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Optimization of Nonlinear VAD Method in the Low-level Wind Retrieval
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摘要: 结合理论和SoWMEX试验 (西南气流试验，Southwest Monsoon Experiment) 的连续多普勒天气雷达观测资料和广东省阳江雷达资料, 对非线性速度方位显示 (非线性VAD) 方法反演低层低于2 km垂直风廓线精度和能力进行定量分析。结果表明：非线性VAD基本能反演出低层风廓线在空间和时间上的演变。但当雷达径向速度数据在方位存在较大的连续性缺测、体积扫描仰角较少时，因传统非线性VAD采用的速度方位显示 (VAD) 方法拟合阶数和垂直拟合阶数过高，反演的低层风廓线会存在较大误差，造成不合理高风速区和风廓线不连续。通过实际观测资料统计分析反演参数对非线性VAD的影响，提出基于连续性数据缺测间隔和不同仰角的多少的VAD和垂直拟合阶数动态调整方法。同锋面降水和台风降水两典型个例的实际探空比对显示，调整后的非线性VAD显著改进低层风廓线反演精度，反演的风廓线结构和变化与实况相符，反演平均误差小于2 m·s-1。Abstract: The performance of nonlinear velocity azimuth display method in the vertical wind profile retrieval at low levels (below 2 km) is quantitatively examined by combing the theoretical analysis and cases observed by SoWMEX S-Pol radar and Yangjiang radar in Guangdong Province. Results show that the general structure and evolution of the low-level wind profile can be reasonably deduced by traditional nonlinear VAD method. The root mean square error can be used to evaluate orders of velocity azimuth display (VAD) fitting, but small error does not always mean the better performance especially with big continuous data absence, and a specific example is given. When setting the VAD fitting order to 3 instead of 2, coefficients which represent the horizontal wind u and v are closer to the wind derived from radial velocity image. However, when the fitting order comes to 4, coefficients lost their physical meaning. The wind direction differs a lot and the speed is much smaller than the value before. At the same time, the root mean square error decreases compared with the order of 3. Besides, data used in nonlinear VAD fitting come from the whole volume, which decreases quite a lot and leads to nonlinear VAD fitting error when the volume coverage pattern (VCP) only has some lower elevations (e.g., two elevations). Therefore, the retrieved wind could contain large error in certain situations, such as for a region with large continuous data absence or a volume scan with fewer elevations.After carefully evaluating the impact of the corresponding parameters on the nonlinear VAD retrievals by analyzing radar measurements, a modified nonlinear VAD method is proposed which takes account of the maximum fitting order in horizontal (VAD) and vertical adaptively according to the size of continuous data absence and the number of sweeps in a volume scan. VAD fitting is abandoned when the data absence is larger than 90°; the order is set to 3 when the data absence is between 60° and 90°; and the order is set to 4 when the data absence is smaller than 60°. The order of nonlinear VAD fitting is reduced when the VCP only has low elevations. Apply the method in two cases: One is a front case passing through Taiwan, China, the other is a typhoon case landfall in Guangdong Province, with both of them having nonlinearity in the low level wind profile. The wind profile after adjusted can significantly improve the wind retrieval, as compared with the traditional nonlinear VAD. Both wind speed and direction from modified nonlinear VAD agree with those from sounding observations, with the root mean square of the wind less than 2 m·s-1, which is obviously better than nonlinear VAD before adjusted.
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Key words:
- nonlinear VAD;
- low-level vertical wind profile;
- Doppler radar
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图 1 本研究中两个例多普勒天气雷达和探空站位置
(圆圈代表多普勒天气雷达150 km观测半径；阴影表示地形)
Fig. 1 The distribution of radar and sounding stations in this study
(the maximum Doppler range of 150 km, the shaded shows the terrain height)
图 2 2008年6月2日00：00—23:52 S-Pol雷达反演的非线性VAD垂直风廓线 (a) 不考虑数据缺测，垂直拟合阶数为三阶, (b) 考虑数据缺测，垂直拟合阶数为三阶, (c) 考虑数据缺测，垂直拟合阶数为二阶
(*表示体扫模式为VCP1, 其余为VCP2)
Fig. 2 The vertical wind profile retrieved by nonlinear VAD of S-Pol radar from 0000 UTC to 2352 UTC on 2 June 2008(a) without considering data absence, the order in z is 3, (b) considering data absence, the order in z is 3, (c) considering data absence, the order in z is 2
(* indicates the VCP1 scan mode, the others are VCP2 scan mode)
图 3 2008年6月2日15:00 VAD与非线性VAD反演低层风廓线与屏东站GPS探空比较
Fig. 3 The low-level wind profile retrived from VAD and nonliner VAD at 1500 UTC 2 June 2008 as compared with the GPS observeraion of Pingdong Station
图 4 2012年7月23日01:00—24:00阳江雷达非线性VAD反演出的垂直风廓线 (a) 不考虑数据缺测，垂直拟合阶数为三阶，(b) 考虑数据缺测，垂直拟合阶数为三阶
Fig. 4 Nonlinear VAD wind profile of Yangjiang radar from 0100 UTC to 2400 UTC on 23 July 2012 (a) without considering data absence, order in z is 3, (b) considering data absence, order in z is 3
图 5 2012年7月23日11:00 VAD与非线性VAD反演低层风廓线与阳江GTS探空比较
Fig. 5 The low-level wind profile retrived from VAD and nonliner VAD at 1100 UTC 23 July 2012 as compared with the GTS observeraion of Yangjiang
表 1 不同阶数傅氏拟合系数以及拟合均方根误差
Table 1 The Fourier coefficients and the aprroximation error for the VAD with the different numer of harmonics
谐波系数 a0 a1 b1 a2 b2 a3 b3 a4 b4 均方根误差/(m·s-1) 二阶 -0.8 8.3 2.3 -0.3 0.0 2.19 三阶 -1.6 7.2 0.9 -2.0 0.6 -0.3 2.2 1.92 四阶 -5.2* 0.6* 0.3* -3.1 5.6* 2.7* 3.1 0.5 -1.5 1.87 注：*表示拟合系数明显与实际联系的物理量大小不符。 
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表 2 2008年6月2日00：00仰角为0.5°和1.5°的水平风速u和v的非线性VAD拟合系数
Table 2 Nonlinear VAD coefficients for u and v with elevation of 0.5° and 1.5° at 0000 UTC 2 June 2008
系数 1 z z2 z3 r2 r2z 均方根误差/(m·s-1) 二阶u -2.2 11.6 -11.5 -0.001 0.004 1.32 二阶v 0.4 -1.5 3.3 0.0006 -0.001 1.12 三阶u -2.6 13.4 -24.2 44.0 0.006 -0.024 1.31 三阶v 0.09 0.09 -7.7 38.1 0.007 -0.026 1.11
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