Areal reduction factor assessment for extreme rainfalls through a new empirical fixed-area formulation

In the hydraulic structures design against extreme events a proper estimate of the areal reduction factor (ARF) is required. Specifically, rainfall-runoff models widely used need to be fed with information on areal-average rainfall over a watershed surface, while rainfall data is typically available at a point scale. The ARF allows to convert rainfall data from point to areal scale.

In this work, a new fixed-area and deterministic approach for estimating the ARF is proposed; it involves ratios between observed annual maxima with specific duration of average rainfall occurring in a specific area and those referring to all the available point rainfalls in the same area. The approach was applied to the Umbria region in Central Italy where, using high-quality and validated rainfall data (with a temporal resolution of 1 minute), a parametric relation expressing ARFs as function of duration and area was found. The outcomes were then compared with those of the most widespread empirical approaches available in literature, often applied when rainfall data are lacking, obtaining substantial over- or underestimation of empirical ARFs. This confirms that the transposition of ARF relations from a geographic area to another could have not-negligible impacts on the design of hydraulic structures. In addition, indications aimed at selecting the most suitable method to be applied for ARF estimation are provided. Specifically, the proposed approach is suitable when a limited number of years of rainfall observations is available. In this regard, the robustness of the methodology was tested by varying the length of the rainfall observation period; a minimum number of about 6 years was found to make the derived empirical formulation sufficiently accurate in a specific area.