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Hao S.-F.,Zhejiang Meteorology Observatory | Cui X.-P.,CAS Institute of Atmospheric Physics
Wuli Xuebao/Acta Physica Sinica | Year: 2012

Total mass conservation is a basic property of advection-diffusion differential equation. Since the difference schemes is not positive-definite, total mass is not conserved, caused by negative mass in numerical integration. Aiming at this problem, a new positive-definite renormalization scheme is proposed based on the physical meaning of negative mass. Experiments of point-source advection-diffusion show that the new renormalization scheme not only solves the positive-definite problem of advection-diffusion differential equation, but also keeps the property of total mass conservation. Compared with the renormalization scheme in the WRF model, the new positive-definite renormalization scheme has virtues of clear physical meaning and easier mannpulation. © 2012 Chinese Physical Society. Source

Hao S.-F.,Zhejiang Meteorology Observatory | Pan J.-S.,Zhejiang Meteorology Observatory | Yue C.-J.,Shanghai Typhoon Institute of China Meteorological Administration | Cui X.-P.,CAS Institute of Atmospheric Physics | Yang S.-F.,Zhejiang Meteorology Observatory
Journal of Tropical Meteorology | Year: 2010

Based on the barotropic primitive equation in the polar coordinate system and the appropriate assumption, we obtained the mathematical equation of orographic forcing on unit mass air parcel. With the consideration of the frictional stress of the sea and land, supposing that parcel velocity in tropical cyclones is in linear variation and that the distribution of surface pressure is circular, a set of equations are derived, which describe the impact of orographic slope error, the central pressure error and position error of tropical cyclones on the wind field in the tropical cyclone. Typhoon Wipha (2007) is selected to verify the above interpretation method. The results show that the orographic slope, the frictional coefficient, the intensity and position of the cyclone are the important factors which have great influence on the interpretation of wind information about tropical cyclones. The dynamic interpretation method gives very good results, especially for the coastal area. It is applicable to improving the forecasts of the wind field in tropical cyclones. Source

Hao S.-F.,Zhejiang Meteorology Observatory | Yang S.-F.,Zhejiang Meteorology Observatory | Lou M.-Y.,Zhejiang Meteorology Observatory
Chinese Journal of Geophysics (Acta Geophysica Sinica) | Year: 2014

The algorithm for calculating parcel trajectory is very important in semi-Lagrangian weather prediction models, in which the traditional method is finite difference scheme. Since only the velocity at the end point of the parcel trajectory can be calculated, the displacement is obtained by wind speed extrapolation method. By referring to the semi-analytical solution (SAS) used in the precise integration method, the possibility of constructing a numerical weather prediction model by using the SAS method is raised. For this purpose, the SAS of the first and second order differential kinematics equations are obtained, then the displacement of air parcel can be obtained by integrating the SAS. The numerical experiments show that the result of the SAS of the first order kinematics equations is a little better than that of the finite difference scheme, and the SAS of the second order kinematics equations can get more accurate result and save the computing time by using a long integration time step. Source

Hao S.-F.,Zhejiang Meteorology Observatory | Lou M.-Y.,Zhejiang Meteorology Observatory | Yang S.-F.,Zhejiang Meteorology Observatory | Li C.,Zhejiang Meteorology Observatory | And 2 more authors.
Wuli Xuebao/Acta Physica Sinica | Year: 2015

To solve atmospheric primitive equations, the finite difference approach would result in numerous problems, compared to the differential equations. Taking the semi-Lagrange model as an example, there exist two difficult problems-the particle trajectory computation and the solutions of the Helmholtz equations. In this study, based on the substitution of atmosphere pressure, the atmospheric primitive equations are linearized within an integral time step, which are broadly seen as ordinary differential equations and can be derived as semi-analytical solutions (SASs). The variables of SASs are continuous functions of time and discretized in a special direction, so the gradient and divergence terms are solved by the difference method. Since the numerical solution of the SASs can be calculated via a highly precise numerical computational method of exponential matrix-the precise integration method, the numerical solution of SASs at any time in the future can be obtained via step-by-step integration procedure. For the SAS methodology, the pressure, as well as the wind vector and displacement, can be obtained without solving the Helmholtz formulations. Compared to the extrapolated method, the SAS is more reasonable as the displacements of the particle are solved via time integration. In order to test the validity of the algorithms, the SAS model is constructed and the same experiment of a non-linear density current as reported by Straka in 1993 is implemented, which contains non-linear dynamics, transient features and fine-scale structures of the fluid flow. The results of the experiment with 50 m spatial resolution show that the SAS model can capture the characters of generation and development process of the Kelvin-Helmholtz shear instability vortex; the structures of the perturbation potential temperature field are very close to the benchmark solutions given by Straka, as well as the structures of the simulated atmosphere pressure and wind field. To further test the convergence of the numerical solution of the SAS model, the 100 m spatial resolution experiment of the non-linear density current is also implemented for comparison. Although the results from both experiments are similar, the former one is better and the property of mass-energy conservation is comparatively reasonable, and furthermore, the SAS model has a convergent property in the numerical solutions. Therefore, the SAS method is a new tool with efficiency for solving the atmospheric primitive equations. © 2015 Chinese Physical Society. Source

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