An explicit four-dimensional variational data assimilation method based on the proper orthogonal decomposition: Theoretics and evaluation |
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| Authors: | XiangJun Tian ZhengHui Xie |
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| Institution: | (1) Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, 100029, China |
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| Abstract: | The proper orthogonal decomposition (POD) method is used to construct a set of basis functions for spanning the ensemble of
data in a certain least squares optimal sense. Compared with the singular value decomposition (SVD), the POD basis functions
can capture more energy in the forecast ensemble space and can represent its spatial structure and temporal evolution more
effectively. After the analysis variables are expressed by a truncated expansion of the POD basis vectors in the ensemble
space, the control variables appear explicitly in the cost function, so that the adjoint model, which is used to derive the
gradient of the cost function with respect to the control variables, is no longer needed. The application of this new technique
significantly simplifies the data assimilation process. Several assimilation experiments show that this POD-based explicit
four-dimensional variational data assimilation method performs much better than the usual ensemble Kalman filter method on
both enhancing the assimilation precision and reducing the computation cost. It is also better than the SVD-based explicit
four-dimensional assimilation method, especially when the forecast model is not perfect and the forecast error comes from
both the noise of the initial filed and the uncertainty of the forecast model.
Supported by the National Natural Science Foundation of China (Grant No. 40705035), National High Technology Research and
Development Program of China (Grant No. 2007AA12Z144), Knowledge Innovation Project of Chinese Academy of Sciences (Grant
Nos. KZCX2-YW-217 and KZCX2-YW-126-2), and National Basic Research Program of China (Grant No. 2005CB321704) |
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| Keywords: | POD data assimilation 4DVAR explicit method |
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