The hydrologic response of urban catchments is sensitive to small scale space-time rainfall variations. A stochastic space-time rainfall model used for design purposes must reproduce important statistics at these small scales. In this paper, a new phenomenological stochastic rainfall model is proposed to simulate rainfall fields consistent with 10-minute 1-km² pixel radar images. A power transformation is applied to the rainfield to ensure the transformed field is Gaussian. The transformed latent Gaussian rain fields conditioned on the previous time step are simulated, and are then transformed back into real rainfall fields. This model is continuous over space and time, allowing for model parameters (e.g., spatial and temporal correlation, storm advection velocity, wet area ratio) to evolve during the storm. A Toeplitz Block Circulant technique is used to achieve fast and accurate simulations of large Gaussian random fields (with lattice of 256 by 256), and is shown to be much more efficient than the traditional Cholesky decomposition method. Two different model calibration strategies, namely the method of moments and the method of generalized moments, are investigated and the corresponding validation results compared. The results suggest that the method of generalized moments produces more realistic images and is able to reproduce aggregated statistics over a wide range of space and time scales. The proposed space-time model also has potential for short-term rainfall forecasting.
Water Down Under 2008. Proceedings of Water Down Under 2008: Incorporating 31st Hydrology and Water Resources Symposium, and, 4th International Conference on Water Resources and Environment Research (Adelaide, S.A. 15-17 April, 2008) p. 1582-1594