# Wave Orbital Velocity Effects on Radar Doppler
## 1 Introduction  
Radar altimetry is a widely acknowledged and largely diffused tool for open sea monitoring. Its basic principles are well known, and need not be described here, since they have been the object of extensive literature [1; 2; 3].  
Conventional radar altimeters (low resolution mode (LRM)), with their along-track resolution on the order of a few kilometres, have indeed proven to be essential in monitoring sea parameters such as significant wave height (SWH) and sea surface height (SSH) from satellites such as ERS-1, ERS-2, Envisat, Jason-1, etc. They have thus become an essential tool in ocean forecasting, climate analysis, and sea level monitoring [4].  
Recent developments have led to a widespread adoption of radar Doppler altimeters (also known as delay Doppler altimeter (DDA)), which provide a much higher along-track resolution (on the order of a few hundred metres); while this potentially improves the possibility of monitoring the ocean parameters, it also enhances some problems related to sea surface data analysis.  
Over the years, a number of difficulties have indeed arisen in assessing how various physical effects may impact the reliability of the measurements. For instance, a well-known problem--common to both conventional and Doppler altimetry--is the so-called electromagnetic bias [5], through which the SWH influences the SSH; also, the presence of foam on the sea surface may influence both SWH and SSH measurements [6; 7].  
The possible influence of sea state on the oscillation of measured SSH was investigated by different authors [8; 9; 10], who showed that 10 Hz root mean square SSH is statistically linked to the value of SWH itself.  
An aspect that recently was shown to be of considerable importance for DDA is the influence of very long waves upon the monitoring of SWH and SSH; the along-track resolution of DDA is indeed on the same order of, or even lower than, wavelength of the ocean swell.  
[PERSON] et al. [11; 12; 13] compared eight months of CryoSat-2 data over long ocean swell and found that, on the one hand, the waveforms derived from DDA are dissimilar from those obtained through conventional altimetry, and on the other hand, the shape of such waveforms is considerably different from the usual shape. By investigating such shapes, they found that sometimes--but not always--the presence of swell is highlighted by a double peak in DDA measurements (Figure 1). It is worth noting that most SWH retrieving algorithms assume a Gaussian distribution of the instantaneous water height--which is not true in a swell dominated sea.  
These results raise concerns about the potential impact of such ocean wave effects on the monitoring of sea state conditions.  
The present paper deals with a related problem, i.e., the interference of wave orbital velocity on the DDA algorithm. Such an effect, first reported in 2016 by [PERSON] et al. [14; 15; 16], was recently (2019) also tackled in [17; 18; 19; 20]. In the following, after a brief recall of the principles of DDA, a numerical procedure is implemented to show the influence of such an effect on the DDA response, and, where possible, to confirm its presence on the basis of published results.