Use R! for estimating forest parameters based on Airborne ... fileIntroduction Methods and Results Ongoing research and summary Use R! for estimating forest parameters based on Airborne

IntroductionMethods and Results

Ongoing research and summary

Use R! for estimating forest parameters basedon Airborne Laser Scanner Data

Johannes Breidenbach

Forest Research Institute Baden-Württemberg,Department of Biometrics

Forstliche Versuchs- und Forschungsanstalt Baden-WürttembergAbteilung Biometrie und Informatik; Wonnhaldestr. 4; 79100 Freiburg

Fon: +49 (0)761-4018-315; [email protected]

J. Breidenbach Use R! for estimating forest parameters based on ALS



Inhalt

1 IntroductionBackgroundAirborne Laser ScanningAnalyzing laser data

2 Methods and ResultsA mixed model (lme) for timber volume estimationA GAMLSS for diameter distribution estimation

3 Ongoing research and summary




BackgroundAirborne Laser ScanningAnalyzing laser data








Sample Plot Inventory

Forest inventory → statistical sound information on theenterprize-level (Stands are too small)





Forest Inventory

Forest inventory → statistical sound information on theenterprize-level (Stands are too small)





Motivation

High costs

Insufficient information on stand level

Staff reduction

Increased economical interest in timber products

⇒ Greater information-need on the stand level





Motivation

High costs


Staff reduction







Motivation

High costs


Staff reduction







Motivation

High costs


Staff reduction







Motivation

High costs


Staff reduction




Aim ⇒ Regionalization (small area estimation): From apoint-wise to a wall-to-wall information

3422500 3423000 3423500

5327

000

5327

500

5328

000

Rechtswert [m]

Hoc

hwer

t [m

]

Vorrat [Vfm ha−1]

0454966

FoGIS Bestandesgrenzen











Airborne Laser Scanning

http://www.geokosmos.com/technologies/airbornscan.jpg

Active remote sensingsystem

Laser for distancemeasurement

Pointcloud with XYZ-rawdata























Digital Terrain Model

Software: TreesVis, FELIS Uni Freiburg





Digital Surface Model

Software: TreesVis, FELIS Uni Freiburg












Area-based method

Aggregation of laser data on sample plot level → metricsStatical relation between

MetricsSample plot attributes (volume, diameter distribution, treeheight)





Area-based method







Area-based method







Area-based method







Computation of metrics





Computation of metrics - basic R

Vegetationshöhe [m]

Häu

figke

it

10 15 20 25 30

010

2030

4050







Häu

figke

it

10 15 20 25 30

010

2030

4050 0% Perzentil

25% Perzentil

50% Perzentil

75% Perzentil

100% Perzentil







Häu

figke

it

10 15 20 25 30

010

2030

4050 0% Perzentil

25% Perzentil

50% Perzentil

75% Perzentil

100% Perzentil

Mittelwert





Other predictor variables - ArcGIS

Crown cover

Coniferous proportion




A mixed model (lme) for timber volume estimationA GAMLSS for diameter distribution estimation








Hierarchical data structure





Hierarchical data structure





Linear mixed model - lme

y ij = X ijβ + U i,jγ i + U ijγ ij + εij

with

γ i ∼ N(0, D(1)), γ ij ∼ N(0, D(2)), εij ∼ N(0,Σij)

where

Σij =

σ2y2δij1 · · · Kov(εij1, εijnij )

.... . .

...Kov(εijnij , εij1) · · · σ2y2δ

ijnij

andKov(εijk , εijk ′) = exp(−s/ρ) σyδ

ijk σyδijk ′


Regionalization - Maptools

3422500 3423000 3423500

5327

000

5327

500

5328

000

Rechtswert [m]

Hoc

hwer

t [m

]

LaubwaldMischwaldNadelwaldLichter BereichStarke vertikale Strukur



3422500 3423000 3423500

5327

000

5327

500

5328

000

Rechtswert [m]

Hoc

hwer

t [m

]

Vorrat [Vfm ha−1]

0454966



3422500 3423000 3423500

5327

000

5327

500

5328

000

457.13

278.87

199.27

346.96

588.60 412.67

397.51

537.47

431.40

515.96

323.84

521.79

556.95

482.69

428.28

143.29

563.85

261.38

337.48

138.01

391.16

518.55

281.84590.42

134.58

521.74

356.49

608.37

176.22

686.29(67.8)

(0.1)

(3.6)

(3.7)

(1.0)

(0.1) (0.3)

(0.3)

(0.2)

(0.8)

(0.7)

(0.4)

(0.2)

(0.1)

(1.4)

(0.7)

(12.2)

(0.1)

(0.3)

(0.1)

(11.1)

(12.9)

(0.5)

(0.6)(0.1)

(9.4)

(0.2)

(4.5)

(0.2)

(3.5)

(0.1)

506.52

NA

289.10

388.83 282.85

420.70

599.50

582.90

534.70

413.80

542.25

395.82

NA

NA

NA

710.20

183.47

407.66

NA

NA

256.50

200.05514.00

NA

510.70

485.60

805.40

NA

473.55(NA)

(8.7)

(NA)

(NA)

(8.9) (21.9)

(28.3)

(20.8)

(NA)

(NA)

(5.1)

(10.2)

(13.4)

(NA)

(NA)

(NA)

(15.4)

(30.3)

(13.0)

(NA)

(NA)

(NA)

(9.2)(17.4)

(NA)

(36.9)

(NA)

(29.6)

(NA)

(29.4)

Rechtswert [m]

Hoc

hwer

t [m

]

Vorrat [Vfm ha−1]

98.36 − 293.22293.22 − 406.69406.69 − 521.75521.75 − 686.29Stichprobenpunkte











Modeling I





Modeling II

Generalized additive model for location, scale and shape -GAMLSSBe

y ∼ Weibull(a, b, c), a = 7, b, c > 0

with density

f (y |b, c) =cb

(yb

)c−1exp

[

−(y

b

)c]

,

thenb = h−1(η) und c = h−1(η).

Where a = Location-, b = Scale- and c = Shape parameter,ηi = x ′

i β as well as h = link function.


Qu1: (24,26.8] Qu3: (28.9,32.7] Plots: 20 Trees: 242

Den

sity

0 20 40 60 80

0.00

0.04

0.08

Qu1: (18.2,21.1] Qu3: (25.2,28.9] Plots: 45 Trees: 472

Den

sity

0 20 40 60 80

0.00

0.04

0.08

Qu1: (21.1,24] Qu3: (25.2,28.9] Plots: 33 Trees: 436

DBH (cm)

Den

sity

0 20 40 60 80

0.00

0.04

0.08

Qu1: (15.4,18.2] Qu3: (21.5,25.2] Plots: 58 Trees: 725

0 20 40 60 80

0.00

0.04

0.08

Qu1: (18.2,21.1] Qu3: (21.5,25.2] Plots: 38 Trees: 561

0 20 40 60 80

0.00

0.04

0.08

Qu1: (12.5,15.4] Qu3: (17.7,21.5] Plots: 51 Trees: 676

DBH (cm)0 20 40 60 80

0.00

0.04

0.08

Qu1: (15.4,18.2] Qu3: (17.7,21.5] Plots: 29 Trees: 430

0 20 40 60 80

0.00

0.04

0.08

Qu1: (9.67,12.5] Qu3: (14,17.7] Plots: 40 Trees: 449

0 20 40 60 80

0.00

0.04

0.08

Qu1: (6.81,9.67] Qu3: (10.3,14] Plots: 22 Trees: 228

DBH (cm)0 20 40 60 80

0.00

0.04

0.08









Ongoing research

20 40 60 80

1020

3040

DBH (cm)

Hei

ght (

m)

Bivariate height- anddiameter distribution

Random forests toestimate tree-speciesspecific timber volume(multivariate)




Ongoing research

Fi Bu Ta Dgl BAh

Vor

rat (

m3 ha

−1)

050

100

150

200

Bivariate height- anddiameter distribution

Random forests toestimate tree-speciesspecific timber volume(multivariate)




Summary

R is well suited for analyzing laser data due to its...functionality to call other programs - shell()flexibility (writing own functions)state-of-the-art statistical methods

Still learning R after 5 years of use...




Summary






Summary






Summary






Summary






Thanks go to...

Christian Gläser, Drs. Edgar Kublin, MatthiasSchmidt, Arne Nothdurft, Gerald Kändler

You for your attention!


Documents

Use R! for estimating forest parameters based on Airborne ... fileIntroduction Methods and Results Ongoing research and summary Use R! for estimating forest parameters based on Airborne