Large Biases in Regression-Based Constituent Flux Estimates: Causes and Diagnostic Tools

Journal of the American Water Resources Association

Volumn 50, Issue 6, 2014, Pages 1401-1424

  Hirsch, Robert M ^a  

^a U S GEOLOGICAL SURVEY   (United States)

Author keywords

Computational methods; Nutrients; Statistics; Transport and fate

Indexed keywords

COMPUTATIONAL METHODS; DIAGNOSTIC PRODUCTS; NUTRIENTS; STATISTICS;

BIASED ESTIMATES; FIVE-PARAMETER MODEL; FLUX COMPUTATION; MULTI-YEAR PERIODS; REGRESSION-BASED MODEL; TOTAL PHOSPHORUS; TRANSPORT AND FATE; WEIGHTED REGRESSION;

LARGE DATASET;

EID: 84898539684     PISSN: 1093474X     EISSN: 17521688     Source Type: Journal    
DOI: 10.1111/jawr.12195     Document Type: Article

References (38)

1. Alameddine, I., S.S. Qian, and K.H. Reckhow, 2011. A Bayesian Changepoint-Threshold Model to Examine the Effect of TMDL Implementation on the Flow-Nitrogen Concentration Relationship in the Neuse River Basin. Water Research 45:51-62, doi: 10.1016/j.watres.2010.08.003.
2. Alexander, R.B., J.K. Böhlke, E.W. Boyer, M. David, J.W. Harvey, P.J. Mulholland, S.P. Seitzinger, C.R. Tobias, C. Tonitto, and W.M. Wollheim, 2009. Simulating Temporal Variations of Nitrogen Losses in River Networks with a Dynamic Transport Model Unravels the Coupled Effects of Hydrological and Biogeochemical Processes. Biogeochemistry 93:91-116. http://www.springerlink.com/content/441650023u7k58u9/, accessed August 2013.
3. Böhlke, J.K., R.C. Antweiler, J.W. Harvey, A.E. Laursen, L.K. Smith, R.L. Smith, and M.A. Voytek, 2009. Multi-Scale Measurements and Modeling of Denitrification in Streams with Varying Flow and Nitrate Concentration in the Upper Mississippi River Basin, USA. Biogeochemistry 93:117-141. http://www.springerlink.com/content/f00r657809770131/, accessed August 2013.
4. Böhlke, J.K., M.E. O'Connell, and K.L. Prestegaard, 2007. Ground-Water Stratification and Delivery of Nitrate to an Incised Stream in Varying Flow Conditions. Journal of Environmental Quality 36:664-680. https://dl.sciencesocieties.org/publications/jeq/abstracts/36/3/664, accessed August 2013.
5. Cohn, T.A., 2005. Estimating Contaminant Loads in Rivers: An Application of Adjusted Maximum Likelihood to Type 1 Censored Data. Water Resources Research 41:W07003, doi: 10.1029/2004WR003833, 13 pp.
6. Cohn, T.A., D.L. Caulder, E.J. Gilroy, L.D. Zynjuk, and R.M. Summers, 1992. The Validity of a Simple Statistical Model for Estimating Fluvial Constituent Loads: An Empirical Study Involving Nutrient Loads Entering Chesapeake Bay. Water Resources Research 28(9):2353-2363.
7. Cohn, T.A., L.L. DeLong, E.J. Gilroy, R.M. Hirsch, and D.K. Wells, 1989. Estimating Constituent Loads. Water Resources Research 25(5):937-942.
8. Crawford, C.G., 1991. Estimation of Suspended-Sediment Rating Curves and Mean Suspended-Sediment Loads. Journal of Hydrology 129:331-348.
9. Crowder, D.W., M. Demissie, and M. Markus, 2007. The Accuracy of Sediment Loads When Log-Transformation Produces Nonlinear Sediment Load-Discharge Relationships. Journal of Hydrology 336:250-268, doi: 10.1016/j.jhydrol.2006.12.024.
10. Dolan, D.M. and R.P. Richards, 2008. Analysis of Late 90s Phosphorus Loading Pulse to Lake Erie. In: Checking the Pulse of Lake Erie, M. Munawar and R. Heath (Editors). Ecovision World Monograph Series, Schweizerbart Science Publishers, Stuttgart, Germany, pp. 79-96.
11. Dolan, D.M., A.K. Yui, and R.D. Geist, 1981. Evaluation of River Load Estimation for Total Phosphorus. Journal of Great Lakes Research 7(3):207-214.
12. Fenelon, J.M. and R.C. Moore, 1998. Transport of Agrichemicals to Ground and Surface Water in a Small Central Indiana Watershed. Journal of Environmental Quality 27:884-894.
13. Ferguson, R.I., 1986. River Loads Underestimated by Rating Curves. Water Resources Research 22(1):74-76.
14. Ferguson, R.I., 1987. Accuracy and Precision of Methods for Estimating River Loads. Earth Surface Processes and Landforms 12(1):95-104.
15. Garrett, J.D., 2012. Concentrations, Loads, and Yields of Selected Constituents from Major Tributaries of the Mississippi and Missouri Rivers in Iowa, Water Years 2004-2008. U.S. Geological Survey Scientific Investigations Report 2012-5240, 61 pp. http://pubs.usgs.gov/sir/2012/5240/.
16. Guo, Y., M. Markus, and M. Demissie, 2002. Uncertainty of Nitrate-N Load Computations for Agricultural Watersheds. Water Resources Research 38(10):1185, doi: 10.1029/2001WR001149.
17. Hirsch, R.M., 1988. Statistical Methods and Sampling Design for Estimating Step Trends in Surface-Water Quality. Water Resources Bulletin 24(3):493-503.
18. Hirsch, R.M., 2012. Flux of Nitrogen, Phosphorus, and Suspended Sediment from the Susquehanna River Basin to the Chesapeake Bay during Tropical Storm Lee, September 2011, as an Indicator of the Effects of Reservoir Sedimentation on Water Quality. U.S. Geological Survey Scientific Investigations Report 2012-5185, 17 pp. http://pubs.usgs.gov/sir/2012/5185/.
19. Hirsch, R.M., D.L. Moyer, and S.A. Archfield, 2010. Weighted Regressions on Time, Discharge, and Season (WRTDS), with an Application to Chesapeake Bay River Inputs. Journal of the American Water Resources Association 46(5):857-880, doi: 10.1111/j.1752-1688.2010.00482.x.
20. Medalie, L., R.M. Hirsch, and S.A. Archfield, 2012. Use of Flow-Normalization to Evaluate Nutrient Concentration and Flux Changes in Lake Champlain Tributaries, 1990-2009. Journal of Great Lakes Research 38(Suppl. 1):58-67. http://dx.doi.org/10.1016/j.jglr.2011.10.002, accessed August 2013.
21. Montgomery, D.C., E.A. Peck, and G.G. Vining, 2012. Introduction to Linear Regression Analysis (Fifth Edition). John Wiley and Sons, Hoboken, New Jersey, 672 pp.
22. Moyer, D.L., R.M. Hirsch, and K.E. Hyer, 2012. Comparison of Two Regression-Based Approaches for Determining Nutrient and Sediment Fluxes and Trends in the Chesapeake Bay Watershed. U.S. Geological Survey Scientific Investigations Report 2012-5244, 118 pp. http://pubs.usgs.gov/sir/2012/5244.
23. Preston, S.D., R.B. Alexander, G.E. Schwarz, and C.G. Crawford, 2011. Factors Affecting Stream Nutrient Loads: A Synthesis of Regional SPARROW Model Results for the Continental United States. Journal of the American Water Resources Association 47(5):891-915, doi: 10.1111/j.1752-1688.2011.00577.x/full.
24. Preston, S.D., V.J. Bierman, Jr., and S.E. Sillman, 1989. An Evaluation of Methods for the Estimation of Tributary Mass Loads. Water Resources Research 25:1379-1389.
25. Qian, S.S., 2010. Environmental and Ecological Statistics with R. Chapman and Hall/CRC Press, Boca Raton, Florida, 421 pp.
26. Richards, R.P., 2004. Improving TMDLs with Lessons Learned from Long-Term Detailed Monitoring. Journal of Environmental Engineering 130:657-663.
27. Richards, R.P., I. Alameddine, J.D. Allan, D.B. Baker, N.S. Bosch, R. Confesor, J.V. DePinto, D.M. Dolan, J.M. Reutter, and D. Scavia, 2012. Discussion of "Nutrient Inputs to the Laurential Great Lakes by Source and Watershed Estimated Using SPARROW Watershed Models" by Dale M. Robertson, and David Saad. Journal of the American Water Resources Association 49(3):715-724, doi: 10.1111/jawr.12006/full, downloaded March 4, 2013.
28. Richards, R.P. and J. Holloway, 1987. Monte Carlo Studies of Sampling Strategies for Estimating Tributary Loads. Water Resources Research 23:1939-1948.
29. Robertson, D.M. and E.D. Roerish, 1999. Influences of Various Water Quality Sampling Strategies on Load Estimates for Small Streams. Water Resources Research 35(12):3747-3759.
30. Runkel, R.L., C.G. Crawford, and T.A. Cohn, 2004. Load Estimator (LOADEST) - A FORTRAN Program for Estimating Constituent Loads in Streams and Rivers. U.S. Geological Survey Techniques and Methods, Book 4, Chap. A5, 75 pp. http://pubs.er.usgs.gov/publication/tm4A5, accessed August 2013.
31. Smith, R.A., G.E. Schwarz, and R.B. Alexander, 1997. Regional Interpretation of Water-Quality Monitoring Data. Water Resources Research 33:2781-2798.
32. Sprague, L.A., R.M. Hirsch, and B.T. Aulenbach, 2011. Nitrate in the Mississippi River and Its Tributaries, 1980-2008: Are We Making Progress? Environmental Science and Technology 45(17):7209-7216, doi: 10.1021/es201221s/, accessed August 2013.
33. Stenback, G.A., W.G. Crumpton, K.E. Schilling, and M.J. Helmers, 2011. Rating Curve Estimation of Nutrient Loads in Iowa Rivers. Journal of Hydrology 396:158-169, doi: 10.1016/j.jhydrol.2010.11.006.
34. Tobin, J., 1958. Estimation of Relationships for Limited Dependent Variables. Econometrica 26:24-36.
35. Vecchia, A.V., R.J. Gilliom, D.J. Sullivan, D.L. Lorenz, and J.D. Martin, 2009. Trends in Concentrations and Use of Agricultural Herbicides for Corn Belt Rivers, 1996-2006. Environmental Science and Technology 43(24):9096-9102.
36. Verma, S., M. Markus, and R.A. Cooke, 2012. Development of Error Correction Techniques for Nitrate-N Load Estimation Methods. Journal of Hydrology 12-25:432-433, doi: 10.1016/j.jhydrol.2012.02.011.
37. Wang, P. and L.C. Linker, 2008. Improvement of Regression Simulation in Fluvial Sediment Loads. Journal of Hydraulic Engineering 134(10):1527-1531.
38. Zhang, Q., D.C. Brady, and W.P. Ball, 2013. Long-Term Seasonal Trends of Nitrogen, Phosphorus, and Suspended Sediment Load from the Non-Tidal Susquehanna River Basin to Chesapeake Bay. Science of the Total Environment 452(3):208-221, doi: 10.1016/j.scitotenv.2013.02.012.