Kriging-based techniques for forest characterization

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Dr. Gyimóthy Szabolcs
Department of Broadband Infocommunications and Electromagnetic Theory

A common reason for making radar measurements of forested areas is to retrieve the distribution, quality and quantity of the above-ground biomass. From a measurement one should determine the mean diameter of the trunks, the height of the trees and other characterizing variables of the forest that are useful for the biomass description. During a measurement one compares the relation of the emitted and the backscattered wave in different polarizations.

The explanation and accurate processing of the radar data requires numerous and extensive observations, but the number of observations is limited by their difficulty and cost. This is the reason for the development of numerical simulators, which can compute the radar response of a virtual forest.

The problem of using such simulators, is that these simulators are computationally expensive and for the computation one has to give the value of the forest parameters, so it requires the knowledge of the variables that are the subject of retrieval. The simulators can be used for the retrieval of the forest parameters (i.e. the solving of the inverse problem) only with an optimization algorithm that usually requires a high number of simulations, so the solution needs a high computational time.

The computational time can be reduced by using surrogate models, that can approximate the result of a numerical simulator with a low computational time. The main idea of surrogate modeling is to evaluate the objective function (in this case the simulator) at given values of the input parameters, and make predictions for any output based on this precalculated information. The generated model is assumed to be appropriately accurate and many magnitudes faster to compute.

In this thesis, I present the process of the surrogate model generation for the COSMO simulator. COSMO was developed in SONDRA Laboratory at Sup\'elec for the study of the radar backscattering of forested areas. The trees of the modeled forest used in the numerical studies are represented only with their trunks. The forest is described with the age of the trees (that is proportional to the diameter of the trunks) and the moisture of the ground, and the radar configuration is described with the frequency and the incident angle. The age of the forest, and the ground moisture are the subject of retrieval in the inverse problem.

For the generation of the surrogate model a two-level adaptive sampling method was used to fit the characteristics of the presented problem with the best accuracy. The upper level of adaptive sampling is responsible for the selection of the samples in the age-moisture plain, and the lower level is responsible for the sample selection in the frequency-incident angle plain. For the prediction of the output (based on the adaptively generated samples) the kriging interpolation were used. Kriging is an approximation method based on stochastic processes. The adaptive sampling is based on the approximated uncertainty of the model and aims to reduce this uncertainty.

The result of the adaptively generated surrogate model is validated with the result of

the simulator. The model is used for the solution of the inverse problem to retrieve the

forest characterization parameters from a radar response.


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