How many measurements are required to construct an accurate sand budget in a large river? Insights from analyses of signal and noise

Morphological change in river channels is frequently evaluated in the context of mass balance sediment budgets. In a closed sediment budget, measurements of sediment influx and efflux are coupled with measured changes in channel topography to provide both spatial and temporal resolution, and independent estimates of the mass balance. For sediment budgets constructed over long river segments (~102 channel widths or greater) and long periods (~2 years or longer), spatial and temporal accumulation of measurement uncertainty, compounded by inadequate sampling frequency or spatial coverage, may produce indeterminate results. The degree of indeterminacy may be evaluated in the context of a signal‐to‐noise ratio (SNR), which is a function of the magnitude of the mass balance and the magnitudes of potential systematic uncertainties associated with measurements and incomplete sampling. We report on a closed sand budget consisting of measurements of flux and two morphological surveys for a 50‐km segment of a large river over a 3‐year period. Accurate reporting of the magnitude and sign of the change in sand storage was only possible by using state‐of‐the‐art techniques with high temporal frequency and large spatial extent. Together, a sand flux and morphological mass balance revealed that sand evacuation was temporally concentrated (~100% of mass change occurred during 19% of the study period) and highly localized (70% of mass change occurred in 12% of the study segment). A SNR analysis revealed that uncertainty resulting from undersampling may approach or exceed that caused by measurement uncertainty and that daily sampling of suspended‐sand concentration or repeat mapping of at least 50% of the river segment was required to determine the sand budget with SNR > 1. The approach used here to analyze sand budget uncertainty is especially applicable to other river systems with large temporal variability in sediment transport and large spatial variability in erosion and deposition. © 2018 John Wiley & Sons, Ltd. Comprehensive sand budget based on high‐resolution measurements of sediment flux, channel morphology, and bed composition for 50‐km segment of Colorado River demonstrates erosion. Uncertainty, evaluated by a signal‐to‐noise analysis shows that sub‐daily sampling of suspended‐sediment concentration and repeat mapping of at least 50% of the study area are required to determine a sand budget with signal‐to‐noise ratio > 1.