Phase-Correcting Data Assimilation and Application to Storm-Scale Numerical Weather Prediction. Part I: Method Description and Simulation Testing

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Abstract
An objective method of determining and correcting phase or position errors in numerical weather prediction is described and tested in a radar data observing system simulation experiment (OSSE) addressing the forecasting of ongoing thunderstorms. Such phase or position errors are common in numerical forecasts at grid resolutions of 2–20 km (meso-γ scale). It is proposed that the process of correcting a numerical forecast field can be simplified if such errors are addressed directly. An objective method of determining the phase error in the forecast by searching for a field of shift vectors that minimizes a squared-error difference from high-resolution observations is described. Three methods of applying a phase error correction to a forecast model are detailed. The first applies the entire correction at the initial time, the second in discrete steps during an assimilation window, and the third applies the correction continuously through the model's horizontal advection process. It is shown that the phase correction method is effective in producing an analysis field that agrees with the data yet preserves the structure developed by the model. The three methods of assimilating the correction in the forecast are successful, and a long-term positive effect on the thunderstorm simulation is achieved in the simulations, even as the modeled storms go through a cycle of decline and regeneration.