Statistical Nonparametric Model for Natural Salt Estimation
Publication: Journal of Environmental Engineering
Volume 131, Issue 1
Abstract
Many rivers in the Western U.S. suffer from high salinity content due to both natural and human-induced causes. Computer simulation models are often used to estimate future salinity levels and identify mitigation needs. To date, estimation of future natural salt loading has utilized linear relationships between natural flow and natural salt. We develop a nonparametric regression technique to fit a functional relationship between natural flow and natural salt. The main advantages of the nonparametric technique are: (1) No prior assumptions have to be made as to the underlying form of the relationship and (2) any arbitrary relationship (linear or nonlinear) can be modeled. In addition, we develop a resampling scheme to provide confidence intervals of the natural salt estimates from the nonparametric model. We apply this model to data from a stream gauge at Glenwood Springs, Colo., on the Colorado River. We show that the new natural salt model reduces the average overprediction of salt mass shown in the existing natural salt model for the period 1941–1995 by approximately 15% .
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The BOR funded this work. The writers would like to thank Dave Trueman for his strong support and encouragement. Valuable comments from three anonymous reviewers in improving the manuscript are thankfully acknowledged.
References
Adamoski, K., and Feluch, W. (1991). “Application of nonparametric regression to groundwater level prediction.” Can. J. Civ. Eng., 18, 600–606.
Brown, R. D. (1984). “Economic evaluation of salinity control.” Salinity in watercourses and reservoirs, R. H. French, ed., Butterworth, Boston 125–134.
Bureau of Reclamation (BOR). (1983). “Draft report—Grand Valley salt pickup calculations.” United States Department of the Interior, Grand Junction, Colo.
Bureau of Reclamation (BOR). (1987). “Colorado River simulation system, system overview.” United States Department of the Interior, Denver.
Butler, D. L. (1996). “Trend analysis of selected water-quality data associated with salinity-control projects in the Grand Valley, in the Lower Gunnison River basin, and at Meeker Dome, western Colorado.” United States Geological Survey, Water Resources Investigation Rep. No. 95-4274, Denver.
Craven, P., and Wahba, G. (1979). “Smoothing noisy data with spline functions.” Numer. Math., 31, 377–403.
Eubank, R. (1999). Spline smoothing and nonparametric regression. Marcel Dekker, New York.
Helsel, D. R., and Hirsch, R. M. (1992). Statistical methods in water resources. Elsevier, Reston, Va.
Huizenga, L. J. (1980). “The River Rhine as an example of international environmental policy in Europe.” Water Services, 84, 1013–1018.
Irons, W. V., Hembree, C. H., and Oakland, G. L. (1965). “Water resources of the upper Colorado River basin—technical report.” United States Geological Survey, Professional Paper, United States Government Printing Office, Washington, D.C., 441.
Lall, U. (1995). “Recent advances in nonparametric function estimation: hydraulic applications.” U.S. Natl. Rep. Int. Union Geod. Geophys. 1991–1994, Rev. Geophys., 33, 1093–1102.
Lall, U., Rajagopalan, B., and Tarboton, D. G. (1996). “A nonparametric wet/dry spell model for resampling daily precipitation.” Water Resour. Res., 32(9), 2803–2823.
Lall, U., and Sharma, A. (1996). “A nearest neighbor bootstrap for resampling hydrologic time series.” Water Resour. Res., 32(3), 679–693.
Lall, U., Moon, Y.-I., and Bosworth, K. (1993). “Kernel flood frequency estimators: Bandwidth selection and kernel choice.” Water Resour. Res.29(4), 1003–1015.
Lee, D. (1989). “Salinity in the Colorado River basin: A dynamic modeling approach to policy analysis.” PhD thesis, Univ. of California at Davis, Davis, Calif.
Lee, D., Howitt, R., and Marino, M. (1993). “A stochastic model of river water quality: application to salinity in the Colorado River.” Water Resour. Res., 29(12), 3917–3923.
Loader, C. (1999). Local regression and likelihood. Springer, New York.
Malone, R. F., Bowles, D. S., Grenney, W. J., and Windham, M. P. (1979). “Stochastic analysis of water quality.” Utah Water Research Laboratory, Utah State Univ., Logan, Utah.
Moon, Y.-I., and Lall, U. (1994). “Kernel function estimator for flood frequency analysis.” Water Resour. Res., 30(11), 3095–3103.
Mueller, D. K., and Osen, L. L. (1988). “Estimation of natural dissolved-solids for the upper Colorado River basin.” Water Resources Investigation Rep. No. 87–4069, United States Geological Survey, Denver.
Nathanson, M. N. (1978). “Updating the Hoover Dam documents.” Bureau of Reclamation, United States Department of the Interior, Denver.
Olson, K. W. (1980). “Economics of controlling natural salt sources in the Arkansas River Basin.” Water Resour. Bull., 16(2), 295–299.
Owosina, A. (1992). “Methods for assessing the space and time variability of ground water data.” MS thesis, Utah State Univ., Logan, Utah.
Prairie, J. R. (2002). “Long-term salinity prediction with uncertainty analysis: Application for Colorado River above Glenwood Springs, CO.” MS thesis, Univ. of Colorado, Boulder, Colo.
Rajagopalan, B., and Lall, U. (1998). “Locally weighted polynomial estimation of spatial precipitation.” J. Geograph. Inf. Decision Anal., 2(3), 48–57.
Rajagopalan, B., and Lall, U. (1999). “A K-nearest-neighbor simulator for daily precipitation and other weather variables.” Water Resour. Res., 35(10), 3089–3101.
Saleh, I. (1993). “Synthesis of streamflow and salt loads.” MS thesis, Texas A&M University, College Station, Tex.
Sharma, A., Tarboton, D. G., and Lall, U. (1997). “Streamflow simulation: A nonparametric approach.” Water Resour. Res., 33(2), 291–308.
Smith, J. A. (1991). “Long-range streamflow forecasting using nonparametric regression.” Water Resour. Res., 27(1), 39–46.
Tarboton, D. G., Sharma, A., and Lall, U. (1998). “Disaggregation procedures for stochastic hydrology based on nonparametric density estimation.” Water Resour. Res., 34(1), 107–119.
U.S. Department of the Interior. (2001). “Quality of water Colorado River basin: Progress report 20.” ⟨http://www.uc.usbr.gov/progact/salinity/index.html⟩ (October 15, 2001).
Vaill, J. E., and Butler, D. L. (1999). “Streamflow and dissolved-solids trends, through 1996, in the Colorado River basin upstream from Lake Powell—Colorado, Utah, and Wyoming.” U.S. Geological Survey, Water Resources Investigation, Rep. No. 99-4097, Denver.
Wurbs, R. A., and Karma, A. S. (1995). “Salinity and water-supply reliability.” J. Water Resour. Plan. Manage., 121(5), 352–358.
Wurbs, R. A., Saleh, I., and Karma, A. S. (1995). “Reservoir system reliability constrained by salinity.” Water Resour. Dev., 11(3), 273–287.
Yates, D., Gangopadhyay, S., Rajagopalan, B., and Strzepek, K. (2003). “A technique for generating regional climate scenarios using a nearest neighbor bootstrap.” Water Resour. Res., 39(7), 1199.
Information & Authors
Information
Published In
Journal of Environmental Engineering
Volume 131 • Issue 1 • January 2005
Pages: 130 - 138
Copyright
© 2005 ASCE.
History
Received: Aug 20, 2002
Accepted: Nov 18, 2003
Published online: Jan 1, 2005
Published in print: Jan 2005
Notes
Note. Associate Editor: Mark J. Rood
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.