An extrapolation algorithm for estimating river bed grain size distributions across basins

Abstract. Values representing grain size distributions of stream reaches are essential for estimating sediment transport at the reach scale. Various modeling frameworks exist that attempt to simulate reach-scale sediment transport across entire drainage basins to characterize sediment dynamics at a watershed scale. Such frameworks require estimates of grain size at each reach. Because obtaining direct measurements at this scale is impractical and logistically difficult, methods to estimate or extrapolate grain size measurements are needed, however, few currently exist. Here I present an extrapolation algorithm that uses one or more pebble counts to extrapolate full grain size distributions to each reach of a drainage network. In addition to the pebble count measurements, the tool requires a stream network geospatial feature class, attributed with values for reach-averaged slope and some consistent measure of relative flow magnitude (or a proxy for flow). I tested the tool in a set of sub-watersheds in the Bitterroot River basin of western Montana, US, with varying valley morphologies, and compared predictions to measurements at 16 sites. When using multiple measurements for calibration, mean absolute percent error averaged 5.8 % of the measured grain sizes in the phi scale. When using a single measurement for calibration, error averaged 8.4 %.