tolerances

The main purpose of this thesis was to determine how forest managers couldmaintain a mixture of species with contrasting shade tolerances in uneven-aged and mixed forests that are managed using continuous-cover forestrysystems

The results suggest that maintaining a mixture of species with contrastingshade tolerances requires ne control of understory light to promote regen-eration of the dierent species Such a control of understory light can beachieved by controlling the density and structure of the overstory with par-tial cutting Moreover regeneration cleaning may be essential to suppressregeneration of the shade-tolerant species and to promote regeneration ofthe less shade-tolerant species

Understory light was found to be a key parameter in the dynamics of het-erogeneous stands as it aects regeneration growth and composition There

86 general discussion

are interspecic dierences in survival and growth response to the availabil-ity of light Under the deep shade of a closed canopy (PACL lt 5 ) only smallseedlings of shade-tolerant species are able to survive (Madsen and Larsen1997 Emborg 1998 Le Duc and Havill 1998 Lieers et al 1999 von Luumlpkeand Hauskeller-Bullerjahn 1999 Emborg et al 2000 Collet et al 2001 vonLuumlpke and Hauskeller-Bullerjahn 2004 Collet and Chenost 2006 Petriţanet al 2007) Consistent with other studies as understory light increases(PACL = 10ndash20 ) the seedlings of less shade-tolerant species are able to sur-vive and grow but the seedlings of shade-tolerant species grow faster andsuppress the seedlings of less shade-tolerant species After canopy release(PACL = 20ndash40 ) the regeneration of both shade-tolerant and less shade-tolerant species develops well (Dineur 1951 Emborg 1998 von Luumlpke 1998Stancioiu and OrsquoHara 2006a) Less shade-tolerant species require indeedgreater amount of radiation than shade-tolerant species Additionally lessshade-tolerant likely require sucient amount of direct radiation that canbe obtained after such canopy release (Diaci 2002 Diaci et al 2007) Follow-ing further canopy opening (PACL gt 40 ) the growth of the regenerationsaturates and becomes less sensitive to variations in light availability (Stan-cioiu and OrsquoHara 2006a Van Couwenberghe et al 2013) Such large canopyopenings alter the microclimate of the understory and regeneration can ad-ditionally suer from the development of competitive herbaceous species(Gaudio et al 2008)

The control of understory light is consequently an important issue al-though it is also a dicult task I explored dierent strategies that forestmanagers could apply to increase the availability of light to the understoryThis work provided indications of how partial cutting can be manipulatedto change stand composition and structure and how such changes aect un-derstory light The control of understory light requires controlling harvestintensity jointly with the location size and species of the harvested treesDierent silvicultural treatments can be utilized to control understory lightFor example forest managers can preferentially harvest small or large treestrees of shade-tolerant species or aggregated groups of trees All of thesesilvicultural strategies could provide satisfactory results as long as harvestintensity is adapted to the chosen strategy (Figure 61)

The results of this thesis also underscore the problem that even undergood light conditions (PACL gt 20 ) regeneration of less shade-tolerantspecies might not overcome the regeneration of shade-tolerant speciesThis nding goes against the theory of shade tolerance as proposed byKobe et al (1995) and the results of greenhouse experiments (Dreyer et al2005) Indeed according to Kobe et al (1995) there is a tradeo betweenhigh-light growth and low-light survival In low-light environments shade-tolerant species survive better than less shade-tolerant species whereasin high-light environments shade-tolerant species grow slower than lessshade-tolerant species Nevertheless the results of this thesis are in accor-dance with the observations of forest managers within the study area andwith the recently published results of Van Couwenberghe et al (2013) and

62 silvicultural recommandations 87

of microsite favorable to

less shade-tolerant species

no harvest

60 basal areaharvested

by speciesgap uniformfrom below from above

Cutting intensity

oak tree

beech tree

Figure 61 Post-harvest understory light conditions depend upon cutting intensityand cutting type To maximize the understory surface that is favorableto regeneration of less shade-tolerant species forest managers need tochoose an adequate combination of cutting type and cutting intensity

Petriţan et al (2014) who studied the same two species in France and inRomania respectively Additionally the suppression of the regenerationof less shade-tolerant species by regeneration of shade-tolerant speciesin high-light environments has been reported in other mixed forests inFrance with mixtures of Quercus pubescens-Fagus sylvatica (Kunstler et al2005) in central Europe with mixtures of Acer pseudoplatanus-Fraxinusexcelsior-Fagus sylvatica (Petriţan et al 2009) or in Quebec with mixturesof Acer saccharumndashFagus grandifolia (Delagrange et al 2010)

Consequently maintaining less shade-tolerant species in stands withshade-tolerant species might require silvicultural interventions jointlyin the overstory and regeneration layers Establishing saplings of lessshade-tolerant species may require competition from the saplings of shade-tolerant species to be decreased manually The dominant saplings of lessshade-tolerant regeneration would have a greater chance of survival if theyare taller than any neighboring saplings of shade-tolerant species

62 silvicultural recommendations for maintaining mix-tures of oak and beech

Beech saplings naturally outgrow oak saplings under a partially closedcanopy In addition beech saplings usually establish before oak saplingsand require half as much light to reach an optimum growth than do oaksaplings In these conditions oaks are rapidly suppressed and mixed standsof oak and beech evolve naturally toward pure beech stands The two speciesmainly coexist because beech naturally regenerates under well-establishedoak stands where oak has previously been favored by selective thinningcoppicing and plantations (Claessens et al 2010) The reverse situation isunlikely to occur naturally without frequent disturbances (Messier et al

1999) and (or) disturbances that damage the beech regeneration (Reyes et al2010)

As a result foresters applying continuous-cover silviculture need to pro-ceed in three phases

First in waiting for the emergence of oak seedlings they must maintainlow-light levels in the understory (PACL lt 5 ) to reduce the developmentof beech seedlings that continuously emerge under the canopy Indeed ger-mination does not depend upon light conditions (Turbang 1954 Welanderand Ottosson 1998 Chaar and Colin 1999 Nicolini et al 2000)

Second reducing overstory density is essential to promote oak regenera-tion This can be achieved with partial cutting that increases the availabilityof radiation to oak regeneration to about 20ndash40 PACL The target basal areaafter partial cutting ranges between 10 m2 haminus1 and 25 m2 haminus1 dependingupon residual stand structure The creation of gaps of about 500 m2 provideslocally large amounts of radiation while minimizing the reduction of standstocking Preferential cutting of small trees and individuals of shade-tolerantspecies provides sucient amounts of light with a target basal area of about15ndash20 m2 haminus1 Cutting without consideration of tree species size and loca-tion requires a lower target basal area ie about 10ndash15 m2 haminus1 Preferen-tially cutting large trees maintains large areas in the understory with low-light availability which favors shade-tolerant species However as saplingsbecome taller foresters need to gradually open the gaps and reduce residualstand density to satisfy the increasing light requirements of older saplings(Messier et al 1999)

Third given the ecological conditions of the Belgian Ardennes oak couldnot be promoted over beech by only managing the overstory Foresters needto frequently remove or break manually the dominant and co-dominantbeech competitors that will systematically overtop oak saplings (von Luumlpke1998) especially if beech seedlings were established before oak seedlings Atthe end of this treatment the dominant oak saplings must indeed dominateall remaining beech saplings

63 study limitations and perspectives

This study provides us with a better understanding of the regeneration dy-namics of uneven-aged stands with a mixture of species with contrastingshade tolerances I was not able to study all of the processes that drive thedynamics of such a complex ecosystem In the following discussion I ac-knowledge the limitations of my work and consequently indicate remain-ing knowledge gaps and interesting research perspectives

I assumed that the coexistence between tree species depends mainly uponinterspecic dierences in the development of established regeneration asonly the dominant saplings survive and reach the upper canopy layers Eventhough the evolution of stand composition does not depend only upon com-petition between saplings of dierent species the suppression of all saplingsof a given species from the regeneration layer certainly aects future stand

63 study limitations and perspectives 89

composition because new regeneration establishment usually does not oc-cur where there is abundant advance regeneration (Reyes et al 2010) Thecomposition of tree recruitment could additionally depend upon interspe-cic competition between poles and trees interspecic dierences in treesurvival seed production seed dispersal and seed germination

I assumed that sapling survival depends upon the capacity of saplingsto grow taller than their neighbors and consequently to capture a largeramount of solar radiation Consequently the analysis of regenerationheight growth (primary growth) was prioritized over the analysis of re-generation diameter growth (secondary growth) and regeneration survivalVan Couwenberghe et al (2013) studied the growth of regeneration ofsessile oak and European beech in France and found that diameter growthis closely related to height growth In their study diameter growth of oaksaplings was less than the diameter growth of beech saplings under allinvestigated light levels Baudry (2013) had studied the survival of sessileoak and European beech in Belgium and demonstrated that sapling survivaldepends largely upon sapling capacity to dominate neighboring individualsMoreover a relationship can usually be found between sapling mortalityand diameter growth (Kobe et al 1995 Pacala et al 1996) The probabilityof sapling mortality decreases as sapling radial growth increases Sustainedgrowth indicates good photosynthetic activity and reduces the period inwhich saplings are exposed to competition with neighboring vegetationor other agents that could cause damage such as wild game (eg deer) ordisease (eg oak powdery mildew)

I assumed that the development of advance regeneration mostly dependsupon light quantity as expressed by the percentage of above canopy lightThe ndings of this thesis corroborate the paramount importance of theamount of light that is required for regeneration development and com-position Nevertheless other factors certainly drive competition betweenspecies with contrasting shade tolerances because some of the results ofthis thesis are in contradiction with the results of other studies Particularlyin a greenhouse experiments (Dreyer et al 2005) saplings of sessile oakoutgrew beech saplings in high-light conditions While in the eld experi-ments that was performed for this thesis project beech saplings dominatedoak saplings under all of the study conditions even though regenerationwas measured over a wide gradient of light availability In stands that aremanaged with continuous-cover forestry systems the availability of lightdoes not necessarily allow conditions to be identied in which the saplingsof less shade-tolerant species outgrow saplings of shade-tolerant species Ihypothesize that other factors drive competition between species with con-trasting shade tolerances and subsequently explain why the saplings of lessshade-tolerant species do not outgrow saplings of shade-tolerant species inbright understories Dierent results could therefore be obtained in otherareas or with other tree species In particular a rank reversal between thegrowth of species with contrasting shade tolerances along a light gradienthas been observed and modeled in other mixed forests (Pacala et al 1994)

Site conditions might also aect species performance ranks (Kobe 2006 Val-ladares and Niinemets 2008) Consequently the promotion of less shade-tolerant species over shade-tolerant species does not automatically requireregeneration tending Among the factors that have already been identiedas modifying the performance rank of species of diering shade tolerancethe availability of water likely plays a key role The other factors that shouldbe considered are tree ontogeny nutrient availability and suneck durationand frequency (Valladares and Niinemets 2008)

Regeneration of less shade-tolerant species likely requires direct radiationwhereas diuse radiation can be enough for regeneration of shade-tolerantspecies (Diaci 2002) Further investigations are required to better identifythe requirements of regenerations to direct radiation and how forest man-ager can control the amount of transmitted direct radiation I hypothesizethat (i) an increase in the availability of direct radiation promotes the regen-eration of less shade-tolerant species (ii) post-harvest availability of directradiation depends upon cutting type and (iii) gap creation is the cutting typethat induce the greatest increase in the availability of direct radiation

The availability of understory light was investigated under particular con-ditions The availability of understory light depends upon complex inter-actions between latitude canopy height topography and foliage orienta-tion and aggregation (Canham et al 1990 Kuuluvainen 1992 Preacutevost andRaymond 2012) In the northern hemisphere maximum solar elevation de-creases with latitude and maximum light penetration through canopy gapsis oset northwards from the gap center (Figure 62) At high latitudes thearea receiving the largest gains in understory light is located closer to thenorthern gap edge or even under closed canopy Consequently the area re-ceiving the largest gain in understory light does not coincide with the areaof increased nutrient and water availability (Lieers et al 1999) Moreoversouth-facing surfaces (sloping ground and leaves) receive greater amounts ofenergy from direct radiation than north-facing surfaces because direct radia-tion strikes the surface at an angle closer to the perpendicular In hilly areassome of the radiation entering at low elevation angles is also intercepted bythe horizon For example west-facing slopes do not receive direct radiationat the beginning of sunrise The study forests were around 50degN latitudehad a canopy height of about 30 m and were present on gentle slopes In dif-ferent forest types at dierent latitudes and (or) on hilly terrain dierentresults could be obtained regarding the eects of partial cutting on under-story light For example I hypothesize that (i) smaller gaps (and higher standdensities) are required on south-facing slopes or at lower latitudes in orderto promote the regeneration of less shade-tolerant species and (ii) cuttingfrom below induces a lower increase in understory light at low latitude thanat high latitude

Furthermore the availability of light for regenerating stems evolvesthrough time due to canopy closure and growth of regeneration In irregu-lar forest stands that are managed with continuous-cover forestry systemssaplings poles and trees react to canopy release The crowns of poles

Low latitude High latitude High latitude + high canopy

closed canopy

directradiations

max solar elevation angle

closed canopy

gap gap

gapgapgap

gap gap gap

Figure 62 The transmission of direct radiation through canopy gaps depends upon the interaction between site lati-tude forest type (eg canopy height) slope and aspect For each combination of these factors the gureschematically depicts the spatial distribution of direct radiation along a North-South transect that is cen-tered on a canopy gap The angular distribution of diuse radiation can be considered as relatively uniformConsequently microsites in gap center receive the greatest amount of diuse radiation

and trees expand laterally and vertically As saplings become taller theavailability of light does not necessarily increase because of the proximityof the crowns of poles and trees (Ban et al 1998) Regeneration growingunder the canopy or at the edge of canopy gaps can therefore face morerapid and more severe competition from the remaining trees and poles thandoes regeneration growing in the center of a canopy gap When analyz-ing the eects of partial cutting I considered understory light conditionsimmediately after the harvest whereas dierent ndings could have beenobtained if I had considered understory light conditions several years afterthe harvest Further work is required to tackle the modeling of canopyclosure and investigate the evolution of understory light conditions withcanopy closure As gap centers northern gap edges and southern gap edgesare microsites with dierent light regimes (Diaci 2002)(Figure 63) someinteresting hypotheses that could be tested are that (i) the availability oflight to regenerating stems at gap edges decreases as regenerating stemsbecome taller because of the competition with dominated trees and canopyclosure and (ii) there is a rank reversal over time in the availability of lightbetween the gap center and northern gap edge

The studied regeneration was protected from game browsing by fencesas browsing by wildlife is known to aect regeneration composition (Hid-ding et al 2013 McGarvey et al 2013) Indeed palatable species are prefer-entially browsed by deer and less palatable species are therefore promotedThis is a severe limitation to the results of this thesis especially if gamepopulations are abundant Depending upon the shade tolerance of the palat-able species game browsing can either promote shade-tolerant species (egEuropean beech versus sessile oak in the study area) or less shade-tolerantspecies (eg spruce versus r in the Vosges mountains (Heuze et al 2005) oron Anticosti Island (Casabon and Pothier 2007 Hidding et al 2013)) Withinthe studied area I hypothesize that (i) abundant deer populations acceleratethe transition of secondary forests to late-successional forests (ii) densityof deer populations is a more important factor than understory light avail-ability to the diversity of understory regeneration and (iii) maintaining thecoexistence of beech and oak requires control of the density of wild gamepopulations

Competition between species is likely aected by changes in environmen-tal conditions Climate change displaces the ecological niches of species andecosystem boundaries Depending upon site conditions species autecologyand interspecic interactions species will either benet or suer from cli-mate change which in the long run can modify stand composition (Bon-temps et al 2012 Mette et al 2013) However the eects of climate changeon the dynamics of uneven-aged and mixed stands require further investiga-tion Interactions between the admixed species can attenuate the sensitivityof species to climate change (Pretzsch et al 2013b) Therefore it is unclear

directradiations

maximum solarelevation angle

Figure 63 Northern gap edge (a) gap center (b) and southern gap edge (c) are mi-crosites with dierent light regimes The availability of light to saplingshypothetically decreases as saplings grow because of competition withdominated trees at gap edges a rank reversal over time of the availabilityof light between the gap center and northern gap edge can be expected

whether the ndings about interspecic competition in the understory arelikely hold under a future climate Further studies should identify whetherinterspecic competition in the understory of uneven-aged forests whenmanaged with a continuous-cover forestry system is sensitive to climatechange

The reaction of regeneration to a sudden increase in solar radiation due tocanopy disturbances or silvicultural treatments was not investigated Modi-cation of stem allometry is expected in the years following canopy release(Collet et al 2001) but further work is required to quantify the reaction ofsaplings to canopy release and assess the eciency of regeneration clean-ing In particular the growth of released saplings should be further studiedin order to provide more precise silvicultural recommendations such as theappropriate timing for regeneration tending

In order to further generalize the ndings of this thesis the simulation ap-proach that was outlined in this study should be replicated for other forestecosystems with dierent species compositions stand structures topogra-phy and at dierent latitudes With this in mind developing models of standstructure and crown dimensions would be particularly helpful Such modelswould enable us to simulate the dynamics of stands with controlled densitycomposition and structure with limited eld work Rigorous experimentalplanning could hence be elaborated to identify clearly the importance of thevarious factors of understory light regime

64 conclusion

The increasing awareness of decision makers and forests managers withrespect to the necessity of preserving biodiversity and ecosystem serviceswith sustainable management practices have provided the impetus for pro-moting a silviculture of mixed and uneven-aged stands that mimics naturalprocesses However a lack of knowledge of the natural dynamics of suchstands has hindered our ability to manage for some desired mixture of treespecies

In order to ll this gap I modeled some key processes of the dynamicsof mixed and uneven-aged stands I modeled the development of mixed re-generation under partially closed canopies and the interception of light byheterogeneous canopies I implemented these models in a simulation pro-gram to explore how these factors aect stand dynamics and how varioussilvicultural treatments can be manipulated to provide or maintain favor-able understory light conditions for natural regeneration The results pro-vide guidelines for forest managers who want to maintain the coexistenceof species with contrasting shade tolerances

Finally maintaining mixtures of species with dierent shade tolerancesoers many advantages but at the same time runs contrary to natural forestsuccession Mixtures preserve forest biodiversity forest productivity andecosystem services and enhance forest resilience In the context of pursu-ing sustainable forest management practices combined with global changemaintaining species mixtures is a good strategy However continuous-cover silviculture of mixed stands with species of dierent shade tolerancesrequires many eorts to ght against the natural transition of secondaryforests towards late-successional forests Despite the numerous silvicul-tural advantages of mixed stands maintaining such species mixtures isquestionable since they do not mimic natural forest dynamics mightprove to be labor intensive and therefore partly contradict the essence ofclose-to-nature forestry the goal of which is to rely upon natural processesover human interventions At the end of this thesis I therefore wonderwhether the management of mixed stands should accommodate naturalforest succession rather than maintaining by any and all means unstableecological communities

B I B L I O G R A P H Y

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Aussenac G 2000 Interactions between forest stands and microclimateEcophysiological aspects and consequences for silviculture Ann For Sci57(3)287ndash301 doi 101051forest2000119

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Balandier P Collet C Miller J H Reynolds P E and Zedaker S M 2006aDesigning forest vegetation management strategies based on the mecha-nisms and dynamics of crop tree competition by neighbouring vegetationForestry 79(1)3ndash27 doi 101093forestrycpi056

Balandier P Sonohat G Sinoquet H Varlet-Grancher C and DumasY 2006b Characterisation prediction and relationships between dier-ent wavebands of solar radiation transmitted in the understorey of even-aged oak (Quercus petraea Q robur) stands Trees 20(3)363ndash370 doi101007s00468-006-0049-3

Balandier P Sinoquet H Frak E Giuliani R Vandame M Descamps SColl L Adam B Prevosto B and Curt T 2007 Six-year time courseof light-use eciency carbon gain and growth of beech saplings (Fagussylvatica) planted under a Scots pine (Pinus sylvestris) shelterwood TreePhysiol 27(8)1073ndash1082 doi 101093treephys2781073

Balandier P Marquier A Gaudio N Wehrlen L Casella E Coll LKiewitt A and Harmer R 2009 Methods for describing light captureby understorey weeds in temperate forests consequences for tree regen-eration In Bentsen N editor Final COST E47 Conference Forest vegetationmanagement towards environmental sustainability pages 73ndash75

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Bartelink H H 1997 Allometric relationships for biomass and leaf areaof beech (Fagus sylvatica L) Ann For Sci 54(1)39ndash50 doi 101051for-est19970104

Bartelink H H 1998a A model of dry matter partitioning in trees TreePhysiol 18(2)91ndash101 doi 101093treephys18291

Bartelink H H 1998b Radiation interception by forest trees a simula-tion study on eects of stand density and foliage clustering on absorp-tion and transmission Ecol Model 105(2-3)213ndash225 doi 101016S0304-3800(97)00165-8

Bartoli M Tran-Ha M Largier G Dume G and Larrieu L 2000 Ecooreun logiciel simple de diagnostic eacutecologique Rev For Fr 56(6)530ndash547 doi10426720425386

Bates D Maechler M Bolker B and Walker S 2013 lme4 Linear mixed-eects models using Eigen and S4 R package version 10-4

Baudry O 2013 Reacuteponse de la reacutegeacuteneacuteration naturelle de checircne et de hecirctreau stade fourreacute agrave la refermeture du couvert PhD thesis UCL Louvain-la-Neuve Belgique

Beaudet M and Messier C 1998 Growth and morphological responses ofyellow birch sugar maple and beech seedlings growing under a naturallight gradient Can J For Res 28(7)1007ndash1015 doi 101139cjfr-28-7-1007

Beaudet M and Messier C 2002 Variation in canopy openness and lighttransmission following selection cutting in northern hardwood stands anassessment based on hemispherical photographs Agric For Meteorol 110(3)217ndash228 doi 101016S0168-1923(01)00289-1

Beaudet M Messier C and Canham C D 2002 Predictions of understoreylight conditions in northern hardwood forests following parameterizationsensitivity analysis and tests of the SORTIE light model For Ecol Man-age 165(1-3)235ndash248 doi 101016S0378-1127(01)00621-1

Beaudet M Harvey B D Messier C Coates K D Poulin J KneeshawD D Brais S and Bergeron Y 2011 Managing understory light condi-tions in boreal mixedwoods through variation in the intensity and spatialpattern of harvest a modelling approach For Ecol Manage 261(1)84ndash94doi 101016jforeco201009033

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Bock J Vinkler I Duplat P Renaud J Badeau V and Dupouey J 2005Stabiliteacute au vent des hecirctraies les enseignements de la tempecircte de 1999Rev For Fr 57(2)143ndash158 doi 10426720425032

Boivin F Paquette A Racine P and Messier C 2011 A fast and reliablemethod for the delineation of tree crown outlines for the computation ofcrown openness values and other crown parameters Can J For Res 41(9)1827ndash1835 doi 101139x11-107

Bonhomme R 1993 The solar radiation characterization and distributionin the canopy In Varlet-Grancher C Bonhomme R and Sinoquet Heditors Crop structure and light microclimate Characterization and appli-cations pages 17ndash28 INRA Paris doi 101002qj49712052020

Bontemps J-D Herve J-C Duplat P and Dhocircte J-F 2012 Shifts in theheight-related competitiveness of tree species following recent climatewarming and implications for tree community composition The case ofcommon beech and sessile oak as predominant broadleaved species in Eu-rope Oikos 121(8)1287ndash1299 doi 101111j1600-0706201120080x

Branquart E and De Keersmaeker L 2010 Eet du meacutelange drsquoessences surla biodiversiteacute forestiegravere Forecirct Wallonne 10617ndash26

Breacuteda N Cochard H Dreyer E and Granier A 1993 Field comparisonof transpiration stomatal conductance and vulnerability to cavitation ofQuercus petraea and Quercus robur under water stress Ann For Sci 50(6)571ndash582 doi 101051forest19930606

Breda N 2003 Ground-based measurements of leaf area index a reviewof methods instruments and current controversies J Exp Bot 54(392)2403ndash2417 doi 101093jxberg263

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Brunner A 1998 A light model for spatially explicit forest stand modelsFor Ecol Manage 107(1-3)19ndash46 doi 101016S0378-1127(97)00325-3

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Canham C D Finzi A C Pacala S W and Burbank D H 1994 Causesand consequences of resource heterogeneity in forests - interspecic vari-ation in light transmission by canopy trees Can J For Res 24(2)337ndash349doi 101139x94-046

Canham C D Coates K D Bartemucci P and Quaglia S 1999 Measure-ment and modeling of spatially explicit variation in light transmissionthrough interior cedar-hemlock forests of British Columbia Can J ForRes 29(11)1775ndash1783 doi 101139x99-151

Casabon C and Pothier D 2007 Browsing of tree regeneration by white-tailed deer in large clearcuts on Anticosti Island Quebec For Ecol Man-age 253(1-3)112ndash119 doi 101016jforeco200707009

Cavin L Mountford E P Peterken G F and Jump A S 2013 Extremedrought alters competitive dominance within and between tree speciesin a mixed forest stand Funct Ecol 27(6)1424ndash1435 doi 1011111365-243512126

Cescatti A 1997a Modelling the radiative transfer in discontinuouscanopies of asymmetric crowns I Model structure and algorithms EcolModel 101(2-3)263ndash274 doi 101016S0304-3800(97)00050-1

Cescatti A 1997b Modelling the radiative transfer in discontinuouscanopies of asymmetric crowns II Model testing and application in aNorway spruce stand Ecol Model 101(2-3)275ndash284 doi 101016S0304-3800(97)00055-0

Chaar H and Colin F 1999 Deacuteveloppement en hauteur des reacutegeacuteneacuterationsde checircne sessile Rev For Fr 51(2)341ndash354 doi 10426720425441

Chazdon R and Pearcy R 1991 The importance of sunecks for forestunderstory plants BioScience 41(11)760ndash766 doi 1023071311725

Chen J M Blanken P D Black T A Guilbeault M and Chen S 1997Radiation regime and canopy architecture in a boreal aspen forest AgricFor Meteorol 86(1-2)107ndash125 doi 101016S0168-1923(96)02402-1

Chen J M Liu J Cihlar J and Goulden M L 1999 Daily canopyphotosynthesis model through temporal and spatial scaling for remotesensing applications Ecol Model 124(2-3)99ndash119 doi 101016S0304-3800(99)00156-8

Claessens H Peacuterin J Latte N Lecomte H and Brostaux Y 2010 Unechecircnaie nrsquoest pas lrsquoautre analyse des contextes sylvicoles du checircne enforecirct wallonne Forecirct Wallonne 1083ndash18

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Coates K D Canham C D Beaudet M Sachs D L and Messier C 2003Use of a spatially explicit individual-tree model (SORTIEBC) to explorethe implications of patchiness in structurally complex forests For EcolManage 186(1-3)297ndash310 doi 101016S0378-1127(03)00301-3

Coll L Balandier P Picon-Cochard C Prevosto B and Curt T 2003Competition for water between beech seedlings and surrounding vege-tation in dierent light and vegetation composition conditions Ann ForSci 60(7)593ndash600 doi 101051forest2003051

Coll L Balandier P and Picon-Cochard C 2004 Morphological and phys-iological responses of beech (Fagus sylvatica) seedlings to grass-inducedbelowground competition Tree Physiol 24(1)45ndash54 doi 101093treep-hys24145

Collet C and Chenost C 2006 Using competition and light estimates to pre-dict diameter and height growth of naturally regenerated beech seedlingsgrowing under changing canopy conditions Forestry 79(5)489ndash502 doi101093forestrycpl03

Collet C and Frochot H 1996 Eects of interspecic competition on peri-odic shoot elongation in oak seedlings Can J For Res 26(11)1934ndash1942doi 101139x26-218

Collet C Colin F and Bernier F 1997 Height growth shoot elongationand branch development of young Quercus petraea grown under dierentlevels of resource availability Ann For Sci 54(1)65ndash81 doi 101051for-est19970106

Collet C Lanter O and Pardos M 2001 Eects of canopy opening onheight and diameter growth in naturally regenerated beech seedlingsAnn For Sci 58(2)127ndash134 doi 101007s00468-001-0159-x

Courbaud B Goreaud F Dreyfus P and Bonnet F R 2001 Evaluat-ing thinning strategies using a tree distance dependent growth modelsome examples based on the CAPSIS software ldquouneven-aged spruceforestsrdquo module For Ecol Manage 145(1-2)15ndash28 doi 101016S0378-1127(00)00571-5

Courbaud B de Coligny F and Cordonnier T 2003 Simulating radiationdistribution in a heterogeneous Norway spruce forest on a slope AgricFor Meteorol 116(1-2)1ndash18 doi 101016S0168-1923(02)00254-X

Da Silva D Boudon F Godin C and Sinoquet H 2008 Multiscale frame-work for modeling and analyzing light interception by trees MultiscaleModel Simul 7(2)910ndash933 doi 10113708071394X

Da Silva D Balandier P Boudon F Marquier A and Godin C 2011Modeling of light transmission under heterogeneous forest canopy anappraisal of the eect of the precision level of crown description AnnFor Sci 69(2)191ndash193 doi 101007s13595-011-0139-2

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Delagrange S Messier C Lechowicz M J and Dizengremel P 2004 Phys-iological morphological and allocational plasticity in understory decidu-ous trees importance of plant size and light availability Tree Physiol 24(7)775ndash784 doi 101093treephys247775

Delagrange S Nolet P and Bannon K 2010 Eet de lrsquoouverture du cou-vert du deacutegagement et du chaulage sur la composition et la croissance dela reacutegeacuteneacuteration drsquoeacuterabliegraveres envahies par le hecirctre Remesure 3 ans apregravessa mise en place Technical report Institut queacutebeacutecois drsquoAmeacutenagement dela Forecirct feuillue

Diaci J Gyoerek N Gliha J and Nagel T 2007 Response of Quercusrobur L seedlings to north-south asymmetry of light within gaps in ood-plain forests of Slovenia Ann For Sci 65(1)105ndash105 doi 101051for-est2007077

Diaci J 2002 Regeneration dynamics in a Norway spruce plantation on asilver r-beech forest site in the Slovenian Alps For Ecol Manage 161(1-3)27ndash38 doi 101016S0378-1127(01)00492-3

Dineur P 1951 Quelques donneacutees sur lrsquoeacutecologie de la reacutegeacuteneacuteration du checircnerouvre Bull Soc For Belg 58(2)38ndash50

Dolling A 1996 Interference of bracken (Pteridium aquilinum L Kuhn)with Scots pine (Pinus sylvestris L) and Norway spruce (Picea abies LKarst) seedling establishment For Ecol Manage 88(3)227ndash235 doi101016S0378-1127(96)03846-7

Doucet J L Kouadio Y L Monticelli D and Lejeune P 2009 En-richment of logging gaps with moabi (Baillonella toxisperma Pierre) ina Central African rain forest For Ecol Manage 258(11)2407ndash2415 doi101016jforeco200908018

Dreyer E Collet C Montpied P and Sinoquet H 2005 Caracteacuterisationde la toleacuterance agrave lrsquoombrage des jeunes semis de hecirctre et comparaison avecles essences associeacutees Rev For Fr 57(2)175ndash188 doi 10426720425034

Dufour-Kowalski S Courbaud B Dreyfus P Meredieu C and de ColignyF 2012 Capsis an open software framework and community for forestgrowth modelling Ann For Sci 69(2)221ndash233 doi 101007s13595-011-0140-9

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Ellenberg H 1974 Indicator values of vascular plants in central Europe vol-ume 9 of Scripta geobotanica Germany

Emborg J 1998 Understorey light conditions and regeneration with re-spect to the structural dynamics of a near-natural temperate deciduousforest in Denmark For Ecol Manage 106(2-3)83ndash95 doi 101016S0378-1127(97)00299-5

Emborg J Christensen M and Heilmann-Clausen J 2000 The struc-tural dynamics of Suserup Skov a near-natural temperate deciduous for-est in Denmark For Ecol Manage 126(2)173ndash189 doi 101016S0378-1127(99)00094-8

Essery R Bunting P Rowlands A Rutter N Hardy J Melloh R Link TMarks D and Pomeroy J 2008 Radiative transfer modeling of a conif-erous canopy characterized by airborne remote sensing J Hydrometeor9(2)228ndash241 doi 1011752007jhm8701

Farque L Sinoquet H and Colin F 2001 Canopy structure and light inter-ception in Quercus petraea seedlings in relation to light regime and plantdensity Tree Physiol 21(17)1257ndash1267 doi 101093treephys21171257

Finegan B 1984 Forest succession Nature 312(8)109ndash114 doi101038312109a0

Fournier R A Landry R August N M Fedosejevs G and Gauthier R P1996 Modelling light obstruction in three conifer forests using hemispher-ical photography and ne tree architecture Agric For Meteorol 82(1-4)47ndash72 doi 1010160168-1923(96)02345-3

Frazer G Canham C and Lertzman K 1999 Gap Light Analyzer (GLA)Version 20 Imaging software to extract canopy structure and gap light trans-mission indices from true-colour sheye photographs users manual and pro-gram documentation Simon Fraser University British Columbia and theInstitute of Ecosystem Studies New York

Galen C Rabenold J J and Liscum E 2007 Functional ecology of ablue light photoreceptor eects of phototropin-1 on root growth enhancedrought tolerance in Arabidopsis thaliana New Phytol 173(1)91ndash99 doi101111j1469-8137200601893x

Garciacutea-Plazaola J and Becerril J 2000 Eects of drought on photoprotec-tive mechanisms in European beech (Fagus sylvatica L) seedlings fromdierent provenances Trees 14(8)485ndash490 doi 101007s004680000068

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Gaudio N Balandier P Philippe G Dumas Y Jean F and Ginisty C2011 Light-mediated inuence of three understorey species (Callunavulgaris Pteridium aquilinum Molinia caerulea) on the growth of Pinussylvestris seedlings Eur J For Res 130(1)77ndash89 doi 101007s10342-010-0403-2

Gersonde R Battles J J and OrsquoHara K L 2004 Characterizing the lightenvironment in Sierra Nevada mixed-conifer forests using a spatially ex-plicit light model Can J For Res 34(6)1332ndash1342 doi 101139x04-013

Gill R M A 1992 A review of damage by mammals in north temperateforests 1 Deer Forestry 65(2)145ndash169 doi 101093forestry652145

Goudriaan J 1977 Crop micrometeorology a simulation study PhD thesisWageningen University Nederland

Govind A Guyon D Roujean J-L Yauschew-Raguenes N Kumari JPisek J and Wigneron J-P 2013 Eects of canopy architectural param-eterizations on the modeling of radiative transfer mechanism Ecol Model251114ndash126 doi 101016jecolmodel201211014

Groot A 2004 A model to estimate light interception by tree crowns ap-plied to black spruce Can J For Res 34(4)788ndash799 doi 101139x03-242

Grubb P 1977 The maintainance of species-richness in plant communitiesThe importance of the regeneration niche Biol Rev 52(1)107ndash145 doi101111j1469-185X1977tb01347x

Gruselle M-C 2002 Etude des potentialiteacutes de production de checircne de qualiteacuteen Ardenne belge Meacutemoire de n drsquoeacutetude

Hall J S 2008 Seed and seedling survival of African mahogany(Entandrophragma spp) in the Central African Republic Implicationsfor forest management For Ecol Manage 255(2)292ndash299 doi101016jforeco200709050

Hector A Schmid B Beierkuhnlein C Caldeira M C Diemer M Dimi-trakopoulos P G Finn J A Freitas H Giller P S Good J Harris RHoumlgberg P Huss-Danell K Joshi J Jumpponen A Koumlrner C LeadleyP W Loreau M Minns A Mulder C P H OrsquoDonovan G Otway S JPereira J S Prinz A Read D J Scherer-Lorenzen M Schulze E-DSiamantziouras A-S D Spehn E M Terry A C Troumbis A Y Wood-ward F I Yachi S and Lawton J H 1999 Plant diversity and produc-tivity experiments in European grasslands Science 286(5442)1123ndash1127doi 101126science28654421123

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Henin J Huart O and Rondeux J 2003 Biogeographical observations onfour scolytids (Coleoptera Scolytidae) and one lymexylonid (ColeopteraLymexylonidae) in Wallonia (Southern Belgium) Belg J Zool 133(2)175ndash180

Heuze P Schnitzler A and Klein F 2005 Is browsing the major factor ofsilver r decline in the Vosges Mountains of France For Ecol Manage217(2ndash3)219ndash228 doi 101016jforeco200506003

Hidding B Tremblay J P and Coteacute S D 2013 A large herbivore triggersalternative successional trajectories in the boreal forest Ecology 94(12)2852ndash2860 doi 10189012-20151

Huston M 1979 A general hypothesis of species diversity Am Nat 113(1)81ndash101

IPCC 2007 Contribution of working groups I II and III to the fourth as-sessment In Pachauri R and Reisinger A editors Climate Change 2007Synthesis Report page 104p IPPC Geneva

IPCC Working group I 2013 Climate change 2013 the physical science basissummary for policymaker page 27 Switzerland

Jabiol B Brecircthes A Ponge J Toutain F and Brun J 1995 Lrsquohumus soustoutes ses formes ENGREF Nancy

Jactel H Brockerho E and Duelli P 2005 A test of the biodiversity-stability theory meta-analysis of tree species diversity eects on insectpest infestations and re-examination of responsible factors For Diversityand Funct 176235ndash262 doi 1010073-540-26599-6_12

Jaderlund A Zackrisson O and Nilsson M C 1996 Eects of bilberry(Vaccinium myrtillus L) litter on seed germination and early seedlinggrowth of four boreal tree species J Chem Ecol 22(5)973ndash986 doi101007BF02029948

Jarret P 2004 La checircnaie atlantique Lavoisier Paris

Jarvis P G and Leverenz J W 1983 Productivity of temperate deciduousand evergreen forests In Lange O L Nobel P S and Osmond C Beditors Encyclopedia of Plant Physiology volume 12 chapter 8 pages 234ndash280 Springer Berlin doi 101007978-3-642-68156-1_9

Jonard M Andre F and Ponette Q 2006 Modeling leaf dispersal in mixedhardwood forests using a ballistic approach Ecology 87(9)2306ndash2318 doi1018900012-9658(2006)87[2306MLDIMH]20CO2

Jonard M Andre F and Ponette Q 2008 Tree species mediated eectson leaf litter dynamics in pure and mixed stands of oak and beech CanJ For Res 38(3)528ndash538 doi 101139X07-183

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Jonckheere I Fleck S Nackaerts K Muys B Coppin P Weiss M andBaret F 2004 Review of methods for in situ leaf area index determina-tion - Part I Theories sensors and hemispherical photography Agric ForMeteorol 121(1-2)19ndash35 doi 101016jagrformet200308027

Keenan R J and Kimmins J P 1993 The ecological eects of clear-cuttingEnvironmental Reviews 1(2)121ndash144 doi doi101139a93-010

Kim H S Palmroth S Theacutereacutezien M Stenberg P and Oren R 2011 Anal-ysis of the sensitivity of absorbed light and incident light prole to variouscanopy architecture and stand conditions Tree Physiol 31(1)30ndash47 doi101093treephystpq098

Kobe R 2006 Sapling growth as a function of light and landscape-levelvariation in soil water and foliar nitrogen in northern Michigan Oecologia147(1)119ndash133 doi 101007s00442-005-0252-8

Kobe R Pacala S Silander J and Canham C 1995 Juvenile tree sur-vivorship as a component of shade tolerance Ecol Appl 5(2)517ndash532doi 1023071942040

Koop H and Sterck F J 1994 Light penetration through structurally com-plex forest canopies - an example of a lowland tropical rain-forest ForEcol Manage 69(1-3)111ndash122 doi 1010160378-1127(94)90223-2

Kunstler G Curt T Bouchaud M and Lepart J 2005 Growth mortalityand morphological response of European beech and downy oak along alight gradient in sub-Mediterranean forest Can J For Res 35(7)1657ndash1668 doi 101139x05-097

Kuuluvainen T 1992 Tree architectures adapted to ecient light utiliza-tion is there a basis for latitudinal gradients Oikos 65(2)275ndash284 doi1023073545019

Kuuluvainen T and Pukkala T 1991 Interaction between canopy architec-ture and photosynthetically active direct radiation at dierent latitudessimulation experiments and their ecological implications Lrsquoarbre Biolo-gie et deacuteveloppement hs277ndash291

Kuusk A 1993 Simulation of crop reectance (including hot spot eect) InVarlet-Grancher C Bonhomme R and Sinoquet H editors Crop struc-ture and light microclimate pages 263ndash270 INRA Lusignan France

Lafond V Lagarrigues G Cordonnier T and Courbaud B 2013 Uneven-aged management options to promote forest resilience for climate changeadaptation eects of group selection and harvesting intensity Ann ForSci 71(2)173ndash186 doi 101007s13595-013-0291-y

Landsberg J J and Sands P 2010 Physiological ecology of forest productionprinciples processes and models volume 4 Academic Press

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Laurent C Perrin D Bemelmans D Carnol M Claessens H De Can-niegravere C Franccedilois L Gerard E Greacutegoire J and Herman M 2009 Lechangement climatique et ses impacts sur les forecircts wallonnes Recom-mandations aux deacutecideurs et aux proprieacutetaires et gestionnaires Technicalreport Ministre de lrsquoAgriculture de la Ruraliteacute de lrsquoEnvironnement et duTourisme

Law B E Cescatti A and Baldocchi D D 2001 Leaf area distri-bution and radiative transfer in open-canopy forests implications formass and energy exchange Tree Physiol 21(12-13)777ndash787 doi101093treephys2112-13777

Le Duc M G and Havill D C 1998 Competition between Quercus petraeaand Carpinus betulus in an ancient wood in England seedling survivor-ship J Veg Sci 9(6)873ndash880 doi 1023073237052

Lecomte H Florkin P Morimont J-P and Thirion M 2003 La forecirct wal-lonne eacutetat de la ressource agrave la n du 20e siegravecle Technical report Ministegraverede la Reacutegion Wallonne Division de la nature et des forecircts

Lemaire J 2001 Checircnaies wallonnes Eacutetat des lieux apregraves un siegravecle de con-version et perspectives sylvicoles Forecirct wallonne 5320ndash30

Leroy C Sabatier S Wahyuni N Barczi J-F Dauzat J Laurans Mand Auclair D 2009 Virtual trees and light capture a method for op-timizing agroforestry stand design Agroforest Syst 77(1)37ndash47 doi101007s10457-009-9232-z

Licoppe A 2005 Reacuteexion sur le rocircle du cerf dans des programmes deconservation de la nature Forecirct wallonne 74(1)32ndash37

Lieers V J Messier C Stadt K J Gendron F and Comeau P G 1999Predicting and managing light in the understory of boreal forests Can JFor Res 29(6)796ndash811 doi 101139x98-165

Ligot G Courbaud B de Coligny F and Jonard M 2013 SamsaraLighthttpcapsisciradfrcapsishelp_ensamsaralight

Lochhead K D and Comeau P G 2012 Relationships between foreststructure understorey light and regeneration in complex Douglas-r dom-inated stands in south-eastern British Columbia For Ecol Manage 284(0)12ndash22 doi 101016jforeco201207029

Loumlf M and Welander N T 2004 Inuence of herbaceous competitors onearly growth in direct seeded Fagus sylvatica L and Quercus robur L AnnFor Sci 61(8)781ndash788 doi 101051forest2004075

Madsen P and Larsen J B 1997 Natural regeneration of beech (Fagus syl-vatica L) with respect to canopy density soil moisture and soil carbon con-tent For Ecol Manage 97(2)95ndash105 doi 101016S0378-1127(97)00091-1

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Mariscal M J Martens S N Ustin S L Chen J Weiss S B andRoberts D A 2004 Light-transmission proles in an old-growth for-est canopy simulations of photosynthetically active radiation by usingspatially explicit radiative transfer models Ecosystems 7(5)454ndash467 doi101007s10021-004-0137-4

McGarvey J C Bourg N A Thompson J R McShea W J and ShenX 2013 Eects of twenty years of deer exclusion on woody vegetationat three life-history stages in a mid-Atlantic temperate deciduous forestNortheastern Naturalist 20(3)451ndash468 doi 1016560450200301

Messier C Doucet R Ruel J C Claveau Y Kelly C and Lechowicz M J1999 Functional ecology of advance regeneration in relation to light inboreal forests Can J For Res 29(6)812ndash823 doi 101139x99-070

Mette T Dolos K Meinardus C Braumluning A Reineking B BlaschkeM Pretzsch H Beierkuhnlein C Gohlke A and Wellstein C 2013Climatic turning point for beech and oak under climate change in CentralEurope Ecosphere 4(12)art145 doi 101890ES13-001151

Moumllder I and Leuschner C 2014 European beech grows better and is lessdrought sensitive in mixed than in pure stands tree neighbourhood eectson radial increment Trees 28(3)1ndash16 doi 101007s00468-014-0991-4

Moulia B and Sinoquet H 1993 Three-dimensional digitizing systems forplant canopy geometrical structure a review In Varlet-Grancher C Bon-homme R and Sinoquet H editorsCrop structure and light microclimatepages 183ndash193 INRA Lusignan France

Newbold A Goldsmith F and Harding J 1981 The regeneration of oakand beech a literature review Discussion Papers in Conservation 33 Uni-versity College London

Nicolini E Barthelemy D and Heuret P 2000 Eects of canopy densityon architectural development of young sessile oakQuercus petraea (Matt)Liebl (Fagaceae) during forest regeneration Can J Bot 78(12)1531ndash1544doi 101139cjb-78-12-1531

Niinemets U 2006 The controversy over traits conferring shade-tolerancein trees ontogenetic changes revisited J Ecol 94(2)464ndash470 doi101111j1365-2745200601093x

Niinemets U 2010 A review of light interception in plant stands from leafto canopy in dierent plant functional types and in species with varyingshade tolerance Ecol Res 25(4)693ndash714 doi 101007s11284-010-0712-4

Nock C A Caspersen J P and Thomas S C 2008 Large ontogeneticdeclines in intra-crown leaf area index in two temperate deciduous treespecies Ecology 89(3)744ndash753 doi 10189007-05311

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Nyland R D 1996 Silviculture concepts and applications McGraw-HillNew-York

Pacala S W Canham C D Silander J A and Kobe R K 1994 SaplingGrowth as a Function of Resources in a North Temperate Forest Can JFor Res 24(11)2172ndash2183 doi 101139x94-280

Pacala S W Canham C D Saponara J Silander J A Kobe R K andRibbens E 1996 Forest models dened by eld measurements esti-mation error analysis and dynamics Ecol Monogr 66(1)1ndash43 doi1023072963479

Paquette A Messier C Perinet P and Cogliastro A 2008 Simulatinglight availability under dierent hybrid poplar clones in a mixed intensiveplantation system For Sci 54(5)481ndash489

Parker G G 1997 Canopy structure and light environment of an old-growth Douglas-rwestern hemlock forest Northwest Sci 71(4)261ndash270

Pedersen B S 1998 The role of stress in the mortality of midwestern oaks asindicated by growth prior to death Ecology 79(1)79ndash93 doi 1018900012-9658(1998)079[0079TROSIT]20CO2

Petriţan A M von Luumlpke B and Petriţan I C 2007 Eects of shadeon growth and mortality of maple (Acer pseudoplatanus) ash (Fraxinusexcelsior) and beech (Fagus sylvatica) saplings Forestry 80(4)397ndash412doi 101093forestrycpm030

Petriţan A M von Luumlpke B and Petriţan I C 2009 Inuence of light avail-ability on growth leaf morphology and plant architecture of beech (Fagussylvatica L) maple (Acer pseudoplatanus L) and ash (Fraxinus excelsior L)saplings Eur J For Res 128(1)61ndash74 doi 101007s10342-008-0239-1

Petriţan I C Marzano R Petriţan A M and Lingua E 2014 Overstorysuccession in a mixed Quercus petraea-Fagus sylvatica old growth forestrevealed through the spatial pattern of competition and mortality ForEcol Manage 3269ndash17 doi 101016jforeco201404017

Phattaralerphong J Sathornkich J and Sinoquet H 2006 A photographicgap fraction method for estimating leaf area of isolated trees Assessmentwith 3D digitized plants Tree Physiol 26(9)1123ndash1136 doi 101093treep-hys2691123

Piboule A Aoucirct 2001 Validation et analyse de sensibiliteacute drsquoun mod-egravele de transfert radiatif en vue de son application agrave la cartographie delrsquoeacuteclairement en peuplement forestier DEA ENGREF-INRA

Piboule A 2005 Inuence de la structure du peuplement forestier sur la dis-tribution de lrsquoeacuteclairement sous couvert Cas drsquoune forecirct heacuteteacuterogegravene feuilluesur plateau calcaire PhD thesis UMR INRA-ENGREF Nancy France

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Piedallu C Perez V Geacutegout J-C Lebourgeois F and Bertrand R 2009Impact potentiel du changement climatique sur la distribution de lrsquoEacutepiceacuteadu Sapin du Hecirctre et du Checircne sessile en France Rev For Fr 61(6)567ndash593 doi 104267204232924

Pierce L L and Running S W 1988 Rapid estimation of coniferous forestleaf area index using a portable integrating radiometer Ecology 69(6)1762ndash1767 doi 1023071941154

Pinheiro J Bates D DebRoy S and Sarkar D 2011 nlme Linear andnonlinear mixed eects models R package version 31-109

Pinno B D Lieers V J and Stadt K J 2001 Measuring and modellingthe crown and light transmission characteristics of juvenile aspen Can JFor Res 31(11)1930ndash1939 doi 101139cjfr-31-11-1930

Plak S 1987 Recherche de relations entre la qualiteacute du bois de checircne et lesparamegravetres de ses stations drsquoorigine Meacutemoire de n drsquoeacutetude

Pommerening A and Murphy S 2004 A review of the history def-initions and methods of continuous cover forestry with special at-tention to aorestation and restocking Forestry 77(1)27ndash44 doi101093forestry77127

Porte A and Bartelink H H 2002 Modelling mixed forest growth a reviewof models for forest management Ecol Model 150(1-2)141ndash188 doi101016S0304-3800(01)00476-8

Poskin A 1934 Le checircne peacutedonculeacute et le checircne rouvre Leur culture en Bel-gique Bibliothegraveque Agronomique Belge Gembloux

Pretzsch H Bielak K Block J Bruchwald A Dieler J Ehrhart H PKohnle U Nagel J Spellmann H Zasada M and Zingg A 2013a Pro-ductivity of mixed versus pure stands of oak (Quercus petraea (Matt) Liebland Quercus robur L) and European beech (Fagus sylvatica L) along anecological gradient Eur J For Res 132(2)263ndash280 doi 101007s10342-012-0673-y

Pretzsch H Schuumltze G and Uhl E 2013b Resistance of European treespecies to drought stress in mixed versus pure forests Evidence of stressrelease by inter-specic facilitation Plant Biol 15(3)483ndash495 doi101111j1438-8677201200670x

Preacutevost M and Raymond P 2012 Eect of gap size aspect and slope onavailable light and soil temperature after patch-selection cutting in yellowbirch-conifer stands Quebec Canada For Ecol Manage 274210ndash221 doi101016jforeco201202020

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Preacutevost M Raymond P and Lussier J M 2010 Regeneration dynamicsafter patch cutting and scarication in yellow birch - Conifer stands CanJ For Res 40(2)357ndash369 doi 101139X09-192

Preacutevost M and Pothier D 2003 Partial cuts in a trembling aspen coniferstand eects on microenvironmental conditions and regeneration dynam-ics Can J For Res 33(1)1ndash15 doi 101139x02-147

Preacutevosto B and Balandier P 2007 Inuence of nurse birch and Scots pineseedlings on early aerial development of European beech seedlings inan open-eld plantation of Central France Forestry 80(3)253ndash264 doi101093forestrycpm017

Pukkala T Becker P Kuuluvainen T and Okerblom P 1991 PredictingSpatial-Distribution of Direct-Radiation Below Forest Canopies Agric ForMeteorol 55(3-4)295ndash307 doi 1010160168-1923(91)90067-Z

Pukkala T Kuuluvainen T and Stenberg P 1993 Below-canopy distri-bution of photosynthetically active radiation and its relation to seedlinggrowth in a boreal Pinus sylvestris stand a simulation approach Scand JFor Res 8(3)313ndash325 doi 10108002827589309382780

R Core Team 2013 R A Language and Environment for Statistical Comput-ing

Rameau J-C 1999 Accrus successions veacutegeacutetales et modegraveles de dynamiquelineacuteaire forestiegravere In Boisement naturels des espaces agricoles pages 33ndash48Ingeacutenieries EAT Nancy

Rey H Dauzat J Chenu K Barczi J-F Dosio G A A and Lecoeur J2008 Using a 3-D virtual sunower to simulate light capture at organplant and plot levels contribution of organ interception impact of he-liotropism and analysis of genotypic dierences Ann Bot 101(8)1139ndash1151 doi 101093aobmcm300

Reyes G P Kneeshaw D De Grandpreacute L and Leduc A 2010 Changesin woody vegetation abundance and diversity after natural disturbancescausing dierent levels of mortality J Veg Sci 21(2)406ndash417 doi101111j1654-1103200901152x

Ross J 1981 The radiation regime and architecture of plant stands volume 3of Tasks for vegetation sciences Springer Boston doi 101007978-94-009-8647-3

Rugani T Diaci J and Hladnik D 2013 Gap dynamics and structure oftwo old-growth beech forest remnants in slovenia PloS one 8(1)1ndash13 doi101371journalpone0052641

Scharnweber T Manthey M Criegee C Bauwe A Schroumlder C andWilmking M 2011 Drought mattersndashDeclining precipitation inuencesgrowth of Fagus sylvatica L and Quercus robur L in north-eastern Ger-many For Ecol Manage 262(6)947ndash961 doi 101016jforeco201105026

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Schuumltz J-P 1999 Close-to-nature silviculture is this concept com-patible with species diversity Forestry 72(4)359ndash366 doi101093forestry724359

Schuumltz J-P Pukkala T Donoso P and Gadow K 2012 Historical Emer-gence and Current Application of CCF In Pukkala T and Gadow K ed-itors Continuous Cover Forestry volume 23 of Continuous Cover Forestrypages 1ndash28 Springer Netherlands doi 101007978-94-007-2202-6_1

Shinozaki K Yoda K Hozumi K and Kira T 1964 A quantitative analysisof plant form-the pipe model theory I Basic analyses Jpn J Ecol 14(3)97ndash105

Sinoquet H Varlet-Grancher C and Bonhomme R 1993 Modelling ra-diative transfer within homogeneous canopies basic concepts In Varlet-Grancher C Bonhomme R and Sinoquet H editors Crop structure andlight microclimate pages 207ndash228 INRA Lusignan France

Sinoquet H Le Roux X Adam B Ameglio T and Daudet F A 2001RATP a model for simulating the spatial distribution of radiation absorp-tion transpiration and photosynthesis within canopies application to anisolated tree crown Plant Cell Environ 24(4)395ndash406 doi 101046j1365-3040200100694x

Sinoquet H Sonohat G Phattaralerphong J and Godin C 2005 Foliagerandomness and light interception in 3-D digitized trees an analysis frommultiscale discretization of the canopy Plant Cell Environ 28(9)1158ndash1170 doi 101111j1365-3040200501353x

Smith T and Huston M 1989 A theory of the spatial and tempo-ral dynamics of plant communities Vegetatio 83(1-2)49ndash69 doi101007BF00031680

Sprugel D G Rascher K G Gersonde R Dovciak M Lutz J A andHalpern C B 2009 Spatially explicit modeling of overstory manipula-tions in young forests Eects on stand structure and light Ecol Model220(24)3565ndash3575 doi 101016jecolmodel200907029

Stadt K J and Lieers V J 2000 MIXLIGHT a exible light transmissionmodel for mixed-species forest stands Agric For Meteorol 102(4)235ndash252 doi 101016S0168-1923(00)00128-3

Stancioiu P T and OrsquoHara K L 2006a Morphological plasticity of regen-eration subject to dierent levels of canopy cover in mixed-species mul-tiaged forests of the Romanian Carpathians Trees 20(2)196ndash209 doi101007s00468-005-0026-2

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Stancioiu P T and OrsquoHara K L 2006b Leaf area and growth eciency of re-generation in mixed species multiaged forests of the Romanian Carpathi-ans For Ecol Manage 222(1-3)55ndash66 doi 101016jforeco200510018

Stancioiu P and OrsquoHara K 2006 Regeneration growth in dierent light en-vironments of mixed species multiaged mountainous forests of RomaniaEur J For Res 125(2)151ndash162 doi 101007s10342-005-0069-3

Theacutereacutezien M Palmroth S Brady R and Oren R 2007 Estimation of lightinterception properties of conifer shoots by an improved photographicmethod and a 3D model of shoot structure Tree Physiol 27(10)1375ndash1387doi 101093treephys27101375

Tian H Chen G Liu M Zhang C Sun G Lu C Xu X Ren W PanS and Chappelka A 2010 Model estimates of net primary productivityevapotranspiration and water use eciency in the terrestrial ecosystemsof the southern United States during 1895ndash2007 For Ecol Manage 259(7)1311ndash1327 doi 101016jforeco200910009

Timbal J Gelpe J and Garbaye J 1990 Preliminary study of the depres-sive eect of Molinia caerulea (L) Moench on early growth and mycor-rhizal status of Quercus rubra seedlings Ann For Sci 47(6)643ndash649 doi101051forest19900609

Touzet G 1996 La sylviculture proche de la nature poleacutemique actuellevieux deacutebats Rev For Fr sp23ndash30 doi 104267204226798

Turbang J 1954 Contribution agrave lrsquoeacutetude de la reacutegeacuteneacuteration naturelle duchecircne en Lorraine belge Bull Inst Agron Gembloux 22(12)90ndash133

Tychon B 2000 Preacutevention des productions veacutegeacutetales agrave lrsquoeacutechelle nationalebaseacutee sur un systegraveme integreacute ldquomodegravele agromeacuteteacuteorologique-teacuteleacutedeacutetactionrdquoanalyse de sensibiliteacute et domaine de validiteacute en tant qursquooutil drsquoaide agrave ladeacutecision en politique agricole Technical report Fondation UniversitaireLuxembourgeoise (FUL) Vlaamse Instelling voor Onderzoek (VITO) etCentre de Recherches Agronomiques (CRA)

Tyler G 1992 Tree species anity of decomposer and ectomycorrhizalmacrofungi in beech (Fagus sylvatica L) oak (Quercus robur L) and horn-beam (Carpinus betulus L) forests For Ecol Manage 47(1-4)269ndash284 doi1010160378-1127(92)90279-I

Valladares F and Niinemets U 2008 Shade Tolerance a Key Plant Featureof Complex Nature and Consequences Annu Rev Ecol Evol Syst 39(1)237ndash257 doi doi101146annurevecolsys39110707173506

Van Couwenberghe R Geacutegout J-C Lacombe E and Collet C 2013 Lightand competition gradients fail to explain the coexistence of shade-tolerantFagus sylvatica and shade-intermediate Quercus petraea seedlings AnnBot 112(7)1421ndash1430 doi 101093aobmct200

112 bibliography

von Luumlpke B 1998 Silvicultural methods of oak regeneration with specialrespect to shade tolerant mixed species For Ecol Manage 106(1)19ndash26doi 101016S0378-1127(97)00235-1

von Luumlpke B and Hauskeller-Bullerjahn K 1999 Production forestry with-out clear felling will oak become marginalized Forst und Holz 54(18)563ndash568

von Luumlpke B and Hauskeller-Bullerjahn K 2004 A contribution to mod-elling juvenile growth examplied by mixed oak-beech regeneration All-gemeine Forst Und Jagdzeitung 175(4-5)61ndash69

Wagner S Collet C Madsen P Nakashizuka T Nyland R andSagheb-Talebi K 2010 Beech regeneration research from ecologicalto silvicultural aspects For Ecol Manage 259(11)2172ndash2182 doi101016jforeco201002029

Walters M B and Reich P B 1996 Are shade tolerance survival andgrowth linked Low light and nitrogen eects on hardwood seedlingsEcology 77(3)841ndash853 doi 1023072265505

Wang Y P and Jarvis P G 1990 Description and validation of an arraymodel MAESTRO Agric For Meteorol 51(3)257ndash280 doi 1010160168-1923(90)90112-J

Webb W L and Ungs M J 1993 Three dimensional distribution of needleand stem surface area in a Douglas-r Tree Physiol 13(2)203ndash212 doi101093treephys132203

Weiss M Baret F Smith G J Jonckheere I and Coppin P 2004 Reviewof methods for in situ leaf area index (LAI) determination Part II Estima-tion of LAI errors and sampling Agric For Meteorol 121(1-2)37ndash53 doi101016jagrformet200308001

Welander N T and Ottosson B 1998 The inuence of shading on growthand morphology in seedlings of Quercus robur L and Fagus sylvatica LFor Ecol Manage 107(1-3)117ndash126 doi 101016S0378-1127(97)00326-5

Williams D L 1991 A comparison of spectral reectance properties at theneedle branch and canopy level for selected conifer species Remote SensEnviron 35(2-3)79ndash93 doi 1010160034-4257(91)90002-N

Summary

Remerciements

Publications

Contents

List of Figures

List of Tables

Acronyms

1 General introduction

2 Study area and species

21 Ecological conditions

22 Reduction of oak population

23 Why maintain oak

231 Biodiversity

232 Resilience

233 Productivity

234 Wood quality

235 Climate change

24 Forest management


31 Methods

311 Study sites




32 Results



323 Diffuse and direct radiation

324 Analyzing site effect

33 Discussion


332 Competition



34 Conclusion

4 Model of light interception

41 Literature review

411 Classification of FRTMs

412 Input variables




416 Discussion

42 Implementing a radiative transfer model

421 Crown geometry

422 Crown radius

423 Tree Height




5 Managing understory light

51 Methods

511 Study sites




52 Results

521 Tree inventory


523 Simulation

53 Discussion

531 Mean light response


6 General discussion

61 Maintaining species diversity

62 Silvicultural recommandations

63 Study limitations and perspectives

64 Conclusion

Bibliography

Gauthier LIGOT

S U M M A R Y

HE Luccock

C O N T E N T S

34 Conclusion 28

xviii contents

bibliography 95

A C R O N Y M S

1D One-dimensional

LAI Leaf Area Index

PE Porous Envelope

TM Turbid Medium

William Wordsworth

John Muir

Belgium

France

Luxembourg

Germany

Belgian Ardennes

0 10050 Km

number of plotsHigh

soil moisture

soil pH

Acidic Alkaline

23 why maintain oak

231 Biodiversity

232 Resilience

Quercus sp

Fagus sylvatica

Girth classes (cm)

Number of trees

233 Productivity

234 Wood quality

235 Climate change

Saint Bernard

31 methods

311 Study sites

square grid

31 methods 19

2 (31)

20 5 7 - 92 19 37 159 - 231 11 - 18 14 ndash 19 10 - 274 7 6 - 74 25 73 168 - 255 13 - 18 4 ndash 95 13 - 20

31 methods 21

c )+ ϵi j (32)

cSDOM)+ ϵi j (33)

32 results

32 results 23

heightincrement

cm cm year

Beech 149 153 (23277) 26 (-962) 10 (421) 120Oak 174 125 (13273) 16 (-1052) 10 (119) 70Other 93 118 (7285) 20 (-6684) 51

Oak 2059(16422476)

6058(34688648)

10257(646914046)

7255 6759

Beech 2431(20352828)

3964(23785550)

7261 10491

33 discussion 25

33 discussion

33 discussion 27

332 Competition

34 conclusion

34 conclusion 29

Heraclitus

Output variables

Input variables

τ (ηγ ) = p (42)

412 Input variables

4125 Crown openness

4151 1D model

4152 3D crown model

416 Discussion

PorousEenvelopep

processes

Applications

Radiative transfer

Canopy geometry

4163 Applications

421 Crown geometry

(x minus x0)2

(y minus y0)2

(z minus z0)2

c= 1 (44)

(a) 1 ellipsoid

aeastawest

bnorth

bsouth

422 Crown radius

423 Tree Height

AL2 + B L+C = 0 (45)

a2 +cos2 (θ ) sin2 (α )

b2 +sin2 (θ )

b2 +z2

1c2 minus 1

tanθ (47)

tree height

path length

crown base height

4261 Method

4263 Conclusion

a R2 = 68 b R

2 = 87

Ralph Waldo Emerson

51 methods

511 Study sites

51 methods 71

51 methods 73

were randomly added

mapped and measured

Plot center part

scoret = β +u

05radicAN

52 results 77

52 results

521 Tree inventory

523 Simulation

stand oak beech

19 983 1494 4398 096 1494 4398 1273 843525 1272 2184 4675 105 2184 4675 1305 843527 353 782 5313 105 645 5297 1273 725728 514 747 4304 119 028 4742 4170 5252 719 4289 1273 649426 617 1460 5489 127 194 7576 7576 7576 1263 5362 1432 78303 1136 1810 4503 107 317 3942 2801 6016 1493 4657 1432 6557

18 467 752 4529 097 140 6232 5443 6430 606 4533 1273 79901 872 1115 4034 118 286 4433 2706 6525 790 3935 1273 71622 1139 1633 4273 097 435 4930 1623 5921 1195 4135 1273 7226

14 1245 2121 4657 128 670 6564 5443 8276 1451 4200 1273 697120 1439 1949 4152 104 697 7187 5570 9231 1252 3546 1273 805329 1270 2056 4541 120 1114 5542 4043 6812 942 3853 1273 652513 1338 1537 3825 109 869 6021 4615 7289 668 2870 1273 69715 2178 2051 3462 103 1195 5387 1783 7130 856 2567 1273 6812

12 1566 2265 4292 116 1361 5324 3947 8085 904 3474 1273 75764 2073 2416 3852 097 1670 5773 3820 7226 746 2572 1273 8403

22 2165 1531 3000 112 1107 2902 1369 4966 362 4336 1751 779921 1203 1954 4548 097 1471 7306 5761 9486 391 3151 1273 763923 1215 1631 4135 100 1241 4387 1464 7576 276 4531 1432 770315 1905 2469 4062 106 1980 5721 3215 7162 006 1305 1273 133717 1885 2689 4262 131 2227 5485 2451 7385 176 2913 1273 49346 1075 2079 4962 112 1738 6659 2897 8976 251 2771 1273 4902

10 1352 2165 4515 129 1929 4899 1655 5952 106 3041 2960 31198 2153 1906 3358 108 1731 4077 1655 6303 023 2135 1305 3056

24 1119 1180 3664 130 1085 4035 2005 550711 1146 1444 4005 100 1351 4822 1273 6685 023 1969 1751 21659 1225 1274 3640 125 1246 3754 1324 6971

52 results 79

Cutting type

Estimate CI

53 discussion

10 20 40 60

10 20 40 60 10 20 40 60

10 20 40 60

beforeharvest

5-10 10-15 15-20 20-25 5-10 10-15 15-20 20-25

5-10 10-15 15-20 20-25 5-10 10-15 15-20 20-250

53 discussion 83

George Wald

no harvest

Cutting intensity

oak tree

beech tree

closed canopy

directradiations

closed canopy

gap gap

gapgapgap

gap gap gap

directradiations

64 conclusion

96 bibliography

bibliography 97

98 bibliography

bibliography 99

100 bibliography

bibliography 101

102 bibliography

bibliography 103

104 bibliography

bibliography 105

106 bibliography

bibliography 107

108 bibliography

bibliography 109

110 bibliography

bibliography 111

112 bibliography

Summary

Remerciements

Publications

Contents

List of Figures

List of Tables

Acronyms



23 Why maintain oak

231 Biodiversity

232 Resilience

233 Productivity

234 Wood quality

235 Climate change



31 Methods

311 Study sites




32 Results





33 Discussion


332 Competition



34 Conclusion




412 Input variables




416 Discussion


421 Crown geometry

422 Crown radius

423 Tree Height





51 Methods

511 Study sites




52 Results

521 Tree inventory


523 Simulation

53 Discussion







64 Conclusion

Bibliography

S U M M A R Y

HE Luccock

C O N T E N T S

34 Conclusion 28

xviii contents

bibliography 95

A C R O N Y M S

1D One-dimensional

LAI Leaf Area Index

PE Porous Envelope

TM Turbid Medium

William Wordsworth

John Muir

Belgium

France

Luxembourg

Germany

Belgian Ardennes

0 10050 Km

number of plotsHigh

soil moisture

soil pH

Acidic Alkaline

23 why maintain oak

231 Biodiversity

232 Resilience

Quercus sp

Fagus sylvatica

Girth classes (cm)

Number of trees

233 Productivity

234 Wood quality

235 Climate change

Saint Bernard

31 methods

311 Study sites

square grid

31 methods 19

2 (31)

20 5 7 - 92 19 37 159 - 231 11 - 18 14 ndash 19 10 - 274 7 6 - 74 25 73 168 - 255 13 - 18 4 ndash 95 13 - 20

31 methods 21

c )+ ϵi j (32)

cSDOM)+ ϵi j (33)

32 results

32 results 23

heightincrement

cm cm year

Beech 149 153 (23277) 26 (-962) 10 (421) 120Oak 174 125 (13273) 16 (-1052) 10 (119) 70Other 93 118 (7285) 20 (-6684) 51

Oak 2059(16422476)

6058(34688648)

10257(646914046)

7255 6759

Beech 2431(20352828)

3964(23785550)

7261 10491

33 discussion 25

33 discussion

33 discussion 27

332 Competition

34 conclusion

34 conclusion 29

Heraclitus

Output variables

Input variables

τ (ηγ ) = p (42)

412 Input variables

4125 Crown openness

4151 1D model

4152 3D crown model

416 Discussion

PorousEenvelopep

processes

Applications

Radiative transfer

Canopy geometry

4163 Applications

421 Crown geometry

(x minus x0)2

(y minus y0)2

(z minus z0)2

c= 1 (44)

(a) 1 ellipsoid

aeastawest

bnorth

bsouth

422 Crown radius

423 Tree Height

AL2 + B L+C = 0 (45)

a2 +cos2 (θ ) sin2 (α )

b2 +sin2 (θ )

b2 +z2

1c2 minus 1

tanθ (47)

tree height

path length

crown base height

4261 Method

4263 Conclusion

a R2 = 68 b R

2 = 87

Ralph Waldo Emerson

51 methods

511 Study sites

51 methods 71

51 methods 73

were randomly added

mapped and measured

Plot center part

scoret = β +u

05radicAN

52 results 77

52 results

521 Tree inventory

523 Simulation

stand oak beech

19 983 1494 4398 096 1494 4398 1273 843525 1272 2184 4675 105 2184 4675 1305 843527 353 782 5313 105 645 5297 1273 725728 514 747 4304 119 028 4742 4170 5252 719 4289 1273 649426 617 1460 5489 127 194 7576 7576 7576 1263 5362 1432 78303 1136 1810 4503 107 317 3942 2801 6016 1493 4657 1432 6557

18 467 752 4529 097 140 6232 5443 6430 606 4533 1273 79901 872 1115 4034 118 286 4433 2706 6525 790 3935 1273 71622 1139 1633 4273 097 435 4930 1623 5921 1195 4135 1273 7226

14 1245 2121 4657 128 670 6564 5443 8276 1451 4200 1273 697120 1439 1949 4152 104 697 7187 5570 9231 1252 3546 1273 805329 1270 2056 4541 120 1114 5542 4043 6812 942 3853 1273 652513 1338 1537 3825 109 869 6021 4615 7289 668 2870 1273 69715 2178 2051 3462 103 1195 5387 1783 7130 856 2567 1273 6812

12 1566 2265 4292 116 1361 5324 3947 8085 904 3474 1273 75764 2073 2416 3852 097 1670 5773 3820 7226 746 2572 1273 8403

22 2165 1531 3000 112 1107 2902 1369 4966 362 4336 1751 779921 1203 1954 4548 097 1471 7306 5761 9486 391 3151 1273 763923 1215 1631 4135 100 1241 4387 1464 7576 276 4531 1432 770315 1905 2469 4062 106 1980 5721 3215 7162 006 1305 1273 133717 1885 2689 4262 131 2227 5485 2451 7385 176 2913 1273 49346 1075 2079 4962 112 1738 6659 2897 8976 251 2771 1273 4902

10 1352 2165 4515 129 1929 4899 1655 5952 106 3041 2960 31198 2153 1906 3358 108 1731 4077 1655 6303 023 2135 1305 3056

24 1119 1180 3664 130 1085 4035 2005 550711 1146 1444 4005 100 1351 4822 1273 6685 023 1969 1751 21659 1225 1274 3640 125 1246 3754 1324 6971

52 results 79

Cutting type

Estimate CI

53 discussion

10 20 40 60

10 20 40 60 10 20 40 60

10 20 40 60

beforeharvest

5-10 10-15 15-20 20-25 5-10 10-15 15-20 20-25

5-10 10-15 15-20 20-25 5-10 10-15 15-20 20-250

53 discussion 83

George Wald

no harvest

Cutting intensity

oak tree

beech tree

closed canopy

directradiations

closed canopy

gap gap

gapgapgap

gap gap gap

directradiations

64 conclusion

96 bibliography

bibliography 97

98 bibliography

bibliography 99

100 bibliography

bibliography 101

102 bibliography

bibliography 103

104 bibliography

bibliography 105

106 bibliography

bibliography 107

108 bibliography

bibliography 109

110 bibliography

bibliography 111

112 bibliography

Summary

Remerciements

Publications

Contents

List of Figures

List of Tables

Acronyms



23 Why maintain oak

231 Biodiversity

232 Resilience

233 Productivity

234 Wood quality

235 Climate change



31 Methods

311 Study sites




32 Results





33 Discussion


332 Competition



34 Conclusion




412 Input variables




416 Discussion


421 Crown geometry

422 Crown radius

423 Tree Height





51 Methods

511 Study sites




52 Results

521 Tree inventory


523 Simulation

53 Discussion







64 Conclusion

Bibliography

HE Luccock

C O N T E N T S

34 Conclusion 28

xviii contents

bibliography 95

A C R O N Y M S

1D One-dimensional

LAI Leaf Area Index

PE Porous Envelope

TM Turbid Medium

William Wordsworth

John Muir

Belgium

France

Luxembourg

Germany

Belgian Ardennes

0 10050 Km

number of plotsHigh

soil moisture

soil pH

Acidic Alkaline

23 why maintain oak

231 Biodiversity

232 Resilience

Quercus sp

Fagus sylvatica

Girth classes (cm)

Number of trees

233 Productivity

234 Wood quality

235 Climate change

Saint Bernard

31 methods

311 Study sites

square grid

31 methods 19

2 (31)

20 5 7 - 92 19 37 159 - 231 11 - 18 14 ndash 19 10 - 274 7 6 - 74 25 73 168 - 255 13 - 18 4 ndash 95 13 - 20

31 methods 21

c )+ ϵi j (32)

cSDOM)+ ϵi j (33)

32 results

32 results 23

heightincrement

cm cm year

Beech 149 153 (23277) 26 (-962) 10 (421) 120Oak 174 125 (13273) 16 (-1052) 10 (119) 70Other 93 118 (7285) 20 (-6684) 51

Oak 2059(16422476)

6058(34688648)

10257(646914046)

7255 6759

Beech 2431(20352828)

3964(23785550)

7261 10491

33 discussion 25

33 discussion

33 discussion 27

332 Competition

34 conclusion

34 conclusion 29

Heraclitus

Output variables

Input variables

τ (ηγ ) = p (42)

412 Input variables

4125 Crown openness

4151 1D model

4152 3D crown model

416 Discussion

PorousEenvelopep

processes

Applications

Radiative transfer

Canopy geometry

4163 Applications

421 Crown geometry

(x minus x0)2

(y minus y0)2

(z minus z0)2

c= 1 (44)

(a) 1 ellipsoid

aeastawest

bnorth

bsouth

422 Crown radius

423 Tree Height

AL2 + B L+C = 0 (45)

a2 +cos2 (θ ) sin2 (α )

b2 +sin2 (θ )

b2 +z2

1c2 minus 1

tanθ (47)

tree height

path length

crown base height

4261 Method

4263 Conclusion

a R2 = 68 b R

2 = 87

Ralph Waldo Emerson

51 methods

511 Study sites

51 methods 71

51 methods 73

were randomly added

mapped and measured

Plot center part

scoret = β +u

05radicAN

52 results 77

52 results

521 Tree inventory

523 Simulation

stand oak beech

19 983 1494 4398 096 1494 4398 1273 843525 1272 2184 4675 105 2184 4675 1305 843527 353 782 5313 105 645 5297 1273 725728 514 747 4304 119 028 4742 4170 5252 719 4289 1273 649426 617 1460 5489 127 194 7576 7576 7576 1263 5362 1432 78303 1136 1810 4503 107 317 3942 2801 6016 1493 4657 1432 6557

18 467 752 4529 097 140 6232 5443 6430 606 4533 1273 79901 872 1115 4034 118 286 4433 2706 6525 790 3935 1273 71622 1139 1633 4273 097 435 4930 1623 5921 1195 4135 1273 7226

14 1245 2121 4657 128 670 6564 5443 8276 1451 4200 1273 697120 1439 1949 4152 104 697 7187 5570 9231 1252 3546 1273 805329 1270 2056 4541 120 1114 5542 4043 6812 942 3853 1273 652513 1338 1537 3825 109 869 6021 4615 7289 668 2870 1273 69715 2178 2051 3462 103 1195 5387 1783 7130 856 2567 1273 6812

12 1566 2265 4292 116 1361 5324 3947 8085 904 3474 1273 75764 2073 2416 3852 097 1670 5773 3820 7226 746 2572 1273 8403

22 2165 1531 3000 112 1107 2902 1369 4966 362 4336 1751 779921 1203 1954 4548 097 1471 7306 5761 9486 391 3151 1273 763923 1215 1631 4135 100 1241 4387 1464 7576 276 4531 1432 770315 1905 2469 4062 106 1980 5721 3215 7162 006 1305 1273 133717 1885 2689 4262 131 2227 5485 2451 7385 176 2913 1273 49346 1075 2079 4962 112 1738 6659 2897 8976 251 2771 1273 4902

10 1352 2165 4515 129 1929 4899 1655 5952 106 3041 2960 31198 2153 1906 3358 108 1731 4077 1655 6303 023 2135 1305 3056

24 1119 1180 3664 130 1085 4035 2005 550711 1146 1444 4005 100 1351 4822 1273 6685 023 1969 1751 21659 1225 1274 3640 125 1246 3754 1324 6971

52 results 79

Cutting type

Estimate CI

53 discussion

10 20 40 60

10 20 40 60 10 20 40 60

10 20 40 60

beforeharvest

5-10 10-15 15-20 20-25 5-10 10-15 15-20 20-25

5-10 10-15 15-20 20-25 5-10 10-15 15-20 20-250

53 discussion 83

George Wald

no harvest

Cutting intensity

oak tree

beech tree

closed canopy

directradiations

closed canopy

gap gap

gapgapgap

gap gap gap

directradiations

64 conclusion

96 bibliography

bibliography 97

98 bibliography

bibliography 99

100 bibliography

bibliography 101

102 bibliography

bibliography 103

104 bibliography

bibliography 105

106 bibliography

bibliography 107

108 bibliography

bibliography 109

110 bibliography

bibliography 111

112 bibliography

Summary

Remerciements

Publications

Contents

List of Figures

List of Tables

Acronyms



23 Why maintain oak

231 Biodiversity

232 Resilience

233 Productivity

234 Wood quality

235 Climate change



31 Methods

311 Study sites




32 Results





33 Discussion


332 Competition



34 Conclusion




412 Input variables




416 Discussion


421 Crown geometry

422 Crown radius

423 Tree Height





51 Methods

511 Study sites




52 Results

521 Tree inventory


523 Simulation

53 Discussion







64 Conclusion

Bibliography

HE Luccock

C O N T E N T S

34 Conclusion 28

xviii contents

bibliography 95

A C R O N Y M S

1D One-dimensional

LAI Leaf Area Index

PE Porous Envelope

TM Turbid Medium

William Wordsworth

John Muir

Belgium

France

Luxembourg

Germany

Belgian Ardennes

0 10050 Km

number of plotsHigh

soil moisture

soil pH

Acidic Alkaline

23 why maintain oak

231 Biodiversity

232 Resilience

Quercus sp

Fagus sylvatica

Girth classes (cm)

Number of trees

233 Productivity

234 Wood quality

235 Climate change

Saint Bernard

31 methods

311 Study sites

square grid

31 methods 19

2 (31)

20 5 7 - 92 19 37 159 - 231 11 - 18 14 ndash 19 10 - 274 7 6 - 74 25 73 168 - 255 13 - 18 4 ndash 95 13 - 20

31 methods 21

c )+ ϵi j (32)

cSDOM)+ ϵi j (33)

32 results

32 results 23

heightincrement

cm cm year

Beech 149 153 (23277) 26 (-962) 10 (421) 120Oak 174 125 (13273) 16 (-1052) 10 (119) 70Other 93 118 (7285) 20 (-6684) 51

Oak 2059(16422476)

6058(34688648)

10257(646914046)

7255 6759

Beech 2431(20352828)

3964(23785550)

7261 10491

33 discussion 25

33 discussion

33 discussion 27

332 Competition

34 conclusion

34 conclusion 29

Heraclitus

Output variables

Input variables

τ (ηγ ) = p (42)

412 Input variables

4125 Crown openness

4151 1D model

4152 3D crown model

416 Discussion

PorousEenvelopep

processes

Applications

Radiative transfer

Canopy geometry

4163 Applications

421 Crown geometry

(x minus x0)2

(y minus y0)2

(z minus z0)2

c= 1 (44)

(a) 1 ellipsoid

aeastawest

bnorth

bsouth

422 Crown radius

423 Tree Height

AL2 + B L+C = 0 (45)

a2 +cos2 (θ ) sin2 (α )

b2 +sin2 (θ )

b2 +z2

1c2 minus 1

tanθ (47)

tree height

path length

crown base height

4261 Method

4263 Conclusion

a R2 = 68 b R

2 = 87

Ralph Waldo Emerson

51 methods

511 Study sites

51 methods 71

51 methods 73

were randomly added

mapped and measured

Plot center part

scoret = β +u

05radicAN

52 results 77

52 results

521 Tree inventory

523 Simulation

stand oak beech

19 983 1494 4398 096 1494 4398 1273 843525 1272 2184 4675 105 2184 4675 1305 843527 353 782 5313 105 645 5297 1273 725728 514 747 4304 119 028 4742 4170 5252 719 4289 1273 649426 617 1460 5489 127 194 7576 7576 7576 1263 5362 1432 78303 1136 1810 4503 107 317 3942 2801 6016 1493 4657 1432 6557

18 467 752 4529 097 140 6232 5443 6430 606 4533 1273 79901 872 1115 4034 118 286 4433 2706 6525 790 3935 1273 71622 1139 1633 4273 097 435 4930 1623 5921 1195 4135 1273 7226

14 1245 2121 4657 128 670 6564 5443 8276 1451 4200 1273 697120 1439 1949 4152 104 697 7187 5570 9231 1252 3546 1273 805329 1270 2056 4541 120 1114 5542 4043 6812 942 3853 1273 652513 1338 1537 3825 109 869 6021 4615 7289 668 2870 1273 69715 2178 2051 3462 103 1195 5387 1783 7130 856 2567 1273 6812

12 1566 2265 4292 116 1361 5324 3947 8085 904 3474 1273 75764 2073 2416 3852 097 1670 5773 3820 7226 746 2572 1273 8403

22 2165 1531 3000 112 1107 2902 1369 4966 362 4336 1751 779921 1203 1954 4548 097 1471 7306 5761 9486 391 3151 1273 763923 1215 1631 4135 100 1241 4387 1464 7576 276 4531 1432 770315 1905 2469 4062 106 1980 5721 3215 7162 006 1305 1273 133717 1885 2689 4262 131 2227 5485 2451 7385 176 2913 1273 49346 1075 2079 4962 112 1738 6659 2897 8976 251 2771 1273 4902

10 1352 2165 4515 129 1929 4899 1655 5952 106 3041 2960 31198 2153 1906 3358 108 1731 4077 1655 6303 023 2135 1305 3056

24 1119 1180 3664 130 1085 4035 2005 550711 1146 1444 4005 100 1351 4822 1273 6685 023 1969 1751 21659 1225 1274 3640 125 1246 3754 1324 6971

52 results 79

Cutting type

Estimate CI

53 discussion

10 20 40 60

10 20 40 60 10 20 40 60

10 20 40 60

beforeharvest

5-10 10-15 15-20 20-25 5-10 10-15 15-20 20-25

5-10 10-15 15-20 20-25 5-10 10-15 15-20 20-250

53 discussion 83

George Wald

no harvest

Cutting intensity

oak tree

beech tree

closed canopy

directradiations

closed canopy

gap gap

gapgapgap

gap gap gap

directradiations

64 conclusion

96 bibliography

bibliography 97

98 bibliography

bibliography 99

100 bibliography

bibliography 101

102 bibliography

bibliography 103

104 bibliography

bibliography 105

106 bibliography

bibliography 107

108 bibliography

bibliography 109

110 bibliography

bibliography 111

112 bibliography

Summary

Remerciements

Publications

Contents

List of Figures

List of Tables

Acronyms



23 Why maintain oak

231 Biodiversity

232 Resilience

233 Productivity

234 Wood quality

235 Climate change



31 Methods

311 Study sites




32 Results





33 Discussion


332 Competition



34 Conclusion




412 Input variables




416 Discussion


421 Crown geometry

422 Crown radius

423 Tree Height





51 Methods

511 Study sites




52 Results

521 Tree inventory


523 Simulation

53 Discussion







64 Conclusion

Bibliography

HE Luccock

C O N T E N T S

34 Conclusion 28

xviii contents

bibliography 95

A C R O N Y M S

1D One-dimensional

LAI Leaf Area Index

PE Porous Envelope

TM Turbid Medium

William Wordsworth

John Muir

Belgium

France

Luxembourg

Germany

Belgian Ardennes

0 10050 Km

number of plotsHigh

soil moisture

soil pH

Acidic Alkaline

23 why maintain oak

231 Biodiversity

232 Resilience

Quercus sp

Fagus sylvatica

Girth classes (cm)

Number of trees

233 Productivity

234 Wood quality

235 Climate change

Saint Bernard

31 methods

311 Study sites

square grid

31 methods 19

2 (31)

20 5 7 - 92 19 37 159 - 231 11 - 18 14 ndash 19 10 - 274 7 6 - 74 25 73 168 - 255 13 - 18 4 ndash 95 13 - 20

31 methods 21

c )+ ϵi j (32)

cSDOM)+ ϵi j (33)

32 results

32 results 23

heightincrement

cm cm year

Beech 149 153 (23277) 26 (-962) 10 (421) 120Oak 174 125 (13273) 16 (-1052) 10 (119) 70Other 93 118 (7285) 20 (-6684) 51

Oak 2059(16422476)

6058(34688648)

10257(646914046)

7255 6759

Beech 2431(20352828)

3964(23785550)

7261 10491

33 discussion 25

33 discussion

33 discussion 27

332 Competition

34 conclusion

34 conclusion 29

Heraclitus

Output variables

Input variables

τ (ηγ ) = p (42)

412 Input variables

4125 Crown openness

4151 1D model

4152 3D crown model

416 Discussion

PorousEenvelopep

processes

Applications

Radiative transfer

Canopy geometry

4163 Applications

421 Crown geometry

(x minus x0)2

(y minus y0)2

(z minus z0)2

c= 1 (44)

(a) 1 ellipsoid

aeastawest

bnorth

bsouth

422 Crown radius

423 Tree Height

AL2 + B L+C = 0 (45)

a2 +cos2 (θ ) sin2 (α )

b2 +sin2 (θ )

b2 +z2

1c2 minus 1

tanθ (47)

tree height

path length

crown base height

4261 Method

4263 Conclusion

a R2 = 68 b R

2 = 87

Ralph Waldo Emerson

51 methods

511 Study sites

51 methods 71

51 methods 73

were randomly added

mapped and measured

Plot center part

scoret = β +u

05radicAN

52 results 77

52 results

521 Tree inventory

523 Simulation

stand oak beech

19 983 1494 4398 096 1494 4398 1273 843525 1272 2184 4675 105 2184 4675 1305 843527 353 782 5313 105 645 5297 1273 725728 514 747 4304 119 028 4742 4170 5252 719 4289 1273 649426 617 1460 5489 127 194 7576 7576 7576 1263 5362 1432 78303 1136 1810 4503 107 317 3942 2801 6016 1493 4657 1432 6557

18 467 752 4529 097 140 6232 5443 6430 606 4533 1273 79901 872 1115 4034 118 286 4433 2706 6525 790 3935 1273 71622 1139 1633 4273 097 435 4930 1623 5921 1195 4135 1273 7226

14 1245 2121 4657 128 670 6564 5443 8276 1451 4200 1273 697120 1439 1949 4152 104 697 7187 5570 9231 1252 3546 1273 805329 1270 2056 4541 120 1114 5542 4043 6812 942 3853 1273 652513 1338 1537 3825 109 869 6021 4615 7289 668 2870 1273 69715 2178 2051 3462 103 1195 5387 1783 7130 856 2567 1273 6812

12 1566 2265 4292 116 1361 5324 3947 8085 904 3474 1273 75764 2073 2416 3852 097 1670 5773 3820 7226 746 2572 1273 8403

22 2165 1531 3000 112 1107 2902 1369 4966 362 4336 1751 779921 1203 1954 4548 097 1471 7306 5761 9486 391 3151 1273 763923 1215 1631 4135 100 1241 4387 1464 7576 276 4531 1432 770315 1905 2469 4062 106 1980 5721 3215 7162 006 1305 1273 133717 1885 2689 4262 131 2227 5485 2451 7385 176 2913 1273 49346 1075 2079 4962 112 1738 6659 2897 8976 251 2771 1273 4902

10 1352 2165 4515 129 1929 4899 1655 5952 106 3041 2960 31198 2153 1906 3358 108 1731 4077 1655 6303 023 2135 1305 3056

24 1119 1180 3664 130 1085 4035 2005 550711 1146 1444 4005 100 1351 4822 1273 6685 023 1969 1751 21659 1225 1274 3640 125 1246 3754 1324 6971

52 results 79

Cutting type

Estimate CI

53 discussion

10 20 40 60

10 20 40 60 10 20 40 60

10 20 40 60

beforeharvest

5-10 10-15 15-20 20-25 5-10 10-15 15-20 20-25

5-10 10-15 15-20 20-25 5-10 10-15 15-20 20-250

53 discussion 83

George Wald

no harvest

Cutting intensity

oak tree

beech tree

closed canopy

directradiations

closed canopy

gap gap

gapgapgap

gap gap gap

directradiations

64 conclusion

96 bibliography

bibliography 97

98 bibliography

bibliography 99

100 bibliography

bibliography 101

102 bibliography

bibliography 103

104 bibliography

bibliography 105

106 bibliography

bibliography 107

108 bibliography

bibliography 109

110 bibliography

bibliography 111

112 bibliography

Summary

Remerciements

Publications

Contents

List of Figures

List of Tables

Acronyms



23 Why maintain oak

231 Biodiversity

232 Resilience

233 Productivity

234 Wood quality

235 Climate change



31 Methods

311 Study sites




32 Results





33 Discussion


332 Competition



34 Conclusion




412 Input variables




416 Discussion


421 Crown geometry

422 Crown radius

423 Tree Height





51 Methods

511 Study sites




52 Results

521 Tree inventory


523 Simulation

53 Discussion







64 Conclusion

Bibliography

HE Luccock

C O N T E N T S

34 Conclusion 28

xviii contents

bibliography 95

A C R O N Y M S

1D One-dimensional

LAI Leaf Area Index

PE Porous Envelope

TM Turbid Medium

William Wordsworth

John Muir

Belgium

France

Luxembourg

Germany

Belgian Ardennes

0 10050 Km

number of plotsHigh

soil moisture

soil pH

Acidic Alkaline

23 why maintain oak

231 Biodiversity

232 Resilience

Quercus sp

Fagus sylvatica

Girth classes (cm)

Number of trees

233 Productivity

234 Wood quality

235 Climate change

Saint Bernard

31 methods

311 Study sites

square grid

31 methods 19

2 (31)

20 5 7 - 92 19 37 159 - 231 11 - 18 14 ndash 19 10 - 274 7 6 - 74 25 73 168 - 255 13 - 18 4 ndash 95 13 - 20

31 methods 21

c )+ ϵi j (32)

cSDOM)+ ϵi j (33)

32 results

32 results 23

heightincrement

cm cm year

Beech 149 153 (23277) 26 (-962) 10 (421) 120Oak 174 125 (13273) 16 (-1052) 10 (119) 70Other 93 118 (7285) 20 (-6684) 51

Oak 2059(16422476)

6058(34688648)

10257(646914046)

7255 6759

Beech 2431(20352828)

3964(23785550)

7261 10491

33 discussion 25

33 discussion

33 discussion 27

332 Competition

34 conclusion

34 conclusion 29

Heraclitus

Output variables

Input variables

τ (ηγ ) = p (42)

412 Input variables

4125 Crown openness

4151 1D model

4152 3D crown model

416 Discussion

PorousEenvelopep

processes

Applications

Radiative transfer

Canopy geometry

4163 Applications

421 Crown geometry

(x minus x0)2

(y minus y0)2

(z minus z0)2

c= 1 (44)

(a) 1 ellipsoid

aeastawest

bnorth

bsouth

422 Crown radius

423 Tree Height

AL2 + B L+C = 0 (45)

a2 +cos2 (θ ) sin2 (α )

b2 +sin2 (θ )

b2 +z2

1c2 minus 1

tanθ (47)

tree height

path length

crown base height

4261 Method

4263 Conclusion

a R2 = 68 b R

2 = 87

Ralph Waldo Emerson

51 methods

511 Study sites

51 methods 71

51 methods 73

were randomly added

mapped and measured

Plot center part

scoret = β +u

05radicAN

52 results 77

52 results

521 Tree inventory

523 Simulation

stand oak beech

19 983 1494 4398 096 1494 4398 1273 843525 1272 2184 4675 105 2184 4675 1305 843527 353 782 5313 105 645 5297 1273 725728 514 747 4304 119 028 4742 4170 5252 719 4289 1273 649426 617 1460 5489 127 194 7576 7576 7576 1263 5362 1432 78303 1136 1810 4503 107 317 3942 2801 6016 1493 4657 1432 6557

18 467 752 4529 097 140 6232 5443 6430 606 4533 1273 79901 872 1115 4034 118 286 4433 2706 6525 790 3935 1273 71622 1139 1633 4273 097 435 4930 1623 5921 1195 4135 1273 7226

14 1245 2121 4657 128 670 6564 5443 8276 1451 4200 1273 697120 1439 1949 4152 104 697 7187 5570 9231 1252 3546 1273 805329 1270 2056 4541 120 1114 5542 4043 6812 942 3853 1273 652513 1338 1537 3825 109 869 6021 4615 7289 668 2870 1273 69715 2178 2051 3462 103 1195 5387 1783 7130 856 2567 1273 6812

12 1566 2265 4292 116 1361 5324 3947 8085 904 3474 1273 75764 2073 2416 3852 097 1670 5773 3820 7226 746 2572 1273 8403

22 2165 1531 3000 112 1107 2902 1369 4966 362 4336 1751 779921 1203 1954 4548 097 1471 7306 5761 9486 391 3151 1273 763923 1215 1631 4135 100 1241 4387 1464 7576 276 4531 1432 770315 1905 2469 4062 106 1980 5721 3215 7162 006 1305 1273 133717 1885 2689 4262 131 2227 5485 2451 7385 176 2913 1273 49346 1075 2079 4962 112 1738 6659 2897 8976 251 2771 1273 4902

10 1352 2165 4515 129 1929 4899 1655 5952 106 3041 2960 31198 2153 1906 3358 108 1731 4077 1655 6303 023 2135 1305 3056

24 1119 1180 3664 130 1085 4035 2005 550711 1146 1444 4005 100 1351 4822 1273 6685 023 1969 1751 21659 1225 1274 3640 125 1246 3754 1324 6971

52 results 79

Cutting type

Estimate CI

53 discussion

10 20 40 60

10 20 40 60 10 20 40 60

10 20 40 60

beforeharvest

5-10 10-15 15-20 20-25 5-10 10-15 15-20 20-25

5-10 10-15 15-20 20-25 5-10 10-15 15-20 20-250

53 discussion 83

George Wald

no harvest

Cutting intensity

oak tree

beech tree

closed canopy

directradiations

closed canopy

gap gap

gapgapgap

gap gap gap

directradiations

64 conclusion

96 bibliography

bibliography 97

98 bibliography

bibliography 99

100 bibliography

bibliography 101

102 bibliography

bibliography 103

104 bibliography

bibliography 105

106 bibliography

bibliography 107

108 bibliography

bibliography 109

110 bibliography

bibliography 111

112 bibliography

Summary

Remerciements

Publications

Contents

List of Figures

List of Tables

Acronyms



23 Why maintain oak

231 Biodiversity

232 Resilience

233 Productivity

234 Wood quality

235 Climate change



31 Methods

311 Study sites




32 Results





33 Discussion


332 Competition



34 Conclusion




412 Input variables




416 Discussion


421 Crown geometry

422 Crown radius

423 Tree Height





51 Methods

511 Study sites




52 Results

521 Tree inventory


523 Simulation

53 Discussion







64 Conclusion

Bibliography

HE Luccock

C O N T E N T S

34 Conclusion 28

xviii contents

bibliography 95

A C R O N Y M S

1D One-dimensional

LAI Leaf Area Index

PE Porous Envelope

TM Turbid Medium

William Wordsworth

John Muir

Belgium

France

Luxembourg

Germany

Belgian Ardennes

0 10050 Km

number of plotsHigh

soil moisture

soil pH

Acidic Alkaline

23 why maintain oak

231 Biodiversity

232 Resilience

Quercus sp

Fagus sylvatica

Girth classes (cm)

Number of trees

233 Productivity

234 Wood quality

235 Climate change

Saint Bernard

31 methods

311 Study sites

square grid

31 methods 19

2 (31)

20 5 7 - 92 19 37 159 - 231 11 - 18 14 ndash 19 10 - 274 7 6 - 74 25 73 168 - 255 13 - 18 4 ndash 95 13 - 20

31 methods 21

c )+ ϵi j (32)

cSDOM)+ ϵi j (33)

32 results

32 results 23

heightincrement

cm cm year

Beech 149 153 (23277) 26 (-962) 10 (421) 120Oak 174 125 (13273) 16 (-1052) 10 (119) 70Other 93 118 (7285) 20 (-6684) 51

Oak 2059(16422476)

6058(34688648)

10257(646914046)

7255 6759

Beech 2431(20352828)

3964(23785550)

7261 10491

33 discussion 25

33 discussion

33 discussion 27

332 Competition

34 conclusion

34 conclusion 29

Heraclitus

Output variables

Input variables

τ (ηγ ) = p (42)

412 Input variables

4125 Crown openness

4151 1D model

4152 3D crown model

416 Discussion

PorousEenvelopep

processes

Applications

Radiative transfer

Canopy geometry

4163 Applications

421 Crown geometry

(x minus x0)2

(y minus y0)2

(z minus z0)2

c= 1 (44)

(a) 1 ellipsoid

aeastawest

bnorth

bsouth

422 Crown radius

423 Tree Height

AL2 + B L+C = 0 (45)

a2 +cos2 (θ ) sin2 (α )

b2 +sin2 (θ )

b2 +z2

1c2 minus 1

tanθ (47)

tree height

path length

crown base height

4261 Method

4263 Conclusion

a R2 = 68 b R

2 = 87

Ralph Waldo Emerson

51 methods

511 Study sites

51 methods 71

51 methods 73

were randomly added

mapped and measured

Plot center part

scoret = β +u

05radicAN

52 results 77

52 results

521 Tree inventory

523 Simulation

stand oak beech

19 983 1494 4398 096 1494 4398 1273 843525 1272 2184 4675 105 2184 4675 1305 843527 353 782 5313 105 645 5297 1273 725728 514 747 4304 119 028 4742 4170 5252 719 4289 1273 649426 617 1460 5489 127 194 7576 7576 7576 1263 5362 1432 78303 1136 1810 4503 107 317 3942 2801 6016 1493 4657 1432 6557

18 467 752 4529 097 140 6232 5443 6430 606 4533 1273 79901 872 1115 4034 118 286 4433 2706 6525 790 3935 1273 71622 1139 1633 4273 097 435 4930 1623 5921 1195 4135 1273 7226

14 1245 2121 4657 128 670 6564 5443 8276 1451 4200 1273 697120 1439 1949 4152 104 697 7187 5570 9231 1252 3546 1273 805329 1270 2056 4541 120 1114 5542 4043 6812 942 3853 1273 652513 1338 1537 3825 109 869 6021 4615 7289 668 2870 1273 69715 2178 2051 3462 103 1195 5387 1783 7130 856 2567 1273 6812

12 1566 2265 4292 116 1361 5324 3947 8085 904 3474 1273 75764 2073 2416 3852 097 1670 5773 3820 7226 746 2572 1273 8403

22 2165 1531 3000 112 1107 2902 1369 4966 362 4336 1751 779921 1203 1954 4548 097 1471 7306 5761 9486 391 3151 1273 763923 1215 1631 4135 100 1241 4387 1464 7576 276 4531 1432 770315 1905 2469 4062 106 1980 5721 3215 7162 006 1305 1273 133717 1885 2689 4262 131 2227 5485 2451 7385 176 2913 1273 49346 1075 2079 4962 112 1738 6659 2897 8976 251 2771 1273 4902

10 1352 2165 4515 129 1929 4899 1655 5952 106 3041 2960 31198 2153 1906 3358 108 1731 4077 1655 6303 023 2135 1305 3056

24 1119 1180 3664 130 1085 4035 2005 550711 1146 1444 4005 100 1351 4822 1273 6685 023 1969 1751 21659 1225 1274 3640 125 1246 3754 1324 6971

52 results 79

Cutting type

Estimate CI

53 discussion

10 20 40 60

10 20 40 60 10 20 40 60

10 20 40 60

beforeharvest

5-10 10-15 15-20 20-25 5-10 10-15 15-20 20-25

5-10 10-15 15-20 20-25 5-10 10-15 15-20 20-250

53 discussion 83

George Wald

no harvest

Cutting intensity

oak tree

beech tree

closed canopy

directradiations

closed canopy

gap gap

gapgapgap

gap gap gap

directradiations

64 conclusion

96 bibliography

bibliography 97

98 bibliography

bibliography 99

100 bibliography

bibliography 101

102 bibliography

bibliography 103

104 bibliography

bibliography 105

106 bibliography

bibliography 107

108 bibliography

bibliography 109

110 bibliography

bibliography 111

112 bibliography

Summary

Remerciements

Publications

Contents

List of Figures

List of Tables

Acronyms



23 Why maintain oak

231 Biodiversity

232 Resilience

233 Productivity

234 Wood quality

235 Climate change



31 Methods

311 Study sites




32 Results





33 Discussion


332 Competition



34 Conclusion




412 Input variables




416 Discussion


421 Crown geometry

422 Crown radius

423 Tree Height





51 Methods

511 Study sites




52 Results

521 Tree inventory


523 Simulation

53 Discussion







64 Conclusion

Bibliography

Documents

Managing understory light to maintain the coexistence of forest tree species with different shade