Uncertainty in modeling

Deque M, Rowell DP, Liithi D, Giorgi E, Christensen JH, Rockel B, Jacob D, Kjellstrom E, de Castro M, van den Hurk B (2007) An intercomparison of regional climate simulations for Europe assessing uncertainties in model projections. Clim Change 81 53-70 doi 10.1007/ S10584-006-9228-X... 

Since the uncertainty in model parameters Hmits the model accuracy, a deviation of 10% is generally considered a very good result. The measurements therefore demonstrate the validity of the presented model, in particular when considering that the temperature-dependent parameters are extracted from data that are only valid in a temperature range between 0 °C and 100 °C. 

Otherwise, the mixture is called a nonazeotrope. A nonazeotropic mixture has a temperature distribution parallel to that of the thermal reservoir. Note that one of the requirements for the nonazeotropic mixture energy conversion improvement is to have a nonconstant temperature heat source and heat sink. The proper choice of best combination of the nonazeotropic mixture is still not entirely understood. Uncertainties in modeling the thermodynamic and heat-transfer aspects of the nonazeotropic mixture refrigeration cycle are such that the probability of realizing significant net benefits in actual application is also not fully known. 

Cullen, A.C. and H.C. Frey. 1999. Probabilistic Techniques in Exposure Assessment A Handbook for Dealing with Variability and Uncertainty in Models and Inputs. New York Plenum Publishing Corporation. 

In stochastic optimization, Cv can be purposefully employed to investigate, denote, and compare the relative uncertainty in models being studied. In a risk minimization model, as the expected value is reduced, the variability in the expected value (for example, as measured by variance or standard deviation) is reduced. The ratio of this change can be captured and described by Cv. Consequently, a comparison of the relative merit of models in terms of their robustness can be represented by their respective values of Cv, in the sense that a model with a lower Cv is favored since there is less uncertainty associated with it. In fact, Markowitz (1952) advocates that the use of Cy as a measure of risk would equally ensure that the outcome of a decisionmaking process still lies in the set of efficient portfolios for the case of operational investments. 

Schwander, H P. Koepke, and A. Ruggaber, Uncertainties in Modeled UV Irradiances Due to Limited Accuracy and Availability of Input Data, J. Geophys. Res., 102, 9419-9429 (1997). 

Extrapolation between the population and community levels of biological organization and between community and ecosystem levels may be greatly confounded by the occurrence of contaminant-induced indirect interactions between organisms, leading to a high level of uncertainty in model predictions. In practice, the most... 

In the prospective context, a common and simple way to handle uncertainty is the use of uncertainty factors (UFs). These may suffice to derive a safe concentration of a substance associated to a predefined protection level to be used generically — that is, it is safe even in worst-case conditions. The greater the uncertainty in models or data for the extrapolations, the larger the overall UF in the lower tiers. The UF is applied to the risk assessment to account for unquantified uncertainties. In some cases, the factor depends on the amount of available data, or UFs per extrapolation are multiplied to provide the final factor (e.g., 10 x 10 x 10 as the UF for 3 assessment steps yields an overall factor of 1000). 

Structural uncertainties in models can be dealt with in a variety of ways, including (1) parameterization of a general model that can be reduced to alternative functional forms (e.g. Morgan Henrion, 1990), (2) enumeration of alternative models in a probability tree (e.g. Evans et al., 1994), (3) assessment of critical assumptions within a model, (4) assessment of the pedigree of a model and (5) assessment of model quality. The first two of these are quantitative methods, whereas the others are qualitative. In practice, a typical approach is to compare estimates made separately with two or more models. However, the models may not be independent of each other with respect to their basis in theory or data. Thus, an apparently favourable comparison of models may indicate only consistency, rather than accuracy. 

Cullen AC, Frey HC (1999) The use of probabilistic techniques in exposure assessment A handbook for dealing with variability and uncertainty in models and inputs. New York, NY, Plenum Press. 

Hebrard E, Dobrijevic M, Benilan Y, Raulin F. Photochemical kinetics uncertainties in modeling Titan s atmosphere a review. J Photochem Photobiol C Photochem Rev 2006 7 211-30. 

Jones J. H. (1998) Uncertainties in modeling core formation. Meteorit. Planet. Sci. 33, A79-A80. 

The rate constant data for the various channels of the H + HO2 reaction are shown in Figs 3.6 to 3.8. The branching ratios have been extensively studied at ambient temperatures because of the importance of the reaction in atmospheric chemistry and are believed to be well known (the results of Keyser [20], which agree with those of Sridharan et al. [21], are usually taken as definitive). However, there are very few studies at higher temperatures and no reliable values above 1000 K. This is not unusual. In most cases there is no information at all for combustion conditions. Current ignorance of reaction pathways in multichannel reactions is possibly the major uncertainty in modelling high-temperature processes. 

R.G. Derwent, Treating Uncertainty in Models of the Atmospheric Chemistry of Nitrogen-Compounds, Atm. Environ. 21 (1987) 1445-1454. 

Characterizing the overall uncertainties associated with the PBPK model estimates is also an important component of the PBPK model evaluation and application. This includes characterizing the uncertainties in model outputs resulting from the uncertainty in the PBPK model parameters. Traditionally, Monte Carlo has been employed for performing uncertainty analysis of PBPK models (39, 40). Some of the recent techniques that have been applied for the uncertainty analysis of PBPK models include the stochastic response surface method (SRSM) (38, 41) and the high-dimensional model reduction (HDMR) technique (42). 

Process alternatives for hydrogen cyanide production Maximization of economic benefit and minimization of environmental inq)act. A preference-based approach Hoffmann et al. (2001) considered total annualized profit per service unit (TAPPS) and material intensity per service (MIPS) as economic and environmental indicator respectively, while Hoffmann et al. (2004) considered Eco-indicator 99 (E199) for environmental objective as well as uncertainty in model parameters. Hoffmann et al. (2001)... 

Stochastic (Probabilistic) Models. One of the most significant advances in exposure estimation in the past 15 to 20 years has been the application of probabilistic statistical methods to many types of data analyses (Duan and Mage 1997 Finley and Paustenbach 1994 Morgan and Henrion 1990 US ERA 1995, 1997, 2000a). Stochastic or probabilistic techniques can help quantify variability and uncertainty in model inputs and outputs, can be used to better characterize the possible range of exposures for a particular scenario when measured data are minimal, and can be employed to better understand the uncertainty inherent in estimates developed from many different types of sources, whether quantitative or qualitative. 

---