Abstract. The flow duration curve (FDC) is a classical method used to graphically represent the relationship between the frequency and magnitude of streamflow. In this sense it represents a compact signature of temporal runoff variability that can also be used to diagnose catchment rainfall-runoff responses, including similarity and differences between catchments. This paper is aimed at extracting regional patterns of the FDCs from observed daily flow data and elucidating the physical controls underlying these patterns, as a way to aid towards their regionalization and predictions in ungauged basins. The FDCs of total runoff (TFDC) using multi-decadal streamflow records for 197 catchments across the continental United States are separated into the FDCs of two runoff components, i.e., fast flow (FFDC) and slow flow (SFDC). In order to compactly display these regional patterns, the 3-parameter mixed gamma distribution is employed to characterize the shapes of the normalized FDCs (i.e., TFDC, FFDC and SFDC) over the entire data record. This is repeated to also characterize the between-year variability of "annual" FDCs for 8 representative catchments chosen across a climate gradient. Results show that the mixed gamma distribution can adequately capture the shapes of the FDCs and their variation between catchments and also between years. Comparison between the between-catchment and between-year variability of the FDCs revealed significant space-time symmetry. Possible relationships between the parameters of the fitted mixed gamma distribution and catchment climatic and physiographic characteristics are explored in order to decipher and point to the underlying physical controls. The baseflow index (a surrogate for the collective impact of geology, soils, topography and vegetation, as well as climate) is found to be the dominant control on the shapes of the normalized TFDC and SFDC, whereas the product of maximum daily precipitation and the fraction of non-rainy days was found to control the shape of the FFDC. These relationships, arising from the separation of total runoff into its two components, provide a potential physical basis for regionalization of FDCs, as well as providing a conceptual framework for developing deeper process-based understanding of the FDCs.
Observation of anti-parity-time-symmetry, phase transitions and exceptional points in an optical fibre
