Combining Phase Error Correction and 3DVAR in Storm—Scale Data Assimilation

In three-dimensional variational (3DVAR) analysis, the background term in the cost function measures the objective distance, usually via a Euclidean norm, between the analysis and background while the observation term measures the distance between the analysis and observations. The goal of the analysis is to minimize the cost function, or the error of the analysis relative to the background and observations subjecting to the weightings that are related to their respective errors. For a forecast system whose predictions often contain discrete features such as individual thunderstorms, the standard formulation of the background term, defined in terms of Euclidean norm, often makes little sense, because large errors can result from errors in the positioning of such discrete features as much as from those in their amplitude. It is usually much more difficult to reduce position than amplitude error. The end result of analysis is often two sets of weak thunderstorms, one at the correct and one at the wrong locations, instead of one set at the right location and with correct intensities. One approach towards solving this problem is to correct the position error first before performing the final analysis. More sophisticated approaches would involve constructing the cost function in a way that would allow for the effective and simultaneous reduction of both phase and amplitude errors. Performing phase correction also allows us to retrain more valuable information about the structure of the background features whose main error lies with their position. In this study, we apply phase correction methods to the assimilation of radar data for convective-scale numerical weather prediction (NWP). We formulate the background term in terms of both displacement (phase) and amplitude errors. As the first step, an existing phase error correction algorithm is applied to first correct the displacement error in the background, the resultant field is then used as the new background of 3DVAR analysis. The impact of phase error correction on the data analysis and the subsequent forecast will be examined for real cases.