# Ka-Band Doppler Scatterometry: A Strong Wind Case Study
## 4 Sea Surface Doppler Centroid  
The Doppler spectrum centroid (DC) is the main parameter for sea surface current retrieval from Doppler scatterometer measurements [68; 69; 70; 71; 72; 73; 74; 75; 76]. In our previous study based on the same experimental setup, we have demonstrated [26] the possibility of sea surface current retrieval from DC measurements using the radar Modulation Transfer Function (MTF) approach [25; 77; 78] for \"regular\" winds, \(U<15\)-18 m s\({}^{-1}\), and long fetches, \(\geq\)100 km. The present data provide a way to check if this approach is still applicable at stronger winds, \(\approx\)20-30 m s\({}^{-1}\), and limited fetches, \(\approx\)1 km. From the above Doppler spectra analysis (Figure 4), no essential sea spray impacts are expected, but other factors, including MTF applicability at strong wind/short fetches, need further examination.  
For space/air-borne scatterometer set up with a large ground footprint size, the DC is \"automatically\" measured when the footprint size exceeds a few peak wavelengths, i.e., surface waves are not spatially resolved. For tower-based measurements, the effective radar footprint size is several meters long and wide (see Appendix A, Figure 14 in [25] for details), and energy-containing surface waves (typically 40 m, 5-s period at the platform site) are resolved. In this case, the DC is based on _temporal_ rather than _spatial_ averaging. In terms of instantaneous Doppler spectra, \(S(f_{d},t)\), and ignoring possible non-ergodicity of the wave field, the DC reads,  
\[V_{\rm D}=\frac{\iint f_{\rm d}S(f_{d},t)\,df_{\rm d}dt}{\iint S(f_{\rm d},t)\, df_{\rm d}dt}, \tag{10}\]  
where time averaging is performed over an interval sufficiently exceeding the peak wave period. We select 1 min averaging interval corresponding to \(\approx\)12 or more characteristic peak wave periods.  
The DC reflects the footprint-averaged sea surface motion that is mainly governed by waves and currents [56; 79; 69], which are entirely, or in part, forced by winds. As a first guess and following [69], the measured DC is compared in Figure 10 with the line-of-sight (LOS) wind vector projection, \(U_{\rm LOS}=U\sin\theta\cos(\varphi-\varphi_{U})\). There is a visually good correlation between the two, but with different slopes (or gain factors in terms of [22]) for different incidence angles (compare Record #7 data collected at \(\theta=45^{\circ}\) with other records collected at \(\theta=20^{\circ}\)). Firstly, this close correlation is explained by weak non-wind-driven background currents (see Figure 2c for 10 m current speed) and, secondly, by a close relationship between wind and waves at the experiment site. The exception from this is  
Figure 9: Folded curvature spectrum, \(B=(B_{0}(k)+B_{0}(-k))/2\), estimated for upwind direction from radar GMFs and our present data versus wind speed and wave number. Spectrum estimate uncertainty is shown by transparent shading in (**a**) wind speed; (**b**) wave number.  
seen for a downwind (negative) part of Record #5 (Figure 10, green dots), for which the relationship between the DC and LOS wind velocity differs for \(-5\) m s\({}^{-1}<U_{\text{LOS}}<0\) m s\({}^{-1}\). This part of Record #5 was acquired during an abrupt switch in wind speed and direction between 22:20 and 23:00 UTC on 25 October 2018 (Figure 2) at virtually constant wave height and direction.  
To achieve deeper insights into the physics of Doppler imaging mechanisms, the DC is further analyzed in terms of the MTF-based Ka-band Doppler (KaDOP) model [26], which is briefly summarized below.