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Recently, non-contact current meters (radar, image-based) are widely used to measure the discharge of rivers, and research and cases of calculating discharge by applying surface velocity-based index velocity method and velocity distribution method are increasing. To apply index velocity or velocity distribution methods based on surface velocity, the relationship between the surface velocity used as the index velocity and the cross-sectional average velocity must be known. In general, in straight channels with sufficiently large channel width, the ratio of the cross-sectional average velocity to the maximum velocity (ϕ(M)) is known to be between 0.6 and 0.7.In this study, the relationship between the maximum surface velocity and the cross-sectional average velocity was analyzed. Using 179 flow measurement data from 60 sites, the ratio of the cross-sectional average velocity to the maximum surface velocity (≈ϕ(M)) was calculated. As a result, ϕ(M) was analyzed to have an average of 0.64(correlation coefficient R=0.86). When the relationship between the two elements was established as a linear equation, the slope was calculated to be 0.6306 (R=0.74). The ratio of ϕ(M) and the velocity coefficient α (ratio of reference discharge/surface velocity discharge (α=1 applied)) was calculated to be 0.75 on average (range 0.51 to 0.91), and when the relationship between the two elements was established as a linear equation, the slope was calculated to be 0.7586 (R= 0.68). The correlation coefficient between ϕ(M) and the maximum surface velocity/average surface velocity of the cross-section was calculated to be -0.84, indicating that ϕ(M) shows a strong correlation with the distribution characteristics of the surface velocity. When the relationship between the two factors was established as an exponential equation, the coefficient of determination was calculated to be 0.76, confirming that the value of ϕ(M) can be estimated and used through surface velocity measurements.keyword : average velocity, surface velocity, index velocity, ϕ(M)AcknowledgementsThis work was supported by Korea Environment Industry & Technology Institute (KEITI) through Research and development on the technology for securing the water resources stability in response to future change Program, funded by Korea Ministry of Climate, Energy and Enviroment (MCEE)(RS-2024-00336020)