Uncertainty In Model Parameter Values Research Articles

Continuous reactive crystallization of β-lactam antibiotics catalyzed by penicillin G acylase. Part II: Case study on ampicillin and product purity

Continuous reactive crystallization of β-lactam antibiotics can ease shortage and contamination concerns for an important class of medicines. With a model of continuous reactive crystallization catalyzed by penicillin G acylase (PGA), a process is developed to ensure purity of the antibiotic product. Guaranteeing the solid-phase purity of ampicillin and cephalexin is important because PGA produces a slightly soluble byproduct, phenylglycine, which can contaminate the antibiotic crystals. In a single well-mixed reactive crystallizer, productivity is optimized and nearly two-fold greater than the non-crystallizing maximum productivity. Process robustness is essential because multiple steady states, only one of which produces pure ampicillin crystals, exist in the well-mixed reactive crystallizer. By combining well-mixed and plug-flow reactive crystallizers in series, crystallization of phenylglycine can be suppressed while high yield and comparable productivity are still achieved. The reactive crystallizer series demonstrates high purity with uncertainty in model parameter values and variability in operating conditions.

A state-space approach to analyze structural uncertainty in physical models

Physics-based computer models, such as fluid flow simulations, seek to approximate the behavior of a real system based on the physical equations that govern the evolution of that system. The model approximation of reality, however, is imperfect because it is subject to uncertainties coming from different sources: finite model resolution, uncertainty in model parameter values, uncertainty in input data such as external forgings, and uncertainty in the structure of the model itself. Many studies to date have considered the effects of parameter and data uncertainty on model outputs, and have offered solutions to obtain the best fitted parameter values for a model. However, much less effort has been devoted to the study of structural uncertainty, which is caused by our incomplete knowledge about the true physical processes, and manifests itself as missing dynamics in the model. This paper seeks to understand structural uncertainty by studying the observable errors, i.e. the discrepancies between the model solutions and measurements of the physical system. The dynamics of these errors is modeled using a state-space approach, which enables one to identify the source of uncertainty and to recognize the missing dynamics inside model. Furthermore, the model solution can be improved by correcting it with the error predicted by the state-space approach. The proposed methodology is applied to two test problems, Lorenz-96 and a stratospheric chemistry model.

The Mayak Worker Dosimetry System (MWDS-2013): A Bayesian Analysis to Quantify Pulmonary Binding of Plutonium in Lungs Using Historic Beagle Dog Data

The revised human respiratory tract model, published in Part 1 of the International Commission on Radiological Protection's (ICRP) report on Occupational Intakes of Radionuclides (OIR), includes a bound fraction, fb, to represent radionuclides that have become chemically bound in the lungs following dissolution of particulates in lung fluid. Bound radionuclides are not subject to particle transport clearance but can be absorbed to blood at a rate, sb. The occurrence of long-term binding of plutonium can greatly increase lung doses, particularly if it occurs in the bronchial and bronchiolar regions. However, there has been little evidence that currently supports the existence of a long-term bound state for plutonium. The present work describes the analysis of measurements of lung data obtained from a life span study of Beagle dogs that were exposed by inhalation to different concentrations of plutonium-239 (239Pu) nitrate aerosol at Pacific Northwest Laboratories, USA. The data have been analysed to assess whether a bound state was required to explain the data. A Bayesian approach was adopted for the analysis that accounts for uncertainties in model parameter values, including uncertainties in the rates of particle transport clearance. Furthermore, it performs the analysis using two different modelling hypotheses: a model based on the current ICRP human respiratory tract model and its treatment of alveolar particle transport clearance; and a model of particle transport clearance that is based on the updated model developed by ICRP to calculate dose coefficients for the OIR. The current model better represents clearance in dogs at early times (up to 1 year following intake) and the latter better represents retention at greater times (>5 years following intake). The results indicate that a long-term bound fraction of between 0.16 and 1.1%, with a mean value of between 0.24 and 0.8% (depending on the model) is required to explain the data.

THE MAYAK WORKER DOSIMETRY SYSTEM (MWDS 2013): A RE-ANALYSIS OF USTUR CASE 0269 TO DETERMINE WHETHER PLUTONIUM BINDS TO THE LUNGS.

Radionuclides in ionic form can become chemically bound in the airways of the lungs following dissolution of inhaled particulates in lung fluid. The presence of long-term binding can greatly increase lung doses from inhaled plutonium, particularly if it occurs in the bronchial and bronchiolar regions. However, the only published evidence that plutonium binding occurs in humans comes from an analysis of the autopsy and bioassay data of United States Transuranium and Uranium Registries Case 0269, a plutonium worker who experienced a very high (58 kBq) acute inhalation of plutonium nitrate. This analysis suggested a bound fraction of around 8 %, inferred from an unexpectedly low ratio of estimated total thoracic lymph node activity:total lung activity, at the time of death. However, there are some limitations with this study, the most significant being that measurements of the regional distribution of plutonium activity in the lungs, which provide more direct evidence of binding, were not available when the analysis was performed. The present work describes the analysis of new data, which includes measurements of plutonium activity in the alveolar-interstitial (AI) region, bronchial (BB) and bronchiolar (bb) regions, and extra-thoracic (ET) regions, at the time of death. A Bayesian approach is used that accounts for uncertainties in model parameter values, including particle transport clearance, which were not considered in the original analysis. The results indicate that a long-term bound fraction between 0.4 and 0.7 % is required to explain this data, largely because plutonium activity is present in the extra-thoracic (ET2), bronchial and bronchiolar airways at the time of death.

Investigating the usefulness of satellite-derived fluorescence data in inferring gross primary productivity within the carbon cycle data assimilation system

Abstract. Simulations of carbon fluxes with terrestrial biosphere models still exhibit significant uncertainties, in part due to the uncertainty in model parameter values. With the advent of satellite measurements of solar induced chlorophyll fluorescence (SIF), there exists a novel pathway for constraining simulated carbon fluxes and parameter values. We investigate the utility of SIF in constraining gross primary productivity (GPP). As a first test we assess whether SIF simulations are sensitive to important parameters in a biosphere model. SIF measurements at the wavelength of 755 nm are simulated by the Carbon-Cycle Data Assimilation System (CCDAS) which has been augmented by the fluorescence component of the Soil Canopy Observation, Photochemistry and Energy fluxes (SCOPE) model. Idealized sensitivity tests of the SCOPE model stand-alone indicate strong sensitivity of GPP to the carboxylation capacity (Vcmax) and of SIF to the chlorophyll AB content (Cab) and incoming short wave radiation. Low sensitivity is found for SIF to Vcmax, however the relationship is subtle, with increased sensitivity under high radiation conditions and lower Vcmax ranges. CCDAS simulates well the patterns of satellite-measured SIF suggesting the combined model is capable of ingesting the data. CCDAS supports the idealized sensitivity tests of SCOPE, with SIF exhibiting sensitivity to Cab and incoming radiation, both of which are treated as perfectly known in previous CCDAS versions. These results demonstrate the need for careful consideration of Cab and incoming radiation when interpreting SIF and the limitations of utilizing SIF to constrain Vcmax in the present set-up in the CCDAS system.

Parameter uncertainty analysis of a biokinetic model of caesium.

Parameter uncertainties for the biokinetic model of caesium (Cs) developed by Leggett et al. were inventoried and evaluated. The methods of parameter uncertainty analysis were used to assess the uncertainties of model predictions with the assumptions of model parameter uncertainties and distributions. Furthermore, the importance of individual model parameters was assessed by means of sensitivity analysis. The calculated uncertainties of model predictions were compared with human data of Cs measured in blood and in the whole body. It was found that propagating the derived uncertainties in model parameter values reproduced the range of bioassay data observed in human subjects at different times after intake. The maximum ranges, expressed as uncertainty factors (UFs) (defined as a square root of ratio between 97.5th and 2.5th percentiles) of blood clearance, whole-body retention and urinary excretion of Cs predicted at earlier time after intake were, respectively: 1.5, 1.0 and 2.5 at the first day; 1.8, 1.1 and 2.4 at Day 10 and 1.8, 2.0 and 1.8 at Day 100; for the late times (1000 d) after intake, the UFs were increased to 43, 24 and 31, respectively. The model parameters of transfer rates between kidneys and blood, muscle and blood and the rate of transfer from kidneys to urinary bladder content are most influential to the blood clearance and to the whole-body retention of Cs. For the urinary excretion, the parameters of transfer rates from urinary bladder content to urine and from kidneys to urinary bladder content impact mostly. The implication and effect on the estimated equivalent and effective doses of the larger uncertainty of 43 in whole-body retention in the later time, say, after Day 500 will be explored in a successive work in the framework of EURADOS.

Evaluation of approaches for estimation of rainfall and the unit hydrograph

The impact of rainfall interpolation techniques and unit hydrograph estimation has been explored for four gauged locations in the Brahmani basin in east India. The use of ground-based and satellite-based data, coupled with testing two interpolation techniques (Thiessen polygon and inverse distance weighting), can yield improved rainfall estimates and fits to observed flows. Due to the presence of significant errors in the areal rainfall estimate it was found that identification of known errors in rainfall data can assist in focusing model calibration on catchment response, thereby reducing the uncertainty in model parameter values. Similarly, using several approaches to estimate the unit hydrograph can assist in reducing uncertainty. The resulting performance of the model for the gauged sites in the Brahmani basin gave Nash–Sutcliffe efficiency (NSE) values for the calibration period of 0.6–0.7. For this basin, the inverse distance weighting approach corrected for spatial variation in rainfall distribution generally gave the best fits to the observed streamflow. Sensitivity to errors in the rainfall surface limits the applicability for this approach in modelling the flows in ungauged basins, however.

Comparative Calibration of a Complex Hydrologic Model by Stochastic Methods GLUE and PEST

Hydrologic and environmental models are useful for prediction and understanding of processes. Model calibration often faces the problem of equifinality, by which empirical observations validate one set of model parameter values almost to the same degree as another very different set. This uncertainty in model parameter values implies uncertainty in model predictions. A stochastic approach to calibration is therefore appropriate to establish the likely range or probability distribution of model parameters and predictions. In the literature, two commonly used methods are the Generalized Likelihood Uncertainty Estimation (GLUE) approach and the Parameter Estimation (PEST) software (a nonlinear parameter estimation and optimization package). This study makes a side-by-side comparison of GLUE and PEST applied to two models, the first a simple two-parameter sinusoidal temperature model and the second a complex multi-parameter multi-purpose hydrologic model, the Soil and Water Assessment Tool (SWAT) model, applied to the Salt Creek watershed in Illinois. The SWAT model is calibrated for stream flow, corn and soybean yields, and nitrate load. The GLUE and PEST calibrations for the simple model are straightforward. The same is not true, however, of the complex SWAT model, for which both GLUE and PEST are found to require some level of prior information to be effective. In this study, that information is obtained from a deterministic calibration of the system using a genetic algorithm (GA). The results indicate that generally there is a greater flexibility in problem specification in GLUE than in PEST. This is desirable, although it also means that there is a greater level of subjectivity. This flexibility, together with GLUE's independence from any assumption of model structure, makes GLUE suitable for calibrating large complex models where computational resources are available. On the other hand, for problems where the presence of local optima is not significant, PEST is an attractive option, as it is able to identify the optimal set of adjustable model parameters at just a fraction of the computational cost of GLUE.

Bond graph models of structured parameter uncertainties

Taking into account uncertainties in model parameter values is a crucial point for studying robustness in modeling and in control. This paper proposes to construct in a systematic and graphical procedure two forms of the linear state equation usually found in the literature for dealing with the robustness problem in the case of structured uncertainties on parameters. It is shown how to model uncertainties in a bond graph approach, in the case of additive or multiplicative parametric variations.

Towards reduced uncertainty in catchment nitrogen modelling: quantifying the effect of field observation uncertainty on model calibration

Abstract. The value of nitrogen (N) field measurements for the calibration of parameters of the INCA nitrogen in catchment model is explored and quantified. A virtual catchment was designed by running INCA with a known set of parameters, and field "measurements" were selected from the model run output. Then, using these measurements and the Shuffled Complex Evolution Metropolis algorithm (SCEM-UA), four of the INCA model parameters describing N transformations in the soil were optimised, while the measurement uncertainty was increased in subsequent steps. Considering measurement uncertainty typical for N field studies, none of the synthesised datasets contained sufficient information to identify the model parameters with a reasonable degree of confidence. Parameter equifinality occurred, leading to considerable uncertainty in model parameter values and in modelled N concentrations and fluxes. Fortunately, combining the datasets in a multi-objective calibration was found to be effective in dealing with these equifinality problems. With the right choice of calibration measurements, multi-objective calibrations resulted in lower parameter uncertainty. The methodology applied in this study, using a virtual catchment free of model errors, is proposed as a useful tool foregoing the application of a N model or the design of a N monitoring program. For an already gauged catchment, a virtual study can provide a point of reference for the minimum uncertainty associated with a model application. When setting up a monitoring program, it can help to decide what and when to measure. Numerical experiments indicate that for a forested, N-saturated catchment, a fortnightly sampling of NO3 and NH4 concentrations in stream water may be the most cost-effective monitoring strategy. Keywords: INCA, nitrogen model, parameter uncertainty, multi-objective calibration, virtual catchment, experimental design

Stochastic modelling of phosphorus transfers from agricultural land to aquatic ecosystems

This paper describes a simple model of phosphorus (P) transfer from agricultural land to surface waters which incorporates the effects of spatial variability in catchment properties and uncertainty in model parameter values. TOPMODEL concepts are used to estimate water, solute and sediment fluxes to water bodies. The model predicts the spatial distribution of water table depth and saturation-excess overland flow based on topography. Dissolved P (DP) transfer is assumed to occur vertically in the unsaturated zone and laterally in the saturated zone. Readily soluble P is assumed to decrease exponentially with soil depth. Particulate P (PP) transfers are modelled by estimating overland flow discharge and associated sediment transport capacity. Uncertainty in the distribution of soil surface P concentrations and model parameters controlling the mobility of soil P are incorporated using Monte Carlo simulation. Predicted losses of DP are well correlated with discharge and those of PP are episodic. Highest losses of P tended to be predicted near to the stream where the water table is close to the surface. The combination of a deterministic model core with a stochastic generation of model parameters or state variables provides an attractive way of embracing variability and uncertainty in models of this kind.

Imprecision of dose predictions for radionuclides released to the environment: An application of a Monte Carlo simulation technique

An evaluation of the imprecision in dose predictions has been performed using current dose assessment models and present knowledge of the variability or uncertainty in model parameter values. The propagation of parameter uncertainties is demonstrated using a Monte Carlo technique for elemental 131I transported via the pasture-cow-milk-child pathway. The results indicate that when site-specific information is not available the imprecision inherent in the predictions for this pathway is potentially large. Generally, the 99th percentile in thyroid dose for children was predicted to be approximately an order of magnitude greater than the median value. The potential consequences of the imprecision in dose for radiation protection purposes are discussed.