| Advecction is one of the basic dynamical processes in the atmospheric movement. The computation is proved to be very important in both numerical weather prediction and numerical simulation. The numerical scheme of advection computing decides not only the precision of model transport, but also the numerical stability of temporal integration, length of time step and the efficiency of computing. The performance of an advection scheme affects obviously on the numerical weather prediction and simulation, especially on the simulation of extreme weather, such as fronts, Typhoon, vortex and intensly developed subtropical cyclone. The discontinous variation of variables is a challenge for advection computing in numerical prediction, because high-order polynomial in a traditional advection scheme is incapable of dealing with discontinuous case. In addition, the lower order schemes produce numerical dissipation and dispersion error. For high-order scheme, it is must show numerical ossilation and get negative value near the sharp variations, which is fatal for specific humidity of water vapor in the atmosphere. Discontinuty or sharp variation of variables becomes more popular in the high-resolution numerical model with the development of computer and refinement of model resolution. Improving the computational ability of describing sharp gradient is much more important for atmospheric numerical prediction.Besides the finite deferencing method which is popular in meteorological model, there are still a couple of high performance schemes that act as candidates for numerical models. Out of those, the CIP (Constrained Interpolation Profiles) is a kind of semi-Lagrangian scheme. It makes use multi-moment variables on grid points, and comput the advection using Hermit-type interpolation. We can therefor construct high-order (3-order) smooth polynomial on a cell with very short stencil, which serves to improve the computational accuracy. In this dissertation, one of the primary works is on the CIP scheme, including numerical test of the CUP scheme on 1-D and 2-D space, installation to the mesoscale non-hydrostatic model MM5, and the impact on a simulation of the heavy Meiyu rainfall in 2006. Another important work is the application of the CIP to solve gravity waves explicitly in a Characteristic method on sphere. The third part in the paper is on numerical test of refined numerical prediction making use of the mesoscale non-hydrostatic model WRF and nesting grid system. In this research, the CIP is firstly tested in 1-D and 2-D idealized advective issues. After the certification of the multi-dimensional CIP computation, adjustment of the 3-D CIP scheme that is installed into MM5 (Peng et al.2003) is carried out, and impact on the heavy rainfall simulation in a Meiyu heavy rainfall case is shown. The results show very good effect of the CIP scheme on the Meiyu front and corresponding rainfall. More realistic mesoscale structure of the precipitation is displayed, and also the vertical structure of Meiyu front and vapor distribution. The convective structure in front zone shows the CIP is strong for large gradient distribution and strong convection in instable area. It illustrates clearly the effect of high performace scheme on the accuracy improvement of simulation.The Gravity wave is meaningful dynamical process to weather system. The gravity wave can not be filtered out in atmospheric models, because it often corresponding to important weather processes, such as topographical rainfall, convection and energy transportation. Due to its rapid wave speed, the gravity wave limits the model integarating time step seriously. To overturn the limitation and enlarge time step, semi-implicit computation of gravity wave is usually used in numerical model. For high-resolution model, however, it is quite expensive because transformation of a large matrix is inavoidable. A CIP characteristic method on sphere is developed in this study, where the semi-implicit method is insteaded with semi-Lagrange CIP scheme. Because of the strong stability of se’mi-Lagrange, the CIP Chracteristic method performs efficient computing in addition to accurate advection. No matrix transformation is needed in the Characteristic method, and the method ensures unconditional stable advection computing. Taking shallow water model as an example, numerical solution of idealized experiment is shown with the CIP Characteristic method. No matrix computation is needed in this algorithm, and which ensures high efficiency and high accuracy of the numerical results. Computational cost is cut largly when used large Courant number in the interation. An example of the numerical solution on Yin-Yang mesh system is given here, and the CIP characteristic method is shown to be accurate, economic and simple in the high resolution model. Stable integration with large Courant number (CFL>1.0) is tested, which is very important for development and application of high resolution numerical model.High resolution and high accuracy numerical weather prediction or simulation is the focus of numerical model. With the improvement of computional condition and accumulation of observation data and analysis data, the difficulty is how to use the data thoroughly and correctly to gain realized numerical results. The mesoscale numerical weather prediction is affected by initial, boundary condition and model dynamics and physics. The initial data and boundary condition are focused here to show the impact on refined downscaling numerical simulation. Taking T639 (known as a glocal spectral model) forecast as the background, a regional downscaling high resolution run of WRF is done with different restarting technique for the simulation of a heavy rainfall case in lower reaches of Yellow River. Two kinds of run are carried out. The first one performs a 48-h run continually that initiates at a point with horizontal and vertical interpolation from the T639 output. Just the same as it restart from the WRF output. The second, however, performs four 12-h run continously, and restarts every time by interpolating T639 output. The results illustrate that the first run gives better simulation of the rainfall, and "cool restart" of the model from T639 forecast shows worse result even within 24 hours. It indicates that the WRF model can describe properly the development of weather system, due to the plenty physics processes and higher resolution of the nonhydrostatic model. On the other hand, the global spectral T639 model is designed for general circulation. Its hydrostatic feature and physics for large-scale simulation, in addition to the relatively lower resolution make the second run not so powerful for the heavy rainfall. It is worthy noting that the result is base on only one case study. It is hard to show a popular conclusion, and more experiments are desired to verify the issue. |
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