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USE OF MATLAB FOR RADAR REMOTE SENSING OF FORESTS

Gustaf Sandberg, PhD student

Chalmers University of Technology

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Matlab is used in all parts of the research process

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Radars are more than target detection

Military radars Air traffic control Speed control Maritime navigation Weather radar Wind speed (at sea) Crop/forest biomass and more

The CARABAS and LORA system. Developed and operated by the Swedish defence research agency (FOI). Used for forest biomass estimation.

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Research in the radar remote sensing group at Chalmers Effects of the ionosphere Sea ice monitoring Wind over oceans Ocean waves Signal processing algorithms Calibration and validation Forest biomass retrieval Advanced modelling of backscatter from forests

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Radar signal depends on forest biomass

Penetrates clouds Independent of light conditions Low frequencies (

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The BIOSAR experiment: A case study

Access precision of forest biomass measurements

Swedish test site near Skara

International collaboration Funded by ESA Image shows radar image

(7 x 8 km2 , courtesy DLR)

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The data needs to be processed before it is analyzed

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Many different kinds of data available.

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Data processing example: Combine in-situ and lidar data In-situ measurements

for 10 stands (blue) Lidar measurements

for 59 stands (red) Wish to combine the

datasets Problem: overlapping

standsImage size is 4 by 1 km2

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Data processing example: Combine in-situ and laser data In-situ measurements

more accurate Remove overlapping

lidar stands Find intersections

using polybool(Mapping toolbox)

Remove stands with non-empty intersection Red defines the intersection found

using polybool. Example from the Matlab help.

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Data processing example: Combine in-situ and laser data Example code:% Extract the vertices for the in-situ stands[x1, y1] = poly2cw(trees(n).polygon_UTM33(:,1),trees(n).polygon_UTM33(:,2));for k=1:length(forest_stands_lidar)

% Extract the vertices for the "Lidar stands"[x2,y2]=deal(forest_stands_lidar(k).polygon(:,1),forest_stands_lidar(k).polygon(:,2));% Find the polygon vertices for the area covered by both the in-situ% and the "Lidar stands".[x,y]=polybool('and',x1,y1,x2,y2);% If this common polygon exists, the areas overlapif ~isempty(x)

include_stand(k)=false;end

end

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The initial data analysis is needed to get to know the data

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Matlab is well suited for initial data analysis No need to initialize variables Easy to plot data and view images Cells are very useful for experiment code Variable editor for examination of variables Fast enough calculations for most purposes

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Initial data analysis example: Examine stand polygons Want to check the stand polygons Visual inspection suitable Example code:% Load the stands for which lidar estimates existload('C:\Work\RS_BIOMASS\Biomass_map_lidar\biomass_map\forest_stands_Lidar.mat','

forest_stands_lidar')% Look at the polygonsfigurefor k=1:length(forest_stands_lidar)

plot(forest_stands_lidar(k).polygon(:,1),forest_stands_lidar(k).polygon(:,2))title(forest_stands_lidar(k).stand_id)axis equalpause

end

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Statistical analysis is an essential part of the research

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Strong support for statistical analysis

Linear regression is often used Extensive support in Matlab Very easy to use Non-linear regression also supported Many probability distributions supported A multitude of statistical tests possible

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Statistical analysis example: Linear regression Assume backscatter linearly dependent on biomass Estimate parameters Calculate confidence bounds Calculate backscatter estimates from model Calculate mean squared error Calculate adjusted R2 coefficient

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Statistical analysis example: Linear regression Example code:% Define the linear modelgamma0L=@(b,biomass) [ones(size(biomass)),biomass]*b;% Estimate parameters and CI[b_Lband_L,bint_Lband_L]=regress(gamma0_Lband,[ones(size(biomass)) biomass]);% Calculate the estimated backscatter using the linear modelgamma0_insitu_Lband_Lest=gamma0L(b_Lband_L,biomass_insitu);gamma0_Lidar_Lband_Lest=gamma0L(b_Lband_L,biomass_Lidar);% Calculate the mean squared errorMSE_Lband_L=mean(abs(gamma0_Lband-gamma0L(b_Lband_L,biomass)).^2);% Calculate adjusted R2 coefficientR2_Lband_L=1-MSE_Lband_L/MSE_Lband_C;R2adj_Lband_L=1-(1-R2_Lband_L)*(Nsamples-1)/(Nsamples-1-1);

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Statistical analysis example: Hypothesis testing Null hypothesis: Constant backscatter Alternate hypothesis: Linear dependence on biomass Use generalized likelihood ratio test The test variable is chi-2 distributed Can test for significance of alternate hypothesis

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Statistical analysis example: Hypothesis testing Example code:% Number of samplesNsamples=length(biomass);% Significance level 5 %a=0.05;% Test variable limit for tests with 1 degree of freedomtestvar_lim=chi2inv(1-a,1);% H0: Constant model. H1: Linar model% The test variable is chi-squared distributed, 1 degree of freedomtestvar_Pband_CvsL=Nsamples/sigma2*(MSE_Pband_C-MSE_Pband_L);

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The final stage: visualization and presentation

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Visualization of results is necessary

Matlab allows easy plotting of data Custom settings nice plots Possible to change most settings Many image formats supported

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Visualization example: The basic plot

The basic plot is frequently used Plot backscatter vs. biomass Include models with estimated parameters Set axis limits Define legends and axis labels

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Visualization example: The basic plot Example code:biomass_lin=linspace(0,bmax,200)';plot(biomass_insitu,gamma0_insitu_Lband,'*',...

biomass_Lidar,gamma0_Lidar_Lband,'x',...biomass_lin,gamma0L(b_Lband_L,biomass_lin),'--',...biomass_lin,gamma0WC(gamma0_veg_Lband,gamma0_gr_Lband,c_Lband_WC,...biomass_lin/cos(mean([incang_insitu_Lband;incang_Lidar_Lband]))),'-')

xlabel('Biomass [tons/ha]','Interpreter','Latex')ylabel(['$\gamma_{',pol,'}^0 [m^2/m^2]$'],'Interpreter','Latex')gridaxis([0 bmax 0 gmaxLband])legend('In-situ estimated biomass','Lidar estimated biomass',...

'Linear Model','Water cloud model','Location','NorthWest')print(gcf,'-dmeta',fullfile(results_dir,['Forward_',pol,'_Lband',scenario]))

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L-band (1.3 GHz) radar backscatter vs. biomass.

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Same plot for P-band (435 MHz). Lower frequencies better results.

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Conclusion: Matlab is used in all parts of the research process Illustrated by examples from case study Many more examples available Easy solutions to many problems Single programming language reduces complexity Many clever solutions, e.g. cells