Estimation of water cloud model vegetation parameters using a genetic algorithm

Abstract

The water cloud model is used to account for the effect of vegetation water content on radar backscatter data. The model generally comprises two parameters that characterize the vegetated terrain, A and B, and two bare soil parameters, C and D. In the present study, parameters A and B were estimated using a genetic algorithm (GA) optimization technique and compared with estimates obtained by the sequential unconstrained minimization technique (SUMT) from measured backscatter data. The parameter estimation was formulated as a least squares optimization problem by minimizing the deviations between the backscatter coefficients retrieved from the ENVISAT ASAR image and those predicted by the water cloud model. The bias induced by three different objective functions was statistically analysed by generating synthetic backscatter data. It was observed that, when the backscatter coefficient data contain no errors, the objective functions do not induce any bias in the parameter estimation and the true parameters are uniquely identified. However, in the presence of noise, these objective functions induce bias in the parameter estimates. For the cases considered, the objective function based on the sum of squares of normalized deviations with respect to the computed backscatter coefficient resulted in the best possible estimates. A comparison of the GA technique with the SUMT was undertaken in estimating the water cloud model parameters. For the case considered, the GA technique performed better than the SUMT in parameter estimation, where the root mean squared error obtained from the GA was about half of that obtained by the SUMT.Key words vegetation parameter; backscatter coefficient; inverse problem; genetic algorithm; data errors; bias; root mean squared error; sequential unconstrained minimization technique Estimation des paramètres de végétation dans un modèle de nuage utilisant un algorithme génétique Résumé Le modèle de nuage est utilisé pour rendre compte de l'effet de la teneur en eau de la végétation sur les données de rétrodiffusion radar. De manière générale, le modèle comprend deux paramètres qui caractérisent le terrain végétalisé, A et B, et deux paramètres de sol nu, C et D. Dans la prèsente étude, les paramètres A et B ont été estimés en utilisant une technique d'optimisation par algorithme génétique (AG), et comparés aux estimations obtenues par la technique de minimisation séquentielle sans contraintes (MSSC) à partir des données mesurées de rétrodiffusion. L'estimation des paramètres a été formulée comme un problème d'optimisation par moindres carrés, en minimisant les écarts entre les coefficients de rétrodiffusion extraits de l'image ASAR d'ENVISAT et ceux prévus par le modèle de nuage. Le biais induit par trois fonctions objectif différentes a été analysé statistiquement par génération de données de rétrodiffusion synthétiques. Il a été observé que, lorsque les données de coefficient de rétrodiffusion ne contiennent aucune erreur, les fonctions objectif n'induisent pas de biais dans l'estim...

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