Abstract
The four-dimensional variational data assimilation (4D-Var) method has been widely employed as an operational scheme in mainstream numerical weather prediction (NWP) centers. In addition to the ensemble data assimilation method, the randomization technique is still used to diagnose the standard deviations of background error in variational data assimilation (VAR) systems; however, such randomization techniques induce sampling noise, which may contaminate the quality of the standard deviations. First, this paper studies the properties of the sampling noise induced by the randomization technique. The results show that the sampling noise is on a small scale displaying high-frequency oscillations around the estimate compared with the estimate and this difference motivates the use of filtering techniques to eliminate the sampling noise effects. The characteristics of the standard deviation field of the control variables are also investigated, and the standard deviation fields of different model parameters have different scales and vary with the vertical model levels. To eliminate such sampling noise, the spectral filtering method used widely in the operational system and a modified spatial averaging approach are investigated. Although both methods have splendid performance in eliminating sampling noise, the spatial averaging approach is more efficient and easier to implement in operational systems. In addition, the optimal filtered results from the spatial averaging approach are dependent on model parameters and vertical levels, which is consistent with the variation in the standard deviation field. Finally, the spatial averaging approach is tested on the operational system at the global scale based on the YH4DVAR and the global NWP system, and the results indicate that the spatial averaging approach has positive effects on both analysis and forecast quality.
Highlights
A data assimilation system optimizes the combination of observations and a short-term forecast of the state variables to provide the best estimate of the initial state of the atmosphere [1]
E spatial structure of the sampling noise introduced by the randomization technique is explored in the operational version of the B matrix. e estimated standard deviations from a finite sample are deteriorated by sampling noise, and the noise tends to be characterized by a relatively small scale and evenly distributed across the global map compared to the estimated reference field. e absolute value of noise dramatically decreases as the sample size increases, and the large-scale of standard deviations is more visible in the estimated field while the global distribution of sampling noise remains even
Such a difference in the structure between sampling noise and the estimates is the key to designing filtering techniques to filter out the small scale noise and preserve the signal of interest. ere is a spectral filtering method truncated at a fixed wavenumber in an operational setting to resolve the issue of sampling noise in the YH4DVAR system. e application of this truncated spectral method is a kind of low-pass filter in spectral space that enables the small scale noise to be filtered out, preserves the large-scale information, and works well for eliminating sampling noise in the operational system
Summary
E four-dimensional variational data assimilation (4D-Var) method has been widely employed as an operational scheme in mainstream numerical weather prediction (NWP) centers. In addition to the ensemble data assimilation method, the randomization technique is still used to diagnose the standard deviations of background error in variational data assimilation (VAR) systems; such randomization techniques induce sampling noise, which may contaminate the quality of the standard deviations. E characteristics of the standard deviation field of the control variables are investigated, and the standard deviation fields of different model parameters have different scales and vary with the vertical model levels. To eliminate such sampling noise, the spectral filtering method used widely in the operational system and a modified spatial averaging approach are investigated. The spatial averaging approach is tested on the operational system at the global scale based on the YH4DVAR and the global NWP system, and the results indicate that the spatial averaging approach has positive effects on both analysis and forecast quality
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