An uncertainty-based framework for incorporating sediment source fingerprinting into spatially-distributed soil erosion model testing

Evaluating the usefulness of spatially-distributed soil erosion and sediment delivery models is inherently difficult. Complications stem from the uncertainty in models and measurements of system responses, as well as from the scarcity of commensurable spatial data for model testing. Here, we present an approach for evaluating distributed soil erosion and sediment delivery models, which incorporates sediment source fingerprinting into model testing within a stochastic framework. We applied the Generalized Likelihood Uncertainty Estimation (GLUE) methodology to the Sediment Delivery Distributed (SEDD) model for the Mortes River catchment (~6600 km²) in Southeast Brazil. Sediment concentration measurements were used to estimate long-term sediment loads with a sediment rating curve. Regression uncertainty was propagated with posterior simulations of model coefficients. A Monte Carlo simulation was used to generate SEDD model realizations, which were compared against limits of acceptability of model errors derived from the uncertainty in the curve-estimated sediment loads. The models usefulness for identifying the sediment sources in the catchment was assessed by evaluating behavioral model realizations against sediment fingerprinting source apportionments. Accordingly, we developed a hierarchical tributary sampling design, in which sink sediments were sampled from multiple nodes in the main river channel. The relative contributions of the main sub-catchments in the basin were subsequently estimated by solving the fingerprinting un-mixing model with a Monte Carlo simulation. Results indicated that gauging station measurements of sediment loads were fairly uncertain (average annual specific sediment yields = 0.47 – 11.95 ton ha^-1 yr^-1). This led to 23.4 % of SEDD model realizations being considered behavioral system representations. Spatially-distributed estimates of sediment delivery to water courses were also highly uncertain, as grid-based absolute errors of SEDD results were hundredfold the median of the predictions. A comparison of SEDD outputs and fingerprinting source apportionments revealed an overall agreement between modeled contributions from individual sub-catchments to sediment loads, although some large discrepancies were found in a specific tributary. From a falsificationist perspective, the SEDD model could not be rejected, as many model realizations were behavioral. The partial agreement between fingerprinting and SEDD results provide some conditional corroboration of the models capability to identify the sources of sediments in the catchment, at least with some degree of spatial aggregation. However, the uncertainty in the grid-based outputs might dispute the models usefulness for actually quantifying sediment dynamics under the testing conditions. For management purposes, both SEDD and fingerprinting results indicated that most of the sediments reaching the hydroelectric power plant reservoir located at the outlet of the Mortes River originated from mid and upper catchment tributaries. The convergence of model results therefore evince that reducing reservoir sedimentation rates requires widespread soil conservation efforts throughout the catchment, instead of local/proximal interventions. Ultimately, we have shown how sediment source fingerprinting can be incorporated into the evaluation of spatially-distributed soil erosion and sediment delivery models while considering the uncertainty in both models and observational data.