Uncertainty Evaluation of a Groundwater Conceptual Model by Using a Multimodel Averaging Method

ABSTRACT

A groundwater field is a complex and open system. Groundwater simulation and prediction often deviated from true values, which is attributed to the uncertainty of groundwater modeling. The conceptual model (model struture) is one of the main sources of groundwater modeling uncertianty. In this study, the mean Euclidean distance (MED) between model simulations and observations is proposed to assess the integrated likelihood value of a conceptual model in Bayesian model averaging (BMA). Moreover, this proposed BMA method is compared with the traditional generalized likelihood uncertainty estimation (GLUE) BMA method by a synthetical groundwater model, and the characteristics of these two BMA methods are summarized.     

Evaluation of habitat suitability index models by global sensitivity and uncertainty analyses: a case study for submerged aquatic vegetation

Habitat suitability index (HSI) models are commonly used to predict habitat quality and species distributions and are used to develop biological surveys, assess reserve and management priorities, and anticipate possible change under different management or climate change scenarios. Important management decisions may be based on model results, often without a clear understanding of the level of uncertainty associated with model outputs. We present an integrated methodology to assess the propagation of uncertainty from both inputs and structure of the HSI models on model outputs (uncertainty analysis: UA) and relative importance of uncertain model inputs and their interactions on the model output uncertainty (global sensitivity analysis: GSA). We illustrate the GSA/UA framework using simulated hydrology input data from a hydrodynamic model representing sea level changes and HSI models for two species of submerged aquatic vegetation (SAV) in southwest Everglades National Park: Vallisneria americana (tape grass) and Halodule wrightii (shoal grass). We found considerable spatial variation in uncertainty for both species, but distributions of HSI scores still allowed discrimination of sites with good versus poor conditions. Ranking of input parameter sensitivities also varied spatially for both species, with high habitat quality sites showing higher sensitivity to different parameters than low‐quality sites. HSI models may be especially useful when species distribution data are unavailable, providing means of exploiting widely available environmental datasets to model past, current, and future habitat conditions. The GSA/UA approach provides a general method for better understanding HSI model dynamics, the spatial and temporal variation in uncertainties, and the parameters that contribute most to model uncertainty. Including an uncertainty and sensitivity analysis in modeling efforts as part of the decision‐making framework will result in better‐informed, more robust decisions.     

Good modeling practice for PAT applications: Propagation of input uncertainty and sensitivity analysis

The uncertainty and sensitivity analysis are evaluated for their usefulness as part of the model‐building within Process Analytical Technology applications. A mechanistic model describing a batch cultivation of Streptomyces coelicolor for antibiotic production was used as case study. The input uncertainty resulting from assumptions of the model was propagated using the Monte Carlo procedure to estimate the output uncertainty. The results showed that significant uncertainty exists in the model outputs. Moreover the uncertainty in the biomass, glucose, ammonium and base‐consumption were found low compared to the large uncertainty observed in the antibiotic and off‐gas CO₂ predictions. The output uncertainty was observed to be lower during the exponential growth phase, while higher in the stationary and death phases ‐ meaning the model describes some periods better than others. To understand which input parameters are responsible for the output uncertainty, three sensitivity methods (Standardized Regression Coefficients, Morris and differential analysis) were evaluated and compared. The results from these methods were mostly in agreement with each other and revealed that only few parameters (about 10) out of a total 56 were mainly responsible for the output uncertainty. Among these significant parameters, one finds parameters related to fermentation characteristics such as biomass metabolism, chemical equilibria and mass‐transfer. Overall the uncertainty and sensitivity analysis are found promising for helping to build reliable mechanistic models and to interpret the model outputs properly. These tools make part of good modeling practice, which can contribute to successful PAT applications for increased process understanding, operation and control purposes. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009     

MARS Approach for Global Sensitivity Analysis of Differential Equation Models with Applications to Dynamics of Influenza Infection

Differential equation models are widely used for the study of natural phenomena in many fields. The study usually involves unknown factors such as initial conditions and/or parameters. It is important to investigate the impact of unknown factors (parameters and initial conditions) on model outputs in order to better understand the system the model represents. Apportioning the uncertainty (variation) of output variables of a model according to the input factors is referred to as sensitivity analysis. In this paper, we focus on the global sensitivity analysis of ordinary differential equation (ODE) models over a time period using the multivariate adaptive regression spline (MARS) as a meta model based on the concept of the variance of conditional expectation (VCE). We suggest to evaluate the VCE analytically using the MARS model structure of univariate tensor-product functions which is more computationally efficient. Our simulation studies show that the MARS model approach performs very well and helps to significantly reduce the computational cost. We present an application example of sensitivity analysis of ODE models for influenza infection to further illustrate the usefulness of the proposed method.     

A tool for simulating and communicating uncertainty when modelling species distributions under future climates

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Effects of branch length uncertainty on Bayesian posterior probabilities for phylogenetic hypotheses

In Bayesian phylogenetics, confidence in evolutionary relationships is expressed as posterior probability--the probability that a tree or clade is true given the data, evolutionary model, and prior assumptions about model parameters. Model parameters, such as branch lengths, are never known in advance; Bayesian methods incorporate this uncertainty by integrating over a range of plausible values given an assumed prior probability distribution for each parameter. Little is known about the effects of integrating over branch length uncertainty on posterior probabilities when different priors are assumed. Here, we show that integrating over uncertainty using a wide range of typical prior assumptions strongly affects posterior probabilities, causing them to deviate from those that would be inferred if branch lengths were known in advance; only when there is no uncertainty to integrate over does the average posterior probability of a group of trees accurately predict the proportion of correct trees in the group. The pattern of branch lengths on the true tree determines whether integrating over uncertainty pushes posterior probabilities upward or downward. The magnitude of the effect depends on the specific prior distributions used and the length of the sequences analyzed. Under realistic conditions, however, even extraordinarily long sequences are not enough to prevent frequent inference of incorrect clades with strong support. We found that across a range of conditions, diffuse priors--either flat or exponential distributions with moderate to large means--provide more reliable inferences than small-mean exponential priors. An empirical Bayes approach that fixes branch lengths at their maximum likelihood estimates yields posterior probabilities that more closely match those that would be inferred if the true branch lengths were known in advance and reduces the rate of strongly supported false inferences compared with fully Bayesian integration.     

Uncertainty in predicting range dynamics of endemic alpine plants under climate warming

Correlative species distribution models have long been the predominant approach to predict species’ range responses to climate change. Recently, the use of dynamic models is increasingly advocated for because these models better represent the main processes involved in range shifts and also simulate transient dynamics. A well‐known problem with the application of these models is the lack of data for estimating necessary parameters of demographic and dispersal processes. However, what has been hardly considered so far is the fact that simulating transient dynamics potentially implies additional uncertainty arising from our ignorance of short‐term climate variability in future climatic trends. Here, we use endemic mountain plants of Austria as a case study to assess how the integration of decadal variability in future climate affects outcomes of dynamic range models as compared to projected long‐term trends and uncertainty in demographic and dispersal parameters. We do so by contrasting simulations of a so‐called hybrid model run under fluctuating climatic conditions with those based on a linear interpolation of climatic conditions between current values and those predicted for the end of the 21st century. We find that accounting for short‐term climate variability modifies model results nearly as differences in projected long‐term trends and much more than uncertainty in demographic/dispersal parameters. In particular, range loss and extinction rates are much higher when simulations are run under fluctuating conditions. These results highlight the importance of considering the appropriate temporal resolution when parameterizing and applying range‐dynamic models, and hybrid models in particular. In case of our endemic mountain plants, we hypothesize that smoothed linear time series deliver more reliable results because these long‐lived species are primarily responsive to long‐term climate averages.     

Too wet and too dry? Uncertainty of DEM as a potential source of significant errors in a model-based water level assessment in riparian and mire ecosystems

Modelling groundwater depths in floodplains and peatlands remains a basic approach to assessing hydrological conditions of habitats. Groundwater flow models used to compute groundwater heads are known for their uncertainties, and the calibration of these models and the uncertainty assessments of parameters remain fundamental steps in providing reliable data. However, the elevation data used to determine the geometry of model domains are frequently considered deterministic and hence are seldom considered a source of uncertainty in model-based groundwater level estimations. Knowing that even the cutting-edge laser-scanning-based digital elevation models have errors due to vegetation effects and scanning procedure failures, we provide an assessment of uncertainty of water level estimations that remain basic data for wetland ecosystem assessment and management. We found that the uncertainty of the digital elevation model (DEM) significantly influenced the results of the assessment of the habitat’s hydrological conditions expressed as groundwater depths. In extreme cases, although the average habitat suitability index (HSI) assessed in a deterministic manner was defined as ‘unsuitable’, in a probabilistic approach (grid-cell-scale estimation), it reached a value of 40% probability, signifying ‘optimum’ or ‘tolerant’. For the 24 habitats analysed, we revealed vast differences between HSI scores calculated for individual grid cells of the model and HSI scores computed as average values from the set of grid cells located within the habitat patches. We conclude that groundwater-modelling-based decision support approaches to wetland assessment can result in incorrect management if the quality of DEM has not been addressed in studies referring to groundwater depths.     

Assessing uncertainty of nitrate variability in groundwater

Nitrate is the primary form of nitrogen in natural waters and it can easily pass through soil to groundwater. Some levels of nitrate concentration in groundwater can cause some health problems such as methemoglobinemia in infants and several cancers. Since geological structures are not homogeneous, investigation of spatial variability of nitrate concentrations in groundwater is characterized by particularly high uncertainties. In this paper, a novel methodology for measure of uncertainty in groundwater nitrate variability is presented. To appraise the fuzziness, which is a type of uncertainty in spatial models, point cumulative semimadogram (PCSM) measure and a metric distance were employed. Measures of fuzziness have been carried out for each location using the experimental and model PCSMs. Finally an uncertainty map, which defines the regional variation of the uncertainty in different categories, has been composed.     

On the reliability of peptide nonplanarity seen in ultra‐high resolution crystal structures

Ultra‐high resolution protein crystal structures have been considered as relatively reliable sources for defining details of protein geometry, such as the extent to which the peptide unit deviates from planarity. Chellapa and Rose (Proteins 2015; 83:1687) recently called this into question, reporting that for a dozen representative protein structures determined at ～1 Å resolution, the diffraction data could be equally well fit with models restrained to have highly planar peptides, i.e. having a standard deviation of the ω torsion angles of only ～1° instead of the typically observed value of ～6°. Here, we document both conceptual and practical shortcomings of that study and show that the more tightly restrained models are demonstrably incorrect and do not fit the diffraction data equally well. We emphasize the importance of inspecting electron density maps when investigating the agreement between a model and its experimental data. Overall, this report reinforces that modern standard refinement protocols have been well‐conceived and that ultra‐high resolution protein crystal structures, when evaluated carefully and used with an awareness of their levels of coordinate uncertainty, are powerful sources of information for providing reliable information about the details of protein geometry.     

Long-Branch Attraction Bias and Inconsistency in Bayesian Phylogenetics

Bayesian inference (BI) of phylogenetic relationships uses the same probabilistic models of evolution as its precursor maximum likelihood (ML), so BI has generally been assumed to share ML''s desirable statistical properties, such as largely unbiased inference of topology given an accurate model and increasingly reliable inferences as the amount of data increases. Here we show that BI, unlike ML, is biased in favor of topologies that group long branches together, even when the true model and prior distributions of evolutionary parameters over a group of phylogenies are known. Using experimental simulation studies and numerical and mathematical analyses, we show that this bias becomes more severe as more data are analyzed, causing BI to infer an incorrect tree as the maximum a posteriori phylogeny with asymptotically high support as sequence length approaches infinity. BI''s long branch attraction bias is relatively weak when the true model is simple but becomes pronounced when sequence sites evolve heterogeneously, even when this complexity is incorporated in the model. This bias—which is apparent under both controlled simulation conditions and in analyses of empirical sequence data—also makes BI less efficient and less robust to the use of an incorrect evolutionary model than ML. Surprisingly, BI''s bias is caused by one of the method''s stated advantages—that it incorporates uncertainty about branch lengths by integrating over a distribution of possible values instead of estimating them from the data, as ML does. Our findings suggest that trees inferred using BI should be interpreted with caution and that ML may be a more reliable framework for modern phylogenetic analysis.     

Data quality

A methodology is presented that enables incorporating expert judgment regarding the variability of input data for environmental life cycle assessment (LCA) modeling. The quality of input data in the life-cycle inventory (LCI) phase is evaluated by LCA practitioners using data quality indicators developed for this application. These indicators are incorporated into the traditional LCA inventory models that produce non-varying point estimate results (i.e., deterministic models) to develop LCA inventory models that produce results in the form of random variables that can be characterized by probability distributions (i.e., stochastic models). The outputs of these probabilistic LCA models are analyzed using classical statistical methods for better decision and policy making information. This methodology is applied to real-world beverage delivery system LCA inventory models. The inventory study results for five beverage delivery system alternatives are compared using statistical methods that account for the variance in the model output values for each alternative. Sensitivity analyses are also performed that indicate model output value variance increases as input data uncertainty increases (i.e., input data quality degrades). Concluding remarks point out the strengths of this approach as an alternative to providing the traditional qualitative assessment of LCA inventory study input data with no efficient means of examining the combined effects on the model results. Data quality assessments can now be captured quantitatively within the LCA inventory model structure. The approach produces inventory study results that are variables reflecting the uncertainty associated with the input data. These results can be analyzed using statistical methods that make efficient quantitative comparisons of inventory study alternatives possible. Recommendations for future research are also provided that include the screening of LCA inventory model inputs for significance and the application of selection and ranking techniques to the model outputs.     

不同水分条件下胡杨光响应曲线拟合模型比较

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两种预测模型在地下水动态中的比较与应用

预测陕西洛惠渠灌区地下水动态变化情况,在综合分析了各种地下水动态研究方法的基础上,提出了基于支持向量机和改进的BP神经网络模型的灌区地下水动态预测方法,并在MATLAB中编制了相应的计算机程序,建立了相应的地下水动态预测模型。以灌区多年实例数据为学习样本和测试样本,比较了两种模型的地下水动态预测优劣性。研究表明,支持向量机模型和BP网络模型在样本训练学习过程中都具较高的模拟精度,而在样本学习阶段,支持向量机的预测精度明显优于BP网络,可以很好的描述地下水动态复杂的耦合关系。支持向量机方法切实可行,更加适合大型灌区地下水动态预测,是对传统地下水动态研究方法的补充与完善。     

Expanded thermodynamic true yield prediction model: adjustments and limitations

Bacterial yield prediction is critical for bioprocess optimization and modeling of natural biological systems. In previous work, an expanded thermodynamic true yield prediction model was developed through incorporating carbon balance and nitrogen balance along with electron balance and energy balance. In the present work, the application of the expanded model is demonstrated in multiple growth situations (aerobic heterotrophs, anoxic, anaerobic heterotrophs, and autolithotrophs). Two adjustments are presented that enable improved prediction when additional information regarding the environmental conditions (pH) or degradation pathway (requirement for oxygenase- or oxidase-catalyzed reactions) is known. A large data set of reported yields is presented and considered for suitability in model validation. Significant uncertainties of literature-reported yield values are described. Evaluation of the model with experimental yield values shows good predictive ability. However, the wide range in reported yields and the variability introduced into the prediction by uncertainty in model parameters, limits comprehensive validation. Our results suggest that the uncertainty of the experimental data used for validation limits further improvement of thermodynamic prediction models.     

Efficiencies of maximum likelihood methods of phylogenetic inferences when different substitution models are used

Choice of a substitution model is a crucial step in the maximum likelihood (ML) method of phylogenetic inference, and investigators tend to prefer complex mathematical models to simple ones. However, when complex models with many parameters are used, the extent of noise in statistical inferences increases, and thus complex models may not produce the true topology with a higher probability than simple ones. This problem was studied using computer simulation. When the number of nucleotides used was relatively large (1000 bp), the HKY+Gamma model showed smaller d(T) topological distance between the inferred and the true trees) than the JC and Kimura models. In the cases of shorter sequences (300 bp) simpler model and search algorithm such as JC model and SA+NNI search were found to be as efficient as more complicated searches and models in terms of topological distances, although the topologies obtained under HKY+Gamma model had the highest likelihood values. The performance of relatively simple search algorithm SA+NNI was found to be essentially the same as that of more extensive SA+TBR search under all models studied. Similarly to the conclusions reached by Takahashi and Nei [Mol. Biol. Evol. 17 (2000) 1251], our results indicate that simple models can be as efficient as complex models, and that use of complex models does not necessarily give more reliable trees compared with simple models.     

Is my species distribution model fit for purpose? Matching data and models to applications

Species distribution models (SDMs) are used to inform a range of ecological, biogeographical and conservation applications. However, users often underestimate the strong links between data type, model output and suitability for end‐use. We synthesize current knowledge and provide a simple framework that summarizes how interactions between data type and the sampling process (i.e. imperfect detection and sampling bias) determine the quantity that is estimated by a SDM. We then draw upon the published literature and simulations to illustrate and evaluate the information needs of the most common ecological, biogeographical and conservation applications of SDM outputs. We find that, while predictions of models fitted to the most commonly available observational data (presence records) suffice for some applications, others require estimates of occurrence probabilities, which are unattainable without reliable absence records. Our literature review and simulations reveal that, while converting continuous SDM outputs into categories of assumed presence or absence is common practice, it is seldom clearly justified by the application's objective and it usually degrades inference. Matching SDMs to the needs of particular applications is critical to avoid poor scientific inference and management outcomes. This paper aims to help modellers and users assess whether their intended SDM outputs are indeed fit for purpose.     

Measuring stroke volume of the ascending aorta with an extravascular Doppler ultrasound probe in comparison with aortic thermodilution]

Currently, no reliable minimally invasive method of measuring cardiac output continuously in neonates and children undergoing cardiac surgery is available. An extravascular Doppler probe was used to measure cardiac output in 15 New Zealand White rabbits (average weight 3.5 kg, range 2.5-4.5 kg). The results obtained were compared with cardiac outputs determined using the aortic thermodilution principle. The mean cardiac outputs measured with the extravascular Doppler probe was 0.37 +/- 0.01 l/min as compared with 0.39 +/- 0.01 l/min with aortic thermodilution. Regression analysis revealed a close correlation (r = 0.973) between the two techniques. The extravascular Doppler techniques is an option for continuous and reliable cardiac output measurement in small animals used in surgical experiments (open chest models) and in neonates or children during surgical repair of complicated congenital heart conditions.     

A robust fuzzy stochastic programming model for the design of a reliable green closed-loop supply chain network

Recently, governmental legislations, limitation of natural resources and adverse effects of End-of-Life products on ecological system have spurred researchers to design closed-loop supply chains (CLSCs). Accordingly, designing green supply chains (SCs) that manage greenhouse gas emissions and prevent air pollution can be helpful for companies to heighten profitability and customer loyalty, besides, uncertainty of parameters and disruption strikes could adversely affect performance of SCs and lower quality of output decisions. Effective planning prevents great losses and increases reliability of manager's decisions against uncertainties. Therefore, this paper is proceeding to design a reliable bi-objective green CLSC that minimizes total costs of network aside with minimizing harmful gas emissions. The proposed model is capable of controlling adverse effects of disruptions via applying scenario-based stochastic programming approach. Also, an effective hybrid robust fuzzy stochastic programming method is extended to effectively control uncertainty of parameters and risk-aversion level of output decisions. Extended model analyzing is based on lead-acid battery SC case study that output results approve applicability and effectiveness of model.     

Effects of climate change on an emperor penguin population: analysis of coupled demographic and climate models

Sea ice conditions in the Antarctic affect the life cycle of the emperor penguin (Aptenodytes forsteri). We present a population projection for the emperor penguin population of Terre Adélie, Antarctica, by linking demographic models (stage‐structured, seasonal, nonlinear, two‐sex matrix population models) to sea ice forecasts from an ensemble of IPCC climate models. Based on maximum likelihood capture‐mark‐recapture analysis, we find that seasonal sea ice concentration anomalies (SIC_a) affect adult survival and breeding success. Demographic models show that both deterministic and stochastic population growth rates are maximized at intermediate values of annual SIC_a, because neither the complete absence of sea ice, nor heavy and persistent sea ice, would provide satisfactory conditions for the emperor penguin. We show that under some conditions the stochastic growth rate is positively affected by the variance in SIC_a. We identify an ensemble of five general circulation climate models whose output closely matches the historical record of sea ice concentration in Terre Adélie. The output of this ensemble is used to produce stochastic forecasts of SIC_a, which in turn drive the population model. Uncertainty is included by incorporating multiple climate models and by a parametric bootstrap procedure that includes parameter uncertainty due to both model selection and estimation error. The median of these simulations predicts a decline of the Terre Adélie emperor penguin population of 81% by the year 2100. We find a 43% chance of an even greater decline, of 90% or more. The uncertainty in population projections reflects large differences among climate models in their forecasts of future sea ice conditions. One such model predicts population increases over much of the century, but overall, the ensemble of models predicts that population declines are far more likely than population increases. We conclude that climate change is a significant risk for the emperor penguin. Our analytical approach, in which demographic models are linked to IPCC climate models, is powerful and generally applicable to other species and systems.