### I. Introduction

*σ*

^{0}=

*A*+

*B*cos

*φ*+

*C*cos

*2φ*, where

*φ*is the azimuth angle of the wind direction relative to the radar look direction. The coefficients

*A*,

*B*, and

*C*of each GMF model are determined empirically based on the experimental data sets for each frequency band as functions of radar parameters (frequency, angle, and polarization) and wind speed. However, each of these empirical models has limited ranges of frequencies, polarizations, incidence angles, and wind vectors.

*φ*=0°) and downwind (

*φ*=180°) directions, and “peakedness” is defined by the difference between the upwind (

*φ*=0°) and crosswind (

*φ*=90°) directions.

*s*

_{0}(skewness factor) that may be empirically determined for a given wind speed.

*B*(

*k*)=

*B*

*(*

_{S}*k*)+

*jB*

*(*

_{a}*k*) with an unknown parameter (skewness factor), which should be empirically determined for each wind speed, we attempted to generate an empirical expression for representing the skewness effect. In the computation of the first term of the theoretical model [10] associated with the correlation function, the correlation length of a sea surface is represented by the function of the correlation length of the upwind (

*L*

*) and crosswind (*

_{u}*L*

*) directions and the azimuth angle of wind direction*

_{c}*φ*. We found that the correlation length could also include the skewness effect without the complicated second term when the correlation length is multiplied by a Gaussian-type functional form of the wind azimuth angle

*φ*. In other words, the skewness effect can be practically accounted for by controlling the correlation length of a sea surface. The coefficients of the new multiplying function can be obtained by comparing the new model with an extensive experiment database. Unlike the existing model, which is complicated and has skewness factors that are determined for each wind speed, this new model is simple without the complicated bispectrum function and needs only the empirical determination of the coefficients for each frequency and polarization for a wide range of wind speeds. The accuracy of this new model was verified with the extensive experiment database at X-band. Surprisingly, the model agreed well with the Ku-band independent radar measurements [14].

### II. The Existing Model

##### (1b)

*I*

*,*

_{pp}*W*(

*K, φ*),

*f*

*,*

_{pp}*F*

*, and*

_{pp}*B*(

*K*,

*φ*) are given in [11],

*k*

_{1}is the wavenumber,

*θ*is the incidence angle, and

*h*

*is the RMS height of a sea surface. The*

_{rms}*W*

^{(}

^{n}^{)}(

*K, φ*) is the

*n*

*-order surface roughness spectrum, which is the Fourier transform of the*

^{th}*n*

*-power of a correlation function. For an exponential correlation function, the roughness spectrum has the form of*

^{th}*W*

^{(}

^{n}^{)}(

*K, φ*)=

*nl*

*[*

_{c}*n*

*+(*

^{2}*Kl*

*)*

_{c}^{2}]

^{−1.5}with

*K*=2

*k*

*sin*

_{1}*θ*and

*l*

*=*

_{c}*L*

*cos*

_{u}^{2}

*φ*+

*L*

*sin*

_{c}^{2}

*φ*, where the correlation length

*l*

*can be obtained from the upwind and crosswind correlation lengths,*

_{c}*L*

*and*

_{u}*L*

*, respectively, with the azimuth angle*

_{c}*φ*. The upwind and crosswind correlation lengths are given in [11] for the various wind speeds. As previously mentioned, a skewness factor

*s*

_{0}is used when describing the skewness effect. This constant is empirically determined at a wind speed, and thus it does not have the physical characteristics for wind speed. Moreover, Eq. (1b) is complicated, and the accessibility is poor. Therefore, we proposed a new simple model that does not need Eq. (1b) and has the physical characteristics for wind speed.

### III. New Simple Empirical Model

*φ*≤ 360° can be controlled by the surface correlation length. Therefore, we proposed the following form of a modified correlation length with unknown constants:

*a*,

*b*, and

*c*.

*f*=10 GHz, and

*θ*=32° with various values of the unknown constants

*a*,

*b*, and

*c*. The constant

*a*in Eq. (2) mainly controls the skewness effect, as shown in Fig. 1—the solid line (

*a*=0.5) and the dashed line (

*a*=0.1) with fixed

*b*and

*c*. The comparison between the solid line (

*b*=3) and the dotted line (

*b*=1) shows that the constant

*b*controls the peakedness (Fig. 1). The role of the constant

*c*is mainly to control the level of the backscattering coefficient, as shown in Fig. 1—the solid line (

*c*=0.7) and the dash-dot line (

*c*=0.3) with fixed

*a*and

*b*. Therefore, the skewness and peakedness can be simply controlled by selecting the optimum values of

*a*,

*b*, and

*c*.

*u*in the following forms:

*s*

_{0}, which was obtained empirically for a wind speed, was applied, but the new model with (3) became much simpler because the correlation length is a function of wind speed. We can also predict the backscattering coefficients for continuous wind speeds.

### IV. Verification of the New Model

*s*

_{0}was used. Conversely, the new model is simpler than the existing model for computing the backscattering coefficients of skewed sea surfaces.