Integro-Difference Equation Model for Ensemble Precipitation Nowcasting

Abstract:

Nowcasts of severe rainfall have a high societal importance. The conventional method is extrapolation of radar echoes from a CAPPI or a low-angle PPI. However, due to its inability to predict growth or decay of rainfall or uncertainty, this approach is limited to short-range deterministic nowcasts (i.e. the next 30 minutes).

To address the above limitations, the Lagrangian Integro-Difference Equation with Autoregression (LINDA) model is proposed for ensemble precipitation nowcasting. The model consists of 1) optical flow and advection, 2) autoregressive integrated (ARI) model, 3) convolution and 4) stochastic perturbations. Advection is separated from components 2-4 that are applied in the Lagrangian coordinates. The ARI model is applied to differenced input time series to capture growth and decay, and the convolution describes loss of predictability. It is shown that the previously developed Short-Term Ensemble Prediction System (STEPS, Bowler et al. 2006) is a special case of the above model.

LINDA is able to capture the nonstationary nature of rainfall processes. This is achieved by using an elliptical convolution kernel that can describe rainfall bands. A spatially variable kernel is obtained by using window function. The advection field and the model parameters are estimated using a sparse approach, where cell-like features are identified from the input data. Likewise, the perturbations are localized to account for the spatial variability of forecast errors. Their spatial covariance structure is estimated using the short-space Fourier transform (SSFT, Nerini et al. 2017). In addition, LINDA uses vertically integrated liquid (VIL) as a proxy for surface rain rate. This is particularly advantageous for predicting developing rainfall that has not yet been observed at low altitudes.

The operational feasibility of LINDA is evaluated using the NEXRAD WSR-88D radar located in Fort Worth, Texas. The evaluation is done using 10 rainfall events during 2018-2019. Forecast rain rates from LINDA are compared to a low-altitude CAPPI. It is shown that LINDA has low computational requirements and up to 20% improved skill compared to STEPS. Largest improvements can be observed during intense convection. This is attributed to both the improved forecast model and the additional information obtained from the VIL.