非均匀分层下的二阶精度垂直差分方案及其在GRAPES模式中的应用

在非均匀分层下，目前GRAPES（Global/Regional Assimilation and Prediction System）模式中使用的垂直差分方案只能达到一阶精度。本文设计了一种适用于非均匀分层的二阶精度垂直差分方案，并将它应用于改进GRAPES模式动力框架的垂直离散化过程。一维廓线理想试验结果表明:二阶精度方案可以减少差分计算误差，而这种改进的幅度相对于差分计算本身引起的误差来说仍然是比较小的。通过密度流试验对修改后的模式动力框架进行测试，结果表明二阶方案可以保持模式动力框架的准确性和稳定性。进一步利用实际资料开展批量测试，发现二阶方案可以降低模式高空要素场的预报误差，而且这种改进随着预报时间的延长变得更为明显。最后选择一次典型的华南暴雨过程进行模拟，同样发现二阶精度方案对于48小时之后的降水会有一定程度的改进。

A Vertical Second-Order Difference Scheme for Non-uniformly Distributed Layers and Its Application in GRAPES Model

In the case of non-uniformly distributed layers, the vertical difference scheme used in GRAPES (Global/Regional Assimilation and Prediction System) model can only achieve first-order accuracy. A second-order scheme was designed and introduced into the GRAPES model in order to be used in the process of vertical discretization. An ideal test using the 1-D profile showed that the new scheme can improve the accuracy of difference computation obviously. An ideal density flow test was conducted to verify the correctness and stability of the new scheme in GRAPES model. A statistical evaluation of a medium-range forecast using the second-order scheme showed an improvement of forecast skill in large-scale fields, especially for the forecast after 120 h. Additionally, the second-order scheme was tested with a real-case experiment based on the extreme rainfall at South China, which again showed an improvement in the forecast of precipitation after 48 h.