Discontinuities in flood frequency curves, here referred to as flood divides, hinder the estimation of rare floods. In this paper we develop an automated methodology for the detection of flood divides from observations and models, and apply it to a large set of case studies in the USA and Germany. We then assess the reliability of the PHysically-based Extreme Value (PHEV) distribution of river flows to identify catchments that might experience a flood divide, validating its results against observations. This tool is suitable for the identification of flood divides, with a high correct detection rate especially in the autumn and summer seasons. It instead tends to indicate the emergence of flood divides not visible in the observations in spring and winter. We examine possible reasons of this behavior, finding them in the typical streamflow dynamics of the concerned case studies. By means of a controlled experiment we also re-evaluate detection capabilities of observations and PHEV after discarding the highest maxima for all cases where both empirical and theoretical estimates display flood divides. PHEV mostly confirms its capability to detect a flood divide as observed in the original flood frequency curve, even if the shortened one does not show it. These findings prove its reliability for the identification of flood divides and set the premises for a deeper investigation of physiographic and hydroclimatic attributes controlling the emergence of discontinuities in flood frequency curves.

Magnitude and frequency are prominent features of river floods informing design of engineering structures, insurance premiums and adaptation strategies. Recent advances yielding a formal characterization of these variables from a joint description of soil moisture and daily runoff dynamics in river basins are here systematized to highlight their chief outcome: the PHysically-based Extreme Value (PHEV) distribution of river flows. This is a physically-based alternative to empirical estimates and purely statistical methods hitherto used to characterize extremes of hydro-meteorological variables. Capabilities of PHEV for predicting flood magnitude and frequency are benchmarked against a standard distribution and the latest statistical approach for extreme estimation in two ways. The methods are first applied to an extensive dataset to compare their skills for predicting observed flood quantiles in a wide range of case studies. Synthetic time series of streamflow, generated for select river basins from contrasting hydro-climatic regions, are later used to assess performances for rare events. Both analyses reveal fairly unbiased capabilities of PHEV to estimate flood magnitudes corresponding to return periods much longer than the sample size used for calibration. The results also emphasize reduced prediction uncertainty of PHEV for rare floods when the mechanistic hypotheses postulated by the method are fulfilled, notably if the flood magnitude-frequency curve displays an inflection point. These features, arising from the mechanistic understanding embedded in the novel distribution of the largest river flows, are key for a reliable assessment of the actual flooding hazard associated to poorly sampled rare events, especially when lacking long observational records.