Despite widespread use of Curve Number (CN) as main parameter in SCS equations for estimating runoff of statistics-free basins, its capability in appropriate estimation of runoff has always been controversial. In this study, ability of CN method has been studied in estimating runoff through the application of a stochastic optimization method and within the framework of SCS equations. In stochastic method, sensitivity of statistical distributions, number of statistical samples and range of CN changes on accuracy of calculations have been studied through the application of MonteCarlo Simulation.The used stochastic method is stable based on the rainfall and runoff information. For this purpose, rainfall and runoff modeling are first selected and probable distribution functions, governing these events, are specified. Then, rainfall and runoff modeling are produced in different sample sizes within random modeling. Produced samples of rainfall and runoff are evaluated based on the specific criteria and specific runoff modeling is selected. The selective runoffs and number of experimental curves are used in SCS equations, rainfall modeling is calculated and their probable functions are determined. Based on Kolmogrov-Smirnov Test, optimal curve number (CNOPT) is set between produced distribution functions and initial probability distribution function governing rainfall events. Also, average and mean curve number (CNAVG,,CNMEG) has been studied. Statistics of basins representing Kasilian and Emameh has been used with the aim of studying efficiency of stochastic method. In KasilianBasin, the runoffs, calculated through the use of CN OPT, enjoyed the minimum error than observational runoffs. This emphasizes desirable capability of CN method in estimating runoff of the basin but stochastic method was unenforceable in Emameh Basin due to the shortage of rainfall and runoff events.

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