The analysis of unsteady flows in natural rivers is highly complicated. One of the most important factors that causes errors in calculating the flow depth and discharge is the inability to accurately estimate the values of Manning’s roughness coefficient (n) for longitudinal river cross-sections. Most conventional methods for calibrating n only provide a mean value for longitudinal river cross-sections, which can significantly increase errors in flood routing. Therefore, a new method is presented herein for identifying the distribution functions of n along natural rivers based on modified random search optimization and clustering (MRSOC). In this method, only the inflow and outflow hydrographs need be determined to obtain the minimum data required. The proposed method was verified using synthetic, field, and experimental data. The results indicate that using the proposed method, all the gradual and abrupt changes of the n value at longitudinal cross-sections of natural rivers can be estimated with sufficient accuracy, and the equations for these changes can also be obtained. This can eventually lead to a noticeable reduction in errors in flood routing.

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