Evaluation of the Historical Sampling Error for Global Models

Abstract

Various ensemble-based schemes are employed in data assimilation because they can use the ensemble to estimate the flow-dependent background error covariance. The most common way to generate the real-time ensemble is to use an ensemble forecast; however, this is very time-consuming. The historical sampling approach is an alternative way to generate the ensemble, by picking some snapshots from historical forecast series. With this approach, many ensemble-based assimilation schemes can be used in a deterministic forecast environment. Furthermore, considering the time that it saves, the method has the potential for operational application. However, the historical sampling approach carries with it a special kind of sampling error because, in a historical forecast, the way to integrate the ensemble members is different from the way to integrate the initial conditions at the analysis time (i.e., forcing and lateral boundary condition differences, and ‘warm start’ or ‘cold start’ differences). This study analyzes the results of an experiment with the Global Regional Assimilation Prediction System-Global Forecast System (GRAPES-GFS), to evaluate how the different integration configurations influence the historical sampling error for global models. The results show that the sampling error is dominated by diurnal cycle patterns as a result of the radiance forcing difference. Although the RMSEs of the sampling error are small, in view of the correlation coefficients of the perturbed ensemble, the sampling error for some variables on some levels (e.g., low-level temperature and humidity, stratospheric temperature and geopotential height and humidity), is non-negligible. The results suggest some caution must be applied, and advice taken, when using the historical sampling approach.

Keywords:

• ensemble-based data assimilation
• historical sampling approach
• sampling error
• GRAPES-GFS