TECHNICAL PAPERS
Nov 1, 1993

Lake Water Temperature Simulation Model

Publication: Journal of Hydraulic Engineering
Volume 119, Issue 11

Abstract

Functional relationships to describe surface wind mixing, vertical turbulent diffusion, convective heat transfer, and radiation penetration based on data from lakes in Minnesota have been developed. These relationships have been introduced by regressing model parameters found either by analysis of field data or by calibration (minimizing the difference between measured and predicted temperatures) in simulations on individual lakes, against gross lake properties such as surface area or Secchi depth. Results of the deterministic lake water temperature stratification model using the functional relationships are not much different than results using the individual calibrations on a great variety of lake surface areas, depths, and transparencies. The model also requires no on‐lake weather but uses input from existing off‐lake weather stations. First order uncertainty analysis showed moderate sensitivity of simulated lake water temperatures to model coefficients. The numerical model which can be used without calibration has an average 1.1°C root mean square error, and 93% of measured lake water temperatures variability is explained by the numerical simulations, over wide ranges of lake morphometries, trophic levels, and meteorological conditions.

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References

1.
Adams, E. E., Cosler, D. J., and Helfrich, K. R. (1990). “Evaporation from heated water bodies: Predicting combined forced plus free convection.” Water Resour. Res., 26(3), 425–435.
2.
Aldama, A. A., Harleman, D. R. F., and Adams, E. E. (1989). “Hypolimnetic mixing in a weakly stratified lake.” Water Resour. Res., 25(5), 1014–1024.
3.
Bannister, T. T. (1974). “Production equations in terms of chlorophyll concentration, quantum yield, and upper limit to production.” Limnology and Oceanography, 19(1), 1–12.
4.
Bannister, T. T. (1979). “Quantitative description of steady state, nutrient‐saturated algal growth, including adaptation.” Limnology and Oceanography, 24(1), 76–96.
5.
Colman, J. A., and Armstrong, D. E. (1987). “Vertical eddy diffusivity determined with 222Rn in the benthic boundary layer of ice‐covered lakes.” Limnology and Oceanography, 32(3), 577–590.
6.
Dake, J. M. K. (1972). “Evaporative cooling of a body of water.” Water Resour. Res., 8(4), 1087–1091.
7.
Dake, J. M. K., and Harleman, D. R. F. (1969). “Thermal stratification in lakes: Analytical and laboratory studies.” Water Resour. Res., 5(2), 404–495.
8.
Dhamotharan, S. (1979). “A mathematical model for temperature and turbidity stratification dynamics in shallow reservoirs,” PhD thesis, University of Minnesota, 319.
9.
Ellis, C., and Stefan, H. G. (1991). “Water temperature dynamics and heat transfer beneath the ice cover of a lake.” Limnology and Oceanography, 36(2), 324–335.
10.
Ford, D. E. (1976). “Water temperature dynamics of dimictic lakes: Analysis and prediction using integral energy concepts,” PhD thesis, University of Minnesota, 432.
11.
Ford, D. E., and Stefan, H. G. (1980). “Thermal predictions using integral energy model.” J. Hydr. Div., ASCE, 106(1), 39–55.
12.
Gargett, A. E. (1984). “Vertical eddy diffusivity in the ocean interior.” J. Marine Res., 42(2), 359–393.
13.
Gargett, A. E., and Holloway, G. (1984). “Dissipation and diffusion by internal wave breaking.” J. Marine Res., 42(1), 15–27.
14.
Gerhard, H., Ilmberger, J., and Schimmele, M. (1990). “Vertical mixing in Uber‐linger See, western part of Lake Constance. Aquatic Sci., 53(3), 256–268.
15.
Harbeck, G. E., Jr. (1962). “A practical field technique for measuring reservoir evaporation utilizing mass‐transfer theory.” Prof. Paper 272E, U.S. Geological Survey, 101–105.
16.
Harleman, D. R. F. (1982). “Hydrothermal analysis of lakes and reservoirs.” J. Hydr. Div., ASCE, 108, 302–325.
17.
Heiskary, S. A., and Wilson, C. B. (1988). Minnesota lake water quality assessment report, Minnesota Pollution Control Agency, St. Paul, Minn., 49.
18.
Henderson‐Sellers, B., and Davies, A. M. (1989). “Thermal stratification modeling for oceans and lakes.” Annual Review of Numerical Fluid Mechanics and Heat Transfer, Vol. 2, C. L. Tien and T. H. Chawla, eds., Hemisphere, New York, N.Y., 85–156.
19.
Hondzo, M., Ellis, C., and Stefan, H. G. (1991). “Vertical diffusion in small stratified lake: Data and error analysis.” J. Hydraul. Engrg., ASCE, 117(10), 1352–1369.
20.
Hondzo, M., and Stefan, H. G. (1991). “Three case studies of lake temperature and stratification response to warmer climate.” Water Resour. Res., 27(8), 1837–1846.
21.
Hondzo, M., and Stefan, H. G. (1992). “Water temperature characteristics of lakes subjected to climate change.” Project Report No. 329, St. Anthony Falls Hydr. Lab., Univ. of Minnesota, Minneapolis, Minn., 185.
22.
Idso, S. B., and Gilbert, R. G. (1974). “On the universality of the Poole and Atkins Secchi disk‐light extinction equation.” J. Appl. Ecology, 11, 399–401.
23.
Idso, S. B., and Jackson, R. D. (1969). “Thermal radiation from the atmosphere.” J. Geophysical Res., 74(23), 5397–5403.
24.
Imberger, J. (1985). “The diurnal mixed layer.” Limnology and Oceanography, 30(4), 737–770.
25.
Imberger, J., and Patterson, J. C. (1989). “Physical limnology.” Advances in applied mechanics, J. W. Hutchinson and T. Y. Wu, eds., Vol. 27, Academic Press, San Diego, Calif., 303–475.
26.
Jassby, A., and Powell, T. (1975). “Vertical patterns of eddy diffusion during stratification in Castle lake, California.” Limnology and Oceanography, 20(4), 530–543.
27.
Lewis, W. M. Jr. (1983). “Temperature, heat, and mixing in Lake Valencia, Venezuela.” Limnology and Oceanography, 28(2), 273–286.
28.
Megard, R. O., Combs, W. S. Jr., Smith, P. D., and Knoll, A. S. (1979). “Attenuation of light and daily integral rates of photosynthesis attained by planktonic algae.” Limnology and Oceanography, 24(6), 1038–1050.
29.
McCormick, M. J. (1990). “Potential changes in thermal structure and cycle of Lake Michigan due to global warming.” Trans. American Fisheries Society, 119(2), 183–194.
30.
Osgood, R. A. (1984). “A 1984 study of the water quality of 43 metropolitan area lakes.” Publication No. 10‐84‐172, Metropolitan Council, St. Paul, Minn., 40.
31.
Osgood, R. A. (1989). “An evaluation of the effects of watershed treatment systems on summertime phosphorus concentration in metropolitan area lakes.” Publication No. 590‐89‐062, Metropolitan Council, St. Paul, Minn., 85.
32.
Poole, H. H., and Atkins, W. R. G. (1929). “Photo‐electric measurements of submarine illumination throughout the year.” J. Marine Biology Association of United Kingdom, 16, 297–324.
33.
Quay, P. D., Broecker, W. S., Hesslein, R. H., and Schindler, D. W. (1980). “Vertical diffusion rates determined by tritium tracer experiments in the thermocline and hypolimnion of two lakes.” Limnology and Oceanography, 25(2), 201–218.
34.
Riley, M. J., and Stefan, H. G. (1987). “Dynamic lake water quality simulation model ‘Minlake.’” Report No. 263, St. Anthony Falls Hydraulic Laboratory, University of Minnesota, Minneapolis, Minn., 140.
35.
Schertzer, W. M., and Sawchuk, A. M. (1990). “Thermal structure of the lower Great Lakes in a warm year: Implications for the occurrence of hypolimnion anoxia.” Trans. Amer. Fisheries Society, 119(2), 195–209.
36.
Schindler, D. W., Beaty, K. G., Fee, E. J., Cruikshank, D. R., DeBruyn, E. R., Findley, D. L., Londsey, G. A., Sherer, J. A., Stainton, M., and Turner, M. A. (1990). “Effects of climatic warming on lakes of the Central Boreal Forest.” Science, 250(16), 967–970.
37.
Shapiro, J., and Pfannkuch, H. (1973). The Minneapolis chain of lakes: A study of urban drainage and its effects 1971–1973, Limnological Research Center, University of Minnesota, Minneapolis, Minn.
38.
Smith, C. R., and Baker, K. S. (1981). “Optical properties of the clearest natural waters.” Appl. Optics, 20(2), 177–184.
39.
Stefan, H. G., Cardoni, J. J., Schiebe, F. R., and Cooper, C. M. (1983). “Model of light penetration in a turbid lake.” Water Resour. Res., 19(1), 109–120.
40.
Stefan, H. G., Dhamotharan, S., and Schiebe, F. R. (1982). “Temperature/sediment model for a shallow lake.” J. Envir. Engrg. Div., ASCE, 108(4), 750–765.
41.
Stefan, H. G., and Ford, D. E. (1975). “Temperature dynamics in dimictic lakes.” J. Hydr. Div., ASCE, 101(1), 97–114.
42.
Stefan, H. G., Gulliver, J., Hahn, M. G., and Fu, A. Y. (1980a). “Water temperature dynamics in experimental field channels: Analysis and modeling.” Report No. 193, St. Anthony Falls Hydraulic Laboratory, University of Minnesota, Minneapolis, Minn.
43.
Stefan, H. G., Hanson, M. J., Ford, D. E., and Dhamotharan, S. (1980b). “Stratification and water quality predictions in shallow lakes and reservoirs.” Proc. Second Intl. Symp. on Stratified Flows, International Association for Hydraulic Research, 1033–1043.
44.
Sweers, H. E. (1976). “A nomogram to estimate the heat‐exchange coefficient at the air‐water interface as a function of wind speed and temperature; a critical survey of some literature.” J. Hydrol., 30, 375–401.
45.
Ward, P. R. B. (1977). “Diffusion in lake hypolimnia.” Proc. 17th Congress Int. Association for Hydraulic Research, International Association for Hydraulic Research, 103–110.
46.
Willis, R., and Yeh, W.W‐G. (1987). Groundwater systems planning and management. Prentice‐Hall, Englewood Cliffs, N.J., 415.
47.
Wright, D., Lawrenz, R., Popp, W., and Danks, M. (1988). “Acid precipitation mitigation program.” Progress Report Thrush Lake Minnesota, Minnesota Dept. of Natural Resour. Div. of Fish and Wildlife Ecological Services Section, Kear‐neysville, W.V., 177.
48.
Wu, J. (1969). “Wind stress and surface roughness at air‐sea interface.” J. Geophysical Res., 74(2), 444–455.

Information & Authors

Information

Published In

Go to Journal of Hydraulic Engineering
Journal of Hydraulic Engineering
Volume 119Issue 11November 1993
Pages: 1251 - 1273

History

Received: May 26, 1992
Published online: Nov 1, 1993
Published in print: Nov 1993

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Authors

Affiliations

Midhat Hondzo
Res. Assoc., St. Anthony Falls Hydr. Lab., Dept. of Civ. and Min. Engrg., Univ. of Minnesota, Minneapolis, MN 55414
Heinz G. Stefan, Member, ASCE
Prof. and Assoc. Dir., St. Anthony Falls Hydr. Lab., Dept. of Civ. and Min. Engrg., Univ. of Minnesota, Minneapolis, MN

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