# Ka-Band Doppler Scatterometry: A Strong Wind Case Study
## 4 Sea Surface Doppler Centroid
### Small Incidence Angle (Record #5)  
Record #5 (Figure 11) is remarkable due to the fully recorded wind direction turning event, with short interruptions during two strong rain events. During this entire record, the radar was oriented downwind relative to westerly winds. During the first part of Record #5 collected at westerly winds (before 00:00 UTC on 25 October 2018), the combined DC contribution from background current, Bragg velocity, and wind drift is \(\approx\)25% of the total DC (Figure 11a, compare green and blue lines). Hence, the remaining \(\approx\)75% is produced by the WIDV. After the wind direction switch into the northerly direction (after 00:00 UTC on 25 October 2018), the partitioning changes to \(\approx\)50/50% due to changes in wave regime and relative radar azimuth (crosswind). Notice that combined contribution from 10 m currents, wind drift, and Bragg velocity changes its sign but remains \(\approx\)0.1 m s\({}^{-1}\) in magnitude. The measured WIDV estimated as the difference between the total measured DC and the sum of background current, wind drift, and Bragg velocity is shown by the blue line in Figure 11c. An alternative \"direct\" estimate of the WIDV, \(V_{\text{D}}-\overline{\widetilde{v}}\), is consistent with the former estimate but has a smaller magnitude as it only accounts for waves resolved by the radar footprint. As illustrated in Figure 11a, the WIDV is the dominant part of the DC. Hence, inverting the DC into the surface current requires precise knowledge of the WIDV. The present dataset provides a useful testbed to evaluate KaDOP model [26] performance. First, the KaDOP is evaluated using the observed frequency-angular wave spectrum concurrently measured by the triangle wave gauge array. This estimate is apparently below the measured WIDV magnitude for the downwind part of Record #5 and even has wrong WIDV sign for the crosswind part of Record #5 (Figure 11c, purple line). These discrepancies are explained by the geometry of the wave gauge triangle which has a too-long base, \(\approx\)10 m, that significantly limited in-situ wave measurements. While gauge-measured wave frequency spectra are limited by the sampling rate, \(f<2\) Hz, their angular-frequency wave spectra are cut off at \(\lambda\approx 20\) m or \(f\approx 0.3\) Hz (Figure 12a), which results in WIDV underestimation for the westerly wind part of Record #5. During the northerly part of Record #5, the very young (hence short) offshore waves are not resolved by the triangle array that results in erroneous spectra estimates for this wave system (Figure 12b), and thus deficient WIDV estimates. For qualitative demonstrations, we simulate the high frequency part of wave spectra, \(f>0.3\) Hz, using the modified JONSWAP spectrum [82], with wave direction defined by instantaneous wind, and smoothly merge it with the measured low-frequency part, \(f<0.3\) Hz. Wave age and spectrum level parameters of the simulated part are selected to fit its peak frequency and elevation variance with those from observed 1D frequency wave spectra. When these simulated wave spectra are used in Equation (11), the KaDOP WIDV estimates improve, with the correct sign in the cross-wind part of Record #5 (green line in Figure 11c). Figure 11: Data from Record #5 at \(\theta=20^{\circ}\) (24-25 October 2018, see also Figure 2). Time series of 1 min average: (**a**) Doppler centroid (DC) and its contribution due to currents, wind, and Bragg scattering; (**b**) wind speed and wind direction; and (**c**) wave-induced Doppler velocity (WIDV) estimated in different ways: (**blue**)—measurements; (**reddish**)—wave resolving Doppler radar measurements; (**purple**)—KaDOP based on wave gauge array measured wave spectrum and Equation (11); (**green**)—KaDOP based on simulated wave spectrum combining wave gauge array measured wave spectrum with wind-based JONSWAP parametrization for high frequency (\(f>0.3\) Hz) part and Equation (11).