Revisiting the statistical scaling of peak annual discharges with respect to the basin size in the light of rainfall climatology

Over the years, several studies have been carried out to investigate how the statistics of peak annual discharges vary with the size of basins, with diverse findings regarding the observed type of scaling (i.e. simple scaling vs multiscaling), especially in cases where the data originated from regions with significantly different hydroclimatic characteristics. In this context, two important questions arise: a) how rainfall climatology affects the scaling of peak annual discharges, and b) how one can effectively conclude on an approximate type of statistical scaling of annual discharge maxima with respect to the basin size. The present study aims at addressing these two questions, using daily discharges from 805 catchments located in different parts of the United Kingdom, with at least 30 years of recordings. In doing so, we isolate the effects of the catchment area and the local rainfall climatology, and examine how the statistics of the standardized discharge maxima vary with the basin scale. The obtained results show that: a) the local rainfall climatology is an important contributor to the observed statistics of annual peak discharges, and b) when the effects of the local rainfall climatology are properly isolated, the scaling of the standardized annual discharge maxima with the area of the catchment closely follows that of the underlying rainfall process, deviating significantly from the simple scaling rule. The aforementioned findings explain to a large extent the diverse results obtained by previous studies in the absence of rainfall information, shedding light to the approximate type of scaling of peak annual discharges with the basin size.