Calibration Guidelines

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Calibration Guidelines. Model development. Model testing. 9. Evaluate model fit 10. Evaluate optimal parameter values 11. Identify new data to improve parameter estimates 12. Identify new data to improve predictions 13. Use deterministic methods 14. Use statistical methods.
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Calibration GuidelinesModel developmentModel testing9.Evaluate model fit10.Evaluate optimal parameter values 11. Identify new data to improve parameter estimates12. Identify new data to improve predictions13.Use deterministic methods14.Use statistical methods1.Start simple, add complexity carefully2. Use a broad range of information3. Be well-posed & be comprehensive4. Include diverse observation data for ‘best fit’5.Use prior information carefully6. Assign weights that reflect ‘observation’ error7.Encourage convergence by making the model more accurate8. Consider alternative modelsPotential new dataPrediction uncertaintyModel DevelopmentGuideline 7:Encourage convergence of the regression by making the model more accurateNonlinear regression can be difficultEven when composite scaled sensitivities andcorrelation coefficientsindicate the data provide sufficient information to estimate the defined parameters, nonlinear regression may not converge.Substantial insight about the observations, potential model inaccuracies, and model fit can be obtained from values calculated in failed regressions:dimensionless scaled sensitivitiescomposite scaled sensitivitiescorrelation coefficientsinfluence statisticsweighted and unweighted residualsparameter updates during the regression.Learn from Failed Regressions!Working to make the model represent the system more accurately obviously is beneficial to model development, and generally also improves the behavior of the regression.Use the information from failed regressions, or regressions that converge to unrealistic parameter values, to guide changes.The most advantageous modifications for improving model accuracy are usually:Modify the parameter definitionModify other aspects of model construction, such as its physical features or the processes it simulatesEstimate fewer parametersAdd observations to the regressionScrutinize existing observations for error in interpretation Make the model more accurateInsensitivityNonlinearityInconsistenciesThe Main Problems that Plague Convergence…InsensitivitySpecify parameters with small cssCombine existing parametersRedesign the parameterizationCreatively use system information (Guideline 2)NonlinearityEvaluate results from intermediate iterationsEvaluate large weighted residuals, observations omitted because simulated equivalents could not be obtained, whether parameter values are realisticIf forward model nonlinearities are a suspected cause of nonconvergence, consider using a linear approximation InconsistenciesCheck parameter representation, dominant observationsEvaluate observations & prior, and their simulated equivalents…and Possible Solutions to ConsiderCalibration GuidelinesModel developmentModel testing9.Evaluate model fit10.Evaluate optimal parameter values 11. Identify new data to improve parameter estimates12. Identify new data to improve predictions13.Use deterministic methods14.Use statistical methods1.Start simple, add complexity carefully2. Use a broad range of information3. Be well-posed & be comprehensive4. Include diverse observation data for ‘best fit’5.Use prior information carefully6. Assign weights that reflect ‘observation’ error7. Encourage convergence by making the model more accurate8.Consider alternative models (MMA)Potential new dataPrediction uncertaintyDeveloping alternative modelsDeterministic methodsAlternative conceptual models about depositional environmentAlternative theories about rainfall distribution and(or) infiltration dynamicsStochastic methodsAlternative realizations of gravel/sand/clay distribution developed using indicator krigingCombined methodsDiscard some alternative realizations based on deterministic depositional theoriesGenerate stochastic variations within a deterministically derived hydrogeologic frameworkGuideline 8:Consider alternative modelsbook p. 308-314Better models have three attributes:
  • Better fit (But not too good!)
  • Weighted residualsthat are more randomly distributed
  • More realistic optimal parameter values
  • Guideline 8:Consider alternative modelsThis graph shows model discrimination criteria for 5 models of the Maggia Valley, southern Switzerland. SSWR: Sum of squared, weighted residuals. AICc, BIC: Model discrimination criteria.Foglia, in press, GW. Book, p. 311.
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