## 1. Introduction

[2] In the low troposphere, anomalous propagation events occur owing to air movements and water evaporation. Survey radars usually work between 1 and 10 GHz in sea environment, and the detection range strongly depends on the atmospheric conditions at these frequencies. Anomalous propagation can cause “holes” in detection and either increase or decrease the radar detection range. This topic is especially critical for low-flying and floating targets for survey radar. Evaporation ducts, surface-based ducts, elevated ducts, and subrefractive layers are the identified anomalous propagation phenomena. These atmospheric structures are characterized by their vertical refractive index profile (Figure 1) [*Babin et al.*, 1997].

[3] The atmospheric conditions can be measured with radiosondes, rocket sondes, and buoys. Then the refractive index profile can be deduced from these measurements. Besides, refractometers can directly measure the refractive index. However, these techniques are difficult and expensive to implement. Atmospheric measurements also have a very low refreshment frequency and the delay between two measurements is too large for most situations. That is why “refractivity from clutter” (RFC) has been proposed to extract the refractivity directly from the radar clutter return [*Krolik and Tabrikian*, 1998; *Rogers et al.*, 2000; *Gerstoft et al.*, 2003a, 2003b; *Yardim et al.*, 2007]. Inferring the values of the modified refractivity profile from the sea clutter is a complex inverse problem because the relation between modified refractivity profile parameters and sea clutter is clearly nonlinear and ill-posed. Moreover, from a meteorological point of view, it implies several simplifying hypotheses to be solvable as described in section 2.

[4] The choice of the algorithm for the inversion is critical for RFC applications. Operational applications necessitate short computation time, less than ten minutes, to avoid error due to temporal evolution of refractivity [*Rogers*, 1996; *Douvenot et al.*, 2008]. Many fast nonlinear optimization methods exist. Neural networks, Support Vector Machines (SVM), radial basis functions, and kriging are the most common [*Bartoli et al.*, 2006].

[5] In the present paper, a learning method using the least squares support vector machines algorithm (LS-SVM) [*Suykens et al.*, 2002] is proposed. The LS-SVM algorithm is based on a least squares optimization with linear constraints. This kind of problem is convex and avoids the local minima during the learning phase. Therefore, LS-SVM is preferred to neural networks and other optimization methods. The work presented here focuses on obtaining the modified refractivity profile from modeled propagation losses, without taking into account the value of the sea clutter radar cross section (RCS). This paper focuses on the feasibility of such a system, by comparing a LS-SVM method with a genetic algorithm (GA) [*Gerstoft et al.*, 2003a] in ideal conditions, with noiseless simulated propagation losses. RFC using LS-SVM method can provide a system giving a refractivity estimation in real time, which is important for operational conditions.

[6] First, the RFC is introduced and the parameterization of the refractivity profile is presented. Second, the GA and LS-SVM processes are briefly exposed. The two inversion methods for RFC applications are compared in terms of accuracy and speed, and finally, the results are discussed.