# A Novel Method for Ocean Wind Speed Detection Based on Energy Distribution of Beidou Reflections
## 4 Results, Analysis and Discussion
### Discussion  
#### 4.3.1 Threshold Effects  
This paper defined two energy zones in the trailing edge of the normalized power waveform by setting two thresholds as  
\[\left\{\begin{array}{c}\textit{Threshold}1=P_{\textit{noise}}\\ \textit{Threshold}1<\textit{Threshold}2<1\end{array}\right. \tag{15}\]  
where \(P_{\textit{noise}}\) is the noise power, which can be estimated by averaging the samples of the waveform with no scattered signals. Specifically, we used delay values between \(-2\) and \(-1.5\) chips before the specular point to estimate the noise. Since \(\textit{Threshold}2\) is an important factor when defining the energy zones, this section compared different values of \(\textit{Threshold}2\) in order to find the optimal threshold for wind speed retrieval. Table 5 shows the wind speed retrieval performances under different threshold values.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Observable** & \(\textit{R}^{2}\) & **RMSE (m/s)** \\ \hline RA & 0.852 & 2.82 \\ EDR & 0.866 & 2.69 \\ EMR & 0.822 & 3.10 \\ Coherent time & 0.875 & 2.61 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Retrieval performances by different observables during Typhoon UTOR.  
Figure 9: Scatter plots between in situ wind speed and observables during Typhoon UTOR. (**a**) \(RA\). (**b**) Coherent time. (**c**) EMR. (**d**) EDR. EMR and EDR are computed with \(\textit{Threshold}2=0.25\). The red lines are the fitting curves.  
As presented in Table 5, the EMR method shows a fluctuant correlation level with respect to different _Threshold2_ in both scenarios. Alternatively, the EDR method presents a relatively stable correlation value of around 0.73 and 0.85 in two wind scenarios, respectively. Figure 10 illustrates the wind speed retrieval performances with different _Threshold2_ ranging from 0.15 to 0.5. In the gentle wind scenario (Case1, the blue line), the EMR reaches a relatively better correlation of 0.769 when _Threshold2_ is 0.3 and degrades rapidly when _Threshold2_ is increasing from 0.3 to 0.38. In the high wind scenario (Case 2, the red line), the EMR correlation level shows a considerable fluctuation when _Threshold2_ ranges from 0.28 to 0.25. The EDR keeps a stable retrieval performance in both scenarios.  
As shown in Figure 10, in the gentle wind scenario, when _Threshold2_ is 0.3, the wind speed retrieval RMSE by EMR and EDR methods are 0.89 m/s and 0.90 m/s and \(R^{2}\) are 0.769 and 0.765, respectively. In the high wind scenario, when _Threshold2_ is 0.15, the RMSE by EMR and EDR methods are 2.93 m/s  
\begin{table}
\begin{tabular}{c c c c c c c} \hline _Threshold2_ & **0.5** & **0.4** & **0.3** & **0.25** & **0.2** & **0.15** \\ \hline \multicolumn{7}{c}{\(R^{2}\) **and RMSE (m/s) in Case 1**} \\ \hline EMR & 0.523/1.28 & 0.456/1.37 & 0.769/0.89 & 0.608/1.16 & 0.746/0.93 & 0.710/0.98 \\ EDR & 0.723/0.97 & 0.709/1.0 & 0.765/0.90 & 0.723/0.97 & 0.749/0.93 & 0.718/0.98 \\ \hline \multicolumn{7}{c}{\(R^{2}\) **and RMSE (m/s) in Case 2**} \\ \hline EMR & 0.430/5.54 & 0.796/3.32 & 0.702/4.01 & 0.822/3.10 & 0.794/3.31 & 2.93/0.841 \\ EDR & 0.834/2.99 & 0.863/2.72 & 0.852/2.82 & 0.866/2.69 & 0.856/2.79 & 2.63/0.871 \\ \hline \end{tabular}
\end{table}
Table 5: Wind speed retrieval performances under different threshold values. Case 1: In the gentle wind scenario. Case 2: In the high wind scenario.  
Figure 10: (**a**) RMSE and (**b**) coefficient of determination \(R^{2}\) as a function of values of _Threshold2_. Case 1 is in the gentle wind scenario, Case 2 is in the UTOR scenario.  
and 2.63 m/s and \(R^{2}\) are 0.841 and 0.871. According to these results, the optimal value of _Threshold2_ for wind speed retrieval is 0.3 in the gentle and high wind scenarios. In the high wind scenario, the optimal _Threshold2_ is 0.15.