The instantaneous surface elevation is assumed to be represented by 
its Fourier transform (ky, ky), which is obtained from the wave height 
spectrum by applying a random phase to each spectral component (Alpers, 
1983). The radar cross section at each grid point is obtained by multiply- 
ing (ky, ky) by a modulation transfer function (Plant et al., 1983) 
and inverse Fourier transforming. Similarly, the center location and width 
of the Doppler spectrum are obtained by calculating the mean and variance 
of the radial velocities occurring within each grid cell during the SAR 
integration time. 
3. MODEL RESULTS 
In order to illustrate the characteristics of the SAR imaging process, 
as predicted by the model discussed in the previous section, some numerical 
results are presented below. These results have been generated using a 
simple form for the wave height spectrum, given by 
A exp [-2(k,/k cos e)?] 
S(k, e) - 
  
-5 <e< (14) 
OSE 
2 2 
[kw 2kk cos e * kokql 
which has a peak spectral density at k = kg, © = 0, and which has a fre- 
quency spectrum nearly identical to that proposed by Pierson and Moskowitz 
(1964), if A = 0.0013, ko = 0.59 g/u? and ky = 0.4 kg. This spec- 
trum also has a frequency-dependent angular spreading which is similar to 
that inferred by Hasselmann, et al. (1980) from the JONSWAP 1973 data for 
frequencies above the spectral peak. Note also that this form approaches 
the semi-isotropic Phillips spectrum for k >> ko. Thus, this form 
appears to be a reasonable representation of the wave spectrum for a fully 
developed sea. 
The effects of surface motions are dependent on the SAR system para- 
meters (primarily the R/V ratio) as well as the wave conditions, and are 
most critical for waves travelling in the azimuth direction. In order to 
illustrate these effects, the simulation model has been operated for R/V 
values of 30, 60, and 120 sec and for wave spectra having dominant wave- 
lengths (defined by Ap = 2»/kg) of 100, 200, and 400 meters centered in 
the azimuth direction. The nominal SAR resolution was assumed to be 25 x 
6.25 meters in each case, and the corresponding integration times are 0.56, 
1.13, and 2.26 sec. These parameters are typical of spaceborne L-band SAR 
systems such as SIR-B (with R/V ranging from 30 to 60 sec) and Seasat (with 
R/V « 120 sec). 
The wave spectrum defined by Eq. (14), with parameters selected to 
match the Pierson-Moskowitz spectrum, implies a significant wave height 
(Hg) of approximately 2 percent of the dominant wavelength (note that 
this dominant wavelength is roughly 30 percent larger than 27g/w6, 
where wy is the peak frequency). In order to simulate cases where the 
sea is not fully developed, runs were also made with the value of A reduced 
to yield a ratio Hs/Ap = 0.01. 
The results of these simulations are shown in Figures 2 through 4. 
Figure 2 shows the wave height and slope spectra and the corresponding 
image spectra for the case Ap = 200 m and R/V = 30 sec. Figure 3 shows 
the ratio of the image spectrum to the wave height spectrum (hereafter 
referred to as the "transfer function") along the azimuth wavenumber axis, 
430 
  
wn Ino 
KD m Sn a a