Flood frequency analysis using power law approach (Case study: Dez Basin)

Estimation of flood discharge and return period of extreme events is one of the most important factors in design of hydraulic structures. Therefore, conducting researches for improving the accuracy of estimation methods is very important. Nowadays, the fractal behavior of all earth science phenomena, including precipitation and runoff has been accepted. This method is used for modeling of natural phenomena because of its strong physical background. As power law is derived from fractal theory, it can be a suitable method for estimation of design flood. In the annual maxima method, a maximum value is extracted among all the recorded discharge occurred during a year. Therefore, in this method, out of a number of extreme events happened at the end of the year, only one value is chosen and other values are eliminated. The positive point of this method is that the extracted data are independent of each other. However, this method has its own limitations. For example, in years with high flood occurrences, the values that stand in the second and third places in terms of magnitude lose the chance to participate in the annual maxima series. On the other hand, in dry years, the occurred maximum values are far lower than the second or third ranked discharge of wet years. Thus, correspondence of the annual maximum time series with reality is not suitable, and such a selection may result in neglecting the real pattern in the recorded values. In another method, partial time series (the time series greater than a given threshold) is employed. In this sampling method, a certain threshold of flow rate is considered and all flow rates that are above the threshold, are taken into consideration. In this study, power law has been employed to select the flood partial series. Therefore, the main objective of this study is to use power law in a) selection of partial series of flood in Dez Basin, and b) flood frequency analysis. In this study, flood frequency analysis of Dez watershed during the period of 1956- 2012 was performed using two approaches of power law (PL) and ordinary statistical distributions. At first, the partial-duration flood series were extracted using power law with the intervals of 7, 14, 30, and 60 days, and then compared with the annual maxima series. The results indicated that the annual maxima series were not suitable for frequency analysis of the flood in Dez Basin, and the 30-day partial duration series obtained from the power law has a better correspondence with the flow and properties of the Dez Basin. Examining of the independence and stationarity of the 30-d partial duration series by Wald-Wolfowitz (W-W) test, confirmed the independence of the considered series. In the next step, the power distribution and ordinary statistical distributions were fitted onto the flood data of the Dez Basin, and performance of each distribution was investigated using Normalized Root Mean Square Error (NRMSE) and Nash-Sutcliffe (NS) criteria. The results showed that in the Tange Panj Bakhtiari station (TPB), power distribution had a better performance than other considered distributions, and in the Tange Panj Sezar (TPS) and Tale Zang (TZ) stations the power distribution stood in the second rank in terms of the best distribution with a slight difference. The results indicated that the annual maxima within shorter return periods estimate lower values for the flood of the studied stations. However, the partial series extracted using power law solved the problem in the annual maxima, and are in full correspondence with the physics of Dez Basin. Following selection of suitable statistical distributions, flood quintiles were calculated for return periods of 2, 5, 10, 20, 50, and 100 years in each station. Based on the calculated quintiles, it was observed that TPB station is more vulnerable to the flood occurrence, where the amount of flood increases in it with the prolongation of return period. In other words, in basins culminating in TPB station, development of warning systems and implementation of flood control programs are more needed. Since the performance of power distribution in estimating the flood in Dez Basin has been very satisfactory and calculation of its parameters and its application is easier than ordinary probability distributions, it can be suggested as the superior distribution for flood frequency analysis in Dez Basin.