地形追随坐标系下埃特尔位涡的计算

A computational method of Ertel potential vorticity in terrain-following coordinates

随着数值天气预报模式的日益普及以及位涡在不同天气、气候时、空尺度上的广泛应用,对采用模式输出资料计算的埃特尔(Ertel)位涡的精度提出了更高要求。将气象要素从中尺度模式普遍采用的地形追随坐标系向定义位涡的z或p坐标系的插值过程(插值法),是导致埃特尔位涡计算误差的主要原因。文中利用地形追随坐标系与z(p)坐标系的变换关系,导出了z坐标系定义的埃特尔位涡在地形追随坐标系中的表达形式,实现了直接在模式格点上计算埃特尔位涡(直接法),在提高计算精度的同时,保留了其在z坐标系中的物理意义,方便了分析与应用。为了进一步分析直接法在减少计算误差方面的作用,使用WRF模式对2016年7月发生在华北地区复杂地形背景下的一次黄淮气旋爆发过程进行了模拟,利用模式输出资料对此次天气过程中强降水时段插值法计算误差的分布进行了分析。结果表明,利用直接法计算位涡可有效减少插值法引入的计算误差,中低层均方根误差可达0.5 PVU,中高层可达0.3 PVU。将其应用到中小尺度对流性天气精细化结构的分析及气候统计研究中,可以有效减少插值法误差对结果产生的不良影响,提高计算和分析准确度。

With the increasing popularity of Numerical Weather Prediction（NWP）models and the wide applications of Potential Vorticity（PV）at various weather and climate scales,further improvement on the accuracy of the Ertel PV calculation with model output is imperative.The main source of computational errors can be attributed to interpolation（interpolation method）in terrain-following coordinates,which are commonly used in mesoscale models.Variables used for the calculation of Ertel PV need to be interpolated from the zor pcoordinates to terrain-following coordinate first.In order to improve the accuracy of Ertel PV calculation,the algorithm for the Ertel PV defined in zcoordinate is converted to a terrain-following coordinate form using the transformation relation between terrain-following coordinate and z（p）coordinate.In this way,the Ertel PV defined in zcoordinate can be calculated directly on model grids（the direct method）without interpolation.Meanwhile,the physical insight of Ertel PV in the zcoordinate is kept to make it convenient for analyses and applications.To further reveal the effect of the direct method in reducing computational errors,an extratropical cyclone outbreak occurred in the complex terrain area in North China was simulated using the Weather Research Forecasting（WRF）model,and detailed analysis of the computational errors in Ertel PV using the interpolation method was conducted.The result shows that by applying the direct method,the RMS errors in the middle-lower and middle-upper levels can be reduced by 0.5 PVU and 0.3 PVU,respectively,which will benefit the analysis of fine structures of convective storms and the study of climate statistics.