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
A new sequential data assimilation method named "Monte Carlo H ∞ filter" is introduced based on H ∞ filter technique and Monte Carlo method in this paper. This method applies to nonlinear systems in condit...A new sequential data assimilation method named "Monte Carlo H ∞ filter" is introduced based on H ∞ filter technique and Monte Carlo method in this paper. This method applies to nonlinear systems in condition of lacking the statistical properties of observational errors. In order to compare the as- similation capability of Monte Carlo H ∞ filter with that of the ensemble Kalman filter (EnKF) in solving practical problems caused by temporal correlation or spatial correlation of observational errors, two numerical experiments are performed by using Lorenz (1963) system and shallow-water equations re- spectively. The result is that the assimilation capability of the new method is better than that of EnKF method. It is also shown that Monte Carlo H ∞ filter assimilation method is effective and suitable to nonlinear systems in that it does not depend on the statistical properties of observational errors and has better robustness than EnKF method when the statistical properties of observational errors are varying. In addition, for the new method, the smallest level factor founded by search method is flow-dependent.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.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 40275032, 40505005 and 40405019) Opening Foundation of Institute of Heavy Rain, CMA (Grant No. IHR2006G13)
文摘A new sequential data assimilation method named "Monte Carlo H ∞ filter" is introduced based on H ∞ filter technique and Monte Carlo method in this paper. This method applies to nonlinear systems in condition of lacking the statistical properties of observational errors. In order to compare the as- similation capability of Monte Carlo H ∞ filter with that of the ensemble Kalman filter (EnKF) in solving practical problems caused by temporal correlation or spatial correlation of observational errors, two numerical experiments are performed by using Lorenz (1963) system and shallow-water equations re- spectively. The result is that the assimilation capability of the new method is better than that of EnKF method. It is also shown that Monte Carlo H ∞ filter assimilation method is effective and suitable to nonlinear systems in that it does not depend on the statistical properties of observational errors and has better robustness than EnKF method when the statistical properties of observational errors are varying. In addition, for the new method, the smallest level factor founded by search method is flow-dependent.
