User guide to the UNC process and three utility programs for computation of nonlinear confidence and prediction intervals using MODFLOW-2000

Christensen, Steen; Cooley, Richard L.

doi:10.3133/tm6a10

Cited by 7 publications

(24 citation statements)

References 25 publications

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“…Use of the statistics presented in this section assumes that the model in question is linear, that is, that for the current (calibrated) parameters, the sensitivities X accurately represent the action of the model. Tests of model linearity can be made to evaluate this assumption using variants of Beale’s measure (Cooley and Naff 1990; Cooley 2004; Tiedeman et al 2004; Christensen and Cooley 2005; Hill and Tiedeman 2007). Yager (2004) presents measures of total and intrinsic nonlinearity for several practical ground water models.…”

Section: Methodsmentioning

confidence: 99%

“…The Cook's D statistic measures the effect of a single observation on the set of model parameters. It is a linear measure but applies to models with large total nonlinearity if the intrinsic nonlinearity is sufficiently small (Yager 1998;Cooley 2004;Christensen and Cooley 2005). In contrast, CV is a fully nonlinear measure.…”

Section: Cook's D and Dfbetas Statisticsmentioning

confidence: 99%

See 1 more Smart Citation

Testing Alternative Ground Water Models Using Cross‐Validation and Other Methods

Foglia¹,

Mehl

Hill

et al. 2007

Groundwater

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Many methods can be used to test alternative ground water models. Of concern in this work are methods able to (1) rank alternative models (also called model discrimination) and (2) identify observations important to parameter estimates and predictions (equivalent to the purpose served by some types of sensitivity analysis). Some of the measures investigated are computationally efficient; others are computationally demanding. The latter are generally needed to account for model nonlinearity. The efficient model discrimination methods investigated include the information criteria: the corrected Akaike information criterion, Bayesian information criterion, and generalized cross-validation. The efficient sensitivity analysis measures used are dimensionless scaled sensitivity (DSS), composite scaled sensitivity, and parameter correlation coefficient (PCC); the other statistics are DFBETAS, Cook's D, and observation-prediction statistic. Acronyms are explained in the introduction. Cross-validation (CV) is a computationally intensive nonlinear method that is used for both model discrimination and sensitivity analysis. The methods are tested using up to five alternative parsimoniously constructed models of the ground water system of the Maggia Valley in southern Switzerland. The alternative models differ in their representation of hydraulic conductivity. A new method for graphically representing CV and sensitivity analysis results for complex models is presented and used to evaluate the utility of the efficient statistics. The results indicate that for model selection, the information criteria produce similar results at much smaller computational cost than CV. For identifying important observations, the only obviously inferior linear measure is DSS; the poor performance was expected because DSS does not include the effects of parameter correlation and PCC reveals large parameter correlations.

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Section: Methodsmentioning

confidence: 99%

Section: Cook's D and Dfbetas Statisticsmentioning

confidence: 99%

Testing Alternative Ground Water Models Using Cross‐Validation and Other Methods

Foglia¹,

Mehl

Hill

et al. 2007

Groundwater

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“…When undertaking linear error variance analysis as an adjunct to solution of an over-determined inverse problem, a Beale type analysis is often employed to characterise the possible effects of model non-linearity on these analyses; see for example Christensen and Cooley (2004) and references cited therein.…”

Section: Sensitivity Analysismentioning

confidence: 99%

Predictive error analysis for a water resource management model

Gallagher¹,

Doherty²

2007

Journal of Hydrology

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“…As discussed by Cooley and Naff (1990), Hill (1998), and Hill and Tiedeman (2007), the use of linear intervals needs to be accompanied by an analysis of model linearity. Such an analysis can be accomplished using the modified Beale's measure, or the nonlinearity measures developed by Cooley (2004), and discussed by Christensen and Cooley (2004), Poeter and others (2005), and Hill and Tiedeman (2007). These nonlinearity measures need to be calculated for models that dominate the calculation of the model-averaged variance; that is, for the models with the highest posterior probabilities.…”

Section: Model-averaged Linear Confidence and Prediction Intervalsmentioning

confidence: 99%

“…If the most probable models are nonlinear, a satisfactory evaluation of uncertainty may require that nonlinear intervals be calculated using, for example, UCODE_2005, the UNC Process of MODFLOW-2000 (Christensen and Cooley, 2004), or PEST (Doherty, 2004). Nonlinear intervals are discussed by Hill and Tiedeman (2007) and references cited therein.…”

Section: Model-averaged Linear Confidence and Prediction Intervalsmentioning

confidence: 99%

MMA, A Computer Code for Multi-Model Analysis

Poeter¹,

Hill²

2007

Techniques and Methods

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The Multi-Model Analysis (MMA) computer code is designed to evaluate many alternative models of a given system, called multiple models in this work. It can be used to rank the models and calculate posterior model probabilities. The probabilities are used to calculate modelaveraged quantities that account for the variability evident in the alternative models. The modelaveraged quantities can include parameter estimates, predictions, and measures of parameter and prediction uncertainty. Calibration of all models needs to be completed before application of MMA. MMA operates by reading files produced by models developed and calibrated to represent a single system. The models all need to use the same observations with the same weighting. The files needed by MMA can be produced by UCODE_2005 and associated codes (Poeter and others, 2005) run in the Sensitivity-Analysis or Parameter-Estimation mode. The name and structure of the files are simple and follow the conventions of JUPITER API data-exchange files. Thus, it is likely that MMA also will be able to use results from codes other than UCODE_2005. Although the examples presented in this work are from the field of groundwater modeling, MMA (and UCODE_2005) can be used to evaluate results from models of nearly any type of system. The documentation presented in this report describes the methods used and the input and output files. Together, this report, Hill and Tiedeman (2007), and Burnham and Anderson (2002) serve to document the computer code described in this work. Additional information on the methods is provided in Burnham and Anderson (2004), Ye and others (2004, 2005), and Poeter and Anderson (2005). The performance of MMA has been tested in a variety of applications. Future applications, however, might reveal errors that were not detected in the test simulations. Users are requested to notify the originating office of any errors found in the report or the computer program. Updates might occasionally be made to both the report and the computer program. Users can check for updates on the World Wide Web at URL

show abstract

User guide to the UNC process and three utility programs for computation of nonlinear confidence and prediction intervals using MODFLOW-2000

Cited by 7 publications

References 25 publications

Testing Alternative Ground Water Models Using Cross‐Validation and Other Methods

Testing Alternative Ground Water Models Using Cross‐Validation and Other Methods

Predictive error analysis for a water resource management model

MMA, A Computer Code for Multi-Model Analysis

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