The impact of reach averaging Manning’s equation for an in-situ dataset of water surface elevation, width, and slope

Abstract The Surface Water and Ocean Topography Mission (SWOT) will generate global, spatially continuous maps of water surface elevation and extent for large inland water bodies when it launches in 2021. We present an analysis of water surface elevation, width, and bathymetry timeseries data from a medium-sized (average annual discharge 14 m 3 /s) river to explore Manning’s equation, an empirical open channel flow equation, in the context of SWOT discharge algorithms. While this equation is in theory inapplicable to natural channels due to the non-uniform and spatially heterogeneous nature of river systems, we explored approaches to adapt it to this context using reach-averaged variables. At twenty sites along a 6.5 km stretch of the Olentangy River in Ohio, USA, we collected automated and manual measurements of water surface elevation and river width, undertook a full bathymetric survey of the study area, and built a hydraulic model. The stretch of river was divided into five reaches, and hydraulic variables were reach-averaged. Using these variables, we used a modified form of Manning’s equation to compute a reach-averaged roughness coefficient. Reach-averaged roughness coefficients varied nonlinearly with discharge and were 2-10 times larger at low flow than at high flow in the in-situ data, ranging from 0.06 to 0.61 in one of the study reaches. These results were compared with the output of an unsteady flow simulation using a calibrated 1-D hydraulic model which was run with constant roughness coefficients at each cross section. When reach-averaged data was used, model-derived roughness coefficient also varied by more than an order of magnitude, with a range of 0.02 to 0.82 for one reach. For both in-situ and model-derived datasets, using a two-parameter roughness coefficient which scaled with a power law on either discharge or stage reduced discharge estimation error, with error for one reach dropping from 81 % to 8 % relative root-mean square error (rRMSE) in the in-situ data and 58 % to 8 % nRMSE in the modeled data. These results imply that spatial averaging of hydraulic variables leads to large variations in reach averaged Manning’s n , which we term the reach’s “effective resistance”, and suggest that this variability can be accounted for with a simple parameterization in estimates of discharge that use spatially averaged data.