Estimation of areal reduction factors of extreme precipitation based on radar data

Areal Reduction Factor (ARF) is a well-established hydrological concept used to convert point precipitation to areal precipitation. The aim of this work is to develop a dataset of ARFs all over Germany, which can be utilized to convert point precipitation extremes to areal precipitation extremes for different area sizes, using RADKLIM radar Product. Initially, point and areal precipitation quantiles, covering seven distinct area sizes up to 1225 km², are estimated at more than 10000 randomly selected RADKLIM pixels. Following the extreme value analysis, areal depth-duration-frequency (ADDF) curves are derived and pixels with the crossing problem - as defined in Goshtasbpour & Haberlandt (2025)- are filtered out. The remaining pixels are further analyzed as study locations. ARFs are then calculated at these study locations, for nine durations from 5 to 1440 minutes, and eight return periods from 1 to 50 years. ARFs typically increase with increasing duration and decrease with increasing area. To model the calculated ARFs as a function of area and duration, a well-performing four-parameter ARF expression from De Michele et al. (2001) is utilized. This model accurately represents the expected behavior of ARFs in relation to area and duration, and has been widely used in the literature. The application of the De Michele model simplifies the representation of ARFs at each study location and for each return period by representing them with only four estimated parameters, instead of 63 different ARF values considering all durations and area sizes. The estimated ARF fitting parameters show solid performance across most study locations, as indicated by the goodness-of-fit criteria: R², Percent Bias, and normalized Root Mean Square Error. Finally, the estimated parameters are interpolated in the space using various geostatistical techniques to provide countrywide raster based ARFs.