Sensitivity to model parameters

Walter B. and Heimann M. (2000) A process-based, climate-sensitive model to derive methane emissions from natural wetlands application to five wetland sites, sensitivity to model parameters, and climate. Global Biogeochem. Cycles 14, 745-765. 

Once the simulation conditions have been properly defined, the simulations are now ready to execute. One important consideration in interpreting simulation results is the sensitivity of these results to underlying assumptions or uncertainty about the simulation model and parameters. Trial simulation outputs should be viewed relative to their sensitivity to model parameter uncertainty. There are two general methods, local and global, for performing SA. 

Very large values of RGA indicate that the system can be quite sensitive to model parameters. The linearisation of the model should be checked carefully. 

Model predictions can be very sensitive to model parameters. Uncertainties in the parameters can therefore lead to strong differences in the predicted abundances of species. Two aspects of the problem can be considered. First, the model parameters are... 

These data show that both models identify important variables that affect 5 Obody w.ier and 8 Ophospha in mammals. Both serve to identify the dikdik as an outlier which may be explained by their sedentary daytime pattern. On the other hand, the body-size model (Bryant and Froelich 1995), which may reliably predict animal 5 0 in temperate, well-watered regions, does not predict 8 Opho,phaw in these desert-adapted species. The second model (Kohn 1996), by emphasizing animal physiology independent of body size, serves to identify species with different sensitivities to climatic parameters. This, in conjunction with considerations of behavior, indicate that certain species are probably not useful for monitoring paleotemperature because their 5 Obodyw er is not tied, in a consistent way, to The oryx, for example, can... 

A survey of the mathematical models for typical chemical reactors and reactions shows that several hydrodynamic and transfer coefficients (model parameters) must be known to simulate reactor behaviour. These model parameters are listed in Table 5.4-6 (see also Table 5.4-1 in Section 5.4.1). Regions of interfacial surface area for various gas-liquid reactors are shown in Fig. 5.4-15. Many correlations for transfer coefficients have been published in the literature (see the list of books and review papers at the beginning of this section). The coefficients can be evaluated from those correlations within an average accuracy of about 25%. This is usually sufficient for modelling of chemical reactors. Mathematical models of reactors arc often more sensitive to kinetic parameters. Experimental methods and procedures for parameters estimation are discussed in the subsequent section. 

Systems that require two-dimensional treatment are sensitive to the parameters in the model, and, as a result, the transport coefficients (ke and De) must be well known. Consequently, a one-dimensional model is usually used for preliminary process design,... 

Tliis model is simpler that the Kunii-Levenspiel model and eliminates the unsubstantiated expression for cloud-to-emulsion transfer employed by Kunii and Levenspiel (Grace, 1984). Furthermore, compared to the previous models, the introduction of the parameter yb in the model leads to better results as the assumption that there is no solids in the bubble phase may lead to the underestimation of conversion in fast reactions. For slow reactions, the value of yb is of minor importance. However, for fast reactions the model may become sensitive to this parameter and the actual conversion should be bounded between the predicted ones using the upper and lower limits of yh, i.e. 0.01 and 0.001, respectively (Grace, 1984). 

The initial conditions for the sensitivity coefficients are usually taken as zero. At the initial condition of the model problem there is no sensitivity to the parameter values, since the initial conditions are usually specified independently of the parameters. 

In any case, because ion scattering is strongly affected by the thermal vibrations of surface atoms, experimental data must be compared to Monte-Carlo simulations for model surfaces to achieve quantitative results. The available data base for structure-fitting is rather small compared to electron spectroscopies, so the sensitivity to structural parameters is sometimes limited. But when the surface structure is close to the bulk structure, ion channeling data can be strongly sensitive to small variations in structural parameters. 

AW device sensitivity to viscoelastic parameters and electrical pnqieities can be used to advantage in some film characterization techniques. In these situations, a comparison of the AW device response to a model of the AW/thin film interaction is often crucial to the effective evaluation of thin film parameters. These additional interaction mechanisms typically involve changes in both the wave velocity and the wave attenuation for SAW, APM and FPW devices, and changes in both resonant frequency and admittance magnitude in TSM devices. In contrast, mass loading does not contribute to wave attenuation or decreases in admittance since moving mass involves no power dissipation (see Chapter 3). 

In the presentation that follows we will consider the mathematical models that have been developed and the model parameters required to predict concentration changes in the animals. In addition, experimental data will be provided that indicate the sensitivity of model parameters to differences in physicochemical form of the elements in the water and to differences in metabolic responses among species. These kinds of... 

The popularity of the Bode representation stems from its utility in circuits analysis. The phase angle plots are sensitive to system parameters and, therefore, provide a good means of comparing model to experiment. The modulus is much less... 

It can be observed that the bubble diameter comes into play in all these forces at power 2 or 3, making the computation very sensitive to this parameter. There are many other forces which could be considered (compressive force due to the liquid, surface tension forces, wake-related forces exerted by neighbouring bubbles, electrostatic repulsion forces between bubbles, etc.). However, these forces were not taken into account in this numerical model. The physical data used for the two phases are shown in Table 1. 

Just as the models used to predict the transport and fate of chemicals in the environment are sensitive to numerous site-specific parameters such as average rainfall and soil types, the equations used to determine exposures for particular activity patterns are sensitive to demographic parameters. These include general population characteristics (e.g. age distributions), culturally-influenced factors (e.g. rates of fish and vegetable consumption), and location-specific factors (e.g. workplace exposure patterns are generally different from those in the home). EPA has recently published the results of its efforts to determine values for numerous parameters that are characteristic of the average population of the U.S. (4), but the risk assessor must adjust these parameters to fit the specific population she or he is evaluating. 

Sometimes when model validation is not needed, or to supplement already discussed validity checks, model stability is assessed. Model stability determines how robust the model parameters are to slight changes in the data and how robust the model predictions are to changes in the either the model parameters or input data. Collectively these tests are referred to as sensitivity analysis. If model outputs are particularly sensitive to some parameter then greater accuracy needs to be obtained in estimating that parameter. A stable model is one that is relatively robust to changes in the model parameters and the input data. 

Wade et al. (1993) simulated concentration data for 100 subjects under a one-compartment steady-state model using either first-or zero-order absorption. Simulated data were then fit using FO-approximation with a first-order absorption model having ka fixed to 0.25-, 0.5-, 1-, 2-, 3-, and 4 times the true ka value. Whatever value ka was fixed equal to, clearance was consistently biased, but was relatively robust with underpredictions of the true value by less than 5% on average. In contrast, volume of distribution was very sensitive to absorption misspecification, but only when there were samples collected in the absorption phase. When there were no concentration data in the absorption phase, significant parameter bias was not observed for any parameter. The variance components were far more sensitive to model misspecification than the parameter estimates with some... 

The figures reveal a hot spot in the bed, which is typical for strongly exothermic processes. The magnitude of this hot spot depends, of course, on the heat effect of the reaction, the rate of reaction, the heat transfer coefficient and transfer areas as shown by Bilous and Amundson [21]. Its location depends on the flow velocity. It is also observed that the profiles become sensitive to the parameters from certain values onward. If the partial pressure of the hydrocarbon were 0.018 atm an increase of 0.0002 atm woifld raise the hot spot temperature beyond permissible limits. Such a phenomenon is called runaway. Note that for the upper part of the curves with po = 0.0181, 0.0182, and 0.019 (Figs. 11.5.b-l and 2) the model used here is not longer entirely adequate heat and mass transfer effects would have to be taken into account There is no doubt however as to the validity of the lower part indicating excessive sensitivity in this region. 

The uncertainties and risk criteria in the risk assessment methodology need to be more explicitly studied in the future. The uncertainties usually deals with the sensitivity of modeling parameters to the risk assessment results for different rockfall scenarios. The risk criteria needs to be established to assess the acceptable level of rockfall risk for... 

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