Set Of Model Parameter Values Research Articles

Pitfalls in hydrologic model calibration in a data scarce environment with a strong seasonality: experience from the Adyar catchment, India

Process-based hydrologic models can provide necessary information for water resources management. However, the reliability of hydrological models depends on the availability of appropriate input data and proper model calibration. In this study, we demonstrate that common calibration procedures that assume stationarity of hydrological processes can lead to unsatisfactory model performance in areas that experience a strong seasonal climate. Moreover, we develop a more robust calibration procedure for the Soil and Water Assessment Tool (SWAT) in the Adyar catchment of Chennai, India. Calibration was carried out based on seasonal decomposition and by successively shifting the calibration period. Daily and monthly streamflow records were used to investigate how these different calibration procedures influence model parameterization. Results show that SWAT model performance improved when calibrated after separating the streamflow into wet and dry seasons. The wet season calibration increased the Kling Gupta Efficiency coefficient and Nash–Sutcliffe Efficiency coefficient values from 0.56 to 0.68 and 0.19 to 0.51, respectively, compared to calibration based on wet and dry seasons together. In addition, when calibration time periods were shifted, resultant sets of model parameter values and performance metrics differed. Calibration based on the 2004–2009 period resulted in an overestimation of streamflow by 8.2%, whereas the overestimation was 12.1%, 18.3%, and 20.0% for the 2004–2010, 2004–2011, and 2004–2012 periods, respectively. This study underlines that both the availability of observed streamflow data and the way these data are applied to calibration have a strong impact on model parameterization and performance.

Simulation of SMAP and AMSR2 observations and estimation of multi-frequency vegetation optical depth using a discrete scattering model in the Tibetan grassland

Passive microwave observation at multiple frequencies has received increasing research interests due to its capability to provide comprehensive information of land surface properties. This paper contributes to the simulation of land surface emission and estimation of vegetation optical depth (VOD) at multiple frequencies using a discrete scattering model with a single set of model parameter values. Validity of the Tor Vergata (TVG) discrete scattering model in simultaneously reproducing the Soil Moisture Active Passive (SMAP) L-band (1.4 GHz) and Advanced Microwave Scanning Radiometer 2 (AMSR2) C- (6.925 GHz) and X-band (10.7 GHz) observations over the Tibetan grassland ecosystem is evaluated. Frequency-specific and multi-frequency calibration strategies are implemented to find the suitable set of model parameter values and to isolate the impact of frequency on parameter values. On this basis, the calibrated TVG model is further used to estimate the VOD, and to investigate the impact of microwave frequency and observation angle on the emission simulations and VOD parameterization.The results show that both frequency-specific and multi-frequency calibration strategies achieve comparable and reasonable simulations of SMAP and AMSR2 observations, confirming the feasibility of using an identical physically-based model (i.e. the calibrated TVG model) to simulate multi-frequency land emission driven by a single set of model parameter values. As such, the dependence of emission components and VOD on frequency can be elaborated after isolating the impact of frequency on parameter values. The VOD values derived from the TVG simulations generally increase with increasing frequency and can be linearly correlated to the LAI variations, while current satellite-based retrievals have almost the same magnitude at the L-, C-, and X-band. The explanation for this can be that the retrieved VOD is different from the theoretical definition. Sensitivity test performed using the calibrated TVG model further shows that polarization-dependence of VOD becomes more apparent with the increasing observation angle and frequency. New parameterization has thus been developed to characterize the dependence of VOD on the frequency, observation angle, and polarization for grassland based on the results of sensitivity test. This study may provide new insights in improving model of land emission and retrievals of SM and VOD with physical interpretability based on multi-frequency satellite observations.

Phenomenological analysis of simple ion channel block in large populations of uncoupled cardiomyocytes.

Current understanding of arrhythmia mechanisms and design of anti-arrhythmic drug therapies hinges on the assumption that myocytes from the same region of a single heart have similar, if not identical, action potential waveforms and drug responses. On the contrary, recent experiments reveal significant heterogeneity in uncoupled healthy myocytes both from different hearts as well as from identical regions within a single heart. In this work, a methodology is developed for quantifying the individual electrophysiological properties of large numbers of uncoupled cardiomyocytes under ion channel block in terms of the parameters values of a conceptual fast-slow model of electrical excitability. The approach is applied to a population of nearly 500 rabbit ventricular myocytes for which action potential duration (APD) before and after the application of the drug nifedipine was experimentally measured (Lachaud et al., 2022, Cardiovasc. Res.). To this end, drug action is represented by a multiplicative factor to an effective ion conductance, a closed form asymptotic expression for APD is derived and inverted to determine model parameters as functions of APD and $\varDelta $APD (drug-induced change in APD) for each myocyte. Two free protocol-related quantities are calibrated to experiment using an adaptive-domain procedure based on an original assumption of optimal excitability. The explicit APD expression and the resulting set of model parameter values allow (a) direct evaluation of conditions necessary to maintain fixed APD or $\varDelta $APD, (b) predictions of the proportion of cells remaining excitable after drug application, (c) predictions of stimulus period dependency and (d) predictions of dose-response curves, the latter being in agreement with additional experimental data.

Large Isotropic Elastic Deformations: On a Comprehensive Model to Correlate the Theory and Experiments for Incompressible Rubber-Like Materials

A comprehensive model, i.e., a model that: (i) suitably captures the mechanical behaviour of various types of rubber-like materials; (ii) describes the constitutive behaviour of a subject rubber-like specimen under different deformation modes via a single set of model parameter values, and (iii) is parent to many of the existing models of distinct types, is presented in this paper for application to the finite deformation of incompressible isotropic rubber-like materials. The model breaks away from Rivlin’s principal invariants I_{i} and Valanis-Landel’s separable function of principal stretches lambda _{i} representations, and instead adopts a general non-separable functional form W( lambda _{1}, lambda _{2}, lambda _{3} ), subject to the incompressibility constraint. By way of example, the application of the model to extant datasets from four types of rubber-like materials that exhibit discernible mechanical behaviours, namely natural unfilled and filled rubbers, hydrogels and (extremely) soft tissue specimens, will be considered. The favourable correlation between the model predictions and the considered experimental datasets, obtained via simultaneous fitting of the model to the data of various deformations, will be demonstrated. It will be shown that most of the landmark models in the literature including the W( I_{1}, I_{2} ) form Mooney-Rivlin, the Gent-like limiting chain extensibility, the nonaffine tube and the separable principal stretches-based type Ogden models are all a special sub-set of the presented parent model, and are all recovered from this model. An important implication of the non-separable functional form of the model will be conferred, through a specific dataset, where the predictions of the separable functions prove inherently inadequate. The consequences of these improvements for a more accurate modelling of the finite deformation of incompressible isotropic rubber-like materials will also be discussed.

Simulation models for the minimum velocity for foam generation and propagation

Foam injection is a promising means of reducing the relative mobility of gas, and hence improving the sweep efficiency of gas, in CO2 and H2 storage, soil-contaminant removal in aquifer remediation, enhanced oil recovery, and matrix-acid well stimulation. Theory (Rossen and Gauglitz, 1990; Ashoori et al., 2012) and experiments (Gauglitz et al., 2002; Yu et al., 2019, 2020) indicate that both foam generation and propagation in steady flow in porous media require the attainment of a sufficiently large superficial velocity or pressure gradient ∇P. Here we examine several foam-simulation models for their ability to represent a minimum velocity, or trigger, for foam generation. We define criteria for representation of such a trigger. For simplicity, we assume a homogeneous porous medium and absence of an oleic phase. We examine the Population-Balance (PB) models of Kam and Rossen (2003) and one of its variants (Kam, 2008), and the PB model of Chen et al. (2010); and the implicit-texture (IT) models in CMG-STARS (Computer Modeling Group, 2017) and of Lotfollahi et al. (2017).Our result show that the PB models of Kam and Rossen and its variant, and the IT models of CMG-STARS and of Lotfollahi et al. do represent a minimum velocity for foam generation. They achieve this by modeling an abrupt decrease in gas mobility with increasing pressure gradient over some range of ∇P. The model of Chen et al. (2010) is based on the model of Kovscek and Radke (1996), which was not intended to represent a trigger for foam generation (Kovscek and Radke, 1993). We cannot say categorically whether it could predict a trigger for any set of model parameter values. Instead, we derive criteria that must be satisfied by the choice of parameters to represent a trigger for foam generation.In simulations of radial foam propagation the STARS foam model predicts that foam propagation fails at the radius at which local ∇P cannot maintain strong foam, not at a greater velocity and ∇P as seen in experiments (Yu et al., 2020). In addition, we identify a fundamental challenge in representing foam generation at the large ∇P at the wellbore in a numerical simulation: conventional simulators do not represent ∇P at the wellbore. Foam generation at the very high superficial velocity at the well radius is not represented in the absence of truly exceptional grid refinement.

Controls on turnover of marine dissolved organic matter—testing the null hypothesis of purely concentration‐driven uptake: Comment on Shen and Benner, “Molecular properties are a primary control on the microbial utilization of dissolved organic matter in the ocean”

Controls on turnover of marine dissolved organic matter—testing the null hypothesis of purely concentration‐driven uptake: Comment on Shen and Benner, “Molecular properties are a primary control on the microbial utilization of dissolved organic matter in the ocean”

ASSESSMENT OF A NEW ISOTROPIC HYPERELASTIC CONSTITUTIVE MODEL FOR A RANGE OF RUBBERLIKE MATERIALS AND DEFORMATIONS

ABSTRACT The choice of an appropriate strain energy function W is key to accurate modeling and computational finite element analysis of the mechanical behavior of unfilled non-crystalizing rubberlike materials. Despite the existing variety of models, finding a suitable model that can capture many deformation modes of a rubber specimen with a single set of parameter values and satisfy the a priori mathematical and structural requirements remains a formidable task. Previous work proposed a new generalized neo-Hookean W (I1) function (doi: 10.1016/j.ijnonlinmec.2020.103626), showing a promising fitting capability and enjoying a structural basis. In this work we use two extended forms of that model which include an I2 term adjunct, W(I1,I2), for application to various boundary value problems commonly encountered in rubber mechanics applications. Specifically, two functional forms of the I2 invariant are considered: a linear function and a logarithmic function. The boundary value problems of interest include the in-plane uniaxial, equi-biaxial, and pure shear deformations and simple shear, inflation, and nonhomogeneous deformations such as torsion. By simultaneous fitting of each model to various deformation modes of rubber specimens, it is demonstrated that a single set of model parameter values favorably captures the mechanical response for all the considered deformations of each specimen. It is further shown that the model with a logarithmic I2 function provides better fits than the linear function. Given the functional simplicity of the considered W (I1, I2) models, the low number of model parameters (three in total), the structurally motivated bases of the models, and their capability to capture the mechanical response for various deformations of rubber specimens, the considered models are recommended as a powerful tool for practical applications and analysis of rubber elasticity.

Reducing the uncertainty on chilling requirements for endodormancy breaking of temperate fruits by data-based parameter estimation of the dynamic model: a test case in apricot.

The Dynamic model has been described as one of the most accurate models to quantify chill accumulation based on hourly temperatures in nuts and temperate fruits. This model considers that a dynamic process occurs at a biochemical level that determines the endodormancy breaking through the accumulation of the so-called portions. The kinetic parameters present in the model should reflect how the fruit trees integrate chilling exposure and thus they should be characteristic for each species. However, the original parameter values, reported in the late 1980s, are still being used. Even if the use of such parameter values is useful to compare among chilling requirements (CRs) for different species or cultivars, it is not the optimal choice when one intends to explain the CR variations in different years for a given cultivar. In this work we propose a data-based model calibration that makes use of phenological data for different apricot cultivars within different years to obtain model parameters, which minimize the variations among years and that have, at the same time, physical meaning to characterize the incumbent species. Results reveal that the estimation not only reduces the accumulated portion dispersion within the considered time periods but also allows to improve the CR predictions for subsequent years. We propose a set of model parameter values to predict endodormancy breaking dates in the apricot cultivars studied here.

Towards a Multiscale Model of Acute HIV Infection

Human Immunodeficiency Virus (HIV) infection of humans represents a complex biological system and a great challenge to public health. Novel approaches for the analysis and prediction of the infection dynamics based on a multi-scale integration of virus ontogeny and immune reactions are needed to deal with the systems' complexity. The aim of our study is: (1) to formulate a multi-scale mathematical model of HIV infection; (2) to implement the model computationally following a hybrid approach; and (3) to calibrate the model by estimating the parameter values enabling one to reproduce the standard observed dynamics of HIV infection in blood during the acute phase of primary infection. The modeling approach integrates the processes of infection spread and immune responses in Lymph Nodes (LN) to that observed in blood. The spatio-temporal population dynamics of T lymphocytes in LN in response to HIV infection is governed by equations linking an intracellular regulation of the lymphocyte fate by intercellular cytokine fields. We describe the balance of proliferation, differentiation and death at a single cell level as a consequence of gene activation via multiple signaling pathways activated by IL-2, IFNa and FasL. Distinct activation thresholds are used in the model to relate different modes of cellular responses to the hierarchy of the relative levels of the cytokines. We specify a reference set of model parameter values for the fundamental processes in lymph nodes that ensures a reasonable agreement with viral load and CD4 + T cell dynamics in blood.

Calibration of hydrodynamic model-driven sewer maintenance

Sewer performance is typically assessed using hydrodynamic models assuming the absence of in-sewer defects. As a consequence, hydraulic performance calculated by models is likely to be overestimated, while the real hydraulic performance of the sewer system remains unknown. This article introduces the concept of ‘hydraulic fingerprinting’ based on model calibration to identify in-sewer defects affecting hydraulic performance. Model calibration enables detection of changes in hydraulic properties of the sewer system. Each model calibration results in a set of model parameter values, their uncertainties and residuals. The model parameter values also incorporate the antecedent condition of the catchment of the event calibrated and are therefore less suitable to identify in-sewer defects. The residuals on the other hand, and more specifically their absolute values, statistical properties and the correlation between residuals at different monitoring locations are suitable as indicators of the occurrence of in-sewer defects. This allows the application of ‘hydraulic fingerprinting’ based on model calibration, where the ‘fingerprint’ is defined by the model parameters and the residuals. The concept of ‘fingerprinting’ is demonstrated for the combined sewer system ‘Tuindorp’ (Utrecht, the Netherlands). The results show that ‘hydraulic fingerprinting’ can be a powerful tool for directing sewer asset management actions.

Joint probabilistic inference of multi-Gaussian conductivity fields and their associated variograms from indirect hydrological data

PUBLICATIONS Water Resources Research RESEARCH ARTICLE 10.1002/2014WR016395 Key Points: Joint Bayesian inference of Gaussian conductivity fields and their variograms A dimensionality reduction that systematically honors the underlying variogram Distributed multiprocessor implementation is straightforward Correspondence to: E. Laloy, elaloy@sckcen.be Citation: Laloy, E., N. Linde, D. Jacques, and J. A. Vrugt (2015), Probabilistic inference of multi-Gaussian fields from indirect hydrological data using circulant embedding and dimensionality reduction, Water Resour. Res., 51, 4224–4243, doi:10.1002/2014WR016395. Received 10 SEP 2014 Accepted 14 MAY 2015 Accepted article online 19 MAY 2015 Published online 12 JUN 2015 Probabilistic inference of multi-Gaussian fields from indirect hydrological data using circulant embedding and dimensionality reduction Eric Laloy 1,2 , Niklas Linde 3 , Diederik Jacques 1 , and Jasper A. Vrugt 2,4 Institute for Environment, Health and Safety, Belgian Nuclear Research Centre, Mol, Belgium, 2 Department of Civil and Environmental Engineering, University of California, Irvine, California, USA, 3 Applied and Environmental Geophysics Group, Institute of Earth Sciences, University of Lausanne, Lausanne, Switzerland, 4 Department of Earth Systems Science, University of California, Irvine, California, USA Abstract We present a Bayesian inversion method for the joint inference of high-dimensional multi- Gaussian hydraulic conductivity fields and associated geostatistical parameters from indirect hydrological data. We combine Gaussian process generation via circulant embedding to decouple the variogram from grid cell specific values, with dimensionality reduction by interpolation to enable Markov chain Monte Carlo (MCMC) simulation. Using the Mat ern variogram model, this formulation allows inferring the conductivity values simultaneously with the field smoothness (also called Mat ern shape parameter) and other geostatisti- cal parameters such as the mean, sill, integral scales and anisotropy direction(s) and ratio(s). The proposed dimensionality reduction method systematically honors the underlying variogram and is demonstrated to achieve better performance than the Karhunen-Loe`ve expansion. We illustrate our inversion approach using synthetic (error corrupted) data from a tracer experiment in a fairly heterogeneous 10,000-dimensional 2-D conductivity field. A 40-times reduction of the size of the parameter space did not prevent the posterior simulations to appropriately fit the measurement data and the posterior parameter distributions to include the true geostatistical parameter values. Overall, the posterior field realizations covered a wide range of geostatistical models, questioning the common practice of assuming a fixed variogram prior to inference of the hydraulic conductivity values. Our method is shown to be more efficient than sequential Gibbs sampling (SGS) for the considered case study, particularly when implemented on a distributed computing cluster. It is also found to outperform the method of anchored distributions (MAD) for the same computational budget. 1. Introduction High-parameter dimensionality poses considerable challenges for the inversion of groundwater flow and transport data [e.g., Kitanidis, 1995; Hendricks-Franssen et al., 2009; Laloy et al., 2013; Zhou et al., 2014, and references therein]. What is more, conceptual and structural inadequacies of the subsurface model and measurement errors of the model input (boundary conditions) and output (calibration) data introduce uncertainty in the estimated parameters and model simulations. Another important source of uncertainty originates from sparse data coverages that rarely contain sufficient information to uniquely characterize the subsurface at a spatial resolution deemed necessary for accurate modeling. This results in an ill-posed inverse problem with many different sets of model parameter values that fit the data acceptably well. Inver- sion methods should consider this inherent uncertainty and provide an ensemble of model realizations that accurately span the range of possible models that honor the available calibration data and prior information. C 2015. American Geophysical Union. V All Rights Reserved. LALOY ET AL. Hydraulic conductivity (K) fields are typically assumed to be stationary and log-normally distributed with a spatial structure determined by a two-point geostatistical model or variogram [e.g., Rubin, 2003]. Unfortu- nately, a lack of (sufficient) point K measurements (if any) makes it difficult to estimate directly the geostatis- tical parameters (mean, sill, variogram model, integral scales and anisotropy factors) from variographic analysis [Ortiz and Deutsch, 2002; Nowak et al., 2010]. Simultaneous (inverse) inference of conductivity values and associated geostatistical parameters is therefore attractive yet computationally challenging. Indeed, only a few studies can be found in the literature that have attempted simultaneous estimation using global and probabilistic search methods. For example, Jafarpour and Tarrahi [2011] used the Ensemble Kalman JOINT FIELD/VARIOGRAM MCMC INVERSION

Projected finite elements for reaction–diffusion systems on stationary closed surfaces

In this paper we present a robust, efficient and accurate finite element method for solving reaction–diffusion systems on stationary spheroidal surfaces (these are surfaces which are deformations of the sphere such as ellipsoids, dumbbells, and heart-shaped surfaces) with potential applications in the areas of developmental biology, cancer research, wound healing, tissue regeneration, and cell motility among many others where such models are routinely used. Our method is inspired by the radially projected finite element method introduced in [39]. (Hence the name “projected” finite element method.) The advantages of the projected finite element method are that it is easy to implement and that it provides a conforming finite element discretization which is “logically” rectangular. To demonstrate the robustness, applicability and generality of this numerical method, we present solutions of reaction–diffusion systems on various spheroidal surfaces. We show that the method presented in this paper preserves positivity of the solutions of reaction–diffusion equations which is not generally true for Galerkin type methods. We conclude that surface geometry plays a pivotal role in pattern formation. For a fixed set of model parameter values, different surfaces give rise to different pattern generation sequences of either spots or stripes or a combination (observed as circular spot-stripe patterns). These results clearly demonstrate the need for detailed theoretical analytical studies to elucidate how surface geometry and curvature influence pattern formation on complex surfaces.

Effects of climate and nutrient load on the water quality of shallow lakes assessed through ensemble runs by PCLake.

Complex ecological models are used to predict the consequences of anticipated future changes in climate and nutrient loading for lake water quality. These models may, however, suffer from nonuniqueness in that various sets of model parameter values may yield equally satisfactory representations of the system being modeled, but when applied in future scenarios these sets of values may divert considerably in their simulated outcomes. Compilation of an ensemble of model runs allows us to account for simulation variability arising from model parameter estimates. Thus, we propose a new approach for aquatic ecological models creating a more robust prediction of future water quality. We used our ensemble approach in an application of the widely used PCLake model for Danish shallow Lake Arreskov, which during the past two decades has demonstrated frequent shifts between turbid and clear water states. Despite marked variability, the span of our ensemble runs encapsulated 70–90% of the observed variation in lake water quality. The model exercise demonstrates that future warming and increased nutrient loading lead to lower probability of a clear water, vegetation-rich state and greater likelihood of cyanobacteria dominance. In a 6.0°C warming scenario, for instance, the current nutrient loading of nitrogen and phosphorus must be reduced by about 75% to maintain the present ecological state of Lake Arreskov, but even in a near-future 2.0°C warming scenario, a higher probability of a turbid, cyanobacteria-dominated state is predicted. As managers may wish to determine the probability of achieving a certain ecological state, our proposed ensemble approach facilitates new ways of communicating future stressor impacts.

Unified Analytic Model for Current–Voltage Behavior in Amorphous Oxide Semiconductor TFTs

We present a simple and semi-physical analytical description of the current-voltage characteristics of amorphous oxide semiconductor thin-film transistors in the above-threshold and sub-threshold regions. Both regions are described by single unified expression that employs the same set of model parameter values directly extracted from measured terminal characteristics. The model accurately reproduces measured characteristics of amorphous semiconductor thin film transistors in general, yielding a scatter of <;4%.

A guide to sensitivity analysis of quantitative models of gene expression dynamics

We provide a guide to performing a sensitivity analysis (SA) of quantitative models of gene expression dynamics appropriate to the levels of uncertainty in the model: spanning cases where parameters are relatively well-constrained to cases where they are poorly constrained. In the well-constrained case, we present methods to perform “local” SA (LSA), which considers small perturbations for a single set of model parameter values. In the poorly-constrained case, we present methods to perform “global” SA (GSA) as a means to evaluate the sensitivity of a model over large regions of parameter space. We apply these methods to quantitative models of increasing complexity. The models we consider are simple logistic growth, negative feedback in a mRNA–protein model, and two models of decision making within bacteriophage λ. We discuss the best practices for how SA can be utilized in an iterative fashion to advance biological understanding.

Identification of constitutive parameters of soil using an optimization strategy and statistical analysis

The paper at hand investigates a strategy to calibrate different constitutive models for soils via back analysis. The efficiency and reliability of the parameter identification for soil models is worked out. In order to demonstrate of how to utilise identification procedures, results from optimisation against conventional oedometer and drained triaxial compression tests on natural Pappadai clay are presented and discussed. The aim of geotechnical optimisation problems is to obtain a set of model parameter values that provide the best match between soil model simulations and appropriate measurements. For the parameter identification process, a constrained population-based algorithm is chosen, namely the Particle Swarm Optimiser. The identification is carried out in an initial step separately on each test and then simultaneously on oedometer and triaxial tests. The evaluation is performed employing three different constitutive models of varying complexity and number of constitutive parameters.A subsequent residual analysis and the computation of confidence intervals for the parameters provide valuable results to assess the quality of the identified parameters in correlation with the evaluated data. Therefore, criteria of the utility and reliability of the mathematical models for further prognosis computations can be estimated.

A Detailed Polymerization Model for Cerenol® Polyols

AbstractSummary: A mathematical model of the acid catalyzed 1,3‐propanediol polymerization has been developed. Two catalysts investigated include sulfuric acid and superacid (tetrafluoroethane sulfonic acid or triflic acid). Based on a detailed reaction mechanism, population and mass balance equations have been derived for small molecules as well as for polymeric species of numerous chain distributions, which are distinguishable in terms of protonation state and end group functionality. Due to the interaction of the sulfuric acid catalyst with the polymer ends, a novel, dual index polymer chain distribution was derived and implemented.The model has been validated with various sets of experimental data obtained in a lab‐scale reactor setup. Dynamic model outputs such as monomer concentration, molecular weight averages, unsaturated and sulfate end groups, water evaporation rate and sulfate middle groups have been compared with experimental data of sulfuric and super acid catalyzed polymerization runs. Very good agreement between model predictions and experimental data has been obtained for both catalyst systems over an extended range of conditions using the same set of model parameter values. It is worth noting that the model is also capable of predicting polymerization equilibrium.

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.

On the dynamic modeling of mammalian cell metabolism and mAb production

A general optimization-based technique for the estimation of kinetic parameter values in dynamic models of cell metabolism is presented. A discretization strategy is used to transform continuous differential equations given in the model into an approximating set of algebraic equations. The discretized equation set is then used to constrain a non-linear optimization problem, whose solution is an optimal set of model parameter values. As a case study, we examine a simplified dynamic model of mammalian cell culture [Gao, J., Gorenflo, V. M., Scharer, J. M., & Budman, H. M. (2007). Dynamic metabolic modeling for a mab bioprocess. Biotechnology Progress, 23 (1), 168–181]. Our parameter estimation technique is shown to solve the unsimplified variant of this model, and to provide a more accurate simulation of the experimentally observed system behavior than originally reported. We are additionally able to predict physically reasonable system data even in the absence of corresponding experimental measurements, and, finally, to provide a quantitative basis for challenging certain underlying assumptions in the original model solution.

Branched pore kinetic model analysis of geosmin adsorption on super-powdered activated carbon

Super-powdered activated carbon (S-PAC) is activated carbon of much finer particle size than powdered activated carbon (PAC). Geosmin is a naturally occurring taste and odor compound that impairs aesthetic quality in drinking water. Experiments on geosmin adsorption on S-PAC and PAC were conducted, and the results using adsorption kinetic models were analyzed. PAC pulverization, which produced the S-PAC, did not change geosmin adsorption capacity, and geosmin adsorption capacities did not differ between S-PAC and PAC. Geosmin adsorption kinetics, however, were much higher on S-PAC than on PAC. A solution to the branched pore kinetic model (BPKM) was developed, and experimental adsorption kinetic data were analyzed by BPKM and by a homogeneous surface diffusion model (HSDM). The HSDM describing the adsorption behavior of geosmin required different surface diffusivity values for S-PAC and PAC, which indicated a decrease in surface diffusivity apparently associated with activated carbon particle size. The BPKM, consisting of macropore diffusion followed by mass transfer from macropore to micropore, successfully described the batch adsorption kinetics on S-PAC and PAC with the same set of model parameter values, including surface diffusivity. The BPKM simulation clearly showed geosmin removal was improved as activated carbon particle size decreased. The simulation also implied that the rate-determining step in overall mass transfer shifted from intraparticle radial diffusion in macropores to local mass transfer from macropore to micropore. Sensitivity analysis showed that adsorptive removal of geosmin improved with decrease in activated carbon particle size down to 1 μm, but further particle size reduction produced little improvement.