River suspended-sand flux computation with uncertainty estimation using water samples and high-resolution ADCP measurements

Abstract. Measuring suspended-sand fluxes in rivers remains a scientific challenge due to their high spatial and temporal variability. To capture the vertical and lateral gradients of concentration in the cross-section, measurements with point samples are performed. However, the uncertainty related to these measurements is rarely evaluated, as few studies of the major sources of error exist. Therefore, the aim of this study is to develop a method to determine the cross-sectional sand flux and estimate its uncertainty. This SDC (for sand discharge computing) method combines suspended-sand concentrations from point samples with ADCP (acoustic Doppler current profiler) high-resolution depth and velocity measurements. The MAP (for multitransect averaged profile) method allows obtaining an average of several ADCP transects on a regular grid, including the unmeasured areas. The suspended-sand concentrations are integrated vertically by fitting a theoretical exponential suspended-sand profile to the data using Bayesian modeling. The lateral integration is based on the water depth as a proxy for the local bed shear stress to evaluate the bed concentration and sediment diffusion along the river cross-section. The estimation of uncertainty combines ISO standards and semi-empirical methods with a Bayesian approach to estimate the uncertainty due to the vertical integration. The new method is applied to data collected in four rivers under various hydro-sedimentary conditions: the Colorado, Rhône, Isère, and Amazon rivers, with computed flux uncertainties ranging between 18 % and 32 %. The relative difference between the suspended-sand flux in 21 cases calculated with the proposed SDC method compared to the International Organization for Standardization (ISO) 4363 standard method ranges between −40 % and +23 %. This method that comes with a flexible, open-source code is the first to propose an applicable uncertainty estimation that could be adapted to other flux computation methods.