Research On The Improvement Of Vertical Coordinate For The High Resolution GRAPES Model

With the increasing resolution of numerical weather prediction models, the topography of the model is getting finer with steeper terrain slope. In this consequence, the traditional height-based terrain-following vertical coordinate proposed by Gal Chen and Sommerville (hereafter called Gal.C.S coordinate) would cause negative impacts on the high resolution numerical simulations in terms of the bigger errors of the pressure gradient force (PGF for short)calculation due to the model steeper terrain-following surface and the associated distortion of gravity waves. One of the important ways to reduce the height-based terrain-following coordinate calculation error is to reduce the terrain effect on the vertical coordinate surface and the recognition of small scale terrain slope, which also becomes the new hot spot in the current research of terrain-following coordinates.Due to the influence of the Qinghai-Tibet plateau and meso&small-scale mountains, the prediction of GRAPES Model on the east Asia still has problems such as larger southern wind, false vertical velocity and precipitation. The main purpose of the paper is to relieve the above prediction problems by reducing the calculation error of the traditional Gal. C.S coordinate. In this paper, systematic analysis and test on the Smoothed and Hybrid Terrain Following coordinate (S.H.T.F. Coordinate for short) are carried out based on GRAPES model, and a new S.H.T.F.coordinate form suitable for the terrain characteristics of our country is designed for the model, which further improves the ability of the simulation.One-scaled Smoothed Level vertical coordinate(SLEVE1 for short), two-scaled Smoothed Level vertical coordinate (SLEVE2 for short), the hybrid LC1 coordinate, the independently designed hybrid LC2 coordinate and the hybrid Klemp coordinate are selected in the research to compare with the Gal.C.S. coordinate. The following conclusions are made by various tests based on GRAPES Meso and GRAPES_GFS model:(1)The terrain compensation term of the S.H.T.F.coordinate has to be solved specially by choosing appropriate decaying coefficients or smoothing the coordinate planes level by level to decay the terrain effect. Considering the different forms of these coordinates, three schemes of dynamic core and program designs are demonstrated.(2)A series of ideal tests about the coordinates are performed including the PGF error test, 2-D advection test, gravity wave test under complex mountainous terrain, and ideal test for spherical cross-mountain airflow, etc. The results of ideal tests show that:all kinds of S.F.T.H. coordinates can reduce the PGF errors, horizontal flow dissipations, and relief the problem of terrain gravity waves in varying degrees. On the medium and high levels, SLEVE2 coordinate, LC1 coordinate, LC1 coordinate and Klemp coordinate can better reduce the PGF calculation error and flow dissipations, and more correctly simulate the waveform,vertical structure and strength of the terrain gravity waves. The SLEVE2 coordinate, however, is still effected by the large scale terrain on the high levels unlike the other three coordinates. The Gal.C.S coordinate and SLEVE1 coordinate remains large PGF error and dissipations, which are quit different from the analytic result.At the bottom, because of terrain smoothing, the errors caused by small-scale terrains in SLEVE2 and Klemp coordinates are smaller than other coordinates.The errors of the LC1 coordinate is smaller than that of SLEVE1, LC1, and Gal.C.S.coordinate. The boundary problem caused by the vertical difference of Klemp coordinate brings lots difficulties in application, and more research is needed.(3)The simulation of the typical case shows that, the S.H.T.F. coordinate can reduce the PGF errors induced by the complex Qinghai-Tibet plateau terrain so as to reduce the false vertical turbulences and the southern wind, which results in the reduction of the false water vapor transportation and precipitation.In one-month the real case tests of the GRAPES Meso model,the S.H.T.F. coordinates give the better results in terms of smaller forecast bias and root mean square error, and higher anomaly correlation coefficients than the Gal.C.S coordinate.The LC1 coordinate shows advancements only on the high levels, but the LC1 coordinate improve the weak point.In conclusion, the SLEVE2 and the LC1 coordinate perform the best among the four coordinates.In the one-month real case tests of the GRAPES_GFS model, SLEVE2 coordinate meet some difficulties deal to the real terrain. Only the simulations of the SLEVE1 and the LC1 coordinate are performed. Similar to the GRAPES-Meso Model, the SLEVE1 coordinate shows obvious improvements compared to Gal.C.S coordinate. However, the LC1 coordinate have not achieved its goals as expected.