How Well Do Multisatellite Products Capture the Space–Time Dynamics of Precipitation? Part II: Building an Error Model through Spectral System Identification

Abstract

Satellite precipitation products, as all quantitative estimates, come with some inherent degree of uncertainty. To associate a quantitative value of the uncertainty to each individual estimate, error modeling is necessary. Most of the error models proposed so far compute the uncertainty as a function of precipitation intensity only, and only at one specific spatiotemporal scale. We propose a spectral error model that accounts for the neighboring space–time dynamics of precipitation into the uncertainty quantification. Systematic distortions of the precipitation signal and random errors are characterized distinctively in every frequency–wavenumber band in the Fourier domain, to accurately characterize error across scales. The systematic distortions are represented as a deterministic space–time linear filtering term. The random errors are represented as a nonstationary additive noise. The spectral error model is applied to the IMERG multisatellite precipitation product, and its parameters are estimated empirically through a system identification approach using the GV-MRMS gauge–radar measurements as reference (“truth”) over the eastern United States. The filtering term is found to be essentially low-pass (attenuating the fine-scale variability). While traditional error models attribute most of the error variance to random errors, it is found here that the systematic filtering term explains 48% of the error variance at the native resolution of IMERG. This fact confirms that, at high resolution, filtering effects in satellite precipitation products cannot be ignored, and that the error cannot be represented as a purely random additive or multiplicative term. An important consequence is that precipitation estimates derived from different sources shall not be expected to automatically have statistically independent errors.