Characterization of the Systematic and Random Errors in Satellite Precipitation Using the Multiplicative Error Model

Precipitation plays a critical role in the water and energy cycle. The systematic and random errors of precipitation are usually estimated using the additive model. However, various studies have shown that the multiplicative model is more suitable to describe the errors of precipitation than the additive model. This study integrates the multiplicative model with the Willmott-AghaKouchak method to characterize the errors of four selected representative satellite precipitation products in China. Zero precipitation is addressed by adding a tiny increment, which is determined by a sensitivity analysis, enabling the examination of missed precipitation and false alarms compared with the traditional strategy that only considers hit events. The results show that the systematic errors based on the additive model are too sensitive to heavy precipitation, resulting in problems, such as unexpected fluctuations, regional biases, unsteady performance, and reverse seasonal and elevational trends in some cases. In contrast, the multiplicative model resolves these problems through balancing the contributions of light and heavy precipitation and is recommended for systematic and random error estimation.