An un-mixing model to study watershed erosion processes J.F. Fox a, * , A.N. Papanicolaou b,1 a Civil Engineering Department, University of Kentucky, Lexington, KY 40506-0281, USA b IIHR-Hydroscience and Engineering, University of Iowa, Iowa City, IA 52242, USA Received 4 December 2006; received in revised form 27 June 2007; accepted 28 June 2007 Available online 5 July 2007 Abstract 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 km 2 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 exhi- bit non-equilibrium conditions and provide calibration data for process-based watershed models. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Fingerprinting; Soil erosion; Un-mixing model; Bayesian; Probabilistic; Sediment transport 1. Introduction Soil erosion from a watershed during high rainfall events can cause degradation of surface waters in rivers due to excessive fine eroded-soil and soil-bound pollutants coming from the uplands [23]. The problem of assessing and mitigating soil erosion at the watershed scale is com- plex because soil erosion is highly variable both spatially across a watershed and temporally throughout the dura- tion of high rainfall events. Spatially, more than one land-use can exist within a watershed. The existence of more than one land-use, such as both agricultural and for- est land-uses in the same watershed, can produce regions of the watershed with differing erosion rates. Also from a spa- tial perspective, more than one erosion process can occur at different levels of the watershed topography even within the same land-use. For example, an agricultural land-use may have pronounced rill/interrill erosion processes on steep upland slopes and headcut erosion processes in floodplain areas near waterways [10]. Temporal complexity exists dur- ing erosion because soil is often detached in an ‘episodic’ sense rather than continuously throughout the duration of the high rainfall event. Due to the high variability in rainfall intensity, soil erodes intermittently from the soil surface as higher intensity rainfall bursting produces soil detachment. The cumulative effect of the episodic nature of erosion varies based on the intensity and duration of the high rainfall event, but in general erosion occurs from different locations across the landscape during a 0309-1708/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.advwatres.2007.06.008 * Corresponding author. Tel.: +1 859 257 8668; fax: +1 859 257 4404. E-mail addresses: jffox@engr.uky.edu (J.F. Fox), apapanic@engineer- ing.uiowa.edu (A.N. Papanicolaou). 1 Tel.: +1 319 335 6448; fax: +1 319 335 5238. www.elsevier.com/locate/advwatres Available online at www.sciencedirect.com Advances in Water Resources 31 (2008) 96–108