Effect of water surface slope and friction slope on the value of the estimated Manning’s roughness coefficient in gravel-bed streams

The aim of the study was to assess the possibility of using the empirical formulas to determine the roughness coefficient in gravel-bed streams, the bed slopes of which range from 0.006 to 0.047. Another aim was to determine the impact of taking into account the conditions of non-uniform flow on the application of these formulas and to develop the correlation relationships between the roughness coefficient and water surface slope and also between the roughness coefficient and friction slope in order to estimate the roughness coefficient n in gravel-bed streams.

The studies were conducted in eight measuring sections of streams located in the Kraków-Częstochowa Upland, southern Poland. The roughness coefficient n₀ for these sections was calculated from the transformed Bernoulli equation based on the results of surveys and hydrometric measurements. The values of n₀ were compared with the calculation results obtained from fourteen empirical formulas presenting the roughness coefficient as a function of slope.

The Lacey, Riggs, Bray and Sauer formulas were found to provide an approximate estimate of the n value, while the best roughness coefficient estimation results were obtained using the Riggs formula. It was also found that taking into account the non-uniform flow and using the friction slope in the formulas instead of the bed slope or water surface slope did not improve the estimated values of the roughness coefficient using the tested formulas. It was shown that the lack of differences in the RMSE and MAE error values calculated for the developed correlation equations between the roughness coefficient and the friction slope or with the water surface slope also indicate no influence of the assumed friction slope or water surface slope on the value of the estimated roughness coefficient.