三维散度方程及其对暴雨系统的诊断分析

Three-Dimensional Divergence Equation and Its Diagnosis Analysis to Storm Rainfall System

利用WRF模式对中国江淮流域一次典型的江淮梅雨锋暴雨过程进行了数值模拟。在模拟结果比较可信的前提下,利用该模式输出的高时空分辨率资料,分析了三维散度的时空分布特征与降水的关系。分析发现,此次江淮梅雨暴雨过程中,对流层中低层尤其是4.287 km(约600 hPa)高度层的三维散度场非零区与雨带对应较好。其移动趋势也与雨带的移动趋势(相同时段基本位于相同的纬度带内,逐渐南移)一致。暴雨大值中心与三维散度极值中心重合。降水量的增减与三维散度强度变化一致。而无降水的区域为大片的三维散度零值区。三维散度之所以能较好地诊断降水,是因为对流层低层的水汽蒸发和对流层中高层的水汽凝结形成了云,而云导致的质量强迫对三维散度的这种上负下正的分布又有正反馈的作用,而且为降水的发生发展提供了有利条件。在以上分析的基础上,推导了三维散度方程,并通过计算找出影响三维散度变化的主要因子。

By utilizing three-dimensional non-hydrostatic WRF （Weather Research and Forecasting） model, a typical Meiyu frontal rainfall which occurs in the mid-lower reaches of the Yangtze River in China is numerically simulated. Based on credible model output data with higher spatial and time resolution, the correlation between three-dimensional divergence and rainfall is analyzed. It is found that the nonzero zone of three-dimensional divergence field in the middle and lower troposphere, especially at 4. 287 km level （about 600 hPa）, has better corresponding relationship with storm rainfall in the location, stretching orientation as well as range. They move southward gradually, and are basically located within the same latitude zone in the same period. The rainfall centers and centers of three-dimensional divergence are nearly collocated. The precipitation has a positive correspondence to the intensity of mass divergence. The change tendencies of precipitation quantity and intensity of three-dimensional divergence are identical. While regions where there is no precipitation tally with zero-value areas of three-dimensional divergence. Why the collocation between the non-zero value zone of the magnitude of three-dimensional divergence in the lower troposphere and the negative value zone of three-dimensional divergence in the upper troposphere can better diagnose precipitation？ To answer this question, the meridional-vertical cross sections along 118°E of the horizontal and vertical components of three-dimensional divergence and the vertical velocity are analyzed. The horizontal convergence in the lower troposphere couples with the horizontal divergence in the upper troposphere. The vertical component of three-dimensional divergence is out of phase with the horizontal component. Below 7 km, the increase of updraft with height leads to the vertical divergence, whereas the contrary case causes the vertical convergence above 7 kin. Three-dimensional divergence results from the residual between horizontal and vertical components of threedimensional divergence, and its sign is determined by the vertical component of three-dimensional divergence. Above analysis shows that, three-dimensional divergence includes not only horizontal convergence/divergence effect of wind field and the shear of vertical velocity, but also the mass field. It reflects the interaction between three-dimensional wind vector （i. e. , atmospheric dynamic effect） and the mass field. Thus, it has predominance over pure horizontal divergence in theory. Although the horizontal divergence is basically negative within precipitation regions in the frontal rainfall case, the coverage area （negative horizontal divergence zone） is far larger than the precipitation region. For heavy rainfall events, thus, the three-dimensional divergence is superior to horizontal divergence in the diagnosis of precipitation. The better detect of the rainfall by nonzero zone of mass divergence field in the middle and lower troposphere is due to the evaporation in the lower troposphere and the condensation in the middle and upper troposphere determined by the vertical velocity that forms cloud. The cloud-induced mass forcing also leads to the coupling pattern of three- dimensional divergence in the lower levels and three-dimensional convergence in the upper levels, accompanying with heavy precipitation. The threc-dimensional divergence equation is derived to identify the major factors controlling the tendency of three-dimensional divergence. The calculations show that the advection of three-dimensional divergence, the term associated with the interaction between vertical vorticity and Coriolis force, the shear of three-dimensional wind vector, baroclinic term are the major factors controlling the local change of three-dimensional divergence.