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《中国科学(D辑:地球科学)(英文版)》 2007-08
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An explicit four-dimensional variational data assimilation method

QIU ChongJian, ZHANG Lei & SHAO AiMei Key Laboratory of Arid Climatic Changing and Reducing Disaster of Gansu Province, College of Atmospheric Sciences, Lanzhou University, Lanzhou 730000, China  
A new data assimilation method called the explicit four-dimensional variational (4DVAR) method is proposed. In this method, the singular value decomposition (SVD) is used to construct the orthogonal basis vectors from a forecast ensemble in a 4D space. The basis vectors represent not only the spatial structure of the analysis variables but also the temporal evolution. After the analysis variables are ex-pressed by a truncated expansion of the basis vectors in the 4D space, the control variables in the cost function appear explicitly, so that the adjoint model, which is used to derive the gradient of cost func-tion with respect to the control variables, is no longer needed. The new technique significantly simpli-fies the data assimilation process. The advantage of the proposed method is demonstrated by several experiments using a shallow water numerical model and the results are compared with those of the conventional 4DVAR. It is shown that when the observation points are very dense, the conventional 4DVAR is better than the proposed method. However, when the observation points are sparse, the proposed method performs better. The sensitivity of the proposed method with respect to errors in the observations and the numerical model is lower than that of the conventional method.
【Fund】: the 973 Program (Grant No. 2004CB418305);; the National Natural Science Foundation of China (Grant No. 40575049)
【CateGory Index】: P413
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