Effects of terrain-following vertical coordinates on high-resolution NWP simulations

With increasing resolution in numerical weather prediction (NWP) models, the model topography can be described with finer resolution and includes steeper slopes. Consequently, negative effects of the traditional terrain-following vertical coordinate on high-resolution numerical simulations become more distinct due to larger errors in the pressure gradient force (PGF) calculation and associated distortions of the gravity wave along the coordinate surface. A series of numerical experiments have been conducted in this study, including idealized test cases of gravity wave simulation over a complex mountain, error analysis of the PGF estimation over a real topography, and a suite of real-data test cases. The GRAPES-Meso model is utilized with four different coordinates, i.e., the traditional terrain-following vertical coordinate proposed by Gal-Chen and Somerville (hereinafter referred to as the Gal.C.S coordinate), the one-scale smoothed level (SLEVE1), the two-scale smoothed level (SLEVE2), and the COSINE (COS) coordinates. The results of the gravity wave simulation indicate that the GRAPES-Meso model generally can reproduce the mountain-induced gravity waves, which are consistent with the analytic solution. However, the shapes, vertical structures, and intensities of the waves are better simulated with the SLEVE2 coordinate than with the other three coordinates. The model with the COS coordinate also performs well, except at lower levels where it is not as effective as the SLEVE2 coordinate in suppressing the PGF errors. In contrast, the gravity waves simulated in both the Gal.C.S and SLEVE1 coordinates are relatively distorted. The estimated PGF errors in a rest atmosphere over the real complex topography are much smaller (even disappear at the middle and upper levels) in the GRAPES-Meso model using the SLEVE2 and COS coordinates than those using the Gal.C.S and SLEVE1 coordinates. The results of the real-data test cases conducted over a one-month period suggest that the three modified vertical coordinates (SLEVE1, SLEVE2, and COS coordinates) give better results than the traditional Gal.C.S coordinate in terms of forecasting bias and root mean square error, and forecasting anomaly correlation coefficients. In conclusion, the SLEVE2 coordinate is proved to be the best option for the GRAPES-Meso model.