An anisotropic diffusion filter can be used to model a flow-dependent background error covariance matrix,which can be achieved by solving the advection-diffusion equation.Because of the directionality of the advection...An anisotropic diffusion filter can be used to model a flow-dependent background error covariance matrix,which can be achieved by solving the advection-diffusion equation.Because of the directionality of the advection term,the discrete method needs to be chosen very carefully.The finite analytic method is an alternative scheme to solve the advection-diffusion equation.As a combination of analytical and numerical methods,it not only has high calculation accuracy but also holds the characteristic of the auto upwind.To demonstrate its ability,the one-dimensional steady and unsteady advection-diffusion equation numerical examples are respectively solved by the finite analytic method.The more widely used upwind difference method is used as a control approach.The result indicates that the finite analytic method has higher accuracy than the upwind difference method.For the two-dimensional case,the finite analytic method still has a better performance.In the three-dimensional variational assimilation experiment,the finite analytic method can effectively improve analysis field accuracy,and its effect is significantly better than the upwind difference and the central difference method.Moreover,it is still a more effective solution method in the strong flow region where the advective-diffusion filter performs most prominently.展开更多
基金The National Key Research and Development Program of China under contract Nos 2022YFC3104804,2021YFC3101501,and 2017YFC1404103the National Programme on Global Change and Air-Sea Interaction of China under contract No.GASI-IPOVAI-04the National Natural Science Foundation of China under contract Nos 41876014,41606039,and 11801402.
文摘An anisotropic diffusion filter can be used to model a flow-dependent background error covariance matrix,which can be achieved by solving the advection-diffusion equation.Because of the directionality of the advection term,the discrete method needs to be chosen very carefully.The finite analytic method is an alternative scheme to solve the advection-diffusion equation.As a combination of analytical and numerical methods,it not only has high calculation accuracy but also holds the characteristic of the auto upwind.To demonstrate its ability,the one-dimensional steady and unsteady advection-diffusion equation numerical examples are respectively solved by the finite analytic method.The more widely used upwind difference method is used as a control approach.The result indicates that the finite analytic method has higher accuracy than the upwind difference method.For the two-dimensional case,the finite analytic method still has a better performance.In the three-dimensional variational assimilation experiment,the finite analytic method can effectively improve analysis field accuracy,and its effect is significantly better than the upwind difference and the central difference method.Moreover,it is still a more effective solution method in the strong flow region where the advective-diffusion filter performs most prominently.
