Improvement of dual-resolution approach for ensemble data assimilation and tests with simulated data. Part I: Method improving

The ensemble Kalman filter (EnKF) method has the advantage of being able to obtain the flow-dependent background error covariance by using short-term ensemble forecasts; however, huge computational cost of running a large ensemble of forecast and analysis becomes the primary challenge for operational application, especially when the forecast ensemble is run at high spatial resolution (HR). Gao et al. proposed a dual-resolution (DR) EnKF data assimilation strategy, that is, an ensemble of forecast run with lower resolution providing the flow-dependent background error covariance estimation for both the low-resolution (LR) analyses and a single HR analysis. Thus this method can significantly reduce the computational cost of the overall forecasting while trying to maintain the benefits of the EnKF algorithms. And its efficiency in producing quality analyses on the high-resolution grid was tested with simulated Doppler radar data. But there is a difference in a sense between the forecast error covariance estimated from high and low resolution ensemble. The forecast fields of HR model contain more mesoscale information than forecast fields of LR model do, so the relativities of atmospheric factors in HR ensemble are probably higher. If the background error covariance gained from LR ensemble replaces that estimated from HR ensemble for a single-high-resolution assimilating only, the forecast error covariance and variance will be underestimated, and such mismatching can influence the effect of assimilation.