Quantifying the predictive consequences of model error with linear subspace analysis

Jeremy T White, John Doherty, Joseph Hughes

    Research output: Contribution to journalArticlepeer-review

    42 Citations (Scopus)


    All computer models are simplified and imperfect simulators of complex natural systems. The discrepancy arising from simplification induces bias in model predictions, which may be amplified by the process of model calibration. This paper presents a new method to identify and quantify the predictive consequences of calibrating a simplified computer model. The method is based on linear theory, and it scales efficiently to the large numbers of parameters and observations characteristic of groundwater and petroleum reservoir models. The method is applied to a range of predictions made with a synthetic integrated surface-water/groundwater model with thousands of parameters. Several different observation processing strategies and parameterization/regularization approaches are examined in detail, including use of the Karhunen-Loève parameter transformation. Predictive bias arising from model error is shown to be prediction specific and often invisible to the modeler. The amount of calibration-induced bias is influenced by several factors, including how expert knowledge is applied in the design of parameterization schemes, the number of parameters adjusted during calibration, how observations and model-generated counterparts are processed, and the level of fit with observations achieved through calibration. Failure to properly implement any of these factors in a prediction-specific manner may increase the potential for predictive bias in ways that are not visible to the calibration and uncertainty analysis process. Key Points The expression of model error is prediction dependent Structural defects may be invisible during calibration How calibration is implemented influences the expression of model error

    Original languageEnglish
    Pages (from-to)1152-1173
    Number of pages22
    JournalWater Resources Research
    Issue number2
    Publication statusPublished - Feb 2014


    • model structural error
    • parameter compensation
    • uncertainty analyisis


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