Empirical modelling of large scale patterns in river bed surface grain size

The large-scale management of river resources requires an understanding of the spatial distribution of bed surface grain size. According to Sternbergʹs law, bed surface grain size at basin scales (i.e., 102–104 km), reduces in the downstream direction. We tested if such patterns were consistent across multiple large basins, and inferred their potential explanatory variables. Specifically, we fitted random forest regression models to mean grain size estimates (Φ units) derived from visual observations on several occasions in 677 stream and river reaches throughout France. Model predictors included the distance from the headwaters, variables describing rainfall, topography and geology of the upstream watershed and the slope of the valley segment on which the reach was located. We made three sets of independent predictions of mean grain size by 1) withholding each observation reach in turn during model-fitting and making a prediction for the withheld reach, 2) withholding reaches in six subsets defined by large drainage basins during model-fitting and making predictions for the withheld reaches in turn and 3) making predictions for 106 hydraulic habitat survey sites where grain size had been measured using protocols that differed from the fitting data. We also evaluated model consistency by fitting it to the six subsets defined by large drainage basins. Regression of the observed (y) vs. predicted (x) mean grain size generated from our three sets of independent predictions had r2 of 52%, 47%, and 38%, respectively; and were unbiased. The characteristic model error, as defined by root mean squared deviation was 2.9 (Φ units), however, the tests indicated that the model uncertainties for the finer size classes were larger. Contrary to expectations, we found consistently weak relationships between mean grain size and distance from the headwaters. The most important contributors to modelled grain size were (consistently across the 6 large basins) watershed slope, segment slope and watershed variables describing rainfall and geological hardness. This suggests that grain size distribution at the scale of multiple basins is mainly governed by patterns associated with sediment sources and hydraulic sorting. Though uncertain at the reach scale, the high generality of our model supports the research of empirical or simplified physically based models of bed surface grain size distribution in multiple basins.