Estimating Hourly Water Temperatures in Rivers Using Modified Sine and Sinusoidal Wave Functions
Publication: Journal of Hydrologic Engineering
Volume 21, Issue 10
Abstract
Air temperature is often used to estimate stream water temperature by developing regression models. A method using modified sine functions and sinusoidal wave functions (MSSWF) was proposed for estimating hourly water temperatures in rivers. Estimates of daily maximum and minimum water temperatures from sine functions (SFs) were corrected using linear regressions as functions of deviations of estimates of daily maximum and minimum air temperatures from SFs, and then modified sinusoidal wave functions (SWFs) were used to estimate hourly water temperatures. Excellent agreement was found between observed and estimated hourly water temperatures using MSSWF models developed for 13 rivers in Alabama. The average Nash-Sutcliffe efficiency (NSE) for the MSSWF models developed for individual rivers is 0.94. The distance of a river monitoring station from the weather station has very little effect on the performance of individual MSSWF models when the distance is less than approximately 300 km. A lumped MSSWF model was also developed by combining water temperature data from all 13 rivers. The average NSE of 0.87 from the lumped MSSWF model indicates that the model can be applied to other rivers in Alabama that lack water temperature observations. The procedure to develop a MSSWF model was applied to four rivers in other regions.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The author, Gang Chen, wishes to express his gratitude to the Chinese Scholarship Council for financial support pursuing his graduate study at Auburn University. The authors would like to also thank Michael A. Perez, at Auburn University, and two anonymous reviewers for their review comments on this paper.
References
Ahmadi-Nedushan, B., et al. (2007). “Predicting river water temperatures using stochastic models: Case study of the Moisie River (Quebec, Canada).” Hydrol. Process., 21(1), 21–34.
Benyahya, L., St-Hilaire, A., Quarda, T. B., Bobée, B., and Ahmadi-Nedushan, B. (2007). “Modeling of water temperatures based on stochastic approaches: Case study of the Deschutes River.” J. Environ. Eng. Sci., 6(4), 437–448.
Brown, G. W. (1969). “Predicting temperatures of small streams.” Water Resour. Res., 5(1), 68–75.
Caissie, D. (2006). “The thermal regime of rivers: A review.” Freshwater Biol., 51(8), 1389–1406.
Caissie, D., El-Jabi, N., and Satish, M. G. (2001). “Modelling of maximum daily water temperatures in a small stream using air temperatures.” J. Hydrol., 251(1), 14–28.
Caissie, D., El-Jabi, N., and St-Hilaire, A. (1998). “Stochastic modelling of water temperatures in a small stream using air to water relations.” Can. J. Civ. Eng., 25(2), 250–260.
Cesaraccio, C., Spano, D., Duce, P., and Snyder, R. L. (2001). “An improved model for determining degree-day values from daily temperature data.” Int. J. Biometeorol., 45(4), 161–169.
Chapra, S. C. (1997). Surface water-quality modeling, McGraw-Hill, New York.
Chen, G., and Fang, X. (2015). “Accuracy of hourly water temperatures in rivers calculated from air temperatures.” Water, 7(3), 1068–1087.
Chen, G., Fang, X., and Devkota, J. (2015). “Understanding flow dynamics and density currents in a river-reservoir system under upstream reservoir releases.” Hydrol. Sci. J., in press.
Cluis, D. A. (1972). “Relationship between stream water temperature and ambient air temperature.” Nordic Hydrol., 3(2), 65–71.
Cole, T. M., and Wells, S. A. (2010). “CE-QUAL-W2: A two-dimensional, laterally averaged, hydrodynamic and water quality model, version 3.6.” Technical Rep., U.S. Army Corps of Engineers Waterways Experiments Station, Vicksburg, MS.
Crisp, D. (1990). “Water temperature in a stream gravel bed and implications for salmonid incubation.” Freshwater Biol., 23(3), 601–612.
Crisp, D., and Howson, G. (1982). “Effect of air temperature upon mean water temperature in streams in the north Pennines and English Lake District.” Freshwater Biol., 12(4), 359–367.
De Wit, C. T. (1978). “Simulation of assimilation respiration and transpiration of crops.” Simulation monographs, Pudoc, Wageningen, Netherlands, 141.
Erickson, T. R., and Stefan, H. G. (2000). “Linear air/water temperature correlations for streams during open water periods.” J. Hydrol. Eng., 317–321.
Harmeson, R. H., and Schnepper, V. M. (1965). “Temperatures of surface waters in Illinois.”, Illinois State Water Survey, Champaign, IL.
Harvey, R., Lye, L., Khan, A., and Paterson, R. (2011). “The Influence of air temperature on water temperature and the concentration of dissolved oxygen in Newfoundland Rivers.” Can. Water Resour. J., 36(2), 171–192.
Hoogenboom, G., and Huck, M. G. (1986). “Rootsimu v4.0: A dynamic simulation of root growth, water uptake, and biomass partitioning in a soil-plant-atmosphere continuum: Update and documentation.” Agronomy and Soils Departmental series, Auburn Univ., Alabama Agricultural Experiment Station, Auburn, AL, 83.
Johnson, A. C., et al. (2009). “The British river of the future: How climate change and human activity might affect two contrasting river ecosystems in England.” Sci. Total Environ., 407(17), 4787–4798.
Johnson, F. (1971). “Stream temperatures in an alpine area.” J. Hydrol., 14(3), 322–336.
Johnson, M. F., Wilby, R. L., and Toone, J. A. (2014). “Inferring air-water temperature relationships from river and catchment properties.” Hydrol. Process., 28(6), 2912–2928.
Kothandaraman, V. (1971). “Analysis of water temperature variations in large river.” J. Sanitary Eng. Div., 97(1), 19–31.
Kothandaraman, V., and Evans, R. L. (1972). “Use of air-water relationships for predicting water temperature.” Rep. of Investigation 69, Illinois State Water Survey, Urbana, IL, 14.
Lambrechts, L., et al. (2011). “Impact of daily temperature fluctuations on dengue virus transmission by Aedes aegypti.” Proc. Natl. Acad. Sci., 108(18), 7460–7465.
Mackey, A., and Berrie, A. (1991). “The prediction of water temperatures in chalk streams from air temperatures.” Hydrobiologia, 210(3), 183–189.
Martin, J. L., and Wool, T. (2002). “A dynamic one-dimensional model of hydrodynamics and water quality EPD-RIV1 user’s manual.” Georgia Environmental Protection Division, Atlanta.
Mohseni, O., and Stefan, H. (1999). “Stream temperature/air temperature relationship: A physical interpretation.” J. Hydrol., 218(3), 128–141.
Mohseni, O., Stefan, H. G., and Eaton, J. G. (2003). “Global warming and potential changes in fish habitat in U.S. streams.” Clim. Change, 59(3), 389–409.
Mohseni, O., Stefan, H. G., and Erickson, T. R. (1998). “A nonlinear regression model for weekly stream temperatures.” Water Resour. Res., 34(10), 2685–2692.
Morin, G., and Couillard, D. (1990). “Predicting river temperatures with a hydrological model.” Chapter 5, Encyclopedia of fluid mechanic, surface and groundwater flow phenomena, Vol. 10, Gulf Publishing Company, Houston, 171–209.
Morrill, J. C., Bales, R. C., and Conklin, M. H. (2005). “Estimating stream temperature from air temperature: Implications for future water quality.” J. Environ. Eng., 139–146.
Morse, W. L. (1972). “Stream temperature prediction under reduced flow.” J. Hydraul. Div., 98(6), 1031–1047.
Nash, J. E., and Sutcliffe, J. V. (1970). “River flow forecasting through conceptual models: Part I—A discussion of principles.” J. Hydrol., 10(3), 282–290.
Pilgrim, J. M., Fang, X., and Stefan, H. G. (1998). “Stream temperature correlations with air temperatures in Minnesota: Implications for climate warming.” J. Am. Water Resour. Assoc., 34(5), 1109–1121.
Raphael, J. M. (1962). “Prediction of temperature in rivers and reservoirs.” J. Power Div., 88(2), 157–182.
Reicosky, D., Winkelman, L., Baker, J., and Baker, D. (1989). “Accuracy of hourly air temperatures calculated from daily minima and maxima.” Agric. Forest Meteorol., 46(3), 193–209.
Sinokrot, B., and Stefan, H. (1993). “Stream temperature dynamics: Measurements and modeling.” Water Resour. Res., 29(7), 2299-2312.
Sinokrot, B. A., and Gulliver, J. S. (2000). “In-stream flow impact on river water temperatures.” J. Hydraul. Res., 38(5), 339–349.
Smith, K. (1981). “The prediction of river water temperatures/prédiction des températures des eaux de rivière.” Hydrol. Sci. J., 26(1), 19–32.
Stefan, H. G., and Preud’homme, E. B. (1993). “Stream temperature estimation from air temperature.” J. Am. Water Resour. Assoc., 29(1), 27–45.
Texas Water Development Board. (1970). “Reconnaissance of water temperature of selected streams in southern Texas.”, Austin, TX.
Thomann, R. V., and Mueller, J. A. (1987). Principles of surface water quality modeling and control, Harper & Row, New York.
USGS (U.S. Geological Surevey). (2015). “USGS current water data for the nation.” 〈http://waterdata.usgs.gov/nwis/rt〉 (Jan. 23, 2015).
Webb, B., Clack, P., and Walling, D. (2003). “Water-air temperature relationships in a Devon river system and the role of flow.” Hydrol. Process., 17(15), 3069–3084.
Webb, B., and Nobilis, F. (1997). “Long-term perspective on the nature of the air-water temperature relationsihp: A case study.” Hydrol. Process., 11(2), 137–147.
Wool, T. A., Ambrose, R. B., Martin, J. L., and Comer, E. A. (2001). “Water quality analysis simulation program (WASP) user’s manual, version 6.” U.S. EPA, Atlanta.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 21 • Issue 10 • October 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: May 8, 2015
Accepted: Mar 30, 2016
Published online: Jun 14, 2016
Published in print: Oct 1, 2016
Discussion open until: Nov 14, 2016
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.