Application of the SPARROW model in watersheds with limited information: a Bayesian assessment of the model uncertainty and the value of additional monitoring

How can spatially explicit nonlinear regression modelling be used for obtaining nonpoint source loading estimates in watersheds with limited information? What is the value of additional monitoring and where should future data-collection efforts focus on? In this study, we address two frequently asked questions in watershed modelling by implementing Bayesian inference techniques to parameterize SPAtially Referenced Regressions On Watershed attributes (SPARROW), a model that empirically estimates the relation between in-stream measurements of nutrient fluxes and the sources/sinks of nutrients within the watershed. Our case study is the Hamilton Harbour watershed, a mixed agricultural and urban residential area located at the western end of Lake Ontario, Canada. The proposed Bayesian approach explicitly accounts for the uncertainty associated with the existing knowledge from the system and the different types of spatial correlation typically underlying the parameter estimation of watershed models. Informative prior parameter distributions were formulated to overcome the problem of inadequate data quantity and quality, whereas the potential bias introduced from the pertinent assumptions is subsequently examined by quantifying the relative change of the posterior parameter patterns. Our modelling exercise offers the first estimates of export coefficients and delivery rates from the different subcatchments and thus generates testable hypotheses regarding the nutrient export hot spots' in the studied watershed. Despite substantial uncertainties characterizing our calibration dataset, ranging from 17% to nearly 400%, we arrived at an uncertainty level for the whole-basin nutrient export estimates of only 36%. Finally, we conduct modelling experiments that evaluate the potential improvement of the model parameter estimates and the decrease of the predictive uncertainty if the uncertainty associated with the current nutrient loading estimates is reduced. Copyright (c) 2012 John Wiley & Sons, Ltd.