A Dynamic and Flexible State Model for Rainfall Nowcasting

We present a dynamic state model estimation method for rainfall nowcasting in which we assume that the short term spatio-temporal evolution of rainfall can be approximated by a linear state model with stochastic perturbations.  We estimate the model parameters using radar reflectivity measurements for one-step as well as multiple-step ahead rainfall nowcasting. If the rainfall intensity at location x and time index t is given by u_t(x), then the overall rainfall field intensity vector at any time t over N pixels (of the target area) can be represented by u_t = [u_t(x_N),...u_t(x_N)]^T_. Following the aforementioned formalism, the spatio-temporal evolution of the rainfall field can be described by the following linear state model given by
u_t = H_tu_t-1 + q_t
where H_t is an unknown time-varying state-transition matrix of dimensions NxN and q_t is a stochastic process noise vector of length N. We present an iterative least squares based method to estimate H_t and explore simpler algebraic structures (e.g., scaled affine transformations) to reduce the numbers of unknown parameters during estimation. We evaluate the performances of the proposed model using simulations and radar reflectivity data from the Royal Netherlands Meteorological Institute (KNMI). We observe that the nowcasting performances strongly depend on the size of the target area (number of pixels N), the type of events as well as the parameterization of H_t. The key advantage of the proposed approach over classical nowcasting methods based on Lagrangian persistence is the possibility to incorporate prior information about future rainfall evolution from external sources of information such as satellites or numerical weather prediction models during the estimation of the parameters.