Fouad Badran

A neural network approach for modeling nonlinear transfer functions: Application for wind retrieval from spaceborne scatterometer data

The present paper shows that a wide class of complex transfer functions encountered in geophysics can be efficiently modeled using neural networks. Neural networks can approximate numerical and nonnumerical transfer functions. They provide an optimum basis of nonlinear functions allowing a uniform approximation of any continuous function. Neural networks can also realize classification tasks. It is shown that the classifier mode is related to Bayes discriminant functions, which give the minimum error risk classification. This mode is useful for extracting information from an unknown process. These properties are applied to the ERS1 simulated scatterometer data. Compared to other methods, neural network solutions are the most skillful.

Wind ambiguity removal by the use of neural network techniques

This paper deals with the removal of ambiguities existing on the direction of the wind measured by satellite scatterometers. It is shown that neural networks are well adapted to solving this problem. Results using ERS. 1 simulated scatterrometric wind fields are presented. It is found that 99% of the ambiguities can be removed by imposing a rate of 25% ambiguity at 180° and 90°.

A Topological Hierarchical Clustering: Application to Ocean Color Classification

We propose a new criteria to cluster the referent vectors of the self-organizing map. This criteria contains two terms which take into account two different errors simultaneously: the square error of the entire clustering and the topological structure given by the Self Organizing Map. A parameter T allows to control the corresponding influence of these two terms. The efficiency of this criteria is illustrated on the problem of top of the atmosphere spectra of satellite ocean color measurements.

Determination of the Geophysical Model Function of NSCAT and its corresponding variance by the use of Neural Networks

We have computed two geophysical model functions (one for the vertical and one for the horizontal polarization) for the NASA scatterometer (NSCAT) by using neural networks. These neural network geophysical model functions (NNGMFs) were estimated with NSCAT scatterometer σO measurements collocated with European Centre for Medium-Range Weather Forecasts analyzed wind vectors during the period January 15 to April 15, 1997. We performed a student t test showing that the NNGMFs estimate the NSCAT σO with a confidence level of 95%. Analysis of the results shows that the mean NSCAT signal depends on the incidence angle and the wind speed and presents the classical biharmonic modulation with respect to the wind azimuth. NSCAT σO increases with respect to the wind speed and presents a well-marked change at around 7 m s−1. The upwind-downwind amplitude is higher for the horizontal polarization signal than for vertical polarization, indicating that the use of horizontal polarization can give additional information for wind retrieval. Comparison of the σO computed by the NNGMFs against the NSCAT-measured σO show a quite low rms, except at low wind speeds. We also computed two specific neural networks for estimating the variance associated to these GMFs. The variances are analyzed with respect to geophysical parameters. This led us to compute the geophysical signal-to-noise ratio, i.e., Kp. The Kp values are quite high at low wind speed and decrease at high wind speed. At constant wind speed the highest Kp are at crosswind directions, showing that the crosswind values are the most difficult to estimate. These neural networks can be expressed as analytical functions, and FORTRAN subroutines can be provided.

Clustering and Classification Based on Expert Knowledge Propagation Using a Probabilistic Self-Organizing Map: Application to Geophysics

In the present paper we describe a complete methodology to cluster and classify data using Probabilistic Self-Organizing Map (PRSOM). The PRSOM map gives an accurate estimation of the density probabity function of the data, an adapted hierarchical clustering allows to take into account an extra knowledge given by an expert. We present two actual applications of the method taken in the domain of geophysics.

SEMI-AUTOMATIC ADJOINT PE MODELING FOR GEOACOUSTIC INVERSION ∗

Recently, an analytic adjoint-based method of optimal nonlocal boundary control has been proposed for inversion of a waveguide acoustic field using the wide-angle parabolic equation [Meyer and Hermand, J. Acoust. Soc. Am. 117, 2937-2948 (2005)]. In this paper a numerical extension of this approach is presented that allows the direct inversion for the geoacoustic parameters which are embedded in a discrete representation of the nonlocal boundary condition. The adjoint model is generated numerically and the inversion is carried out jointly across multiple frequencies. To demonstrate the effectiveness of the implemented numerical adjoint, an illustrative example is presented for the geoacoustic characterization of a Mediterranean shallow water environment using realistic experimental conditions.

A method to de-alias the scatterometer wind field: a real world application

By the 1990’s several scatterometers are going to fly on board satellites dedicated to earth and ocean observation. The Europeen ERS.l AMI (Advanced Microwave Imager) is planned to be launched in 1991 and the US N.SCAT (Navy SCATterometer) is supposed to be launched in 1992. These scatterometers will provide wind vectors on a grid mesh of 50*50 km with a time and space coverage which will be dramatically improved with respect to conventionnal means of observations (see figure 1). For the first time oceanographers can expect to obtain an adequate description of the forcing of ocean circulation which depends on the wind-stress vector for the surface layers and on the wind-stress curl for the large scale and deep motions. These scatterometers will measure the wind with three antennas oriented in different directions. As the radar backscatter σO varies harmonically with the horizontal angle χ between the wind and the antenna, with maxima backscatter in the upwind and downwind directions and minima at the crosswind angle, it is possible to compute the wind direction [1]. In the absence of noise the determination of the direction of the wind would be unique. As the backscatter signal is noisy ambiguities can arise in its determination. The functional relationship between σ0 and the azimuth angle χ is nearly σO = cos (2χ), which results in two major ambiguities which are approximately 180° apart, and two others which are at 90°. Several techniques have been proposed to remove these ambiguities[2]. In the present paper we propose an alternative approach based on concepts developed in the frame of neural networks. The method we use can be related to image processing and two dimensional filtering. Its conceptuar framework is to determine two optimal filters to dealias the wind direction.