2056 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 40, NO. 9, SEPTEMBER 2002 Retrieval of Land Surface Parameters in the Sahel From ERS Wind Scatterometer Data: A “Brute Force” Method L. Jarlan, P. Mazzega, and E. Mougin Abstract—The retrieval of surface parameters, namely, the soil moisture content and the herbaceous above-ground biomass, from European Remote Sensing (ERS) wind-scatterometer data is in- vestigated for a Sahelian study site during the period 1993–1994. Thanks to the low dimension of the unknown parameter vector, a systematic exploration of the parameter space could be carried out. This method allows the recovery of the optimal parameter set as well as an exhaustive description of the subdomain of accept- able solutions. The mapping of this subdomain points out the lack of constraints brought by the ERS dataset on the determination of the surface parameters. Particularly, additional constraints should be found on the rapid and short-scale variation of the soil mois- ture content. Moreover, it is shown that the distributions of the retrieved parameters are not normal nor log normal, as could be expected from random variables. As a consequence, the optimal parameter set is neither the average nor the maximum likelihood, and the computation of an a posteriori standard deviation of the parameters is meaningless. Index Terms—Backscattering, “brute force” method, nonlinear optimization, Sahel, wind scatterometer. I. INTRODUCTION T HE RETRIEVAL of land surface parameters from remote sensing data is usually achieved through an inverse method. Such a method allows to project the data information content from an abstract data space onto the parameter space via theoretical or semiempirical models. The solution parameters are optimal in the sense that they obey some predefined criterion that is the minimization of a cost function. In many applications, the scalar cost function is computed as the mean-square departure between the observed data and the “predicted” data estimated from the model that is controlled by the parameter vector . Among the inverse methods, the so-called least squares inverse theory (LSIT) [1], [2] is a mature theory that is nowadays widely used in the context of geosciences. This approach has been recently applied with success to the problem of land surface parameter recovery from European Remote Sensing (ERS) wind scatterometer (WSC) data [3]. However, the least squares inverse method (LSIM) Manuscript received June 20, 2001; revised November 9, 2001. This work was supported by the Programme National de Télédétection Spatiale-2000. L. Jarlan and E. Mougin are with the Centre d’Etudes Spatiales de la Biosphère, CNES/CNRS/UPS, 31401 Toulouse Cedex 4, France (e-mail: jarlan@cesbio.cnes.fr). P. Mazzega is with the Laboratoire d’Etude en Géophysique et en Océanogra- phie Spatiale, CNRS/CNES/UPS, 31401 Toulouse Cedex 4, France (e-mail: pierre.mazzega@cnes.fr). Digital Object Identifier 10.1109/TGRS.2002.802500 relies on a few basic assumptions that, in some cases, might not be relevant for estimating model parameters from remote sensing. 1) The model equations are linear or at least can be lin- earized around some good a priori parameter set . 2) The cost function presents a single minimum, the global minimum, and no saddle points. 3) The data errors, the errors associated with , and the er- rors related to the imperfect model equations are normally distributed. As such, these distributions, or densities, are fully specified by their respective mean and covariance. 4) The a posteriori parameters and data residues (not explained by the “best” model) are also normally dis- tributed. Assumptions 1) and 2) are intimately related: the cost func- tion, associated with nonlinear model equations, often appears as a complex landscape in the parameter space with several local minima and saddle points. As a consequence, any cost function minimization relying on descent-gradient algorithms or variants is trapped in the vicinity of the nearest local minimum. Ac- cordingly, the results of data inversion strongly depend on the a priori solution [4]. Moreover, even for weakly nonlinear problems, assumptions 3) and 4) are often violated. The present study aims to demonstrate that a “brute force” approach is better suited when the number of sought parame- ters, or equivalently the dimension of the parameter space , is low. Through a systematic exploration of , this brute-force approach allows not only to recover the optimal parameters but also provides a complete picture of the subdomain cor- responding to all the admissible solutions. Several structural properties of the relationship between the model and the data are also retrieved from this picture. In the present study, the brute-force method is applied to WSC time series acquired over Northern Sahel (Mali), aiming to estimate the temporal varia- tion of two land surface parameters, namely, the above-ground herbaceous biomass and the humidity of the upper soil profile. The considered period is January 1993–December 1994. The paper is organized as follows. The data and the backscattering model are described in Section II. Section III presents the inversion approach. Results are discussed in Section IV. II. DATA AND MODEL A. ERS Scatterometer Data ERS WSCs provide a measure of the C-VV backscattering coefficient of the illuminated surface at incidence angles 0196-2892/02$17.00 © 2002 IEEE