## 1. Introduction

[2] In many maritime regions of the world, such as the Mediterranean, Persian Gulf, East China Sea, and California Coast, atmospheric ducts are common occurrences. They result in various anomalies such as significant variations in the maximum operational radar range and increased sea clutter. Hence radar systems operating in these environments would benefit from knowing the effects of the environment on their system performance. This requires knowledge of the atmospheric refractivity, which is usually represented by the modified refractivity (M profile) in the radar community [see *Skolnik*, 2001].

[3] Evaporation and surface-based ducts are associated with increased sea clutter due to the heavy interaction between the sea surface and the electromagnetic signal trapped within the duct. However, this unwanted clutter is a rich source of information about the environment and can be used to determine the local atmospheric conditions. This can be a valuable addition to other more conventional techniques such as radiosondes, rocketsondes, microwave refractometers and meteorological models such as the Coupled Ocean/Atmospheric Mesoscale Prediction System (COAMPS) that give M profile forecasts [*Rowland and Babin*, 1987; *Thews*, 1990; *Hodur*, 1996; *Skolnik*, 2001]. In a Bayesian framework, the results of one or several of these techniques and regional duct statistics [*Babin*, 1996] can be coupled with the clutter inversion to improve the overall estimation quality. An attractive feature of inferring refractivity from sea surface clutter is that it does not use additional hardware or extra meteorological/electromagnetic measurements. It extracts the information from the radar clutter obtained during normal radar operation, which usually is readily available both as a function of range, direction and time. For a fast inversion algorithm, a near-real-time M profile structure is obtained. The need for a fast algorithm that updates the environmental estimates at intervals of 30 min or less is evident in work by *Rogers* [1996], where the RMS error in propagation factor exceeds 6 dB after 30 min because of temporal decorrelation.

[4] Various techniques that estimate the M profile using radar clutter return are proposed by *Rogers et al.* [2000], *Gerstoft et al.* [2003,2004], *Barrios* [2004], *Rogers et al.* [2005], *Yardim et al.* [2006], and *Vasudevan et al.* [2007]. Most of these refractivity from clutter (RFC) techniques use an electromagnetic fast Fourier transform (FFT) split-step parabolic equation (SSPE) approximation to the wave equation [*Barrios*, 1994; *Levy*, 2000], whereas some also make use of ray-tracing techniques. While the paper by *Rogers et al.* [2000] exclusively deals with evaporation duct estimation, other techniques are applicable to both evaporation, surface-based and mixed type of ducts that contain both an evaporation section and an surface-based type inversion layer. *Vasudevan et al.* [2007] exploits the inherent Markovian structure of the FFT parabolic equation approximation and uses a particle filtering approach, whereas *Barrios* [2004] uses rank correlation with ray tracing to estimate the M profile.

[5] In contrast, *Gerstoft et al.* [2003, 2004] and *Yardim et al.* [2006] use global parameterization within a Bayesian framework. Since the unknown model parameters are defined as random variables in a Bayesian framework, the inversion results will be in terms of the means, variances and marginal, as well as the *n*-dimensional joint posterior probability distributions, where *n* represents the number of unknown duct parameters. This gives the user not only the ability to obtain the maximum a posteriori (MAP) solution, but also the prospect of performing statistical analysis on the inversion results and the means to convert these environmental statistics into radar performance statistics. These statistical calculations can be performed by taking multidimensional integrals of the joint probability distribution functions (PPD). *Gerstoft et al.* [2003] use genetic algorithms to estimate the MAP solution. However, no statistical analysis is performed since classical genetic algorithms (GA) are not suitable for the necessary integral calculations. While *Gerstoft et al.* [2004] use importance sampling, *Yardim et al.* [2006] use Markov chain Monte Carlo (MCMC) samplers to perform the MC integration [*Ó Ruanaidh and Fitzgerald*, 1996; *MacKay*, 2003]. Although they provide the means to quantify the impact of uncertainty in the estimated duct parameters, they require large numbers of forward model runs and hence they lack the speed to be near-real-time methods and are not suitable for models with large numbers of unknowns.

[6] In this paper, a hybrid GA-MCMC technique is implemented. The method reduces the number of forward model runs required to perform the RFC inversion, while still being able to perform MC integration. It is first tested on the synthetic data used by [*Yardim et al.* [2006] with a four-parameter, range-independent, trilinear M profile model (Figure 1). Then data collected during the 1998 Wallops Island experiment (Wallops'98) [see *Gerstoft et al.*, 2003] are analyzed using a 16-parameter range-dependent atmospheric model to show the capabilities and limitations of the method. An evaporative duct structure is not appended in this work but it can be done by introducing a Jeske-Paulus (JP) [*Jeske*, 1973; *Paulus*, 1985] or Liu-Katsaros-Businger (LKB) [*Liu et al.*, 1979] profile using one or more extra evaporation duct parameters, depending on the conditions.