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Climate change and human activities are two important factors affecting surface runoff. In water resource planning and management, it is usually important to separate the contribution of the mentioned factors to the runoff change. In this paper, a new methodology is proposed to obtain the relative impact of human activities and climate change on streamflow under uncertainty. In this methodology, the breakpoint of the annual time series of the observed runoff is estimated and the time series is divided into two study periods; before and after the breakpoint, namely the "natural" and "impacted" periods. The Jazim monthly water balance model is used for monthly runoff simulation. To incorporate the effect of snow in simulating runoff, two Jazim-based monthly water balance models with Rao and Al Wagdany (1995) and McCabe and Markstrom (2007) snow modules are used. Then, the monthly water balance models are calibrated and verified for the natural and impacted periods. The main parameters of the water balance models are optimized using the Genetic Algorithms. The uncertainty of the parameters of the models is analyzed using differential evolution adaptive Metropolis (DREAM) algorithm, which is based on the Markov Chain Monte Carlo (MCMC) algorithm. This algorithm provides the posterior probability distribution functions (PDFs) of parameters of the runoff simulation models. Next, the PDFs of the contribution rate (CR) of the climate change and human activities to runoff are determined using the fixing changing method by taking into account the PDFs of the models' parameters. To show the applicability and efficiency of the proposed methodology, it is applied to the Zayandehrud sub-basin in Iran. Using the Standard Normal Homogeneity Test (SNHT), Pettitt and Buishand range tests, one breakpoint at 2006 is detected in runoff time series. Through the monthly rainfall-runoff simulations and the fixing-changing method, it is estimated that decrease in the runoff after the breakpoint can be attributed to climate change by 57.8% and 45%, using the Jazim-Rao & Al Wagdany model and the Jazim-McCabe & Markstrom model, respectively. The results of the uncertainty analysis of the parameters of the water balance models show that the parameters of LSMX (maximum moisture capacity of the lower soil layer) and K-3 (deep percolation coefficient) are the most significant parameters in the uncertainty of runoff simulated by both the models. According to the PDFs of contribution rate (CR) of climate change and human activities which are obtained using each rainfall-runoff model, it can be inferred that the Jazim-McCabe & Markstrom model significantly decreased the uncertainty of estimations.