## 2 Materials and Methods
### Simulated MWHS Brightness Temperature Data  
To make our research more realistic, the WRF profiles data are used as input of the community radiative transfer model (CRTM version 2.4.0) to simulate the Microwave Humidity Sounder (MWHS) brightness temperature (BT). MWHS is carried on the FengYun-3D, launched on 14 December 2017. It has 15 channels, ranging from 89 to 183 GHz. Figure 2 shows the vertical distribution of weighting functions for MWHS channels. We choose BT at around 183 GHz water vapor absorption band as the tracer to derive winds. The  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Data Scope** & **Experiment Design** \\ \hline Satellite revisiting time & 5–120 min & Sampled every 5 min \\ \hline FOV size & 3–30 km & 3 km, 6 km, 12 km, \\  & & 18 km, 24 km, 30 km \\ \hline  & & 975 hPa, 925 hPa, 900 hPa, 850 hPa, 800 hPa, \\ Moisture height & 975–100 hPa & 700 hPa, 600 hPa, 500 hPa, 400 hPa, 300 hPa, \\  & & 200 hPa, 100 hPa \\ \hline \hline \end{tabular}
\end{table}
Table 1: Wind track experiment design.  
Figure 1: Simulated water vapor field with different spatial resolution of 3 km (**a**) and 30 km (**b**) at 12:00 on 8 August 2019 (UTC) 850 hPa.  
weight function peak level of 183 GHz (shown in Table 2) is mainly at the middle-lower troposphere [22]. Here, we use the weighting function peak as the height of the wind vectors. To analyze the wind-tracking errors, we compare the BT wind fields with the WRF wind fields at the approximate layers. Figure 3 shows the BT of 183.31\(\pm\)7 GHz and the water vapor of 800 hPa. The approximate layers are also shown in Table 2. The purpose of this experiment is to confirm whether our OF wind-tracking algorithm is suitable for the wind retrieval based on MW observations and to compare the wind retrieve error difference between BT and water vapor fields.  
expansion expressed in a local coordinate system to accomplish image modeling. The polynomial expansion is shown as follows:  
\[\text{f(x)}=\mathbf{x}^{\text{T}}\mathbf{A}\mathbf{x}+\text{b}^{\text{T}} \mathbf{x}+\text{c} \tag{1}\]  
The dependent variable \(\mathbf{x}\) represents the two-dimensional coordinate position (x y) T, \(\mathbf{A}\) is a symmetric matrix, b a vector, and c a scalar. The coefficient \(\mathbf{A}\) captures even part of the signal information except direct current (DC), b captures the odd part, and c varies with the local DC level [31]. According to the principle that coefficients can keep constant after a little motion, they are estimated by the weighted least squares method fit to the signal valued in the neighborhood [30].  
The OF method must satisfy the assumption that the variation of the OF (the vector) is approximately smooth [32]. However, when it is applied to the wind track in the typhoon area, the assumption is not out of question due to the rapid changes of water vapor and the high-speed rotation around the typhoon eyewall area. The image pyramid method [33] is incorporated into the Farneback OF algorithm to solve this problem. Basically, the images at different scales are resized so that the algorithm can better capture the displacements at different scales. As shown in Figure 4, the pyramid bottom is of the original image size, and the image is resized 0.5 times its previous size upwards sequentially. The motion scale is also continuously resized so that the large-scale motion around the typhoon's eyewall will be resized to meet the assumption which guarantees the effectiveness of the OF method.