A Bayesian methodological framework for accommodating interannual variability of nutrient loading with the SPARROW model

Abstract

[1] Regression-type, hybrid empirical/process-based models (e.g., SPARROW, PolFlow) have assumed a prominent role in efforts to estimate the sources and transport of nutrient pollution at river basin scales. However, almost no attempts have been made to explicitly accommodate interannual nutrient loading variability in their structure, despite empirical and theoretical evidence indicating that the associated source/sink processes are quite variable at annual timescales. In this study, we present two methodological approaches to accommodate interannual variability with the Spatially Referenced Regressions on Watershed attributes (SPARROW) nonlinear regression model. The first strategy uses the SPARROW model to estimate a static baseline load and climatic variables (e.g., precipitation) to drive the interannual variability. The second approach allows the source/sink processes within the SPARROW model to vary at annual timescales using dynamic parameter estimation techniques akin to those used in dynamic linear models. Model parameterization is founded upon Bayesian inference techniques that explicitly consider calibration data and model uncertainty. Our case study is the Hamilton Harbor watershed, a mixed agricultural and urban residential area located at the western end of Lake Ontario, Canada. Our analysis suggests that dynamic parameter estimation is the more parsimonious of the two strategies tested and can offer insights into the temporal structural changes associated with watershed functioning. Consistent with empirical and theoretical work, model estimated annual in-stream attenuation rates varied inversely with annual discharge. Estimated phosphorus source areas were concentrated near the receiving water body during years of high in-stream attenuation and dispersed along the main stems of the streams during years of low attenuation, suggesting that nutrient source areas are subject to interannual variability.

Leveraging Spatial and Temporal Variability to Probabilistically Characterize Nutrient Sources and Export Rates in a Developing Watershed

“…The point source DC has a mean of 0.87 and a CI that includes 1.0. A value of near 1.0 is expected for point sources, assuming that there are no substantial biases in the point source loading data (Schwarz et al, ; Wellen et al, ). We note that point source DCs below 1.0 are common in many hybrid model applications, including previous applications in this study area (McMahon et al, ; Qian et al, ; Smith et al, ).…”

“…Additional factors, beyond land use change and precipitation-induced nutrient wash-off, may also affect the interannual variability of instream nutrient loads. The previous studies by Wellen et al (2012) and Xia et al (2016) suggest that changes in instream residence time and nutrient retention may also play an important role. In this study, we estimated retention based on available NHD stream characteristics, which reflect average conditions over time.…”

Regional scale selenium loading associated with surface coal mining, Elk Valley, British Columbia, Canada

“…Detail on the calculation of γ i 2 is provided in Section 3.4. See the SI or Wellen et al (2012Wellen et al ( , 2014 …”

Legacy Nutrient Dynamics at the Watershed Scale: Principles, Modeling, and Implications

“…However, currently prevailing watershed models are generally lack of an explicit mechanism to describe the legacy nutrient dynamics and delivery lags (Kleinman et al, 2015;Meals et al, 2010). Lumped or statistical watershed models such as the export coefficient model, GlobalNEWS, GWLF, PolFlow, and SPARROW generally assume that the nutrient cycle to be at a steady state, either on a yearly basis or over a multiyear period (e.g., 5-year average, Alam and Goodall, 2012;De Wit, 2001;Swaney et al, 2012;Wellen et al, 2012). However, a major challenge remains in determining the appropriate length of the multiyear period that should be used to consider nutrient source inputs into models to satisfy the steady-state assumption (Chen et al, 2014b).…”