Nonlinear regression modeling of nutrient loads in streams: A Bayesian approach

[1] A Bayesian nonlinear regression modeling method is introduced and compared with the least squares method for modeling nutrient loads in stream networks. The objective of the study is to better model spatial correlation in river basin hydrology and land use for improving the model as a forecasting tool. The Bayesian modeling approach is introduced in three steps, each with a more complicated model and data error structure. The approach is illustrated using a data set from three large river basins in eastern North Carolina. Results indicate that the Bayesian model better accounts for model and data uncertainties than does the conventional least squares approach. Applications of the Bayesian models for ambient water quality standards compliance and TMDL assessment are discussed.

[1]  Sylvia Richardson,et al.  Markov Chain Monte Carlo in Practice , 1997 .

[2]  C. Richardson,et al.  Estimating the long‐term phosphorus accretion rate in the Everglades: A Bayesian Approach with risk assessment , 1997 .

[3]  J. Brakebill,et al.  Application of spatially referenced regression modeling for the evaluation of total nitrogen loading in the Chesapeake Bay watershed , 1999 .

[4]  J. Mandrup-Poulsen.  Findings of the National Research Council’s Committee on Assessing the TMDL Approach to Water Quality Management , 2002 .

[5]  Gregory E. Schwarz,et al.  Effect of stream channel size on the delivery of nitrogen to the Gulf of Mexico , 2000, Nature.

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

[7]  J. Besag.  Spatial Interaction and the Statistical Analysis of Lattice Systems , 1974 .

[8]  U. Aswathanarayana,et al.  Assessing the TMDL Approach to Water Quality Management , 2001 .

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

[10]  J. Besag,et al.  On conditional and intrinsic autoregressions , 1995 .

[11]  Gregory E. Schwarz,et al.  Regional interpretation of water‐quality monitoring data , 1997 .

[12]  Mark E. Borsuk,et al.  On Monte Carlo methods for Bayesian inference , 2003 .

[13]  H. Jeffreys.  Some Tests of Significance, Treated by the Theory of Probability , 1935, Mathematical Proceedings of the Cambridge Philosophical Society.

[14]  Adrian E. Raftery,et al.  [Practical Markov Chain Monte Carlo]: Comment: One Long Run with Diagnostics: Implementation Strategies for Markov Chain Monte Carlo , 1992 .

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