A Matérn model of the spatial covariance structure of point rain rates

It is challenging to model a precipitation field due to its intermittent and highly scale-dependent nature. Many models of point rain rates or areal rainfall observations have been proposed and studied for different time scales. Among them, the spectral model based on a stochastic dynamical equation for the instantaneous point rain rate field is attractive, since it naturally leads to a consistent space–time model. In this paper, we note that the spatial covariance structure of the spectral model is equivalent to the well-known Matérn covariance model. Using high-quality rain gauge data, we estimate the parameters of the Matérn model for different time scales and demonstrate that the Matérn model is superior to an exponential model, particularly at short time scales.