A Research On Some Key Aspect Of SISL Non-hydrostatic Spectral Numerical Weather Prediction Dynamical Kernel

Over the past decades,most operational numerical weather prediction(NWP)models adopted the hydrostatic approximation which was important for the early development of NWP models.Currently,as the available computer power increasing,the horizontal resolution of NWP models become higher to provide more accuracy prediction service.Once the resolution close to the 10 km horizontal resolution threshold,beyond which the hydrostatic approximation becomes inaccurate.Accordingly,it is essential to develop new efficient non-hydrostatic NWP models for future development.Comparing to hydrostatic models,non-hydrostatic models are more complex for which have more prognostic variables and more constraints for vertical discretization.Furthermore,special numerical techniques are required for prediction of small scale orographically induced local weather features which is resolved with the very high resolution that can be reached by NH models.Based on the current numerical methods for NWP models,the existing works still insufficient for problems such as hight accuracy vertical discretizaton schemes,the evaluation tools for the model error evolution and so on.To address the challenge,in this work we study several key problems for the adiabatic frame of global non-hydrostatic spectral models.The main contribution of our work is as follows:1.We develop a finite differential non-hydrostatic X-Z plane spectral model.The X-Z plane model is a toy model for NWP research which has the same equations with real3 d prediction models.A carefully designed vertical finite differential scheme is adopted.The X-Z plane model uses the two level semi-implicit semi-lagrangian scheme for time and advection discretizaton.The boundary conditions of top and bottom as well as lateral are handled separately to guarantee best results can be generated.A series of test cases such as four types of mountain wave flow and gravity wave test case are carried out to confirm the accuracy and stability of our model.2.We develop a new non-hydrostatic plane spectral model base on a high accuracy hybrid scheme for vertical discritization.Applying finite element vertical discretization for a mass-based non-hydrostatic kernel is proven to be difficult due to the constraints of vertical operators.We propose a novel hybrid finite element vertical discretization method for the semi-implicit mass based non-hydrostatic kernel,which integrates a finite differential scheme and a finite element scheme together.In the hybrid method,the finite differential scheme which satisfies the set of constraints is applied to the linear part,while a cubic finite element scheme with high order accuracy is applied to the non-linear part.Furthermore,to improve the accuracy of the linear part,an enlarged set of vertical levels is employed to the differential scheme.This set of vertical levels is only used to solve semi-implicit equations,and has no impact on the grid point calculation and spectral transformations.A series of 2D realized test cases are conducted to verify the stability and the accuracy of our new method.3.We develop a 3d global non-hydrostatic spectral model,based on aforementioned numerical methods.The dynamic core of the 3d global model keep the same with 2d plane model with the only differentness of basis of the spectral method.The horizontal grid of spherical model uses gauss reduced grid.The curvature terms of the model are introduce by the rotate matrix technology.The coriolis force is treated implicitly.A series 3d test cases such as steady state test,baroclinic instability test case,Rossby-Haurwitz wave test case and mountain wave test case are carried to verify the accuracy and stability of the 3d non-hydrostatic global model.4.We investigate the initial error growth property for chaos models.It is found that there exists a simple linear relationship between the logarithms of saturation value of mean relative growth of initial error and value of initial error that the sum of logarithms of the two is constant.We propose the definition of the mean absolute growth of initial error of with for a specific chaos system the saturation is proven to be a constant.Following this property,a equation for calculating predictability limit quantitatively is given.We investigate the model error growth property for chaos systems.It is found that the mean absolute growth of model error is initially exponential with a growth rate which has no direct relationship with the largest Lyapunov exponent.Afterwards model error growth enters nonlinear phase with a decreasing growth rate,and finally reaches a saturation value.The growth rate can be used to evaluate the predictability of models.