Study On The Improvement Of The Semi-lagrangian Advection Scheme In The GRAPES Model

The transport process is of crucial importance in the at mospheric motions.The accuracy of the advection scheme plays a key role in the performance ofNumerical Weather Prediction (NWP) models. Currently, GRAPES(Global/Regional Assimilation and PrEdiction System), the new-generation o fNWP model developed by the China Meteorological Administration (CMA),adopted the traditional Semi-Lagrangian advection scheme with Cubic Lagrangianinterpolation (referred to as the SL_CL scheme) to deal with the advectionproblems. Although the combination of the SL_CL scheme and the semi-implicittime difference method allows the NWP models to adopt a longer integration timelength, it still has some deficiencies in shape-preserving property and nume ricalaccuracy. Based on the previous research findings, a revised SL advection isdeveloped in this thesis and research emphasis is placed on the shape-preservingproperty and numerical accuracy in the SL scheme expecting to improve theperformance of SL advection scheme in GRAPES model.A SL advection scheme (referred to as the R2007scheme) proposed by Reich (2007)was first analyzed, it was found that when the remapped mesh method between the Lagtangianparticles and the Eulerian grids was applied in the non-uniform grid cells, the factor of gridcell area in the R2007scheme would exert an extremely negative effect on the finalinterpolation, affecting the behavior of the R2007scheme. Given this situation, the RevisedR2007scheme (referred to as the Re_R2007scheme) is developed by confining the grid cellarea in the R2007scheme to unit area, that is, the weight of the grid cell area in thecomputation of the R2007scheme was defined1and only the length of the grid cell wasconsidered in the final interpolation. It was demonstrated that the Re_R2007scheme after thiskind of revision could be applied to the uniform or non-uniform grid cells for computation andperform well in the computation regarding the advection problem. In the Re_R2007scheme,the value at the departure point is interpolated by the cubic and linear B-spline function, andthe value interpolated by the cubic B-spline function is corrected by the value by the linear B-spline function, thus positively leading to the improvement of numerical accuracy in theRe_R2007scheme. The one-and two-dimensional idealized tests in the rectangularcoordinate system with uniform grid cells and two groups of solid-body rotationtests in the latitude-longitude spherical coordinate system with non-uniform gridcells were conducted for inter-comparisons between Re_R2007scheme and SL_CLscheme. The numerical results are as follows:(1) the Re_R2007scheme performe dbetter in the shape-preserving property compared with the SL_CL scheme andcould favorably maintain the initial distribution. The damping effects wereremarkably reduced in the Re_R2007scheme. On the other hand, the spuriousoscillation caused by the interpolation near the discontinuous area wassignificantly weakened in the Re_R2007scheme.(2) Co ntrasted with the SL_CLscheme, the Re_R2007scheme achieved a higher numerical accuracy. In theone-dime nsional sine wave experiment and two-dimensional cosine bellexperiment in the rectangular coordinate system with the uniform grid cells, thenormalized errors of the Re_R2007scheme was about7.5and3times smaller thanthose of the SL_CL scheme, respectively, indicating the higher numerical accuracyof the Re_R2007scheme.(3) Similar to the SL_CL scheme, the numericalaccuracy of the Re_R2007scheme was hardly affected by the flow direction. In thesolid-body rotation tests in the latitude-longitude spherical coordinate system withnon-uniform grid cells, the relevant error terms could almost reach the same levelwhenever the solid-body travelled along the equator or across the poles, but theSL_CL scheme displayed bigger error in the related terms.Furthermore, the Re_R2007scheme was implemented in GRAPES global model byadding and modifying some related programming codes. To evaluate the performance of theRe_R2007scheme, three groups of three-dimensional solid-body rotation tests withoutconsidering the forcing terms in the prognostic equations were first conducted to compare itwith the QMSL scheme in GRAPES global model, and the results show that the Re_R2007scheme displayed a remarkable advantage in the shape-preserving property over the QMSLscheme. Then, three idealized tests by adding the forcing terms in the prognostic equationswere conducted to further check the correctness of the related codes added for Re_R2007scheme in GRAPES global model. The balance flow test shows that the Re_R2007schemecould ensure the long-term steady integration in GRAPES global model. The cross-polar flowtest demonstrates that the Re_R2007scheme could guarantee the integration stability near thepoles. The Rossby_Haurtiz test indicates that the Re_R2007scheme could favorably maintainthe shape of the certain waves after a long integration. Therefore, the added codes concerningRe_R2007scheme in GRAPES global model is basically correct and the Re_R2007scheme could ensure the integration stability in the dynamical core of GRPES global model, whichlays a good foundation for the real simulation using Re_R2007scheme in GRAPES globalmodel.