A high-resolution hierarchical model for space-time rainfall

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. However, current rainfall models make simplifying assumptions about the temporal characteristics of rainfields and thus cannot be expected to reproduce important statistics over various space and time scales. In this study, an extensive investigation of radar rainfall data for the Sydney region motivated the development of a new phenomenological hierarchical stochastic model to robustly simulate rainfall fields consistent with 10-minute 1-km2 pixel radar images. The hierarchical framework consists of three levels. The development of the first two levels which simulate the evolution of rainfall fields for a single storm is the focus of this thesis. The third level, which is designed for simulation of storm sequences, is left for future research. The first level simulates a latent Gaussian random field conditioned on the previous time step, , which is transformed to a rain field using a power transformation. 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 hugely more efficient than the traditional Cholesky decomposition method. In the second level, first-order autoregressive (AR(1)) models are used to describe the within-storm variations of the level-one parameters that control the evolution of the rain fields. Calibration is performed using a generalized method-of-moments approach. The parametric bootstrap validation technique was used to evaluate the performance of the first two levels of the model by comparing the characteristics of interest for four observed storm events (typical of frontal and convective storms experienced in Sydney, Australia) and synthetic storms. It is found that this two-level rainfall model produces realistic sequences of rain images which capture the physical hierarchical structure of clusters, patchiness of rain fields and the persistence exhibited during storm development. A variety of important statistics were adequately reproduced at both 10-min and 1-hr time scales over space scales ranging from 1 km up to 32 km. Finally, application of this model to short-term rainfall forecasting is presented.