On the Computation of Integrals of Bivariate Gaussian Distribution

This paper deals with the computation of integrals<br>of centred bivariate Gaussian densities over any domain defined as an angular sector of R^2. Based on an accessible geometrical approach of the problem, we suggest to transform the double integral into a single one, leading to a tractable closed-form expression only involving trigonometric functions. This solution can also be seen as the angular cumulative distribution of bivariate centered Gaussian variables (X,Y). We aim to provide a didactic approach of our results, and we validate them by comparing with those of the literature.

On the Computation of Integrals of Bivariate Gaussian Distribution

This paper deals with the computation of integrals<br>of centred bivariate Gaussian densities over any domain defined as an angular sector of R^2. Based on an accessible geometrical approach of the problem, we suggest to transform the double integral into a single one, leading to a tractable closed-form expression only involving trigonometric functions. This solution can also be seen as the angular cumulative distribution of bivariate centered Gaussian variables (X,Y). We aim to provide a didactic approach of our results, and we validate them by comparing with those of the literature.

Thunderstorm Strike Probability Nowcasting

To assist in thunderstorm warning, automated nowcasting systems have been developed that detect thunderstorm cells in radar images and propagate them forward in time to generate forecasted threat areas. Current methods, however, fail to quantify the probabilistic nature of the error structure of such forecasts. This paper introduces the Thunderstorm Environment Strike Probability Algorithm (THESPA), which forecasters can use to provide probabilistic thunderstorm nowcasts for risk assessment and emergency decision making. This method accounts for the prediction error by transforming thunderstorm nowcasts into a strike probability, or the probability that a given location will be impacted by a thunderstorm in a given period, by specifying a bivariate Gaussian distribution of speed and direction errors. This paper presents the development and analysis of the THESPA method and verifies performance using experimental data. Results from a statistical analysis of Thunderstorm Identification, Tracking, Analysis, and Nowcasting (TITAN) tracking errors of nowcasts made near Sydney, Australia, were used to specify the distribution, which was then applied to data collected from the World Weather Research Programme (WWRP) Beijing 2008 Forecast Demonstration Project. The results are encouraging and show Brier skill scores between 0.36 and 0.44 with respect to a deterministic advected threat area forecast.