# Validating CYGNSS Wind Speeds with Surface-Based Observations and Triple Collocation Analysis
## 3 Results
### Triple Collocation Analysis
#### 3.2.2 Results of TCA  
A comparison of the TCA metrics for cross correlation and root mean square error are given in Table 4, and Figure 5 presents density plots of the coincident measurements between the three products. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & & & \multicolumn{6}{c}{**Time Thresholds (SAR Speeds \textgreater{} 15 m/s)**} \\
**Pair** & **Metric** & **0.5** & **1** & **1.5** & **2** & **2.5** & **3** & **4** \\ \hline \multirow{3}{*}{SAR CYG} & R & 0.516 & 0.532 & 0.550 & 0.544 & 0.511 & 0.524 & 0.505 \\  & RMSD & 6.343 & 6.044 & 5.960 & 5.861 & 6.067 & 6.033 & 6.001 \\  & \# Meas & 2357 & 4808 & 6893 & 9071 & 11,281 & 13,296 & 17,313 \\ \hline \multirow{3}{*}{SAR SMAP} & R & 0.76 & 0.76 & 0.76 & \multirow{3}{*}{No change} & \multirow{3}{*}{No change} & \multirow{3}{*}{} \\  & RMSD & 4.898 & 4.889 & 4.904 & & & \\ \cline{1-1}  & \# Meas & 81,879 & 101,397 & 102,280 & & & \\ \hline \hline \end{tabular} Note: All correlation results were significant with \(p<<0.001\) using Wald test with T distribution.  
\end{table} 
Table 3: R and RMSD of 1:1 matchups of datasets used in TCA, for areas of SAR wind speeds above 15 m/s. NOAA v1.2 is used for CYGNSS. The Merged product has cross-correlations (CCs) equal or lower than NOAA and significantly lower errors, suggesting good performance for the TC-based product. SMAP had the highest CC and lowest errors, showing high agreement with both CYGNSS and SAR. This does not imply that SMAP is more accurate to the truth than SAR, as the unknown truth is approximated based on the distributions of the three datasets. SAR's performance was considerably lower in the multiplicative than the additive error models, while NOAA's performance improved. The multiplicative error model emphasises errors at lower wind speeds because it is using logarithmic wind speeds. This \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Error Model** & **Metric** & **NOAA** & **MRG** & **Avg. SAR** & **Avg. SMAP** \\ \hline \multirow{2}{*}{Additive} & CC (unitless) & 0.84 (0.02) & 0.84 (0.01) & 0.85 (0.01) & 0.93 (0.01) \\  & RMSE (m/s) & 3.48 (0.24) & 2.71 (0.16) & 3.57 (0.17) & 2.44 (0.22) \\ \hline \multirow{2}{*}{Multiplicative} & CC (unitless) & 0.88 (0.01) & 0.85 (0.02) & 0.79 (0.03) & 0.92 (0.02) \\  & RMSE (m/s) & 3.13 (0.18) & 2.90 (0.15) & 4.84 (0.56) & 2.77 (0.31) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results from TCA showing cross-correlations (CC) and error comparing the two CYGNSS wind retrieval products. SAR and SMAP are the average of the two values calculated in triplets with CYGNSS NOAA or YSLF. The value in smaller brackets is the 99 th percentile confidence interval from bootstrapping n = 1000. Figure 5: Density plots showing numbers of measurements at each cell used in triple collocation, with R, RMSD and bias. (**a–c**) are the matchups with Merged, and (**d–f**) for the NOAA. Displaying matchups between SAR to CYGNSS, SMAP to CYGNSS, and SAR to SMAP respectively. Grey line shows linear trendline. Black line shows 1:1 value. suggests that SAR's performance at higher winds is more similar to SMAP and CYGNSS, while NOAA is more similar to SAR and SMAP at low wind speeds. Table 4 shows that SAR has the highest errors. This could be due to SAR's higher resolution (3 km compared to \(\sim\)25 km) which enables it to more clearly identify TC eyes and other locations of low winds. The opposite is the case for NOAA but less significantly, as the differences are within confidence intervals. Cross-correlation and error values were also calculated for SAR and SMAP against the unknown truth based on the average of CYGNSS NOAA and Merged. Table 4 revealed that SMAP has wind estimates closer to CYGNSS than SAR, and this is demonstrated by the density plots in Figure 5 (comparing Figure 5b,d against Figure 5a,d). In Figure 5, the Merged product had lower RMSD values of 5.22 m/s to SAR and 4.19 m/s to SMAP, compared to the 5.75 m/s comparison to HURF [30].