# Characterization of CYGNSS Ocean Surface Wind Speed Products
## 3 Results
### Sensitivity to Wind Speed Persistence  
Stress caused by wind at the ocean surface imparts energy to the surface roughness at capillary-scale wavelengths. Turbulent energy cascade transfers energy from shorter to longer wavelengths and, after a sufficient length of time, the complete roughness spectrum reaches an equilibrium. The equilibrium state is referred to as a Fully Developed Sea. Prior work has shown that the time required for the roughness spectrum to become fully developed with respect to GNSS-R measurements is 1-2 h [42]. In other words, once the wind has blown at the same speed and in the same direction for \(\sim\)2 h, a GNSS-R measurement will stabilize and the wind speed estimated from it will be consistent with that persistent wind. If, on the other hand, the wind changes in the hours prior to a measurement, the capillary waves will react to the change more quickly than the swell waves and the swell waves at the time of the measurement will not be consistent with the local wind speed. As a result, the wind speed estimated from the measurement may be biased relative to the true wind at the time of the measurement. We consider here the dependence of wind speed bias on wind persistence. The persistence of wind speed at a given time is a measure of its change in the recent past. For our purposes, we use ERA5 winds reported hourly and define _persistence_ at time \(t\) as  
\[persistence(t)=\frac{windspeed(t)-windspeed(t-2 hr)}{windspeed(t)} \tag{1}\]  
where \(windspeed(t)\) is the ERA5 wind speed reported at a given time and \(windspeed(t-2\) h) is the ERA5 wind speed reported at the same location 2 h earlier. We further only considered cases of monotonic change in wind speed between (\(t-2\) h) and the present, i.e., either \(windspeed(t)>windspeed(t-1\) h) \(>windspeed(t-2\) h) for \(persistence>0\) or \(windspeed(t)<windspeed(t-1\) h) \(<windspeed(t-2\) h) for \(persistence<0\). In practice, monotonicity over 2 h was satisfied in the large majority of cases. A full year of matchups between CYGNSS and ERA5 winds during 2022 was used for the persistence analysis. The matchups were divided into 5 m/s increments of wind speed (as defined by the CYGNSS wind speed matchup at time, \(t\)) and then each increment was further divided by the persistence of the wind speed. The results are shown in Figure 18 for the FDS wind product. Figure 17: Dependence of (**a**) ASCAT and (**b**) GMI wind speed bias on SWH. For each wind speed interval, the bias (mean difference between CYGNSS and ERA5) is shown as a function of persistence. Error bars are included to show the standard deviation of the population of samples averaged in each case. Several characteristics apparent in Figure 18 are noteworthy. For all wind speeds above 5 m/s, the bias is within \(\pm\)0.5 m/s of zero when the persistence is small (between \(-\)15% and +15%). For larger positive values of persistence, in which case the prior wind speed was significantly lower than the present wind, there is a small increase in the bias. More notably, for large negative values of persistence, the bias grows dramatically with increasing persistence. These are cases in which the prior wind was significantly higher than the present wind. The explanation of this result is that the longer wave portion of the roughness spectrum is still responding to the higher winds that were there in the past. This increases the overall roughness and decreases the NBRCS. The retrieval algorithm therefore overestimates the wind speed, resulting in a large positive bias (FDS >> ERA5). Figure 19 shows persistence results for the NOAA wind speed product relative to ERA5. Below 15 m/s, the dependence of bias on persistence was similar to that of the FDS product. Above 15 m/s, the relative change in bias with persistence was similar but there is a significant overall positive bias in the NOAA product for all values of persistence.