The Physically-Based Extreme Value (PHEV) distribution of river discharges

Reliable assessment of the flooding hazard of river basins is crucial for many social and economic activities. We present here the Physically-based Extreme Value (PHEV) distribution of river discharges. PHEV is a process-based alternative to empirical estimates and statistical methods hitherto used to characterize extremes of hydrometeorological variables. It arises from a description of key hydro-meteorological processes driving runoff production (e.g., precipitation inputs, evapotranspiration rates, soil moisture states and catchment responses) through solution of the master equation for the probability distribution of streamflow in a catchment. PHEV pairs physical understanding of the mechanisms producing extreme events and defining their chance of occurrence with an easily tractable mathematical descriptions of them, thus providing a theoretical underpinning to the study of manifold flood-related issues, such as the emergence of heavy tails in streamflow and flood distributions, flood rich and poor periods, and the reasons leading to the occurrence of extreme flood events.

In this work we benchmark capabilities of PHEV for predicting odds and magnitudes of floods against a standard distribution and the latest statistical approach for extreme estimation. 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. The analyses outline the domain of applicability of PHEV and reveal less biased capabilities to estimate flood magnitudes with return periods much longer than the sample size used for calibration. Results also show reduced prediction uncertainty of PHEV for rare floods, notably if the flood magnitude-frequency curve displays an inflection point.

Such discontinuities typically hinder estimation of high streamflow quantiles. PHEV reveals itself as a reliable tool to foresee their occurrence in a large set of case studies from the US and Germany, also when using shortened data series where the highest observations were removed. Case studies for which PHEV predicts the occurrence of an inflection point which is not visible in the empirical flood magnitude-frequency curve mostly belong to river flow regimes characterized by values weakly oscillating around their mean, which rarely exhibit extreme flow values by their nature. The limited length of the available data series might be thus constraining the possibility to observe extreme floods that shall be expected. These results indicate the possibility to reliably appraise the propensity of rivers to generate extreme floods by means of a process-based description of watershed dynamics, thus laying the foundation for a better comprehension of their physio-climatic controls.