Lagrangian Integro-Difference Equation Model for Precipitation Nowcasting
Authors: Pulkkinen Seppo , Chandrasekar V. , Niemi Tero 
Published: October 2021

Abstract
Delivering reliable nowcasts (short-range forecasts) of severe rainfall and the resulting flash floods is important in densely populated urban areas. The conventional method is advection-based extrapolation of radar echoes. However, during rapidly evolving convective rainfall this so-called Lagrangian persistence (LP) approach is limited to deterministic and very short-range nowcasts. To address these limitations in the 1-h time range, a novel extension of LP, called Lagrangian Integro-Difference equation model with Autoregression (LINDA), is proposed. The model consists of five components: 1) identification of rain cells, 2) advection, 3) autoregressive process describing growth and decay of the cells, 4) convolution describing loss of predictability at small scales, and 5) stochastic perturbations to simulate forecast uncertainty. Advection is separated from the other components that are applied in the Lagrangian coordinates. The reliability of LINDA is evaluated using the NEXRAD WSR-88D radar that covers the Dallas–Fort Worth metropolitan area, as well as the NEXRAD mosaic covering the continental United States. This is done with two different configurations: LINDA-D for deterministic and LINDA-P for probabilistic nowcasts. The validation dataset consists of 11 rainfall events during 2018–20. For predicting moderate to heavy rainfall (5–20 mm h−1), LINDA outperforms the previously proposed LP-based approaches. The most significant improvement is seen for the ETS and POD statistics with the 5 mm h−1 threshold. For 30-min nowcasts, they show 15% and 16% increases, respectively, to the second-best method and 48% and 34% increases compared to LP. For the 5 mm h−1 threshold, the increase in the relative operating characteristic (ROC) skill score of 30-min nowcasts from the second-best method is 10%.

Significance Statement
Delivering reliable forecasts of severe rainfall for the next few hours has a major societal importance. This is particularly true for densely populated urban areas, where flash floods can cause property damage and loss of lives. Such forecasts are conventionally produced by direct extrapolation of weather radar measurements. However, for intense localized rainfall this approach has low prediction ability beyond 30 min. To extend this limit, we propose a novel method that combines machine vision with a statistical model for growth and decay of rainfall. The method is designed for predicting highly localized rain cells and bands. In addition, a stochastic extension for producing probabilistic forecasts is developed. Using several verification metrics, we demonstrate that for predicting moderate to heavy rainfall (5–20 mm h−1), the proposed method has significantly improved forecast skill compared to the reference methods. The evaluation is done by using the NEXRAD WSR-88D that covers the Dallas–Fort Worth urban metroplex with a population of over 7 million. Demonstration of the applicability of LINDA in a larger domain is done by using the NEXRAD radar network that covers the continental United States.