1

Estimating Forest Biomass Using Geostatistics Techniques: a case Study of

Rondônia, Southern Brazilian Amazon

Marcio SalesCarlos Souza

Phaedon KyriakidsDar RobertsEdson Vidal

2

Biomass estimates diverge: (Houghton et al, 2001)

Preview biomass estimates *

Approachs:

1- Interpolation.

2- Estimation on 44 forest ecossystems

3- Interpolation of field measurements.

4- Modeling

5- Interpolation.

6- Based on satellite data.

7- Purely Based on Satellite data.

• Total biomassa ranged from 78 to 279 PgC.• Resulting biomass profiles also differ.

1 2 3 4

5 6 7

* Picture modified from Houghton et al, 2001

3

Common Methods to Estimate Biomass

• Extrapolation of forest surveys;

• Estimates based on satellite data;

• Estimates based on models relating biomass on environmental parameters: (ex. vegetation type and soil);

4

Problems of the Common Methods

•Do not provide a measure of local uncertainty

•Do not account for spatial correlation

5

Objective

– Evaluate geostatistics to improve biomass estimation in the Amazon region

• Takes into account spatial autocorrelation• Provides a measure of local uncertainty

6

MethodsStudy area and data base

Origin: RADAMBRASIL

Data on timber volume from 330 samples inside and up to a

distance of 100km around Rondônia.

RADAMBRASIL plots:- 1 ha (20 m x 500 m).- All trees which DBH≥45 cm.

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MethodsAuxiliary

data

Volume data

Auxiliary data

Estimating trend

Trend model

ResidualsVariogram

AnalysisVariogram parameters

Kriging

Volume map

VolumeStd error map

BiomassConvertion

Biomass map

BiomassStd error map

1- Trend Estimation 2- Geoestatistics

3- Biomass Mapping

Sample data

Population data

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Methods• Data Layers:

Soil Texture (re-classified from IBGE’s Classification of Soils (1980)).

Forest type (re-classified from IBGE’s vegetation classification).

Topography(SRTM)

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Use information of neighbor samples to predict values atnon-sampled locations

Data Analysis

:)(swi

i

iiSSs ywywywywy 2211ˆ

ii dsw

1)(

Spatial Interpolation Geostatistical Interpolation (Kriging)

Weighting factors of samples nearby location s

Ex.: Classical (inverse distance) interpolation:

Choice of weighting factors :)(swi

min)()()()(ˆ

1)(

sYsYwVarsYsYVar

sw

iii

i

Best Linear Unbiased Estimator!

Kriging Requires:

• Volume values must be free of any trend (regression on external variables or coordinates)

•Estimation of variogram function (Variogram analysis):

))(),(()( huYuYCovhC

w1(s1) w2(s1) w2(s3)

w3(s3)w3(s1)

w4(s2)

w3(s2)

w1(s2)

w2(s2)

w1(s1) w2(s1) w2(s3)

w3(s3)w3(s1)

w4(s2)

w3(s2)

w1(s2)

w2(s2)

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• In the samples:

Trend Model Estimation

• In the population:

Trend Model Application

•Rondônia was divided in a 1km x 1km grid

•Trend model applied using data layers

Data Analysis

Estatistical Model for volume:

)()(ˆ sRsmY

)(,, sRtopogsoiltexttopogfortypetopogsoiltextfortypeVolumes

)(sm )(sR

)(,, sRtopogsoiltexttopogfortypetopogsoiltextfortypeVolumes

)(sm )(sR

fortype: Set of dummy variables for forest classes

soiltext : Set of dummy variables for soil texture classes

topog: Topography

R: Regression residuals

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Sample residual variogram

)(

1

2)()()(2

1)(

hN

iii huyuy

hNh

Sample residual variogram

)(

1

2)()()(2

1)(

hN

iii huyuy

hNh

Variogram Model:Nested Structure: nugget+gaussian+spherical

299.7 Km1855.2 (1.00)Spherical component:

99.9 Km1117.2 (0.60)Gaussian component:

-70.1 (0.04)Nugget:

RangesSillsComponent

299.7 Km1855.2 (1.00)Spherical component:

99.9 Km1117.2 (0.60)Gaussian component:

-70.1 (0.04)Nugget:

RangesSillsComponent

Model Parameters:

Results

00 55.5 111 166.5 222 277.5 333 388.5 444

500

1000

1500

2000

2500

Lag distance (Km)

Sem

ivari

an

ce Sill of spherical component: 1855.2

Sill of gaussiancomponent: 1117.2

Range of Gaussian Component: 99.9 Km

Range of Spherical Component: 299.7 Km

Variogram Model

Sample Variogram

Omnidirectional semivariogramof residuals

0 55.5 111 166.5 222 277.5 333 388.5 444

500

1000

1500

2000

2500

Sill of

Sill of gaussiancomponent:

Range of Gaussian Component: 99.9 Km

Variogram Model

Sample Variogram

Omnidirectional semivariogramof residuals

0

Variogram Analysis of Residuals

Nugget Effect:70.1

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Kriging Results

Volume Estimates

Deforestation up to 2003

Standard Errors (m3/ha)

Degrees West

Deg

ree

s N

ort

h

10

15

20

25

30

35

40

45

50

15.5

16.5

17.5

18.5

19.5

19.5

-72 -71 -70 -69 -68 -67 -66

Expected Volume (m3/ha)

Degrees West

Deg

ree

s N

ort

h

20

40

60

80

100

120

140

160

180

15.5

16.5

17.5

18.5

19.5

19.5

-72 -71 -70 -69 -68 -67 -66

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Converting volume to biomass Fearnside, 1997:

Biomass = SB x BEF x CF

SB = Volume x VEF x WD: Stemwood biomass

Volume Expansion Factor = 1.25 for dense forests

= 1.5 otherwise.

Wood Density = 0.404 for savanas (Barbosa & Fearnside); = 0.68 otherwise (Nogueira et al, 2005).

BEF = exp(3.213-0.506 ln(SB)) if SB<190

= 1.74 o.t.c

CF = 1.68: Sum of correction factors for lianas, non-trees, belowground biomass, trees <10cm DAP, trees with 30<DAP<31.8 cm DAP, hollow trees, bark and palms.

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Results

Biomass Estimates

Deforestation up to 2003

Standard Errors (Mg.C/ha)

Degrees West

Deg

ree

s N

ort

h

20

40

60

80

100

120

140

160

180

200

15.5

16.5

17.5

18.5

19.5

19.5

-72 -71 -70 -69 -68 -67 -66

Expected Biomass (Mg.C/ha)

Degrees West

Deg

ree

s N

ort

h

100

150

200

250

300

350

400

450

500

15.5

16.5

17.5

18.5

19.5

19.5

-72 -71 -70 -69 -68 -67 -66

450

600

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Relative RMSE reduction vs sample size inside variogram range .

0%

5%

10%

15%

20%

25%

30%

0 10 20 30 40 50 60 70 80 90# nearby samples (inside gaussian range of variogram range)

RM

SE

rel

ativ

e re

du

ctio

nResults

Validation

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Conclusions

- Biomass estimation has to take into account the spatial correlation.

- The volume in 1 ha plots is spatially correlated up to 100 km.

- Kriging improves estimation at locations with high samples density.

- The maps can be used to generate confidence intervals for the expected local mean biomass /ha.