Modeling of monthly flow duration curve using nonlinear regression method for un-gauged watersheds of Ardabil Province

The flow duration curve (FDC) represents the frequency distribution of water flow over a period of time, which is widely used in hydrology to evaluate different ranges of river water flow applications. Therefore, it is necessary to develop a suitable estimation model and method in un-gauged watersheds. To this end, in the present study, a modeling method based on nonlinear regression, for the preparation of FDC based on water flow (Q) and precipitation (P) data in the statistical period 2002-2013, area (A) and mean slope (S) of upland watersheds of 30 stations of Ardabil Province were used. For nonlinear regression analysis, about 70 and 30% of the stations were considered for calibration and validation, respectively. The development of the FDC estimation model involved several steps, including nondimensionalization of flow data, normalization, definition of the parameters of nonlinear regression equations, and calculation of required quartiles. According  to the results, after testing different equations, the equation Q=0.00002385(AP)0.571S0.845  considering all input variables with a coefficient of determination (R2) 0.78 and mean absolute error (MAE) 0.021, was introduced as the final equation for FDC modeling in watersheds without statistics.