Abstract
Mainstream numerical weather prediction (NWP) centers usually estimate the standard deviations of background error by using a randomization technique to calibrate specific parameters of the background error covariance model in variational data assimilation (VAR) systems. However, the sampling size of the randomization technique is typically several orders of magnitude smaller than that of model state variables, and using finite-sized estimates as a proxy for the truth can lead to sampling noise, which may contaminate the estimation of the standard deviation. The sampling noise is firstly investigated in an atmospheric model to show that the sampling noise has a symmetrical structure oscillating around the truth on a small scale. To alleviate the sampling noise, a heterogeneous local weighting filtering is proposed based on distance-weighted correlation and similarity-weighted correlation. Local weighting filtering is easy to implement in the VAR operational systems and has a low computational cost in the post-processing of reducing the sampling noise. The validity and performance of local weighting filtering method are examined in a realistic model framework to show that the proposed filtering is able to eliminate most of the sampling noise dramatically, the details of the filtered results are more visible, and the accuracy of the filtered results is almost the same as that estimated from the larger sample. The signal-to-noise ratio of the optimal filtered field is improved by nearly 20%. A comparison with the widely used spectral filtering approach in the operational system is considered, showing that the proposed filtering method is more efficient to implement in the filtering procedure and exhibits very good performance in terms of preserving the local anisotropic features of the estimates. These attractive results show the potential efficiency of the local weighting filtering method for solving the noise issue in the randomization technique.
Highlights
Numerical weather prediction (NWP) can be expressed by a nonlinear equation system, and the accuracy of the initial state determines the quality of the prediction to a large extent
The structure of this paper is organized as follows: in Section 2, a brief introduction of the randomization technique and spectral filtering in the operational variational data assimilation (VAR) system is given, and we present the detailed implementation of the proposed filtering
The standard deviation estimated by the randomization technique in the atmospheric model is presented as well as the sampling noise, and the application of the local weighting filtering on removing sampling noise is examined in a realistic framework
Summary
Numerical weather prediction (NWP) can be expressed by a nonlinear equation system, and the accuracy of the initial state determines the quality of the prediction to a large extent. Mainstream NWP centers generally model the background error covariance matrix in the form of control variable transforms (CVT) in the operational VAR system [4,5,6,7,8,9]. The randomization technique has been widely employed to estimate the standard deviations in numerical meteorological dynamic systems when the covariance matrix is model in the form B = UUT [10,11]. The proposed filtering approach shows very good performance in terms of eliminating sampling noise while preserving the standard deviation estimates and presents an excellent ability to preserve the local anisotropic features of the estimates.
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