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

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.