一种改进的平缓-混合地形追随坐标在GRAPES中尺度模式中的应用研究

A study on application of an improved terrain-following vertical coordinate in the GRAPES model

中文关键词:  GRAPES模式  平缓-混合坐标  动力框架  数值模式

英文关键词:GRAPES model  Terrain-following coordinate  Dynamic core  Numerical modelling

中文摘要:

      平缓-混合地形追随坐标（T-F坐标）可以减小坐标面上的地形影响带来的各种计算误差。以余弦三角函数为基函数的平缓-混合坐标（COS坐标）高层坐标面水平，计算误差较小，但是低层坐标面之间的厚度较薄，增大了计算误差，给模式稳定性及模拟效果带来较大的影响。设计一种改进的COS坐标，使低层坐标面垂直分布更加均匀，应用于GRAPES-Meso模式进行理想试验和实际模拟试验。结果表明，改进的COS坐标相对COS坐标，中高层计算误差相当，低层地形作用衰减的垂直变化更加均匀，减小了计算误差，提高了计算稳定性；地形重力波试验结果显示，改进的COS坐标重力波破碎相对COS坐标有一定缓解，更接近解析值；批量模拟试验结果显示，改进的COS坐标各个层次上的月平均模拟偏差比单尺度双曲函数平缓-混合坐标（简称SLEVE1坐标）更小，均方根误差减小，距平相关系数增大。改进的COS坐标有效地解决了COS坐标的计算问题，提高了模式预报效果。

英文摘要:

      Errors caused by topographic features on the coordinate planes can be reduced using the smoothed-level terrain-following coordinate (T-F coordinate). In upper levels, the coordinate planes of the T-F coordinate, which is based on trigonometric function of cosine (COS coordinate), are horizontal with little error. However, in lower levels, the thickness between two adjacent planes is too small to keep the model numerically stable. At the same time, it also brings in larger calculating errors that result in bad performance of the model. Considering all the above factors, an improved COS coordinate is designed to average the thickness between COS coordinate planes. Ideal and real cases tests are conducted with the GRAPES-Meso model using the improved COS coordinate. The results of the tests indicate that compared with the COS coordinate, the improved COS coordinate can on one hand keep the planes horizontal on higher levels. On the other hand, it leads to a more uniformity distribution of the coordinate planes and greatly reduces errors in lower levels. The model with the original coordinate can reproduce the mountain induced gravity waves that are consistent with the analytic solution. However, the shape, vertical structure and intensity of the waves are better simulated by the model with the improved COS coordinate, especially in lower levels where the COS coordinate doesn't work as expected. One-month real case tests indicate that the improved COS coordinate yields better results in terms of forecast bias, root mean square error and anomaly correlation coefficient. In conclusion, the improved COS coordinate solves the calculation problems of the COS coordinate, and improves the prediction ability.