Multi-resolution incremental 4D-Var for WRF: Implementation and application at convective scale

The current four-dimensional variational (4D-Var) data assimilation (DA) algorithm, available in the community Weather Research and Forecasting (WRF) model's DA (WRFDA) system, can run only at the same resolution as that of the WRF model forecast, which makes it computationally prohibitive for operational applications at convective scale. The Multi-Resolution Incremental 4D-Var (MRI-4DVar) has been developed in this study in order to speed up WRF 4D-Var through a three-stage procedure in each outer loop. One key aspect of WRF MRI-4DVar is the introduction of the inverse control variable transform within WRFDA that allows the proper resolution change between different outer loops for the control variables projected in the vertical empirical orthogonal function (EOF) space. MRI-4DVar's computational efficiency and forecast performance are demonstrated by applying it to an afternoon thunderstorm event over northern Taiwan with a 2 km model resolution setting. Comparing to the full-resolution 4D-Var experiment, two MRI-4DVar configurations with a speed-up of 4.5 and 7.5 times performed similarly well in terms of Fractions Skill Score (FSS) of 6-hr accumulated rainfall forecasts and hourly variation of total rainfall amount, indicating MRI-4DVar's potential for operational applications at convective scale.