Analysis of Prediction Uncertainty: Monte Carlo Simulation and Nonlinear Least-Squares Estimation of a Vertical Transport Submodel for Lake Nantua

  • F. Chahuneau
  • S. des Clers
  • J. A. Meyer


Lake Nantua (see Figure 1 for lake characteristics) is a small eutrophic alpine lake undergoing frequent algal blooms (the blue-green alga Oscillatoria rubescens). The entire water body is thermally stratified from April to December and completely mixed after the late-autumn overturn (the lake is monomictic). Given the rather small lake area and its simple morphometry, the water body is considered horizontally homogeneous and a one-dimensional submodel was developed to describe vertical transport processes (eddy diffusion and advection).


Dispersion Coefficient Eddy Diffusion Global Solar Radiation Prediction Uncertainty Monte Carlo Simulation Result 
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  1. Bella, A.D. (1970). Simulating the effect of sinking and vertical mixing on algal population dynamics. Journal of the Water Pollution Control Federation, 42(5) part 2:140–152.Google Scholar
  2. Bengtsson, L. (1978). Wind induced circulation in lakes. Nordic Hydrology, 9:75–94.Google Scholar
  3. Bowden, K.F. and Hamilton, P. (1975). Some experiments with a numerical model of circulation and mixing in a tidal estuary. Estuarine and Coastal Marine Science, 3:281–301.CrossRefGoogle Scholar
  4. Chahuneau, F. and des Clers, S. (in preparation). Use of routine meteorological data for simulation of thermal seasonal evolution of temperate lakes.Google Scholar
  5. Ford, D.E. and Thornton, K.W. (1979). Time and length scales for the 1-dimensional assumption and its relation to ecological models. Water Resources Research, 15(1): 113–120.CrossRefGoogle Scholar
  6. Lehman, R.S. (1977). Computer Simulation and Modelling. An Introduction. Lawrence Erlbaum Associates, Hillsdale, New Jersey.Google Scholar
  7. Leonard, B.P., Vachtsevanos, G.J., and Abood, K.A. (1978). Unsteady-state two-dimensional salinity intrusion model for an estuary. In C.A. Brebbia (Editor), Applied Numerical Modelling. Pentech Press, Plymouth, UK, pp. 113–123.Google Scholar
  8. Lerman, A. (1979). Geochemical Processes. Water and Sediment Environments. Wiley, New York.Google Scholar
  9. Li,Y.-H. (1973). Vertical eddy diffusion coefficient in Lake Zürich. Schweizerische Zeitschrift für Hydrologie, 35(1): 1–7.CrossRefGoogle Scholar
  10. Marquardt, D.W. (1963). An algorithm for least-squares estimation of non-linear parameters. Journal of the Society for Industrial and Applied Mathematics, 11:431–441.CrossRefGoogle Scholar
  11. Meeter, D.A. (1968). Program GAUSHAUS. Numerical Analysis Laboratory, University of Wisconsin at Madison, Madison, Wisconsin.Google Scholar
  12. Munk, W.H and Anderson, E.R. (1948). Notes on a theory of the thermocline. Journal of Marine Research, 7(3): 276–295.Google Scholar
  13. Newbold, J.D. and Ligget, J.A. (1974). Oxygen depletion model for Cayuga Lake. Journal of the Environmental Engineering Division, American Society of Civil Engineers, 100(1): 41–59.Google Scholar
  14. O’Neill, R.V. and Gardner, R.H. (1979). Sources of uncertainty in ecological models. In B.P. Zeigler, M.S. Elzas, G.J. Klir, and T.I. Ören (Editors), Methodology in Systems Modelling and Simulation. North-Holland, Amsterdam, pp. 447–463.Google Scholar
  15. Orlob, G.T. and Selna, L.S. (1970). Temperature variations in deep reservoirs. Journal of the Hydraulics Division, American Society of Civil Engineers, 96(2): 391–410.Google Scholar
  16. Remson, I., Hornberger, G.H., and Holz, F.J. (1971). Numerical Methods in Subsurface Hydrology. Wiley-Interscience, New York.Google Scholar
  17. Ryan, P.J. and Harleman, D.R.F. (1971). Prediction of the annual cycle of temperature changes in a stratified lake or reservoir: mathematical model and user’s manual. MIT Report 137. MIT Press, Cambridge, Massachusetts.Google Scholar
  18. Svensson, U. (1978). Examination of the summer stratification. Nordic Hydrology, 9(2): 105–120.Google Scholar
  19. Tetra Tech. (1978). Rates, constants and kinetics formulations in surface water quality modeling. Report TC-3689, EPA/600/3-78/105. US Environmental Protection Agency, Duluth, Minnesota.Google Scholar
  20. Tiwari, J.L., Hobbie, J.E., Reed, J.P., Stanley, D.W., and Miller, M.C. (1978). Some stochastic differential equation models of an aquatic ecosystem. Ecological Modelling, 4:3–27.CrossRefGoogle Scholar
  21. Tucker, W.A. and Green, A.W. (1977). A time-dependent model of the lake-averaged vertical temperature distribution of lakes. Limnology and Oceanography, 22(4): 687–699.CrossRefGoogle Scholar
  22. Vila, J.P. (1980). Modélisation non-linéaire. Le problème de l’identification. Considérations numériques et statistiques. Internal Report. Laboratoire de Biométrie, INRA-CNRS, 78350 Jouy-en-Josas, France.Google Scholar
  23. Walters, R.A., Carey, G.F., and Winter, D.K. (1978). Temperature computation for temperate lakes. Applied Mathematical Modelling, 2:41–48.CrossRefGoogle Scholar

Copyright information

© International Institute for Applied Systems Analysis, Laxenburg/Austria 1983

Authors and Affiliations

  • F. Chahuneau
    • 1
  • S. des Clers
    • 2
  • J. A. Meyer
    • 2
  1. 1.Laboratoire de BiométrieINRA-CNRZ Domaine de VilvertJouy-en-JosasFrance
  2. 2.Laboratoire de ZoologieEcole Normale SupérieureCedex 05 ParisFrance

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