Identification of a Function to Fit the Flow Duration Curve and Parameterization of a Semi-Arid Region in North China

Abstract

The discharge process has undergone major changes in many river basins throughout the world as a result of the simultaneous influences of global climate change and human activity. Flow duration curves (FDCs) are crucial indicators of river basins’ hydrological processes. However, it is challenging to compare FDCs in a quantitative way. This study will identify the best function with which to fit the flow duration curve in a semi-arid region of North China, so as to quantify the FDC, and parameterize the function of the FDC of the region in order to describe the FDCs of ungauged basins. In this work, six small- and medium-sized catchments in North China are selected as the study area, and three functions, i.e., log normal, generalized Pareto and H2018 functions, were chosen to fit the FDC at nineteen hydrological stations. The relationship between the parameters of the FDC and the basin characteristics, such as the climatic factors and geographical features, were analyzed. A regression formula of the parameters of the FDC function was established, and its spatial and temporal distributions were examined. Based on the evaluation of four indicators, the Nash–Sutcliffe efficiency, the root mean square relative error, the logarithmic Nash efficiency coefficient and the coefficient of determination, the results demonstrate that the H2018 function can match FDCs the best. Through the annual runoff, annual precipitation, precipitation in summer, potential evapotranspiration, catchment area, mean elevation, length of the main channel and maximum flow frequency, the parameters of a, b, and k in the H2018 function can be formulated. The regression formula constructed in this study can obtain a regional flow duration curve with satisfactory performance, which provides a reference for the validation of remote-sensing-based runoff data in ungauged regions.