Physical controls and regional pattern similarities of precipitation and flow duration curves using the three-parameter gamma distribution

The flow duration curve (FDC) is the cumulative distribution function, which represents the relationship between the frequency and magnitude of streamflow, and the precipitation duration curves (PDC) follows the same principle. Nowadays, the correlation between the shape of PDC and FDCs, their respective physical control factors including human activities, and their fitting conditions in unmeasured catchments across China have not been fully understood. In this paper, daily precipitation and streamflow data with 30 years records from 224 hydrological stations in the middle and lower Yangtze River basin were chosen to fit PDC and FDCs through gamma distribution. Framework was proposed for modelling FDCs to analyse the relationship, similarity, regional patterns and response mechanism of fitting parameters between PDC and FDCs, dividing the streamflow time series into fast and base flow and stations into three categories in consideration of human activities to attribute the shapes of PDC and FDCs to catchment meteorological and geographical characteristics and physical processes under natural conditions. Results indicate that the parameters of PDC and certain FDCs (TFDC, FFDC, SFDC) share similar spatial patterns but vary for the different duration and interactions of the processes. The climate and catchment characteristics such as extreme properties of precipitation, base flow index (BFI), P_max*α_p and concentration ratio index (CIM) will influence the shape of PDC and FDCs. The relationship between BFI and SFDC/TFDC can be better reflected in “Regulated watersheds”, while CIM/P_max*α_p and PDC/FFDC in “watersheds in the mainstream” are more related. This paper provides a deeper understanding and more accurate way of the application of these parameters in describing and predicting hydrological processes and estimation of PDC and FDCs in unmeasured catchments, and can be applied to more future research about processes based on catchment rainfall-runoff responses and physical controls.