ON THE OPTIMAL BACKGROUND ERROR COVARIANCES: DIFFERENT SCALE ERRORS’ CONTRIBUTION

The large-scale and small-scale errors could affect background error covariances for a regional numerical model with the specified grid resolution.Based on the different background error covariances influenced by different scale errors,this study tries to construct a so-called"optimal background error covariances"to consider the interactions among different scale errors.For this purpose,a linear combination of the forecast differences influenced by information of errors at different scales is used to construct the new forecast differences for estimating optimal background error covariances.By adjusting the relative weight of the forecast differences influenced by information of smaller-scale errors,the relative influence of different scale errors on optimal background error covariances can be changed.For a heavy rainfall case,the corresponding optimal background error covariances can be estimated through choosing proper weighting factor for forecast differences influenced by information of smaller-scale errors.The data assimilation and forecast with these optimal covariances show that,the corresponding analyses and forecasts can lead to superior quality,compared with those using covariances that just introduce influences of larger-or smallerscale errors.Due to the interactions among different scale errors included in optimal background error covariances,relevant analysis increments can properly describe weather systems(processes)at different scales,such as dynamic lifting,thermodynamic instability and advection of moisture at large scale,high-level and low-level jet at synoptic scale,and convective systems at mesoscale and small scale,as well as their interactions.As a result,the corresponding forecasts can be improved.

ON THE OPTIMAL BACKGROUND ERROR COVARIANCES: DIFFERENT SCALE ERRORS' CONTRIBUTION

The large-scale and small-scale errors could affect background error covariances for a regional numerical model with the specified grid resolution. Based on the different background error covariances influenced by different scale errors, this study tries to construct a so-called "optimal background error covariances" to consider the interactions among different scale errors. For this purpose, a linear combination of the forecast differences influenced by information of errors at different scales is used to construct the new forecast differences for estimating optimal background error covariances. By adjusting the relative weight of the forecast differences influenced by information of smaller-scale errors, the relative influence of different scale errors on optimal background error covariances can be changed. For a heavy rainfall case, the corresponding optimal background error covariances can be estimated through choosing proper weighting factor for forecast differences influenced by information of smaller-scale errors. The data assimilation and forecast with these optimal covariances show that, the corresponding analyses and forecasts can lead to superior quality, compared with those using covariances that just introduce influences of larger- or smallerscale errors. Due to the interactions among different scale errors included in optimal background error covariances, relevant analysis increments can properly describe weather systems (processes) at different scales, such as dynamic lifting, thermodynamic instability and advection of moisture at large scale, high-level and low-level jet at synoptic scale, and convective systems at mesoscale and small scale, as well as their interactions. As a result, the corresponding forecasts can be improved.