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In some cases these data are observational, provided by nature (e.g., meteorological measurements, supernova luminosities); in other cases, data come from a carefully planned hierarchy of controlled experiments—e.g., the Predictive Engineering and Computational Sciences (PECOS) case study in Section 5.9.

In addition to physical observations, information may come from the literature or expert judgment that may incorporate historical data or known physical behavior.

The list below covers a number of important considerations that will have an impact on the methods and approaches for carrying out validation and prediction: • The amount and relevance of the available physical observations for the assessment, • The accuracy and uncertainty accompanying the physical observations, • The complexity of the physical system being modeled, • The degree of extrapolation required for the prediction relative to the available physical observations and the level of empiricism encoded in the model, • The computational demands (run time, computing infrastructure) of the computational model, • The accuracy of the computational model’s solution relative to that of the mathematical model (numerical error), • The accuracy of the computational model’s solution relative to that of the true, physical system (model discrepancy), • The existence of model parameters that require calibration using the available physical observations, and • The availability of alternative computational models to assess the impact of different modeling schemes or physics implementations on the prediction.Ninety percent of the actual temperatures are within ±14°F for the persistence-model forecasts and within ±6°F for the NWS forecasts.The greater accuracy of the NWS forecasts is due to NWS’s use of computational models and additional meteorological information.Here the concept of “nearness” of the physical observations to the predictions of the intended use of the model becomes relevant, as does the notion of the domain of applicability for the prediction.However, FIGURE 5.1 Daily maximum temperatures for Norman, Oklahoma (left), and histograms of next-day prediction errors (right) using two prediction models.

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