Gridded estimated rainfall intensity values at very high spatial and temporal resolution levels are needed as main inputs for weather prediction models to obtain accurate precipitation forecasts, and to verify the performance of precipitation forecast models. These gridded rainfall fields are also the main driver for hydrological models that forecast flash floods, and they are essential for disaster prediction associated with heavy rain. Rainfall information can be obtained from rain gages that provide relatively accurate estimates of the actual rainfall values at point-referenced locations, but they do not characterize well enough the spatial and temporal structure of the rainfall fields. Doppler radar data offer better spatial and temporal coverage, but Doppler radar measures effective radar reflectivity (Ze) rather than rainfall rate (R). Thus, rainfall estimates from radar data suffer from various uncertainties due to their measuring principle and the conversion from Ze to R. We introduce a framework to combine radar reflectivity and gage data, by writing the different sources of rainfall information in terms of an underlying unobservable spatial temporal process with the true rainfall values. We use spatial logistic regression to model the probability of rain for both sources of data in terms of the latent true rainfall process. We characterize the different sources of bias and error in the gage and radar data and we estimate the true rainfall intensity with its posterior predictive distribution, conditioning on the observed data. Our model allows for nonstationary and asymmetry in the spatio-temporal dependency structure of the rainfall process, and allows the temporal evolution of the rainfall process to depend on the motions of rain fields, and the spatial correlation to depend on geographic features. We apply our methods to estimate rainfall intensity every 10 minutes, in a subdomain over South Korea with a spatial resolution of 1 km by 1 km.
"Spatial–temporal mesoscale modeling of rainfall intensity using gage and radar data." Ann. Appl. Stat. 2 (4) 1148 - 1169, December 2008. https://doi.org/10.1214/08-AOAS166