Estimating the return periods of the flood volume and peak flow based on bivariate rainfall analysis in Barz Palin

Generating a mathematical relationship between rainfall and runoff plays an important role in the decision-making process and control of surface flows. This structure has levels of uncertainty based on the hydrological conditions, land cover, time, depth, and rate of the rainfall events. Uncertainty analysis in systems evaluation and management has been considered as a logical aspect in engineering estimates in recent decades. Uncertainty generally implies that there is no complete knowledge of the behavior of a system and the specific values of its variables. At present, the uncertainty problem has been one of the topics of interest in research, decision-making and design in the field of water science and engineering. Different methods of uncertainty analysis in water resources have been developed. The main purpose of this study was to determine the degree of uncertainty and its role in calculating runoff generated by rainfall.

The hydrological information used in this study includes the amount of rainfall and runoff recorded in daily time steps. Analysis of available data revealed about 37 rainfall events that led to the flood. Rainfall characteristics (maximum daily rate (mm/day) and cumulative rainfall depth in one event (mm)) and two characteristics of runoff hydrograph (hydrograph peak flow (m3/s) and runoff volume (million cubic meters (MCM)) were calculated from daily rainfall and runoff information. Therefore, a probabilistic decision model based on copula multivariate functions was developed to predict the variables at different return periods. The relationship between rainfall rate and depth with peak hydrograph flow and runoff volume for flood events over a 37-year period was formulated through fuzzy set theory. The feasible domain of the fuzzy problem was searched using a multi-objective optimization genetic algorithm based on the non-dominated sorting to find the extreme points. The obtained solutions were used as a fuzzy response to calculate the runoff of the Barz plain in Khuzestan province in southwestern Iran.

The results showed that the correlation between the maximum daily rainfall rate and the peak discharge of runoff hydrograph with a determination of coefficient equal to 0.85 can be described as fuzzy numbers. Therefore, a combined model of fuzzy system and multi-objective genetic algorithm was used to calculate the fuzzy response of runoff characteristics to uncertainty inputs of rainfall. Consequence of the development of this method can analyze the existing uncertainty in estimating the volume and intensity of runoff based on recorded rainfall information and provide an estimate with certain levels of flood reliability. Future research should provide relationships to predict the effect of rainfall duration on runoff output hydrographs and add a new component to this decision structure.