Inverse technique is a widely used method in oceanography, but it has a problem that the retrieved solutions often violate model prior assumptions. To tune the model has consistent solutions, an iteration approach, wh...Inverse technique is a widely used method in oceanography, but it has a problem that the retrieved solutions often violate model prior assumptions. To tune the model has consistent solutions, an iteration approach, which successively utilizes the posterior statistics for next round inverse estimation, is introduced and tested from a real case study. It is found that the consistency may become elusive as the determinants of solution and noise covariance matrices become zero in the iteration process. However, after several steps of such operation, the difference between posterior statistics and the model prior ones can be gradually reduced.展开更多
Considering the characteristics of nonlinear problems,a new method based on the L-curve method and including the concept of entropy was designed to select the regularization parameter in the one-dimensional variationa...Considering the characteristics of nonlinear problems,a new method based on the L-curve method and including the concept of entropy was designed to select the regularization parameter in the one-dimensional variational analysis-based sounding retrieval method.In the first iteration,this method uses an empirical regularization parameter derived by minimizing the entropy of variables.During subsequent iterations,it uses the L-curve method to select the regularization parameter in the vicinity of the regularization parameter selected in the last iteration.The new method was employed to select the regularization parameter in retrieving atmospheric temperature and moisture profiles from Atmospheric Infrared Sounder radiance measurements selected from the first day of each month in 2008.The results show that compared with the original L-curve method,the new method yields 5.5%and 2.5%improvements on temperature and relative humidity profiles,respectively.Compared with the discrepancy principle method,the improvements on temperature and relative humidity profiles are 1.6%and 2.0%,respectively.展开更多
The application of Tikhonov regularization method dealing with the ill-conditioned problems in the regional gravity field modeling by Poisson wavelets is studied. In particular, the choices of the regularization matri...The application of Tikhonov regularization method dealing with the ill-conditioned problems in the regional gravity field modeling by Poisson wavelets is studied. In particular, the choices of the regularization matrices as well as the approaches for estimating the regularization parameters are investigated in details. The numerical results show that the regularized solutions derived from the first-order regularization are better than the ones obtained from zero-order regularization. For cross validation, the optimal regularization parameters are estimated from L-curve, variance component estimation（VCE） and minimum standard deviation（MSTD） approach, respectively, and the results show that the derived regularization parameters from different methods are consistent with each other. Together with the firstorder Tikhonov regularization and VCE method, the optimal network of Poisson wavelets is derived, based on which the local gravimetric geoid is computed. The accuracy of the corresponding gravimetric geoid reaches 1.1 cm in Netherlands, which validates the reliability of using Tikhonov regularization method in tackling the ill-conditioned problem for regional gravity field modeling.展开更多
基金The National Natural Science Foundation of China under contract Nos 41490644 and 41490640
文摘Inverse technique is a widely used method in oceanography, but it has a problem that the retrieved solutions often violate model prior assumptions. To tune the model has consistent solutions, an iteration approach, which successively utilizes the posterior statistics for next round inverse estimation, is introduced and tested from a real case study. It is found that the consistency may become elusive as the determinants of solution and noise covariance matrices become zero in the iteration process. However, after several steps of such operation, the difference between posterior statistics and the model prior ones can be gradually reduced.
基金Supported by the China Meteorological Administration Special Public Welfare Research Fund(GYHY201406011)National Natural Science Foundation of China(41405038)
文摘Considering the characteristics of nonlinear problems,a new method based on the L-curve method and including the concept of entropy was designed to select the regularization parameter in the one-dimensional variational analysis-based sounding retrieval method.In the first iteration,this method uses an empirical regularization parameter derived by minimizing the entropy of variables.During subsequent iterations,it uses the L-curve method to select the regularization parameter in the vicinity of the regularization parameter selected in the last iteration.The new method was employed to select the regularization parameter in retrieving atmospheric temperature and moisture profiles from Atmospheric Infrared Sounder radiance measurements selected from the first day of each month in 2008.The results show that compared with the original L-curve method,the new method yields 5.5%and 2.5%improvements on temperature and relative humidity profiles,respectively.Compared with the discrepancy principle method,the improvements on temperature and relative humidity profiles are 1.6%and 2.0%,respectively.
基金supported by the National Natural Science Foundation of China (Nos.41374023,41131067,41474019)the National 973 Project of China (No.2013CB733302)+2 种基金the China Postdoctoral Science Foundation (No.2016M602301)the Key Laboratory of Geospace Envi-ronment and Geodesy,Ministry of Education,Wuhan University (No.15-02-08)the State Scholarship Fund from Chinese Scholarship Council (No.201306270014)
文摘The application of Tikhonov regularization method dealing with the ill-conditioned problems in the regional gravity field modeling by Poisson wavelets is studied. In particular, the choices of the regularization matrices as well as the approaches for estimating the regularization parameters are investigated in details. The numerical results show that the regularized solutions derived from the first-order regularization are better than the ones obtained from zero-order regularization. For cross validation, the optimal regularization parameters are estimated from L-curve, variance component estimation（VCE） and minimum standard deviation（MSTD） approach, respectively, and the results show that the derived regularization parameters from different methods are consistent with each other. Together with the firstorder Tikhonov regularization and VCE method, the optimal network of Poisson wavelets is derived, based on which the local gravimetric geoid is computed. The accuracy of the corresponding gravimetric geoid reaches 1.1 cm in Netherlands, which validates the reliability of using Tikhonov regularization method in tackling the ill-conditioned problem for regional gravity field modeling.
