Improved rainfall nowcasting using Burgers’ equation

Abstract Nowcasting of surface precipitation from radar data typically relies on algorithms that calculate advection, such as the McGill Algorithm for Precipitation nowcasting by Lagrangian Extrapolation (MAPLE). This method offers high spatial and temporal resolution but it cannot represent the growth-decay of precipitation and non-stationary advection vector fields. In this study, we propose some nowcasting rainfall models based on advection-diffusion equation with non-stationary motion vectors. The diffusion term of this equation gives to smoother rainfall predictions for lead times and increased skill scores. The motion vectors are updated in each time step by solving a system of two-dimensional (2D) Burgers’ equation. The proposed forecasting models use the following three steps. First, an initial motion vector field is approximated using the Variational Echo Tracking (VET) algorithm. Second, a forecast is obtained for each time step by solving a time-dependent advection or advection-diffusion equation. In this step, the motion vectors are updated by solving Burgers’ equation. Lastly, forecasts are evaluated with lead times from 2.5  min to 3 h, and forecasts are compared with rain rate observations for six events over a 250 × 250  km2 region in southeastern South Korea. To observe the effects of the diffusion term and Burgers’ equation, four variants of the proposed modeling methods are considered, depending on the equations: advection equation (Type 1), advection and Burgers’ equations (Type 2), advection-diffusion equation (Type 3), and combination of the advection–diffusion and Burgers’ equations (Type 4). The forecasts from the Type 1 method are very similar to those of MAPLE. The other models (Type 2–4) yielded clearly better skill scores and correlation on average, with up to 3 h’ lead time. Models that use Burgers’ equation (Type 2 and Type 4) give much better scores than other methods using fixed motion vectors when the temporal variation of the motion vectors is large.

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