大气数值预报模式中高度地形追随坐标的设计研究:理论分析与理想试验  

A design of height-based terrain-following coordinates in the atmospheric numerical model:Theoretical analysis and idealized tests

作　　者：李超[1,2,3] 陈德辉[3] 李兴良[3] 

机构地区：[1]中国气象科学研究院,北京100081 [2]中国科学院大学,北京100049 [3]中国气象局数值预报中心,北京100081

出　　处：《气象学报》2012年第6期1247-1259,共13页Acta Meteorologica Sinica

基　　金：GRAPES动力框架关键技术研究(2012BAC22B01);无缝隙强对流天气临近短时预报关键技术和预报系统(2013CB430106);GRAPES中尺度模式改进与升级(201006016);国家自然科学基金项目(41105068;40805045)

摘　　要：采用一种统一的地形追随坐标的形式,对Gal-Chen&Somerville(简称Gal.C.S坐标)、平缓坐标(smoothed levelverti calcoordinate,简称SLEVE坐标)等几种典型的高度地形追随坐标进行了气压梯度力计算误差影响和二维质量平流试验的理论分析,并与一种新提出的高度地形追随坐标——三角函数平缓坐标(简称COS坐标)进行比较。气压梯度力计算误差分析结果显示,与Gal.C.S坐标相比,单尺度平缓坐标(简称SLEVE1坐标)、双尺度平缓坐标(简称SLEVE2坐标)和COS坐标在减小气压梯度力计算误差上有不同程度的改进,SLEVE2坐标和COS坐标比其他两种坐标更具优势,衰减系数b和坐标转换的雅可比项对减小误差起决定性作用。二维质量平流试验也有类似的结果,与无地形的参考试验结果相比,COS坐标的质量输送计算误差最小,且经优化的COS坐标的质量输送计算误差几乎和参考计算误差完全重合,在4种坐标中最优。Several kinds of typical height-based terrain-following coordinates, such as the Gal-Chen＆Somerville coordinate （hereafter ＂Gal. C. S＂ coordinate）, the smoothed level vertical coordinate （hereafter SLEVE coordinate） and a new coordinate called as the cosine-smoothed coordinate （hereafter ＂COS＂ coordinate）, were theoretically analyzed and intercompared with each other via the induced errors by calculations of the PGF （Pressure Gradient Force） and the 2D-ADV （2-dimensional mass advection） tests. The results of calculation of the PGF showed that the errors of the calculation of the PGF induced by using a terrain following coordinates, were significantly decreased by using SLEVE1, SLEVE2 and COS coordinates in comparison to the Gal. C. S coordinate. SLEVE2 and COS coordinates were relatively better in reduction of the errors of the PGF calculation. The decaying coefficient ＂b＂ and its Jocabian derivative played a deterministic role in reduction of the errors. The similar remarks could be made for the tests of the 2D-ADV calculation. The errors of the 2D-ADV calculation by using the COS coordinate were the smallest as compared with those of the reference test in which there were no terrain. The COS coordinate was most advantageous among all the four coordinates in tests.

关 键 词：大气数值预报模式 高度地形追随坐标 气压梯度力计算误差 二维质量平流扩散 

分 类 号：P435.1[天文地球—大气科学及气象学]