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Model calibration/parameter estimation techniques and conceptual model error

  • Petros Gaganis
Conference paper
Part of the NATO Science for Peace and Security Series C: Environmental Security book series (NAPSC)

In a modeling exercise, errors in the model structure cannot be avoided because they arise from our limited capability to exactly describe mathematically the complexity of a physical system. The effect of model error on model predictions is not random but systematic, therefore, it does not necessarily have any probabilistic properties that can be easily exploited in the construction of a model performance criterion. The effect of model error varies in both space and time. It is also different for the flow and the solute transport components of a groundwater model and may have a significant impact on parameter estimation, uncertainty analyses and risk assessments. Structural errors may result in a misleading evaluation of prediction uncertainty associated with parameter error because model sensitivity to uncertain parameters may be quite different than that of the correct model. A substantial model error may significantly degrade the usefulness of model calibration and the reliability of model predictions because parameter estimates are forced to compensate for the existing structural errors. Incorrect uncertainty analyses and estimated parameters that have little value in predictive modeling could potentially lead to an engineering design failure or to a selection of a management strategy that involves unnecessary expenditures. A complementary to classical inverse methods model calibration procedure is presented for assessing the uncertainty in parameter estimates associated with model error. This procedure is based on the concept of a per-datum calibration for capturing the spatial and temporal behavior of model error. A set of per-datum parameter estimates obtained by this new method defines a posterior parameter space that may be translated into a probabilistic description of model predictions. The resulted prediction uncertainty represents a reflection on model predictions of available information regarding the dependent variables and measures the level of confidence in model performance.

Keywords

model calibration parameter estimation conceptual error model error inverse method uncertainty groundwater modeling 

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References

  1. Beck, M.B., 1987, Water quality modeling: A review of the analysis of uncertainty, Water Resources Research, 23: 1393–1442.CrossRefGoogle Scholar
  2. Beckie, R., 1996, Measurement scale, network sampling scale, and ground water model parameters, Water Resources Research, 32: 65–76.CrossRefGoogle Scholar
  3. Beven, K.J. and Binley, A.M., 1992, The future of distributed models: Model calibration and uncertainty prediction, Hydrological Processes, 6: 279–298.CrossRefGoogle Scholar
  4. Beven, K.J. and Freer, J., 2001, Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems using the GLUE methodology, Journal of Hydrology, 249: 11–29.CrossRefGoogle Scholar
  5. Carrera, J. and Neuman, S.P., 1986, Estimation of aquifer parameters under transient and steady state conditions: 1. Maximum likelihood method incorporating prior information, Water Resources Research, 22: 199–210.CrossRefGoogle Scholar
  6. Carrera, J., Alcolea, A., Medina, A., Hidalgo, J., and Slooten, L.J., 2005, Inverse problem in hydrogeology, Hydrogeology Journal, 13: 206–222.CrossRefGoogle Scholar
  7. Cooley, R.L., 1982, Incorporation of prior information on parameters into nonlinear regression groundwater models, 1, Theory, Water Resources Research, 18: 965–976.CrossRefGoogle Scholar
  8. Cooley, R.L., 1983, Incorporation of prior information on parameters into nonlinear regression groundwater models, 2, Applications, Water Resources Research, 19: 662–676.CrossRefGoogle Scholar
  9. Cooley, R.L., Konikow, L.F., and Naff, R.L., 1986, Nonlinear-regression groundwater flow modeling of a deep regional aquifer system, Water Resources Research, 22: 1759–1778.CrossRefGoogle Scholar
  10. Dagan, G., 1989, Flow and Transport in Porous Formations, Springer-Verlag, New York.Google Scholar
  11. Freeze, R.A., Massmann, J., Smith, L., Sperling, T., and James, B., 1990, Hydrological decision analysis: 1. A framework, Ground Water, 28: 738–766.CrossRefGoogle Scholar
  12. Gaganis, P. and Smith, L., 2001, A Bayesian approach to the quantification of the effect of model error on the predictions of groundwater models, Water Resources Research, 37: 2309–2322.CrossRefGoogle Scholar
  13. Gaganis, P. and Smith, L., 2006, Evaluation of the uncertainty of groundwater model predictions associated with conceptual errors: A per-datum approach to model calibration, Advances in Water Resources, 29: 503–514.CrossRefGoogle Scholar
  14. Gaganis, P. and Smith, L., 2008, Accounting for model error in risk assessments: Alternatives to adopting a bias towards conservative risk estimates in decision models, Advances in Water Resources, 31: 1074–1086.CrossRefGoogle Scholar
  15. Gavalas, G.R., Shah, P.C., and Seinfeld, J.H., 1976, Reservoir history matching by Bayesian estimation, Society of Petroleum Engineers Journal, 16: 337–350.CrossRefGoogle Scholar
  16. Gerhar, L.W., 1993, Stochastic Subsurface Hydrogeology, Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
  17. Gupta, H.V., Sorooshian, S., and Yapo, P.O., 1998, Toward improved calibration of hydro-logic models: Multiple and noncommensurable measures of information, Water Resources Research, 34: 751–763.CrossRefGoogle Scholar
  18. Hill, M.C. and Tiedeman, C.R., 2007, Effective Groundwater Model Calibration: With Analysis of Data, Sensitivities, Predictions, and Uncertainty, Wiley-Interscience, London, UK.Google Scholar
  19. Kitanidis, P.K. and Vorvoris, E.G., 1983, A geostatistical approach to the inverse problem in groundwater modeling (steady state) and one-dimensional simulations, Water Resources Research, 19: 677–690.CrossRefGoogle Scholar
  20. Konikow, L.F. and Bredehoeft, J.D., 1992, Ground-water models cannot be validated, Advances in Water Resources, 15: 75–83.CrossRefGoogle Scholar
  21. Luis, S.J. and McLaughlin, D., 1992, A stochastic approach to model validation, Advances in Water Resources, 15: 15–32.CrossRefGoogle Scholar
  22. McLaughlin, D. and Townley, L.R., 1996, A reassessment of the groundwater inverse problem, Water Resources Research, 32: 1131–1161.CrossRefGoogle Scholar
  23. Morgan, M.G., Henrion, M., and Small, M., 1990, Uncertainty: A Guide to Dealing with Uncertainty in Quantitative Risk and Policy Analysis, Cambridge University Press, Cambridge University Press.Google Scholar
  24. Neuman, S.P., 1973, Calibration of distributed groundwater flow models viewed as a multiple-objective decision process under uncertainty, Water Resources Research, 9: 1006–1021.CrossRefGoogle Scholar
  25. Neuman, S.P., 2003, Maximum likelihood Bayesian averaging of uncertain model predictions, Stochastic Environmental Research and Risk Assessment, 17: 291–305.CrossRefGoogle Scholar
  26. Poeter, E.P. and Hill, M.C., 1997, Inverse models: A necessary next step in ground-water modeling, Ground Water, 35: 250–260.CrossRefGoogle Scholar
  27. Schwarz, G., 1978, Estimating the dimension of a model, Annals of Statistics, 6: 461–465.CrossRefGoogle Scholar
  28. Smith, L. and Gaganis, P., 1998, Strontium-90 migration to water wells at the Chernobyl nuclear power plant: Re-evaluation of a decision model, Environmental and Engineering Geoscience, IV: 161–174.Google Scholar
  29. Sun, N.-Z., Yang, S.-L., and Yeh, W.W.-G., 1998, A proposed stepwise regression method for model structure identification, Water Resources Research, 34: 2561–2572.CrossRefGoogle Scholar
  30. Ye M., Neuman, S.P., and Meyer, P.D., 2004, Maximum likelihood Bayesian averaging of spatial variability models in unsaturated fractured tuff, Water Resources Research, 40: W05113.CrossRefGoogle Scholar
  31. Warwick, J.J., 1989, Interplay between parameter uncertainty and model aggregation error, Water Resources Bulletin, 25: 275–283.Google Scholar
  32. Weiss, W. and Smith, L., 1998, Parameter space methods in Joint parameter estimation for groundwater models, Water Resources Research, 24: 647–661.CrossRefGoogle Scholar
  33. Zimmerman, D.A., de Marsily, G., Gotway, C.A., Marieta, M.G., Axness, C.L., Beauheim, R.L., Bras, R.L., Carrera, J., Dagan, G., Davies, P.B., Gallegos, D.P., Galli, A., GomezQQQHernadez, J., Grindrod, P., Gutjahr, A.L., Kitanidis, P.K., Lavenue, A.M., McLaughlin, D., Neuman, S.P., RamaRao, B.S., Ravenne, C., and Rubin, Y., 1998, A comparison of seven geostatistical based inverse approaches to estimate trans-missivities for modeling advective transport by groundwater flow, Water Resources Research, 34: 1373–1413.CrossRefGoogle Scholar

Copyright information

© Springer Science + Business Media B.V 2009

Authors and Affiliations

  • Petros Gaganis
    • 1
  1. 1.Department of the EnvironmentUniversity of the Aegean, University Hill, Xenia BuildingMytileneGreece

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