A hybrid modeling framework for intensively managed Douglas-fir in the Pacific Northwest

1

A hybrid modeling A hybrid modeling framework for framework for

intensively managed intensively managed Douglas-fir in the Douglas-fir in the Pacific NorthwestPacific Northwest

Aaron WeiskittelAaron Weiskittel

Department of Forest Department of Forest ScienceScience

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HypothesesHypotheses Empirical models struggle to predict

growth response to intensive management because: The selected time step can not capture the highly

dynamic nature of growth following management

Dynamics of the crown are inadequately represented

Influence of site physiographic features (aspect, slope, elevation), soils (depth, texture, % rock), or climate are not included in the projections

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Justification/ObjectivesJustification/Objectives All possible combinations of treatments cannot be All possible combinations of treatments cannot be

field tested field tested

Better understanding of physiological mechanisms:Better understanding of physiological mechanisms: improve extrapolations to untested combinations improve extrapolations to untested combinations explain some of the differences in behavior among explain some of the differences in behavior among

data sets and resulting models data sets and resulting models

objective is to build a model that represents key objective is to build a model that represents key ecophysiological processes in a practical yet ecophysiological processes in a practical yet mechanistic mannermechanistic manner responses to a wide array of silvicultural treatments responses to a wide array of silvicultural treatments

and regimes can be tested and regimes can be tested sensitivity to weather and treatment interactions with sensitivity to weather and treatment interactions with

weather weather

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Annualized diameter and Annualized diameter and height growth equations height growth equations for Douglas-fir, western for Douglas-fir, western

hemlock, and red alder in hemlock, and red alder in the Pacific Northwest, the Pacific Northwest,

USAUSAIn Press: Forest Ecology and In Press: Forest Ecology and

ManagementManagement

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IntroductionIntroduction Most regional individual tree growth & Most regional individual tree growth &

yield models operate on a 5-10 year time yield models operate on a 5-10 year time stepstep

Commonly assumed that increasing Commonly assumed that increasing temporal resolution of the model would temporal resolution of the model would decrease overall precisiondecrease overall precision

Annual fluctuations in weather are averaged outAnnual fluctuations in weather are averaged out

Plot remeasurement data are typically Plot remeasurement data are typically collected on a 2-10 year interval, which collected on a 2-10 year interval, which makes getting annual growth difficult and makes getting annual growth difficult and impreciseimprecise

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Objectives/JustificationObjectives/Justification Use the iterative method of Cao (2002; CJFR 32:

2051-2059) to estimate annualized growth equations Diameter and height

fitted with maximum likelihood and multi-level mixed-effects random effects correlated with installation physiographic

features

3 plantation species in western OR and WA Douglas-fir western hemlock red alder

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MethodsMethods Only control (untreated) plots used

Hann et al. (2003; OSU FRL Res. Contrib. 40) model forms used

Site indices were: DF, Bruce (1981; For Sci 4: 711-725) WH, Bonner et al. (1995; Can. For. Serv. Info Report

BC-X-353) RA, Nigh & Courtin (1998; New Forest 16: 59-70)

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Methods: Model fitting Methods: Model fitting techniquetechnique

Requires no modification of the growth data (i.e. Requires no modification of the growth data (i.e. no interpolation to a common remeasurement no interpolation to a common remeasurement length)length)

Constrains predicted periodic growth, which Constrains predicted periodic growth, which reduces the error associated with annually reduces the error associated with annually updating a tree listupdating a tree list

Basically, a simple do loop combined with a Basically, a simple do loop combined with a minimization functionminimization function

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ResultsResults Models fit well (RModels fit well (R22 ~ 0.5 – 0.9) and were ~ 0.5 – 0.9) and were

consistent with biological expectationsconsistent with biological expectations

Multi-level mixed effects (MLME) indicated Multi-level mixed effects (MLME) indicated significant installation and plot variationsignificant installation and plot variation

MLME significantly improved model fitsMLME significantly improved model fits

Diameter growth peaked at 30, 25, and 15 cm Diameter growth peaked at 30, 25, and 15 cm DBH for DF, WH, and RADBH for DF, WH, and RA

Hann et al. (2003) height growth equation Hann et al. (2003) height growth equation worked well for DF, but modifications are worked well for DF, but modifications are required for WH and RArequired for WH and RA

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ResultsResults

initial DBH (cm)

0 20 40 60 80 100

5-yr

dia

met

er g

row

th (

cm y

r-1)

0

1

2

3

4

5

MLMLMEORGANON

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ResultsResults Installation random effects provided a few Installation random effects provided a few

interesting relationships for DF and RA, but fits interesting relationships for DF and RA, but fits were generally poor (Rwere generally poor (R22 < 0.35) < 0.35)

Physiographic variables better predictors than soils or mean Physiographic variables better predictors than soils or mean climate variablesclimate variables

WH showed no relationship with any examined WH showed no relationship with any examined variablevariable

EquationEquation Significant factorsSignificant factors

DF diameter growthDF diameter growth Elevation, slope, aspect, & precipitationElevation, slope, aspect, & precipitation

DF height growthDF height growth Slope, aspect, and soil rock content Slope, aspect, and soil rock content

RA diameter growthRA diameter growth Slope, aspect, and elevationSlope, aspect, and elevation

RA height growthRA height growth Slope & aspectSlope & aspect

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SimulationSimulation 12 SMC Type II installations (not used in fitting) used 12 SMC Type II installations (not used in fitting) used

for model verificationfor model verification Initial BH age: 23.5 – 46.5Initial BH age: 23.5 – 46.5 Site index: 29.3 – 48.0 mSite index: 29.3 – 48.0 m

Growth simulated for 12 – 16 years using the annualized growth equations combined with previously fitted annual mortality function and a static crown recession model

Predictions compared with SMC-variant of ORGANON v8 Distance-independent, individual tree with 5 year time step

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Results: SimulationResults: Simulation

After 12-16 years of simulation, After 12-16 years of simulation, annualized equations were better than annualized equations were better than ORGANON predictionsORGANON predictions

Multi-level mixed effects (MLME) Multi-level mixed effects (MLME) models performed better than models performed better than maximum likelihood (ML)maximum likelihood (ML)

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DBH (cm) HT (m)

Mea

n s

quar

e e

rror

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

ML MLME MLME with predicted ranef ORGANON

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ConclusionConclusion Annualized equations offer an opportunity to

improve the precision of growth projections, while providing several additional benefits: Not restricted to a preconceived time interval Biologically justified Improved chance of capturing the growth dynamics

following intensive management Opportunity to connect empirical equations with a process-

based model

Process-based model is needed to capture the influence of climate, soils, and physiographic features

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In Review: Canadian Journal of In Review: Canadian Journal of Forest ResearchForest Research

Modeling the influence of Modeling the influence of intensive management on intensive management on

Douglas-fir individual branch Douglas-fir individual branch growth and mortality: growth and mortality:

implications for predicting implications for predicting tree growth responsetree growth response

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IntroductionIntroduction Crowns are an important link between Crowns are an important link between

physiological processes and observed growth physiological processes and observed growth responseresponse

Few growth and yield models represent crowns Few growth and yield models represent crowns in a significant amount of detailin a significant amount of detail E.g., most use static height to crown base E.g., most use static height to crown base

equations to predict crown recessionequations to predict crown recession

Capturing the dynamics of crown may be an Capturing the dynamics of crown may be an important step for improving individual tree important step for improving individual tree growth projectionsgrowth projections

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IntroductionIntroduction previous branch work in Douglas-fir is limitedprevious branch work in Douglas-fir is limited

Maguire et al. (1994)Maguire et al. (1994) tree age was young (4-7 yrs at breast height)tree age was young (4-7 yrs at breast height)

Maguire et al. (1999)Maguire et al. (1999) only live branchesonly live branches

Turnblom and Briggs (1999)Turnblom and Briggs (1999) branches at breast height onlybranches at breast height only

branch-level models exists for several other branch-level models exists for several other important commercial species (NZ, FIN, FRA)important commercial species (NZ, FIN, FRA)

few have considered the effects of intensive few have considered the effects of intensive managementmanagement

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ObjectivesObjectives Monitor the growth and mortality of Monitor the growth and mortality of

individual branches on a multitude of individual branches on a multitude of stems across a range of stand typestems across a range of stand type

Understand branch dynamics following Understand branch dynamics following silvicultural treatmentssilvicultural treatments

Develop models the predict branch Develop models the predict branch dynamics using key variablesdynamics using key variables

Integrate these equations into an Integrate these equations into an individual tree modeling frameworkindividual tree modeling framework

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measure branch location and size measure branch location and size in several different PNW in several different PNW installationsinstallations SMCSMC

controlcontrol fertilization (1-4 yrs after)fertilization (1-4 yrs after) thinningthinning fertilization + thinningfertilization + thinning

VMRCVMRC controlcontrol 1.5, 3.3, & 9.3 m1.5, 3.3, & 9.3 m22

of complete veg of complete veg controlcontrol

complete control of woody veg only complete control of woody veg only complete control of herb veg onlycomplete control of herb veg only

PCTPCT 254 stems/ha254 stems/ha 508 stems/ha508 stems/ha controlcontrol

SNCSNC various levels of Swiss needle cast various levels of Swiss needle cast

diseasedisease

methodsmethods

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MethodsMethods Branches on the trees used in a previous analysis Branches on the trees used in a previous analysis

were tagged and remeasured 2 years after initial were tagged and remeasured 2 years after initial measurementmeasurement

Treatment effects were assessed with multi-level Treatment effects were assessed with multi-level mixed effects models with weighting and a mixed effects models with weighting and a correlation structurecorrelation structure

Final models were annualized using the technique Final models were annualized using the technique previously discussedpreviously discussed

Total of 2,828 branches on 103 trees were Total of 2,828 branches on 103 trees were remeasuredremeasured

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Simulation modelSimulation model Final branch equations were combined Final branch equations were combined

with individual tree annualized growth with individual tree annualized growth models and the crown reconstruction models and the crown reconstruction algorithmalgorithm

4-yr growth on 56 plots with varying 4-yr growth on 56 plots with varying levels of silvicultural treatments was levels of silvicultural treatments was simulatedsimulated Control, Thin, Fertilized, & Thin + FertilizedControl, Thin, Fertilized, & Thin + Fertilized

Compared to the use of a static height Compared to the use of a static height to crown base equationto crown base equation

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Results: Branch growthResults: Branch growth Significantly influenced by:Significantly influenced by:

Precommercial thinningPrecommercial thinning Swiss needle cast diseaseSwiss needle cast disease Commercial thinningCommercial thinning FertilizationFertilization

In the case of commercial thinning and In the case of commercial thinning and fertilization, response varied by time since fertilization, response varied by time since treatmenttreatment

Overall, branch growth was related to branch size Overall, branch growth was related to branch size and location as well as tree diameter growth and and location as well as tree diameter growth and crown sizecrown size Variability in the original data high (RVariability in the original data high (R22

~ 0.25)~ 0.25)

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Results: Branch Results: Branch mortality mortality

Significant treatment effect of:Significant treatment effect of: Swiss needle castSwiss needle cast Commercial thinningCommercial thinning FertilizationFertilization Vegetation managementVegetation management

With respect to commercial thinning and With respect to commercial thinning and fertilization, effects dependent on time since fertilization, effects dependent on time since treatmenttreatment

Final model included initial branch size and Final model included initial branch size and location, summation of branch diameters above location, summation of branch diameters above subject branch, tree size, and relative stand densitysubject branch, tree size, and relative stand density Mortality at the branch-level much better predictor Mortality at the branch-level much better predictor

than at the tree-level (i.e. Rthan at the tree-level (i.e. R22 ~ 0.47)~ 0.47)

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Results: SimulationResults: Simulation Predictions of height to crown base Predictions of height to crown base

improvedimproved

Mean bias of diameter and height growth Mean bias of diameter and height growth reduced, but mean square error (MSE) reduced, but mean square error (MSE) not improvednot improved

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ConclusionsConclusions Branch diameter growth and mortality were Branch diameter growth and mortality were

highly dynamic processeshighly dynamic processes Mortality was more predictable than growthMortality was more predictable than growth Growth peaked early (~6 mm in diameter) and Growth peaked early (~6 mm in diameter) and

was relatively nonexistent for the majority of a was relatively nonexistent for the majority of a branch’s lifebranch’s life

Branch dynamics were sensitive to stand Branch dynamics were sensitive to stand conditions imposed by intensive forest conditions imposed by intensive forest management practices, but predictablemanagement practices, but predictable

Improved representation of crown dynamics in Improved representation of crown dynamics in an individual tree growth model slightly an individual tree growth model slightly improved growth predictionsimproved growth predictions

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In Review: Ecological ModellingIn Review: Ecological Modelling

Development of a hybrid Development of a hybrid modeling framework for modeling framework for

predicting intensively predicting intensively managed Douglas-fir managed Douglas-fir

growth at multiple levelsgrowth at multiple levels

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IntroductionIntroduction High variability of climatic and soil conditions in High variability of climatic and soil conditions in

the Pacific Northwestthe Pacific Northwest Proximity to Pacific Ocean + 2 mountain ranges with Proximity to Pacific Ocean + 2 mountain ranges with

different geologic histories = tremendous variationdifferent geologic histories = tremendous variation Steep, broken terrainSteep, broken terrain

Warm, dry Mediterranean climate makes water Warm, dry Mediterranean climate makes water the driving variablethe driving variable

Site index is a crude measure of site productivity Site index is a crude measure of site productivity and relies on information from the current stand and relies on information from the current stand to make predictionsto make predictions Indexes only height growth potentialIndexes only height growth potential

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Process Modeling Process Modeling PhilosophyPhilosophy

Keep the model simple yet mechanistically Keep the model simple yet mechanistically soundsound

Derive parameters from literature and/or Derive parameters from literature and/or available dataavailable data

Flexible enough to accommodate a variety of Flexible enough to accommodate a variety of approachesapproaches i.e. integrate key processes and improve with i.e. integrate key processes and improve with

increased data increased data

No “free” parametersNo “free” parameters All required input must have an empirical basisAll required input must have an empirical basis

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Literature ReviewLiterature Review Indication that the ‘best’ process-based Indication that the ‘best’ process-based

models were those with:models were those with: A daily time step and multiple time periods A daily time step and multiple time periods

during each dayduring each day

Both direct and diffuse radiation consideredBoth direct and diffuse radiation considered

A separation of canopy into sunlit/shaded leaf A separation of canopy into sunlit/shaded leaf areaarea

Soil water and nutrient status connected to Soil water and nutrient status connected to physiological processesphysiological processes

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Development of the Development of the modelmodel

Four basic modeling challenges:Four basic modeling challenges: Simulate LAI from a tree list and basic stand infoSimulate LAI from a tree list and basic stand info

Mechanistically represent key physiological Mechanistically represent key physiological processesprocesses

Estimate stand-level allocation of net primary Estimate stand-level allocation of net primary production (NPP) to several biomass pools production (NPP) to several biomass pools (foliage, stem, etc.)(foliage, stem, etc.)

Predict individual tree dimensional growth and Predict individual tree dimensional growth and mortalitymortality

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Development of the modelDevelopment of the model

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Development of the model Development of the model a. prediction of LAIa. prediction of LAI

Several different approaches for estimating Several different approaches for estimating LAI were comparedLAI were compared BHSAP, constant leaf area per unit of sapwood BHSAP, constant leaf area per unit of sapwood

area at breast heightarea at breast height CBSAP, constant leaf area per unit of sapwood CBSAP, constant leaf area per unit of sapwood

area at crown basearea at crown base Gholz et al. (1979) allometric equationGholz et al. (1979) allometric equation BCACS, simulates size, #, and leaf area of BCACS, simulates size, #, and leaf area of

branchesbranches

Actual LAI was not availableActual LAI was not available Correlated with stand current annual Correlated with stand current annual

incrementincrement

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Development of the model Development of the model a. prediction of LAIa. prediction of LAI

All simulated LAIs were significantly All simulated LAIs were significantly correlated with observed current annual correlated with observed current annual increment (CAI)increment (CAI) CBSAP (r = 0.81)CBSAP (r = 0.81)

Gholz (r = 0.79)Gholz (r = 0.79)

BHSAP (r = 0.78)BHSAP (r = 0.78)

BCACS (r = 0.75)BCACS (r = 0.75)

Correlations all relatively high, but Correlations all relatively high, but their order can be deceivingtheir order can be deceiving

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Development of the model Development of the model b. prediction of current annual b. prediction of current annual

incrementincrement

Model was applied to 56 plots, Model was applied to 56 plots, with the following treatments: with the following treatments: ControlControl FertilizedFertilized ThinnedThinned Thinned + FertilizedThinned + Fertilized

Wide range of growing conditionsWide range of growing conditions Both nitrogen responsive and non-Both nitrogen responsive and non-

responsive locationsresponsive locations

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incrementincrement

VariableVariable Min Min MaxMax

Foliar N%Foliar N% 1.261.26 2.972.97

Avg. Temp (C)Avg. Temp (C) 9.99.9 13.613.6

Avg. Prcp (cm)Avg. Prcp (cm) 120120 290290

Soil water Soil water holding capacity holding capacity (cm)(cm)

7575 226226

AgeAge 1313 2525

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incrementincrement

LAI used in the simulation

BHSAP GHOLZ CBSAP BCACS

Me

an

sq

ua

re e

rro

r (m

3 h

a-1

yr-1

)

0

1

2

3

4

5

6

7

Weiskittel NPP model3-PG

39


incrementincrement

40


incrementincrement

Silvicultural Treatment

CONTROL FERT THIN THIN + FERT

Sta

nd v

olum

e gr

owth

MS

E (

m3 h

a-1 y

r-1)

0.0

0.5

1.0

1.5

2.0EMPIRICAL HYBRID 3-PG SECRETS-3PG

41


incrementincrement

Performance on Swiss Needle Cast Performance on Swiss Needle Cast Cooperative plotsCooperative plots

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Development of the model Development of the model

3-PG’s approach to respiration and carbon 3-PG’s approach to respiration and carbon allocation were more correlated with allocation were more correlated with observed growth than several other methodsobserved growth than several other methods These are important assumptions that require These are important assumptions that require

more examination and refinementmore examination and refinement

Treatment of soil water effects on canopy Treatment of soil water effects on canopy photosynthesis was the primary source of photosynthesis was the primary source of improvementimprovement

Bias of stand CAI projection comparable to a Bias of stand CAI projection comparable to a stand-level empirical modelstand-level empirical model

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Results: Individual tree Results: Individual tree growthgrowth

Disaggregation of stand-level growth to Disaggregation of stand-level growth to individual tree proved quite difficultindividual tree proved quite difficult Best approach was based on weighted leaf areaBest approach was based on weighted leaf area

Mechanistic models of tree diameter and height Mechanistic models of tree diameter and height growth achieved a level of biases comparable, growth achieved a level of biases comparable, but not better than purely empirical equationsbut not better than purely empirical equations Solution was to modify empirical models based on Solution was to modify empirical models based on

annual NPPannual NPP

Tree mortality predicted using growth efficiency Tree mortality predicted using growth efficiency performed as well as an empirical modelperformed as well as an empirical model

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DBH (cm) HT (m)

Mea

n sq

uare

err

or

0

1

2

3

4

5

Empirical Allometric Pipe-model Thornley (1999) Hybrid

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ConclusionsConclusions Reconstructing the crown provides good predictions of Reconstructing the crown provides good predictions of

LAI across a range of stand conditionsLAI across a range of stand conditions LIDAR offers the opportunity to prove initial LAI estimates, LIDAR offers the opportunity to prove initial LAI estimates,

but does not eliminate the need for detailed crown dynamics but does not eliminate the need for detailed crown dynamics

Process-based models were a useful tool for integrating Process-based models were a useful tool for integrating the effects of physiographic features and climate on tree the effects of physiographic features and climate on tree growthgrowth

Considerable error can be experienced with the primary Considerable error can be experienced with the primary physiological processes are not accounted for properlyphysiological processes are not accounted for properly

Understanding individual tree physiological processes is Understanding individual tree physiological processes is key for future progresskey for future progress

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Overall conclusionsOverall conclusions Empirical growth and yield models continue to Empirical growth and yield models continue to

need refinementneed refinement Annual time step and better representation of Annual time step and better representation of

crown dynamics improved performancecrown dynamics improved performance

Hybridization of process-based with an Hybridization of process-based with an empirical model can be a useful tool for both empirical model can be a useful tool for both research and applied useresearch and applied use

Research into crown structure and dynamics Research into crown structure and dynamics provides insights into many key system provides insights into many key system attributesattributes

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AcknowledgementsAcknowledgements Thanks to:Thanks to:

Committee membersCommittee members Doug Maguire, Robert A. Monserud, Doug Maguire, Robert A. Monserud,

Barbara Lachenbruch, Randy Johnson, Barbara Lachenbruch, Randy Johnson, Temesgen Hailemariam, Glenn Murphy, Paul Temesgen Hailemariam, Glenn Murphy, Paul AdamsAdams

Greg JohnsonGreg Johnson

Field and lab crew members (~30 temps over Field and lab crew members (~30 temps over 5 yrs)5 yrs)

USDA Forest Service PNW Research StationUSDA Forest Service PNW Research Station

Dissertation and Dissertation and R library R library

available online:available online:www.holoros.com/www.holoros.com/DF.HGS.htmDF.HGS.htm

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A hybrid modeling framework for intensively managed Douglas-fir in the Pacific Northwest