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

[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.

[1]  Douglas J. Soldat,et al.  Effect of Soil Phosphorus Levels on Phosphorus Runoff Concentrations from Turfgrass , 2009 .

[2]  Murray N. Charlton.  The Hamilton Harbour remedial action plan: eutrophication , 2001 .

[3]  R. Peter Richards,et al.  Monte Carlo studies of sampling strategies for estimating tributary loads , 1987 .

[4]  L. Claessens,et al.  Hydro‐ecological linkages in urbanizing watersheds: An empirical assessment of in‐stream nitrate loss and evidence of saturation kinetics , 2009 .

[5]  Douglas J. Soldat,et al.  The Fate and Transport of Phosphorus in Turfgrass Ecosystems , 2008 .

[6]  Kenneth H. Reckhow,et al.  An Examination of Land Use - Nutrient Export Relationships , 1982 .

[7]  M. Sivapalan,et al.  Spatiotemporal averaging of in‐stream solute removal dynamics , 2011 .

[8]  A statistical approach to estimate nitrogen sectorial contribution to total load. , 2005, Water science and technology : a journal of the International Association on Water Pollution Research.

[9]  Deva K. Borah,et al.  WATERSHED-SCALE HYDROLOGIC AND NONPOINT-SOURCE POLLUTION MODELS: REVIEW OF APPLICATIONS , 2004 .

[10]  M. B. Beck,et al.  On the identification of model structure in hydrological and environmental systems , 2007 .

[11]  M. Charlton,et al.  Water Quality Trends in Hamilton Harbour: Two Decades of Change in Nutrients and Chlorophyll a , 2009 .

[12]  Weitao Zhang,et al.  Addressing equifinality and uncertainty in eutrophication models , 2008 .

[13]  Predicting the Fate and Transport of E. coli in Two Texas River Basins Using a Spatially Referenced Regression Model 1 , 2009 .

[14]  David A Saad,et al.  Nutrient Inputs to the Laurentian Great Lakes by Source and Watershed Estimated Using SPARROW Watershed Models1 , 2011, Journal of the American Water Resources Association.

[15]  George B. Arhonditsis,et al.  Integration of numerical modeling and Bayesian analysis for setting water quality criteria in Hamilton Harbour, Ontario, Canada , 2011, Environ. Model. Softw..

[16]  Bradley P. Carlin,et al.  Bayesian measures of model complexity and fit , 2002 .

[17]  George B. Arhonditsis,et al.  A revaluation of lake-phosphorus loading models using a Bayesian hierarchical framework , 2009, Ecological Research.

[18]  A. N. Strahler.  Hypsometric (area-altitude) analysis of erosional topography. , 1952 .

[19]  Song S. Qian,et al.  Support of Total Maximum Daily Load Programs Using Spatially Referenced Regression Models , 2003 .

[20]  Jennifer G. Winter,et al.  EXPORT COEFFICIENT MODELING TO ASSESS PHOSPHORUS LOADING IN AN URBAN WATERSHED 1 , 2000 .

[21]  W. Stahel,et al.  Log-normal Distributions across the Sciences: Keys and Clues , 2001 .

[22]  George Kuczera,et al.  Understanding predictive uncertainty in hydrologic modeling: The challenge of identifying input and structural errors , 2010 .

[23]  G. Shaddick,et al.  Modelling daily multivariate pollutant data at multiple sites , 2002 .

[24]  Peter Reichert,et al.  Analyzing input and structural uncertainty of nonlinear dynamic models with stochastic, time‐dependent parameters , 2009 .

[25]  Andrew Gelman,et al.  General methods for monitoring convergence of iterative simulations , 1998 .

[26]  Gregory E Schwarz,et al.  Factors Affecting Stream Nutrient Loads: A Synthesis of Regional SPARROW Model Results for the Continental United States1 , 2011, Journal of the American Water Resources Association.

[27]  Robert M. Hirsch,et al.  Mean square error of regression‐based constituent transport estimates , 1990 .

[28]  Craig A Stow,et al.  Will Lake Michigan lake trout meet the Great Lakes Strategy 2002 PCB reduction goal? , 2004, Environmental science & technology.

[29]  Ioannis K. Tsanis,et al.  Mass balance modelling and wetland restoration , 1997 .

[30]  Richard A. Smith,et al.  An initial SPARROW model of land use and in-stream controls on total organic carbon in streams of the conterminous United States , 2010 .

[31]  S. T. Buckland,et al.  An Introduction to the Bootstrap. , 1994 .

[32]  Hans R. Künsch,et al.  A smoothing algorithm for estimating stochastic, continuous time model parameters and its application to a simple climate model , 2009 .

[33]  Kuolin Hsu,et al.  Uncertainty assessment of hydrologic model states and parameters: Sequential data assimilation using the particle filter , 2005 .

[34]  George B. Arhonditsis,et al.  Predicting the response of Hamilton Harbour to the nutrient loading reductions: A modeling analysis , 2011 .

[35]  Hans-Peter Deutsch.  Time Series Modeling , 2004 .

[36]  Robert M. Summers,et al.  The validity of a simple statistical model for estimating fluvial constituent loads: An Empirical study involving nutrient loads entering Chesapeake Bay , 1992 .

[37]  L. Band,et al.  Nitrogen input from residential lawn care practices in suburban watersheds in Baltimore county, MD , 2004 .

[38]  George B. Arhonditsis,et al.  Eutrophication Risk Assessment in Hamilton Harbour: System Analysis and Evaluation of Nutrient Loading Scenarios , 2010 .

[39]  E. Stanley,et al.  Hydrogeomorphic controls on phosphorus retention in streams , 2003 .

[40]  R. Alexander,et al.  Estimates of diffuse phosphorus sources in surface waters of the United States using a spatially referenced watershed model. , 2004, Water science and technology : a journal of the International Association on Water Pollution Research.

[41]  S. P. Bhavsar,et al.  Temporal PCB and mercury trends in Lake Erie fish communities: a dynamic linear modeling analysis. , 2011, Ecotoxicology and environmental safety.

[42]  Gregory E Schwarz,et al.  Differences in phosphorus and nitrogen delivery to the Gulf of Mexico from the Mississippi River Basin. , 2008, Environmental science & technology.

[43]  P. M. Gale,et al.  Phosphorus Retention in Streams and Wetlands: A Review , 1999 .

[44]  M. de Wit,et al.  Nutrient fluxes at the river basin scale. I: the PolFlow model , 2001 .

[45]  Peter C. Young,et al.  Systematic Identification of DO-BOD Model Structure , 1976 .

[46]  Alexander H. Elliott,et al.  Estimating the sources and transport of nutrients in the Waikato River Basin, New Zealand , 2002 .

[47]  Silvia Terziotti,et al.  A Regional Modeling Framework of Phosphorus Sources and Transport in Streams of the Southeastern United States1 , 2011, Journal of the American Water Resources Association.

[48]  Michael Rode,et al.  New challenges in integrated water quality modelling , 2010 .

[49]  Raymond J. Carroll,et al.  Measurement error in nonlinear models: a modern perspective , 2006 .

[50]  Weitao Zhang,et al.  Bayesian calibration of mechanistic aquatic biogeochemical models and benefits for environmental management , 2008 .

[51]  G. Schwarz,et al.  Sources of Suspended‐Sediment Flux in Streams of the Chesapeake Bay Watershed: A Regional Application of the SPARROW Model 1 , 2010 .

[52]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[53]  Satyendra P. Bhavsar,et al.  A Bayesian assessment of the PCB temporal trends in Lake Erie fish communities , 2011 .

[54]  Nicholas G. Aumen,et al.  Concepts and methods for assessing solute dynamics in stream ecosystems , 1990 .

[55]  S. P. Bhavsar,et al.  Detection of temporal trends of α- and γ-chlordane in Lake Erie fish communities using dynamic linear modeling. , 2011, Ecotoxicology and environmental safety.

[56]  Kenneth H. Reckhow,et al.  Nonlinear regression modeling of nutrient loads in streams: A Bayesian approach , 2005 .

[57]  Andrew Thomas,et al.  WinBUGS - A Bayesian modelling framework: Concepts, structure, and extensibility , 2000, Stat. Comput..

[58]  Jeffrey R. Deacon,et al.  Estimation of Total Nitrogen and Phosphorus in New England Streams Using Spatially Referenced Regression Models , 2004 .

[59]  Weitao Zhang,et al.  Predicting the Frequency of Water Quality Standard Violations Using Bayesian Calibration of Eutrophication Models , 2008 .

[60]  Qingyun Duan,et al.  An integrated hydrologic Bayesian multimodel combination framework: Confronting input, parameter, and model structural uncertainty in hydrologic prediction , 2006 .

[61]  M. West,et al.  Bayesian forecasting and dynamic models , 1989 .

[62]  K. A. Krieger.  Effectiveness of a coastal wetland in reducing pollution of a Laurentian Great Lake: Hydrology, sediment, and nutrients , 2003, Wetlands.

[63]  H. Akaike.  A new look at the statistical model identification , 1974 .

[64]  Michael Rode,et al.  Is point uncertain rainfall likely to have a great impact on distributed complex hydrological modeling? , 2010 .

[65]  C. Kucharik,et al.  The influence of climate on in‐stream removal of nitrogen , 2004 .