## 1. Introduction

[2] Radar echoes from natural surfaces are often analyzed using theoretical models for the scattering process. In most cases, these scattering models treat the scattered field as being either “coherent” or “incoherent”. The coherent component is characterized by a deterministic phase behavior (i.e., constructively interfering surface scatterers), such that the mean electric field is nonzero and the average power is given by the squared mean field. The incoherent component assumes random interference between scatterers, such that the mean electric field strength is zero, and the average power is given by the sum of the squared local field strength across the surface.

[3] In practice, there is a transitional behavior between the two components, and the total reflected power is not simply their sum. An example is to consider two point sources that radiate toward the receiving antenna. If their respective complex-valued electric fields at the receiver are given by **E**_{1} and **E**_{2}, then the coherent and incoherent reflected power is

where the asterisk denotes the complex conjugate. For a natural surface, the received echo is the superposition of many such reflections. The difference between the two components lies in the degree of correlation between the electric field vectors. In the case of perfect correlation, the coherent component (1) contains all of the reflected power; the calculated incoherent component does not constitute additional received signal. For a diffusely scattering surface, however, the squared terms in (1) are cancelled by the random signs of the electric field cross-products, and the total reflected power is given by the incoherent component. For backscatter data collected at incidence angles typical of imaging radar systems (>20°), the incoherent echo is safely assumed to dominate the return. The coherent return is only important when the incidence angle is small (the “near-nadir” regime), since this component contributes primarily to “mirror-like” reflections from smooth portions of the surface. In this paper, we examine models for the coherent and incoherent echo components, and discuss their applicability for analysis of near-nadir radar backscatter data.

[4] Our interest in near-nadir scattering processes is motivated by two upcoming Mars radar sounder instruments. The Mars Express Mission carries the Mars Advanced Radar for Subsurface and Ionosphere Sounding (MARSIS), which operates at frequencies from 1.8 to 5 MHz. The Mars Reconnaissance Orbiter, to be launched in 2005, will carry the Shallow Subsurface Radar Sounder (SHARAD), which operates at a center frequency of 20 MHz. These sounders are intended to search for Martian subsurface geologic interfaces, but will also measure the surface return from the nadir region (and potentially from favorably oriented off-nadir regions). The surface echo may obscure subsurface returns, and significant effort is directed toward understanding the dominant scattering mechanisms and possible methods for identifying and suppressing surface reflections [e.g., *Peeples et al.*, 1978; *Orosei et al.*, 2001; *Plaut et al.*, 2001]. An additional motivation comes from the possible inclusion of a radar sounder instrument on the Jupiter Icy Moons Orbiter (JIMO) mission.

[5] This paper examines the relative importance of coherent and incoherent near-nadir radar backscattering, using a fractal description of surface roughness. Section 2 reviews the observing geometry of the MARSIS and SHARAD instruments. In section 3, we discuss existing models for these two components, and correct an error in the normalization of the coherent scattering model of *Shepard and Campbell* [1999]. We also characterize the dependence of normal-incidence backscatter on surface roughness and scattering area. Section 4 assesses the range of validity for models of incoherent scattering, and the conditions under which coherent surface returns may be observed, relative to the operating parameters of the MARSIS and SHARAD sounders.