## 3 Results and Discussion
### Relationship between AMVs Error and Water Vapor Content, Gradient, and Wind Speed  
Different weather conditions possess different atmospheric state parameters, including moisture, wind, temperature, and pressure. To deep-dive the reason that different weather conditions require different time intervals, we explore the relationship between the wind track errors and atmospheric state parameters. [PERSON] et al. (2019) concluded that AMVs errors produced by the local area pattern-matching algorithm are state-dependent on the water vapor content, moisture gradient, wind speed, and wind-moisture angle. To explore whether the OF tracking algorithm could reduce the errors' dependence on these atmospheric state parameters, we plot the wind speed AE at 400 hPa with 5 min revisiting time as a function of water vapor content (Figure 11a), gradient (Figure 11b), wind speed (Figure 11c), and wind-moisture gradient angle (Figure 11d). [PERSON] et al. (2019) found that the largest wind speed AE exists at very low water vapor content, while Figure 9a shows there is no significant relationship between the wind speed AE and water vapor content, indicating that the Farneback OF wind-tracking algorithm is less affected by water  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Satellite Revisiting Time** & **5 min** & **50 min** \\ \hline Wind speed RE & 34.77\% & 19.32\% \\ Wind direction AE & 27.58\({}^{\circ}\) & 14.97\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: The wind-tracking errors of the selected smooth area at 400 hPa with 5 min and 50 min revisiting time.  
Figure 9: WRF wind field (**a**) and OF wind field (**b**) at 400 hPa of the typhoon area with the 5 min revisiting time.  
vapor content. The tracking error tends to be large near the low water vapor gradient, as shown in Figure 11b, which is consistent with [PERSON] et al. (2019). This is because that low water vapor gradient will smooth the difference between two images and cause the OF to be unable to be captured. Figure 11c shows that the AE concentrated in the area with low wind speed. As the wind speed increases, the error gradually becomes larger. The maximum error is linearly related to the wind speed, indicating that the Farneback OF wind-tracking algorithm is closely related to the wind speed, which is also consistent with the poor tracking effect in the typhoon eyewall area. The wind-moisture gradient angle is defined as the derivation between the wind direction and water vapor gradient angle, with \(\pm 90^{\circ}\) indicating the wind direction parallel to the water vapor isolines. [PERSON] et al. (2019) shows that the largest error occurs near \(\pm 90^{\circ}\), while in our study, the error is not related to the angle derivation. The traditional algorithm will smooth and blur the water vapor in a certain area, causing the moisture discontinuity to be excessively eliminated and leading to a very small tracked average wind vector. In comparison, the Farneback OF wind algorithm can achieve pixel-level moisture tracking and is not affected by the relationship between wind direction and moisture gradient.  
Figure 10: The WRF wind field (**a**) and OF wind field (**b**) of the selected smooth area with 5 min revisiting time at 400 hPa. The WRF wind field (**c**) and OF wind field (**d**) of the selected smooth area with 50 min revisiting time at 400 hPa.