# Wave Orbital Velocity Effects on Radar Doppler
## 3 Simulation and Results
### 20 Hz Data--Sea Surface Height  
An important geophysical parameter obtained through satellite altimeter measurement is SSH; in particular, the 20 Hz standard deviation of SSH, also known--perhaps inappropriately--as \"SSH error\", is often used as an index to evaluate the quality of this parameter. In order to investigate the possible mechanisms which govern this phenomenon, the simulation has been carried out as  
Figure 10: Comparison between averaged 20 Hz WF with (green line), and without (dashed red line), R-effect for swell superimposed to a wind sea: (**a**) JONSWAP significant wave height Hs = 4 m, peak wave period Tp = 8 s; swell wave height H = 4 m, period T = 14 s; (**b**) JONSWAP significant wave height Hs = 4 m, peak wave period Tp = 8 s; swell wave height H = 4 m, period T = 16 s.  
Figure 9: Simulated single waveforms with (solid green line), and without (dashed red line), R-effect for swell superimposed to a wind sea: (**a**) JONSWAP significant wave height Hs = 4 m, peak wave period Tp = 8 s; swell wave height H = 4 m, period T = 14 s; (**b**) JONSWAP significant wave height Hs = 4 m, peak wave period Tp = 8 s; swell wave height H = 4 m, period T = 16 s.  
above, with a realistic JONSWAP wind sea state, providing 20 results per second. For each of the 20 measurements, the average value \(\overline{\eta}\) of the sea surface height over each resolution strip was calculated, both by taking into account, and by neglecting, the R-effect. A typical result is reported in Figure 11.  
The SSH errors, i.e., the standard deviations \(\sigma_{\overline{\eta}}\) of the \(\overline{\eta}\) over a second (20 looks) can thus be calculated. Figure 12 yields the results for Hs = 4 m and various values of the peak spectral wavelength Lp, both for main wave direction perpendicular (across-track), and aligned (along-track), to the satellite flight direction.  
The results are interesting, because they provide an entirely different picture according to whether R effect is taken into account or not. Along-track R results provide--for a 200 m peak wavelength--a \(\sigma_{\overline{\eta}}\) of about 5 mm, while non-R give a negligible value. The reverse is true for across-track results. This leads to the possibility that SSH oscillations, or at least parts of them, might be caused by an aliasing effect. Available experimental information by [PERSON] et al. [8; 9], [PERSON] et al. [31], and a simple model by [PERSON] et al. [10] yield very scattered data with an average value of about 1 cm, and a dispersion of the same order of magnitude. Unfortunately, no information is provided in the current literature about the influence of the sea direction with respect to the satellite line of flight, and this is certainly an aspect which should be investigated.  
Figure 11: Sea surface height average values \(\overline{\eta}\) by taking in account (solid green line), and by neglecting (dashed red line), the R-effect.  
Figure 12: Standard deviation values \(\sigma_{\overline{\eta}}\) as a function of peak spectral wavelength Lp by considering (green diamonds), and by neglecting (red circles), R-effect: (**a**) main wave direction across satellite track; (**b**) main wave direction along satellite track.