A Monte Carlo Approach to Estimation and Prediction

  • Kurt Fedra

Abstract

The model representation of complex environmental systems requires numerous simplifications; frequently, arbitrary choices of how to formally represent the relationships between causes and effects have to be made, since these relationships are neither obvious nor easy to detect. Environmental systems in toto do not easily yield to the classical scientific tool of planned experimentation. Consequently, the analyst has to utilize whatever bits of information may be available, which as a rule are very few and not strictly appropriate in terms of the problems addressed. A priori knowledge about the structure and function of any ecosystem is generally poor, and reliable quantitative information on the governing processes and their rates and interrelationships insufficient. Consequently, building and testing models and finally applying them for predictive purposes often consists of a more or less formalized trial-and-error iterative process of estimation, testing, and improvement. The following discussion proposes an approach for formalizing this process of model building, calibration, and application; it emphasizes the interdependences of the individual steps in the process. The approach proposed is based on the recognition of uncertainty as an inevitable element in modeling, and uses straightforward Monte Carlo techniques to cope with this uncertainty.

Keywords

Biomass Phosphorus Chlorophyll Phytoplankton Respiration 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Argentesi, F. and Olivi, L. (1976). Statistical sensitivity analysis of a simulation model for the biomass-nutrient dynamics in aquatic ecosystems. Proceedings of the Summer Computer Simulation Conference, 4th, pp. 389–393.Google Scholar
  2. Attersee Report (1976). Vorläufige Ergebnisse des OECD-Seeneutrophierungs und des MaB-Programms. Weyregg, Austria.Google Scholar
  3. Attersee Report (1977). Vorläufige Ergebnisse des OECD-Seeneu trophierungs und des MaB-Programms. Weyregg, Austria.Google Scholar
  4. Beck, M.B. (1979a). System Identification, Estimation, and Forecasting of Water Quality: Part I: Theory. WP-79–31. International Institute for Applied Systems Analysis, Laxenburg, Austria.Google Scholar
  5. Beck, M.B. (1979b). Applications of System Identification and Parameter Estimation in Water Quality Modeling. WP-79–99. International Institute for Applied Systems Analysis, Laxenburg, Austria.Google Scholar
  6. Beck, M.B., Halfon, E., and van Straten, G. (1979). The Propagation of Errors and Uncertainty in Forecasting Water Quality — Part I: Method. WP-79–100. International Institute for Applied Systems Analysis, Laxenburg, Austria.Google Scholar
  7. Benson, M. (1979). Parameter fitting in dynamic models. Ecological Modelling, 6: 97–115.CrossRefGoogle Scholar
  8. Bierman, V.J., Dolan, D.M., Stoermer, E.F., Gannon, J.E., and Smith, V.E. (1980). The Development and Calibration of a Spatially Simplified Multi-Class Phytoplankton Model for Saginaw Bay, Lake Huron. Contribution No. 33. Great Lakes Environmental Planning Study, US Environmental Protection Agency, Grosse Ile, Michigan.Google Scholar
  9. Biologische Anstalt Helgoland (1964–1979). Jahresberichte. Biologische Anstalt Helgoland, Hamburg.Google Scholar
  10. Conrad, M. (1976). Patterns of biological control in ecosystems. In B.C.Patten (Editor), Systems Analysis and Simulation in Ecology, Volume IV. Academic Press, New York, pp. 431–457.Google Scholar
  11. DiToro, D.M. and van Straten, G. (1979). Uncertainty in the Parameters and Predictions of Phytoplankton Models. WP-79–27. International Institute for Applied Systems Analysis, Laxenburg, Austria.Google Scholar
  12. DiToro, D.M., O’Connor, DJ., and Thomann, R.V. (1971). A dynamic model of phytoplankton populations in the Sacramento-San Joaquin Delta. Advances in Chemistry Series, 106: 131– 180.Google Scholar
  13. Fedra, K. (1979a). Modeling Biological Processes in the Aquatic Environment; With Special Reference to Adaptation. WP-79–20. International Institute for Applied Systems Analysis, Laxenburg, Austria.Google Scholar
  14. Fedra, K. (1979b). A Stochastic Approach to Model Uncertainty: a Lake Modeling Example. WP-79– 63. International Institute for Applied Systems Analysis, Laxenburg, Austria.Google Scholar
  15. Fedra, K. (1980a). Mathematical modeling — a management tool for aquatic ecosystems? Helgoländer Wissenschaftliche Meeresuntersuchungen, 34(2):221–235.Google Scholar
  16. Fedra, K. (1980b). Austrian Lake Ecosystem Case Study: Achievements, Problems and Outlook After the First Year of Research. CP-80–41. International Institute for Applied Systems Analysis, Laxenburg, Austria.Google Scholar
  17. Fedra, K. (1981a). Estimating model prediction accuracy: a stochastic approach to ecosystem modeling. In D.M. Dubois (Editor), Progress in Ecological Engineering and Management by Mathematical Modelling. Cebedoc, Liège.Google Scholar
  18. Fedra, K. (1981b). Pelagic foodweb analysis: hypothesis testing by simulation. Proceedings of the 15th European Marine Biology Symposium. Kieler Meeresforschung, Sonderheft 5:240–258.Google Scholar
  19. Fedra, K. (1982). Environmental Modeling Under Uncertainty: Monte Carlo Simulation. WP-82–42. International Institute for Applied Systems Analysis, Laxenburg, Austria.Google Scholar
  20. Fedra, K., van Straten, G., and Beck, B. (1981). Uncertainty and arbitrariness in ecosystems modeling: a lake modeling example. Ecological Modelling, 13: 87–110.CrossRefGoogle Scholar
  21. Flögl, H. (1974). Die Reinhaltung der Salzkammergutsee. Österreichische Wasserwirtschaft, 26:1–11Google Scholar
  22. Gjessing, D.T. (1979). Environmental remote sensing. Physics in Technology, 10: 266–271.CrossRefGoogle Scholar
  23. Greve,W. (1981). Invertebrate predator control in a coastal marine ecosystem: the significance of Beroe gracilis (Ctenophora). Proceedings of the 15th European Marine Biology Symposium. Kieler Meeresforschung, Sonderheft 5:211–217.Google Scholar
  24. Hagmeier, E. (1978). Variations in phytoplankton near Helgoland. Rapports et Procès Verbaux, Conseil International pour l’Exploration de la Mer, 172: 361–363.Google Scholar
  25. Halfon, E. (Editor) (1979). Theoretical Systems Ecology. Academic Press, New York.Google Scholar
  26. Hornberger, G.M. and Spear, R.C. (1980). Eutrophication in Peel Inlet — I. Problem-defining behavior and a mathematical model for the phosphorus scenario. Water Research, 14: 29–42.CrossRefGoogle Scholar
  27. Imboden, D.M. and Gächter, R. (1978). A dynamic lake model for trophic state prediction. Ecological Modelling, 4: 77–98.CrossRefGoogle Scholar
  28. Kremer, J.N. and Nixon, S.W. (1978). A Coastal Marine Ecosystem. Ecological Studies 24. Springer, New York.Google Scholar
  29. Lewis, S. and Nir, A. (1978). A study of parameter estimation procedures of a model of lake phosphorus dynamics. Ecological Modelling, 4: 99–118.CrossRefGoogle Scholar
  30. Lucht, F. and Gillbricht, M. (1978). Long-term observations on nutrient contents near Helgoland in relation to nutrient input of the river Elbe. Rapports et Procès Verbaux, Conseil International pour l’Exploration de la Mer, 172: 358–360.Google Scholar
  31. Moog, O. (1980). Jahresbericht 1979. Arbeiten aus dem Labor, Weyregg, 4/1980.Google Scholar
  32. Müller, G. (1979). Jahresbericht 1978. Arbeiten aus dem Labor, Weyregg, 3/1979.Google Scholar
  33. Nihoul, J.C.J. (1975). Modelling of Marine Systems. Elsevier Oceanography Series 10. Elsevier, Amsterdam.Google Scholar
  34. O’Neill, R.V. and Gardner, R.H. (1979). Sources of uncertainty in ecological models. In B.P. Zeigler, M.S. Elzas, GJ. Klir, and T.I. Oren (Editors), Methodology in Systems Modelling and Simulation. North-Holland, Amsterdam, pp. 447–463.Google Scholar
  35. O’Neill, R.V. and Rust, B. (1979). Aggregation error in ecological models. Ecological Modelling, 7: 91–105.CrossRefGoogle Scholar
  36. Park, R.A. et al. (1974). A generalized model for simulating lake ecosystems. Simulation, August: 33–56.Google Scholar
  37. Pielou, E.C. (1975). Ecological Diversity. Wiley, New York.Google Scholar
  38. Popper, K.R. (1959). The Logic of Scientific Discovery. Hutchinson, London.Google Scholar
  39. Reckhow, K.H. (1979). The use of a simple model and uncertainty analysis in lake management. Water Resources Bulletin, 15:601–611.Google Scholar
  40. Scavia, D. (1980a). An ecological model of Lake Ontario. Ecological Modelling, 8: 49–78.CrossRefGoogle Scholar
  41. Scavia, D. (1980b). The need for innovative verification of eutrophication models. In R.V. Thomann and T.O. Barnwell, Jr. (Editors), Workshop on Verification of Water Quality Models. EPA-600/9-80-016. US Environmental Protection Agency, Athens, Georgia.Google Scholar
  42. Spear, R.C. and Hornberger, G.M. (1980). Eutrophication in Peel Inlet — II. Identification of critical uncertainties via generalized sensitivity analysis. Water Research, 14: 43–49.CrossRefGoogle Scholar
  43. Steele, J.H. (1962). Environmental control of photosynthesis in the sea. Limnology and Oceanography, 7:137–150.CrossRefGoogle Scholar
  44. Steele, J.H. (1974). The Structure of Marine Ecosystems. Harvard University Press, Cambridge, Massachusetts.Google Scholar
  45. Steele, J.H. (Editor) (1978). Spatial Pattern in Plankton Communities. Plenum Press, New York.Google Scholar
  46. Straskraba, M. (1976). Development of an Analytical Phytoplankton Model with Parameters Empirically Related to Dominant Controlling Variables. Symposium für Umweltbiophysik, Abhandlungen der Akademie der Wissenschaften der DDR, Jg. 1974. Akademieverlag, Berlin, German Democratic Republic.Google Scholar
  47. Straskraba, M. (1979). Natural control mechanisms in models of aquatic ecosystems. Ecological Modelling, 6: 305–321.CrossRefGoogle Scholar
  48. Tiwari, J.L., Hobbie, J.E., Reed, J.P., Stanley, D.W., and Miller, M.C. (1978) Some stochastic differential equation models for an aquatic ecosystem. Ecological Modelling, 4: 3–27.CrossRefGoogle Scholar
  49. van Straten, G. (1980). Analysis of Model and Parameter Uncertainty in Simple Phytoplankton Models for Lake Balaton. WP-80–139. International Institute for Applied Systems Analysis, Laxenburg, Austria.Google Scholar
  50. van Straten, G. and de Boer, B. (1979). Sensitivity to Uncertainty in a Phytoplankton–Oxygen Model for Lowland Streams. WP-79–38. International Institute for Applied Systems Analysis, Laxenburg, Austria.Google Scholar
  51. Vollenweider, R.A. (1969). Possibilities and limits of elementary models concerning the budget of substances in lakes. Archiv für Hydrobiologie, 66 (1): 1–36.Google Scholar
  52. Vollenweider, R.A. (1975). Input–output models with special reference to the phosphorus loading concept in limnology. Schweizerische Zeitschrift für Hydrologie, 37: 53–84.CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  • Kurt Fedra
    • 1
  1. 1.International Institute for Applied Systems AnalysisLaxenburgAustria

Personalised recommendations