Determination of Z-R Relationships for Rainfall Estimation from Weather Radar, Rain Gauges, and Disdrometers

Z-R relationships are a fundamental component of rainfall estimation and are widely applied in radar meteorology and hydrology supporting operational applications such as flood forecasting. Despite their extensive use, the procedures adopted to derive Z-R coefficients are often not described in sufficient detail, and key methodological choices, such as the selection of the dependent variable in the regression analyses, are frequently left implicit.In this study, we analyze the determination of Z-R relationships using rain gauge, disdrometer, and X-band radar observations with solid-state transmitters collected over the Seveso-Olona-Lambro river basin and the Milan metropolitan area (northern Italy). A set of rainfall events recorded in 2023 is examined, including both stratiform and convective events. Z-R coefficients are determined using a regression-based approach following a leave-one-out methodology across events and multiple instrument pairings, to account for differences in sampling volumes and measurement characteristics.The resulting relationships are evaluated by comparing radar-based rainfall estimates against rain gauge observations and estimates obtained using standard Z-R formulations. The analysis focuses on the performance of rainfall estimates for different methodological choices in the regression process and for stratiform and convective events, and includes an assessment of mean areal accumulated rainfall to emphasize the hydrological relevance of properly defining Z-R relationships. The study highlights the sensitivity of rainfall estimation to methodological choices in Z-R coefficient determination and underscores the importance of clearly documenting regression setups.