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 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.展开更多
A variational method based on previous numerical forecasts is developed to estimate and correct non-systematic component of numerical weather forecast error. In the method, it is assumed that the error is linearly dep...A variational method based on previous numerical forecasts is developed to estimate and correct non-systematic component of numerical weather forecast error. In the method, it is assumed that the error is linearly dependent on some combination of the forecast fields, and three types of forecast combination are applied to identifying the forecasting error: 1) the forecasts at the ending time, 2) the combination of initial fields and the forecasts at the ending time, and 3) the combination of the forecasts at the ending time and the tendency of the forecast. The Single Value Decomposition (SVD) of the covariance matrix between the forecast and forecasting error is used to obtain the inverse mapping from flow space to the error space during the training period. The background covariance matrix is hereby reduced to a simple diagonal matrix. The method is tested with a shallow-water equation model by introducing two different model errors. The results of error correction for 6, 24 and 48 h forecasts show that the method is effective for improving the quality of the forecast when the forecasting error obviously exceeds the analysis error and it is optimal when the third type of forecast combinations is applied.展开更多
基金the 973 Program (Grant No. 2004CB418305)the National Natural Science Foundation of China (Grant No. 40575049)
文摘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.
基金Supported by National Natural Science Foundation of China (Grant Nos. 40875063 and 40505022)
文摘A variational method based on previous numerical forecasts is developed to estimate and correct non-systematic component of numerical weather forecast error. In the method, it is assumed that the error is linearly dependent on some combination of the forecast fields, and three types of forecast combination are applied to identifying the forecasting error: 1) the forecasts at the ending time, 2) the combination of initial fields and the forecasts at the ending time, and 3) the combination of the forecasts at the ending time and the tendency of the forecast. The Single Value Decomposition (SVD) of the covariance matrix between the forecast and forecasting error is used to obtain the inverse mapping from flow space to the error space during the training period. The background covariance matrix is hereby reduced to a simple diagonal matrix. The method is tested with a shallow-water equation model by introducing two different model errors. The results of error correction for 6, 24 and 48 h forecasts show that the method is effective for improving the quality of the forecast when the forecasting error obviously exceeds the analysis error and it is optimal when the third type of forecast combinations is applied.
