An un-mixing model to study watershed erosion processes

An un-mixing model is formulated within a Bayesian Markov Chain Monte Carlo framework for use within land-use fingerprinting to study watershed erosion processes. The model has two new components: (1) An equation and erosion process parameter are used to weight tracer signatures from each erosion process within a land-use. (2) An extra tracer distribution and episodic erosion parameter are used to represent soil eroded throughout the sampling duration and thus include the episodic nature of erosion. To test specification of these new parameters, the un-mixing model is applied in the 15 km² Jerome Creek Watershed in the Palouse Region of Northwestern Idaho. Erosion processes include surface erosion upon mountain slopes due to logging in the forest land-use and rill/interrill erosion on cultivated slopes and headcut erosion in riparian floodplains of the agricultural land-use (winter wheat/peas rotation and hay pasture). Episodic erosion occurs for the event where the model is applied. A sensitivity analysis shows that the smallest Bayesian credible set results when the new parameters are specified using hydrologic data and process-based models. The un-mixing model predicts that 90% of the eroded-soil originated from the agricultural land-use and 10% originated from the forest land-use. A comparative study is performed that estimates 90.5% and 9.5% of eroded-soil originated from the agricultural and forest land-uses. Successful performance of the un-mixing model highlights future application as a standalone probabilistic tool to monitor watershed erosion processes that exhibit non-equilibrium conditions and provide calibration data for process-based watershed models.