# Wave Orbital Velocity Effects on Radar Doppler
## 4 Discussion and Conclusions  
A number of numerical simulations were performed to evaluate the influence that the R-effect, i.e., the Doppler shift deriving from sea wave orbital movement, can have on the response of delay Doppler altimeters (DDA).  
A schematic two-wavelength sea state was first considered; in this condition, the effect is occasionally present and visible in some single waveforms. Another numerical experiment was then carried out, by considering 20 Hz DDA simulated measurements on a more realistic sea state, based on a JONSWAP spectral wind sea superimposed to a long swell. The analysis of the results has shown a minor, but consistent, difference between R and non-R simulations of the 20 Hz averaged waveforms, as well as remarkable differences among some single waveforms; in particular, a complex shape waveform was occasionally found, bearing a similarity with experimental data by other researchers.  
A further set of simulations, again based on a JONSWAP wind sea, have provided interesting results on the 20 Hz oscillation \(\sigma_{\overline{\eta}}\) of the SSH. For a sea state orthogonal to the satellite track, the SSH simulated values when the R-effect is considered show a \(\sigma_{\overline{\eta}}\) which could account, at least in part, for the results reported in the literature.  
All the results seem to prove that the vertical orbital velocity component does actually influence DDA response; as per the practical importance, however, the conclusions must be more articulate. As per the evaluation of SWH, current algorithms, at least for wind sea states, should not be affected by any error caused by neglecting the R-effect, considering that they have generally been well tested against sea truth. Further detailed investigations should instead be carried on DDA-based monitoring of SWH in the situation where the sea state includes a long swell, and therefore the Gaussian distribution of the water heights does not hold.  
Another aspect where the consideration of the R-effect could be meaningful is the analysis of SSH and of its oscillations \(\sigma_{\overline{\eta}}\): on the one hand, the accuracy requirements of SSH monitoring are higher than those of SWH, on the other hand the behavior of \(\sigma_{\overline{\eta}}\) is a current, active research field. The effect could be exploited to extract further information on the sea state.  
A further line of investigation should lead to an assessment of the possible limits of the resolution attainable in the future with satellite DDA.  
The consequences of this work might prove to be of relevance, especially taking into account the new generation of sea monitoring satellites, such as Sentinel-3, which are greatly increasing the availability of DDA data over the oceans.  
Conceptualization: F.R. and E.P.C.; methodology: F.R., E.P.C., and F.D.; software: F.R., E.P.C., and A.D.L.; validation: A.D.L. and E.P.C.; formal analysis: E.P.C. and F.R.; writing--original draft preparation: F.R. and E.P.C.; writing--review and editing: A.D.L. and F.D.; supervision: F.D. and F.R. All authors have read and agreed to the published version of the manuscript.  
This research was carried out with University of Salerno Institutional Funds, as well as with the support of CUGRI (University Consortium for Research on Major Hazards).  
The authors are grateful to [PERSON] and [PERSON] for help and advice, as well as for authorizing the reproduction of the results reported in Figure 1. Thanks are also due to [PERSON] and [PERSON] for useful discussion and encouragement over the years, and to the anonymous reviewers for suggesting significant improvements of the approach. Work was partially carried out within ESA EO-Project 1172 \"Remote Sensing of Wave Transformation\".  
The authors declare no conflict of interest.