## Abstract

The Muskingum method is one of hydrological approaches have been using for flood routing for many years thanks to its simplicity and reasonable accuracy over other methods. In engineering works, the calculation of the Peak section of a flood hydrograph is crucially important. In the present study, using the Particle Swarm Optimization (PSO) algorithm, instead of using a single basic flood, the parameters of the linear Muskingum method (X, K, Δt) are calculated by computed arithmetic and geometric means relevant to two basic floods in the form of eight different models for calculating the downstream hydrograph. The results indicate that if the numerical values of the calculated flood inflow are placed in the interval of the inflow and the basic flood which the parameters X, K, Δt are from it, the computation accuracy in approximating the outflow flood related to the peak section of the inflow hydrograph increases for all the mentioned models. In other words, if the arithmetic mean of X, K and the geometric mean of Δt, relevant to the two basic floods are used instead of using values of X, K, Δt of a single basic flood, the computational accuracy in estimating the flood peak section of hydrograph in downstream has the highest increase among all the eight models. Thus, the Mean Relative Error (MRE) relevant to the peak section of the inflow hydrograph of the third flood (observational flood) obtained by the first and second basic floods equal to 4.89% and 2.91%, respectively, while in case of using the arithmetic mean of X and K and the geometric mean of Δt, related to the first and second basic floods (the best models presented in this study), this value is equal to 1.66%.

## HIGHLIGHTS

• Using parameters of two baseline flood simultaneously for flood routing using linear Muskingum method

• In addition to the optimize (X, K), the time interval (Δt) is also optimized using the Particle Swarm Optimization (PSO) algorithm

• Using the arithmetic mean of X, K and the geometric mean of Δt related to two baseline floods is the best to state for flood routing

• Increasing the accuracy of flood routing calculations in estimating the flood peak section using parameters of two baseline floods rather than using parameters of single baseline flood

• Using the presented model in this study compared to the case in which only the first or second baseline flood is used, the Mean Relative Error (MRE) will be decreased by 66% and 43%, respectively

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