Evaluation of the Areal Reduction Factor in an Urban Area through Rainfall Records of Limited Length: A Case Study

Abstract

This paper addresses the determination of the areal reduction factor (ARF) as a function of area and duration. The analysis is carried out using the data recorded in a 10-year period at the rainfall gauge network of the city of Milan (Italy). Four types of probability distributions [exponential, the extreme value type 1 (EV1), the generalized extreme value (GEV), and generalized Pareto], two parameter estimation methods (probability-weighted moments and partial probability-weighted moments), and four different regression models of ARF on area and duration are considered. A sensitivity analysis is carried out to outline the effect exerted on ARF by the choice of probability distribution and the parameter estimation method and by that of the model. The effect of model choice is more important than the choice of the distribution and estimation method. The models that fit the data best are the newly developed ones. The ARF model that has the best fit presents a root-mean-square error (RMSE) equal to 0.0204. This ARF error is very acceptable for practical purposes. The computed areal rainfall quantiles show inconsistencies, which are likely due more to insufficient coverage of the rain gauge network, particularly in the outskirts of the area being considered, than to the limited amount of data. For a proper investigation of the ARF dependence on area and duration, both a longer series and a better gauge distribution are necessary.