Predicting Hourly Stream Temperatures Using the Equilibrium Temperature Model


Water temperature is a key physical habitat determinant in lotic ecosystems as it influences many physical, chemical and biological properties of rivers. Hence, a good understanding of the thermal regime of rivers is essential for effective management of water and fisheries resources. This study deals with the modeling of hourly stream water temperature using the equilibrium temperature model. This water temperature model was applied on two thermally different watercourses, namely, the Little Southwest Miramichi River (LSWM) and Catamaran Brook (CatBk; New Brunswick). The equilibrium temperature model is a simplified version of a deterministic model. As such, in the equilibrium temperature model the total heat flux at the surface is assumed proportional to the difference between the water temperature and an equilibrium temperature. In the present study, the equilibrium temperature was assumed to vary linearly with hourly air temperature. This study showed that there was a good relationship between the equilibrium and air temperature at the hourly time scale. The root-mean-square error (RMSE) obtained with the hourly equilibrium temperature model was similar to results reported in previous studies with values of 1.05°C (CatBk) and 1.36°C (LSWM). The model’s performance was best in late summer and autumn when water levels were low. In contrast, the presence of snowmelt in the spring resulted in poorer performances. This study also showed good results in estimating the daily mean (Tmean) and maximum (Tmax) water temperatures from the predicted hourly water temperatures, which were often required in fishery management.

Share and Cite:

Hébert, C. , Caissie, D. , Satish, M. and El-Jabi, N. (2015) Predicting Hourly Stream Temperatures Using the Equilibrium Temperature Model. Journal of Water Resource and Protection, 7, 322-338. doi: 10.4236/jwarp.2015.74026.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Caissie, D. (2006) The Thermal Regime of Rivers: A Review. Freshwater Biology, 51, 1389-1406.
[2] Webb, B.W., Hannah, D.M., Moore, R.D., Brown, L.E. and Nobilis, F. (2008) Recent Advances in Stream and River Temperature Research. Hydrological Processes, 22, 902-918.
[3] Breau, C., Cunjak, R.A. and Bremset, G. (2007) Age-Specific Aggregation of Wild Juvenile Atlantic Salmon Salmo salar at Cool Water Sources during High Temperature Events. Journal of Fish Biology, 71, 1179-1191.
[4] Raphael, J.M. (1962) Prediction of Temperature in Rivers and Reservoirs. Journal of the Power Division, 88, 157-181.
[5] Brown, G.W. (1969) Predicting Temperatures of Small Streams. Water Resources Research, 5, 68-75.
[6] Markarian, R.K. (1980) A Study of the Relationship between Aquatic Insect Growth and Water Temperature in a Small Stream. Hydrobiologia, 75, 81-95.
[7] Wichert, G.A. and Lin, P. (1996) A Species Tolerance Index of Maximum Water Temperature. Water Quality Resources Journal of Canada, 31, 875-893.
[8] Kinouchi, T., Yagi, H. and Miyamoto, M. (2007) Increase in Stream Temperature Related to Anthropogenic Heat Input from Urban Wastewater. Journal of Hydrology, 335, 78-88.
[9] Bradley, A.A., Holly, F.M., Walker, W.K. and Wright, S.A. (1998) Estimation of Water Temperature Exceedance Probabilities Using Thermo-Hydrodynamic Modeling. Journal of the American Water Association, 34, 467-480.
[10] Moore, R.D., Spittlehouse, D.L. and Story, A. (2005) Riparian Microclimate and Stream Temperature Response to Forest Harvesting: A Review. Journal of the American Water Resources Association, 41, 813-834.
[11] Morrison, J., Quick, M.C. and Foreman, M.G.G. (2002) Climate Change in the Fraser River Watershed: Flow and Temperature Projections. Journal of Hydrology, 263, 230-244.
[12] Tung, C.P., Lee, T.Y. and Yang, Y.C. (2006) Modeling Climate-Change Impacts on Stream Temperature of Formosan Landlocked Salmon Habitat. Hydrological Processes, 20, 1629-1649.
[13] Morin, G. and Couillard, D. (1990) Predicting River Temperatures with a Hydrological Model. In: Cheremisinoff, N.P., Ed., Encyclopedia of Fluid Mechanic, Surface and Groundwater Flow Phenomena, Gulf Publishing Company, Houston, Vol. 10, 171-209.
[14] Edinger, J.E., Duttweiler, D.W. and Geyer, J.C. (1968) The Response of Water Temperatures to Meteorological Conditions. Water Resources Research, 4, 1137-1143.
[15] Caissie, D., Satish, M.G. and El-Jabi, N. (2005) Predicting River Water Temperatures Using the Equilibrium Temperature Concept Method with Applications on Miramichi River Catchments (New Brunswick, Canada). Hydrological Processes, 19, 2137-2159.
[16] Mohseni, O. and Stefan, H.G. (1999) Stream Temperature-Air Temperature Relationships: A Physical Interpretation. Journal of Hydrology, 218, 128-141.
[17] Bogan, T., Mohseni, O. and Stefan, H.G. (2003) Stream Temperature-Equilibrium Temperature Relationship. Water Resources Research, 39, 1245.
[18] Bogan, T., Stefan, H.G. and Mohseni, O. (2004) Imprints of Secondary Heat Sources on the Stream Temperature/Equilibrium Temperature Relationship. Water Resources Research, 40, Article ID: W12510.
[19] Larnier, K., Roux, H., Dartus, D. and Croze, O. (2010) Water Temperature Modeling in the Garonne River (France). Knowledge and Management of Aquatic Ecosystems, 398, 20.
[20] Caissie, D., Satish, M.G. and El-Jabi, N. (2007) Predicting Water Temperatures Using a Deterministic Model: Application on Miramichi River Catchments (New Brunswick, Canada). Journal of Hydrology, 336, 303-315.
[21] Marcotte, N. and Duong, V.L. (1973) Le calcul de la temperature de l’eau des rivières. Journal of Hydrology, 18, 273-287.
[22] Younus, M., Hondzo, M. and Engel, B.A. (2000) Stream Temperature Dynamics in Upland Agricultural Watershed. Journal of Environmental Engineering, 126, 518-526.
[23] Hondzo, M. and Stefan, H.G. (1994) Riverbed Heat Conduction Prediction. Water Resources Research, 30, 1503-1513.
[24] Caissie, D. and El-Jabi, N. (1995) Hydrology of the Miramichi River Drainage Basin. In: Chadwick, E.M.P., Ed., Water, Science, and the Public: The Miramichi Ecosystem, Canadian Special Publication of Fisheries and Aquatic Sciences No. 123. NRC Research Press, Ottawa, 83-93.
[25] Cunjak, R.A., Caissie, D. and El-Jabi, N. (1990) The Catamaran Brook Habitat Research Project: Description and General Design of Study. Canadian Technical Report of Fisheries and Aquatic Sciences, No. 1751, 14 p.
[26] Novotny, V. and Krenkel, P.A. (1973) Simplified Mathematical Model of Temperature Changes in Rivers. Journal of the Water Pollution Control Federation, 45, 240-248.
[27] Gu, R. (1998) A Simplified River Temperature Model and Its Application to Streamflow Management. Journal of Hydrology, 37, 35-54.
[28] Marce, R. and Armengol, J. (2008) Modelling River Water Temperature Using Deterministic, Empirical, and Hybrid Formulations in a Mediterranean Stream. Hydrological Processes, 22, 3418-3430.
[29] Herb, W.R. and Stefan, H.G. (2011) Modified Equilibrium Temperature Models for Cold-Water Streams. Water Resources Research, 47, 13.
[30] Caissie, D., El-Jabi, N. and St-Hilaire, A. (1998) Stochastic Modelling of Water Temperatures in a Small Stream Using Air to Water Relations. Canadian Journal of Civil Engineering, 25, 250-260.
[31] Chenard, J-F. and Caissie, D. (2008) Stream Temperature Modelling Using Artificial Neural Networks: Application on Catamaran Brook, New Brunswick, Canada. Hydrological Processes, 22, 3361-3372.
[32] Beschta, R.L., Bilby, R.E., Brown, G.W., Holtby, L.B. and Hofstra, T.D. (1987) Stream Temperature and Aquatic Habitat: Fisheries and Forestry Interactions. In: Salo, E.O. and Cundy, T.W., Eds., Streamside Management: Forestry and Fishery Interactions, University of Washington, Institute of Forest Resources, Seattle, Contribution No. 57, 191-232.
[33] Erickson, T.R. and Stefan, H.G. (2000) Linear Air/Water Temperature Correlations for Streams during Open Water Periods. Journal of Hydrologic Engineering, 5, 317-321.
[34] Stefan, H.G. and Preud’homme, E.B. (1993) Stream Temperature Estimation from Air Temperature. JAWRA Journal of the American Water Resources Association, 29, 27-45.

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.