Real‐time rainfall prediction at small space‐time scales using a two‐dimensional stochastic advection‐diffusion model

A model based on the two-dimensional stochastic advection-diffusion equation is developed to forecast properties of individual rain cells in urban areas such as speed and spatial rainfall intensity. Two different modeling approaches are employed, and examples of the results are given. The first approach involves a Gaussian distribution as an analytic solution to the advection-diffusion equation, whereas the second one entails a double Fourier series expansion of the rainfall intensity field. Both modeling approaches are used to predict the rainfall intensity field over a small 12-gage urban catchment in southern Sweden. The model parameters are continuously updated by extended Kalman filtering. The Fourier series approach is shown to be the most flexible for practical applications and to give the most accurate forecasts. This model approach gives acceptable forecasts for a lead time of 1-5 min. It gives consistently smaller prediction errors compared to both the Gaussian solution and simple extrapolation calculations. The effect of system noise level on the forecast accuracy and model performance is discussed. The model can be used not only to predict in real time the spatial rainfall, but also to parameterize the variability pattern of small-scale spatial rainfall into a set of physically based parameters, thus separating the effects of advective velocity, turbulent diffusion, and development/decay.