## 3 Results
### Wind Speed-Direction Joint Distribution
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Height (m)** & **k1** & **k2** & **k3** & **u1** & **u2** & **u3** & **w1** & **w2** & **w3** & **R2** \\ \hline
30 & 0.6672 & 147.8000 & 1.3400 & 4.9220 & 5.6180 & 1.5220 & 0.6452 & 0.0135 & 0.3460 & **0.9788** \\
40 & 0.5144 & 2.8280 & 4.6260 & 1.6050 & 4.5070 & 5.5370 & 0.7490 & 0.1400 & 0.1110 & **0.9752** \\
50 & 53.3900 & 2.1320 & 0.5736 & 0.9577 & 1.6970 & 5.1360 & 0.0291 & 0.2269 & 0.7489 & **0.9804** \\
60 & 0.6317 & 1.2940 & 13.5200 & 1.8460 & 5.1140 & 0.8774 & 0.6311 & 0.3480 & 0.0209 & **0.9547** \\
70 & 4.0900 & 2.6680 & 0.4680 & 1.0640 & 2.2170 & 5.1050 & 0.1079 & 0.1783 & 0.7138 & **0.982** \\
80 & 1.6190 & 5.3890 & 0.6176 & 1.3280 & 2.6010 & 4.9860 & 0.2995 & 0.0913 & 0.6092 & **0.9554** \\
90 & 4.0300 & 0.3784 & 1.9930 & 2.5790 & 5.2240 & 1.3990 & 0.1006 & 0.6953 & 0.2041 & **0.9839** \\
100 & 0.4858 & 1.7340 & 4.0630 & 5.1250 & 1.3430 & 2.6130 & 0.6476 & 0.2541 & 0.0984 & **0.9793** \\
110 & 1.2830 & 3.5460 & 0.7891 & 1.2230 & 2.6220 & 5.0040 & 0.3694 & 0.1188 & 0.5119 & **0.9743** \\
120 & 1.2510 & 6.5100 & 0.7259 & 1.3440 & 2.7020 & 4.9620 & 0.3793 & 0.0675 & 0.5532 & **0.9553** \\
130 & 0.2516 & 9.0010 & 4.6660 & 1.1730 & 2.5760 & 4.8990 & 0.8914 & 0.0215 & 0.0871 & **0.9066** \\
140 & 1.1460 & 1.6970 & 0.8594 & 5.0090 & 0.6983 & 2.3080 & 0.3560 & 0.2202 & 0.4238 & **0.9755** \\
150 & 0.2522 & 10.7400 & 5.2870 & 1.0770 & 3.1060 & 4.8310 & 0.9289 & 0.0142 & 0.0569 & **0.9259** \\
160 & 0.7875 & 1.8100 & 1.7690 & 0.8724 & 2.8150 & 4.8900 & 0.5837 & 0.1912 & 0.2252 & **0.9514** \\
170 & 2.8060 & 1.7220 & 0.5832 & 2.8900 & 4.8850 & 1.0080 & 0.1054 & 0.2051 & 0.6895 & **0.9066** \\
180 & 10.9900 & 2.4180 & 0.2066 & 2.2860 & 4.6390 & 0.6778 & 0.0171 & 0.0924 & 0.8906 & **0.959** \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Parameter fitting value of \(g(\zeta)\). Figure 4: Results of the fitting of wind. We grouped the measured samples at the measuring points and calculated the i-th wind speed interval \([v_{i},v_{i+1}]\) and the j-th wind direction interval \([\theta_{j},\theta_{j+1}]\) (number of samples \(n_{ij}\)). The joint probability density of measured wind speed and direction can be expressed as follows:  
\[p_{ij}=\frac{n_{ij}}{N_{\Delta}v_{i\Delta}\theta_{j}} \tag{10}\]  
In the formula, \(N\) is the number of measured wind speed samples, \(\Delta v_{i}=v_{i+1}-v_{i}\), \(\Delta\theta_{j}=\theta_{j+1}-\theta_{j}\). This paper takes \(\Delta v_{i}=1\) m/s, \(\Delta\theta_{j}=22.5\times\pi/180\) rad, divides 21 \(\times\) 16 grids, and calculates the \(p_{ij}\) and the probability density function \(f(v_{i}+\Delta v_{i}/2,\theta_{j}+\Delta\theta_{j}/2)\) corresponding to the midpoint of the grid \((v_{i}+\Delta v_{i}/2,\theta_{j}+\Delta\theta_{j}/2)\). The coefficient of determination, R2, is used to evaluate the wind speed and wind direction joint distribution model:  
\[R^{2}=1-\frac{\sum\limits_{i=1}^{21}\sum\limits_{j=1}^{16}{(p_{ij}-f_{ij})^{2 }}}{\sum\limits_{i=1}^{21}\sum\limits_{j=1}^{16}{(p_{ij}-\overline{p_{ij}})^{ 2}}} \tag{11}\]  
The results are shown in Table 8, which shows that the fitting effect of the two-dimensional joint distribution model is good. Figure 5: Flow chart of parameter determination of mvM model. The fitting effect of the AL model is shown in Figure 6a-d. As can be seen in the figure, the probability of main wind direction decreased with an increase in height, due to the influence of the surface. The model prediction results fitted well with the measured data.