Study On Satellite Data Retrieval And Assimilation With A Singular Value Decomposition Technique

The retrieval of atmospheric temperature and moisture profiles from satellite observations and the atmospheric data assimilation are both the typical inversion problems in Atmospheric Science. In fact, regardless of the atmospheric temperature and moisture profile retrieval, or the atmospheric data assimilation, the ultimate goals of these two inversion problems are same, that is to determine a given atmosphere status as accurately as possible using all available meteorological observations. Like most inversion problems, both the atmospheric temperature and moisture retrieval and atmospheric data assimilation are faced with two intractable problems when resolving the inversion problems: (1) the inversion problem is highly under-determined because the available meteorological observations can not provide all information to accurately determine the atmosphere status; (2) the inversion solutions usually are unstable and sensitive to observation errors.However, many studies have shown that the atmosphere, as a driven-dissipative nonlinear system, has the characteristic of nonlinear adjustment to external forcing. Mathematically speaking, it implies that no matter how the initial condition is, the system status will eventually shrink to an attractor in the status space, which is a point-set with zero measure in the phase space. It means that, if the degree of freedom of the atmospheric states discretized by computation grids is N, the atmosphere state which can appears in real atmosphere only exists in a low-dimensional sub-space which has a much lower freedom degrees than that of the N-dimensional space, and it is the so-called sub-space spanned by attractors. Therefore, an effective way to solving the under-determined problem mentioned above is to restrict the solutions of the retrieval or data assimilation problem in the sub-space which covers the attractor, instead of in the grid space. Because the observation errors usually distribute randomly, so the probability of which the observation errors fall into the sub-space will be very small, as a result, the observation noise can be filtered out effectively and the stability of the inversion solutions can be strengthened. By applying the empirical orthogonal decomposition (EOF) or singular value decomposition (SVD) to a set of the historical observations or model-simulated dataset, the base vectors that support the sub-space can be obtained.Based on above understanding and consideration as well as previous studies, in this paper, more detailed studies on satellite data retrieval and atmospheric data assimilation method based on the singular value decomposition (SVD) technique are made.For the temperature and moisture profiles retrieval problem, in this paper, it is pointed out that the temperature and moisture should be retrieved simultaneously in the three-dimensional (3-D) space instead of the one-dimensional (1-D) space, which is used widely in most conventional retrieval methods. Base on this, a three-dimensional physical-statistical retrieval method is proposed. In this method, by applying SVD to a three-dimensional temperature and moisture dataset, the spatial structure of these atmospheric parameters can be represented by using a few leading eigenvectors. Using model-simulated data and real observations, the new retrieval method has been validated and the results are compared with those of 1-D method. The results show that, comparing to the 1-D method, the 3-D method has the ability to retain much more useful observation information, as a result, more observation noises can be filtered out and the retrieval accuracy can be improved greatly.As for the atmospheric data assimilation problem, firstly, a set of numerical experiments has been designed to testify the original ensemble-based reduced data assimilation (ERDA) method proposed by Qiu and Chou (2006), then improvements have been made and a new ERDA method is developed. The basic difference between the original one and the new one is that in the old method only the model variables at one time level can be analyzed, but in the new method the variables at multiple time levels can be analyzed simultaneously during the analysis process. The models with different complexity levels (three-parameter dynamic model, shallow water model and the advanced synoptic numerical weather forecasting model-MM5) are used to evaluate the feasibility and impact on the initial condition improvements of such kind of ensemble-based data assimilation methods, and the results are compared with those of variational data assimilation methods. Comparing to the variational method, it is shown that the ensemble-based data assimilation method has the ability to spread the observation information among spatial and temporal space as well as different model variables. In most cases the ERDA method will behave better than the variational method. In addition, the ERDA method is not sensitive to observation errors than varitional method. More important, in ERDA method, there is no need to compute the background error covariance matrix B and its inversion, neither to integrate the adjoint model, so the computation is reduced greatly.In the mean time, a mixed four-dimensional variational data assimilation method, which combines the ERDA and 4DVAR method together, is proposed in this paper. The three-parameter dynamic model and the shallow water equation model are used to test this new method and the results are compared with those of the 4DVAR method. The results indicate that the mixed method can provide flow-dependent background error covariance and has some advantages comparing to the conventional 4DVAR method.After that, a set of numerical experiments have been designed to test and implement the ERDA method to improve the precipitation forecast by assimilating the satellite retrieved temperature and moisture observations and assimilating the satellite bright temperatures directly. The results also are compared with those of 4DVAR method. It is shown that ERDA method can make more improvement than that of variational method; it is also shown that the forecast of the location of precipitation in ERDA method is better than variational method. It implies that the ERDA method has some advantages in atmospheric remote sensing data assimilation. So it is a very promising method and deserves further investigation in the future.