Model Uncertainty Analysis Research Articles

A Framework to Identify the Uncertainty and Credibility of GCMs for Projected Future Precipitation: A Case Study in the Yellow River Basin, China

General circulation models could simulate precipitation under climate change and have been recognized as a major tool to project future water resources, but huge inherent uncertainties mean that their credibility is widely questioned. The current analysis mainly focuses on some aspects of uncertainty and few on the whole chain process to yield a more reliable projection. This study proposes a framework to identify the uncertainty and credibility of GCMs, consisting of downscaling, uncertainty analysis (model spread and Taylor diagram), ensemble analysis (grid-based weighted Bayesian model averaging), credibility analysis (signal-to-noise ratio), and probability projection. Based on five selected climate models from the Coupled Model Intercomparison Project Phase 5 (CMIP5), the uncertainties and credibility of simulated precipitation in the Yellow River of China were analyzed. By comparing the models’ output with the observation in the historical period of 1986–2005, we can see that large uncertainty exists among models’ annual precipitation. For different-class precipitation, the uncertainties of the five models are small in relatively weak rain, but large in heavy rainfall, which indicates more risk in future projections and the necessity to explore their credibility. Moreover, in such a large-span basin, GCMs show vast spatial differences in space and even opposite trends in some regions, demonstrating the limits of Bayesian model averaging (BMA) on multi-model ensemble due to one weight group overall whole basin. Thus, a grid-based weighted Bayesian model averaging (GBMA) method is proposed to cope with the spatial inconsistencies of models. Given the multi-model ensemble results, the future precipitation changes of the periods of 2021–2050 and 2061–2090 are projected, and the probability and credibility of future precipitation changes in terms of spatial distribution are identified. Model credibility identification could allow for more reliable projections of precipitation change trends, especially for different spatial regions, which will be very valuable for decision-making related to water resource management and security.

Planning for resilience: Incorporating scenario and model uncertainty and trade-offs when prioritizing management of climate refugia.

Climate change has become the greatest threat to the world's ecosystems. Locating and managing areas that contribute to the survival of key species under climate change is critical for the persistence of ecosystems in the future. Here, we identify ‘Climate Priority’ sites as coral reefs exposed to relatively low levels of climate stress that will be more likely to persist in the future. We present the first analysis of uncertainty in climate change scenarios and models, along with multiple objectives, in a marine spatial planning exercise and offer a comprehensive approach to incorporating uncertainty and trade‐offs in any ecosystem. We first described each site using environmental characteristics that are associated with a higher chance of persistence (larval connectivity, hurricane influence, and acute and chronic temperature conditions in the past and the future). Future temperature increases were assessed using downscaled data under four different climate scenarios (SSP1 2.6, SSP2 4.5, SSP3 7.0 and SSP5 8.5) and 57 model runs. We then prioritized sites for intervention (conservation, improved management or restoration) using robust decision‐making approaches that select sites that will have a benign climate under most climate scenarios and models. The modelling work is novel because it solves two important issues. (1) It considers trade‐offs between multiple planning objectives explicitly through Pareto analyses and (2) It makes use of all the uncertainty around future climate change. Priority intervention sites identified by the model were verified and refined through local stakeholder engagement including assessments of local threats, ecological conditions and government priorities. The workflow is presented for the Insular Caribbean and Florida, and at the national level for Cuba, Jamaica, Dominican Republic and Haiti. Our approach allows managers to consider uncertainty and multiple objectives for climate‐smart spatial management in coral reefs or any ecosystem across the globe.

Hydrological modeling using remote sensing precipitation data in a Brazilian savanna basin

Precipitation is the main input for hydrological models. However, due to limitations of rain gauge stations, satellite precipitation estimates have become a good alternative to precipitation information. In this context, this study aimed to validate the precipitation data with Tropical Rainfall Measuring Mission Multisatellite Precipitation Analysis (TMPA) and Integrated Multi-satellitE Retrievals for Global Precipitation Measurement (IMERG) data, in addition to assessing the uncertainty and performance of the Soil and Water Assessment Tool (SWAT) using observed precipitation (OP), TMPA, and IMERG data. Statistical coefficients were used to validate TMPA and IMERG precipitation data. P-factor and r-factor were considered for the uncertainty analysis, while the Nash-Sutcliffe efficiency (NSE), its logarithmic version (LNSE), and the percent bias (PBIAS) were analyzed to characterize the model performance analysis in monthly time steps. There was an overestimation by TMPA and IMERG in the precipitation estimation, especially in the dry period. OP, TMPA, and IMERG setups presented satisfactory results for uncertainty and performance analysis in hydrological modeling. The IMERG setup generally showed better results than the TMPA setup, being a good alternative for hydrological modeling, especially in regions with scarce precipitation datasets.

Uncertainty analysis for the nuclear liquid drop model and implications for the symmetry energy coefficients

Background: Despite its age, the nuclear liquid drop (LD) model, plus the microscopic corrections, still plays an important role in nuclear mass studies. Especially, the LD model readily correlate the finite nucleus and the nuclear matter through the symmetry energy term.Purpose: To systematically analyze the model uncertainty of the LD mass formula and check the corresponding symmetry energy coefficients.Method: The Monte Carlo bootstrap approach, based on the nonparametric sampling, is applied to determine the statistical uncertainties of the parameter set in two popular LD formulas. The dependence between these parameters is also quantified via the correlation coefficients.Results: The least required proportion of the experimental mass data is fixed for the fitting process of the LD formula. After the statistical deviation is determined for each parameter in the LD formula, the model uncertainty is evaluated as illustrated for one heavy isotopic chain. The Pearson coefficients between each two parameters involved in the LD mass formula are tabulated and figured plus the detailed discussions on the surface and volume symmetry energy coefficients.Conclusion: The uncertainties of the fitted parameters and the LD model itself are smooth, leading to a relatively stable extrapolation. It is necessary to include the Wigner energy term in the LD model when yielding the reasonable symmetry energy coefficients.

Uncertainty and sensitivity analysis of algal-bacterial model under different ranges of parameter variation

Based on the Activated Sludge Model No.3, a comprehensive model consisting of autotrophic bacteria, algae, and heterotrophic bacteria was presented in this work to describe the relationship among microorganisms and substrates in photo-sequencing batch reactors. The proposed model, which is called the algal-bacteria model, has involved a total of 31 parameters. The standard regression coefficient method was used to conduct global sensitivity analysis of the algal-bacteria model proposed was used to reduce the experiment time and energy of the experimenters, which determined that eight sensitivity parameters from analysis results according to the absolute value of sensitivity indices SRC. Analyzing the influence of different parameter value ranges on the sensitivity analysis, it provides a reference for the parameter sensitivity and uncertainty analysis of the algae-bacteria model. The results show that the algal-bacteria model simulates the removal process of complex nutrients well, and the parameter values affect the sensitivity analysis, but the identification of the most sensitive parameters will not be affected. Moreover, in terms of predicting the removal of dissolved oxygen and pollutants, the simulation results were proved to be in good agreement with the experimental data. It was demonstrated that the established model could be used as a valuable tool for optimizing the parameters of photo-sequencing batch reactors. Key findings of this paper include (1) representation of a comprehensive model to describe the interactions among bacteria, algae, and substrates; (2) assessment of the reliability of model parameters; (3) adoption of a novel method to estimate the most sensitive parameters and evaluate the influence of the change of parameters on the sensitivity analysis results. Our findings suggest that the application of the algal-bacterial consortia system may provide a viable technology in wastewater treatment.

Assessment of household air pollution exposure of tribal women

There is a growing evidence that the burning of unprocessed biomass fuels is associated with adverse health impacts. This study estimated the gaseous pollutants (CO, CO2, O3, SO2, and NO2) and particulate matters (PM2.5 and PM10) during the burning of biomass and liquefied petroleum gas (LPG) fuels and their impacts on the health of tribal women. The results revealed that the tribal women mainly used six types of unprocessed biomass fuels (dry leaves, cow dung cake, dry woods, twigs, rice straw, and agricultural residues) along with five types of traditional earthen stoves. The concentration of gaseous and PM was recorded as in the order of CO2 > SO2 > CO > O3 and total suspended particulate matter (TSPM) > PM10 > PM2.5, respectively. The pollutant concentration inside the kitchen room for biomass users was significantly (p < 0.001) higher than LPG users. The biomass using tribal women might be suffering from higher cardiovascular risk than LPG users. The lung function study results also indicated that the mean values of forced expiratory volume in 1 s (FEV1), forced vital capacity (FVC), and FEV1/FVC were lower among biomass users than LPG users. The correlation study shows that tribal women who were exposed to biomass smoke were in a more vulnerable position than those who used LPG. Moreover, the toxicological risk among tribal biomass users was observed high (3.52) compared to LPG users (0.39). On the other hand, the Monte Carlo probabilistic simulation model for uncertainty analysis revealed that the mean value of Hazard Quotient (HQ) for PM2.5 in kitchen room was observed as 4.31E-00 and 9.40E-01 for biomass and LPG users, respectively. Modelling study also revealed that exposure of duration and cooking time are extremely important for toxicological risk assessment. However, further long-term comprehensive studies are extremely important.

Uncertainty and Variability Analysis of Agent-Based Transport Models

This paper presents an analysis of the output variability of agent-based transport models. We simulated a MATSim model of the city of Hanover multiple times with identical input and evaluated the resulting travel times on different level of aggregation. On a global level, we observed minor variations of travel times. However, the results show an increased variation when examining the output on the level of districts or for individual agents. A recommendation for estimating the required number of simulation runs for a stable output of travel time for the purposed aggregation level is derived from our case study.

Uncertainty Analysis of a Numerical Model for Calculating an Effective Source Height

Uncertainty Analysis of a Numerical Model for Calculating an Effective Source Height

Uncertainty Analysis of Digital Elevation Models by Spatial Inference From Stable Terrain

The monitoring of Earth&#x2019;s and planetary surface elevations at larger and finer scales is rapidly progressing through the increasing availability and resolution of digital elevation models (DEMs). Surface elevation observations are being used across an expanding range of fields to study topographical attributes and their changes over time, notably in glaciology, hydrology, volcanology, seismology, forestry and geomorphology. However, DEMs frequently contain large-scale instrument noise and varying vertical precision that lead to complex patterns of errors. Here, we present a validated statistical workflow to estimate, model, and propagate uncertainties in DEMs. We review the state-of-the-art of DEM accuracy and precision analyses, and define a conceptual framework to consistently address those. We show how to characterize DEM precision by quantifying the heteroscedasticity of elevation measurements, i.e. varying vertical precision with terrain- or sensor-dependent variables, and the spatial correlation of errors that can occur across multiple spatial scales. With the increasing availability of high-precision observations, our workflow based on independent elevation data acquired on stable terrain can be applied almost anywhere on Earth. We illustrate how to propagate uncertainties for both pixel-scale and spatial elevation derivatives, using terrain slope and glacier volume changes as examples. We find that uncertainties in DEMs are largely underestimated in the literature, and advocate that new metrics of DEM precision are essential to ensure the reliability of future Earth and planetary surface elevation assessments.

Comparison of the performance and reliability between improved sampling strategies for polynomial chaos expansion.

As uncertainty and sensitivity analysis of complex models grows ever more important, the difficulty of their timely realizations highlights a need for more efficient numerical operations. Non-intrusive Polynomial Chaos methods are highly efficient and accurate methods of mapping input-output relationships to investigate complex models. There is substantial potential to increase the efficacy of the method regarding the selected sampling scheme. We examine state-of-the-art sampling schemes categorized in space-filling-optimal designs such as Latin Hypercube sampling and L1-optimal sampling and compare their empirical performance against standard random sampling. The analysis was performed in the context of L1 minimization using the least-angle regression algorithm to fit the GPCE regression models. Due to the random nature of the sampling schemes, we compared different sampling approaches using statistical stability measures and evaluated the success rates to construct a surrogate model with relative errors of <0.1%, <1%, and <10%, respectively. The sampling schemes are thoroughly investigated by evaluating the y of surrogate models constructed for various distinct test cases, which represent different problem classes covering low, medium and high dimensional problems. Finally, the sampling schemes are tested on an application example to estimate the sensitivity of the self-impedance of a probe that is used to measure the impedance of biological tissues at different frequencies. We observed strong differences in the convergence properties of the methods between the analyzed test functions.

Development of a Dream-Based Inverse Model for Multi-Point Source Identification in River Pollution Incidents: Model Testing and Uncertainty Analysis

Development of a Dream-Based Inverse Model for Multi-Point Source Identification in River Pollution Incidents: Model Testing and Uncertainty Analysis

Bootstrapped Artificial Neural Network Model for Uncertainty Analysis of Melcor Simulations in a Station Blackout Accident

Bootstrapped Artificial Neural Network Model for Uncertainty Analysis of Melcor Simulations in a Station Blackout Accident

Parameter estimation and uncertainty analysis in hydrological modeling

AbstractNowadays, mathematical models of hydrological systems are used routinely to guide decision making in diverse subjects, such as: environmental and risk assessments, design of remediation strategies for contaminated sites, and evaluation of the impact of climate change on water resources. The correct development and use of them is relevant beyond the realm of hydrology. The continuous improvement in computational power and data collection are leading to the development of increasingly complex models, which integrate multiple coupled physical processes to achieve a better representation of the modeled system. Most of the parameters included in models are difficult to measure directly, so they must be estimated from collected data through a calibration procedure. Furthermore, when models are used to make forecasts about future or hypothetical scenarios, it is important to bound the uncertainty of their results. Therefore, the application of systematic approaches for parameter estimation, sensitivity, and uncertainty analysis to integrate data and models and quantify potential errors, is more necessary now than it was in the past. Even though methodological frameworks for these purposes exist, they have had a slow adoption due to their high computational cost and the required technical knowledge to apply them. We analyze existing methodologies, discuss remaining challenges, and present a survey of emerging trends for the application of parameter estimation and uncertainty analysis in hydrological modeling. Thus, the main objective of this overview article is contributing to improving the quality of models and to their correct use as support tools for decision‐making.This article is categorized under: Science of Water Science of Water &gt; Hydrological Processes Science of Water &gt; Methods

Uncertainty analysis and calibration of SST turbulence model for free shear layer in cavity-ramp flow

The development and reattachment of the free shear layer in supersonic flows have been a widely encountered phenomenon in engineering, and are gaining increasing interest from researchers who investigate such complex flow structures using numerical simulation methods. Among these methods, Reynolds Averaged Navier-Stokes (RANS) still plays an important role in application problems. However, the uncertainty of the parameters in RANS turbulence model affects the reliability and accuracy of predictions. Therefore, the purpose of this study is to conduct a detailed uncertainty analysis of the parameters in the shear-stress transport (SST) turbulence model for the free shear layer in a cavity-ramp flow. In the current study, uncertainty quantification was conducted with the construction of a surrogate model between the parameters and calculation results using the non-intrusive polynomial chaos (NIPC) method. Next, for sensitivity analysis, the Sobol index of each parameter was calculated to identify the key parameters mainly responsible for the uncertainty. Based on the above results, Bayesian inference was employed to calibrate these key parameters by leveraging experimental data. The results show that the calculated wall pressure and skin friction of the ramp suffer a non-negligible uncertainty caused by the model parameters, and parameters a1, σω2, β2, κ, and β1 are identified as the key parameters in this type of flow. Subsequently, the calibrated values for the key parameters are obtained through Bayesian inference, which could significantly improve prediction results in the original case. Furthermore, the applicability of the SST model with calibrated parameters is verified under different free-stream conditions.

The pie sharing problem: Unbiased sampling of N+1 summative weights

A simple algorithm is provided for randomly sampling a set of N+1 weights such that their sum is constrained to be equal to one, analogous to randomly subdividing a pie into N+1 slices where the probability distribution of slice volumes are identically distributed. The cumulative density and probability density functions of the random weights are provided. The algorithmic implementation for the random number sampling are made available. This algorithm has potential applications in calibration, uncertainty analysis, and sensitivity analysis of environmental models. Three example applications are provided to demonstrate the efficiency and superiority of the proposed method compared to alternative sampling methods.

Uncertainty analysis of accident causality model using Credal Network with IDM method: A case study of hazardous material road transportation accidents

Bayesian network (BN) is an effective tool for causal inferences of accidents. However, it is often criticized for the difficulty in obtaining accurate/sufficient data needed to get precise probability numbers, and expert knowledge is necessary on this occasion. Such numbers provided by experts lead to great cognitive uncertainty in the model. Credal Network (CN), regarded as an extension of BN, uses imprecise probabilities to well express the cognitive uncertainty, but how to give the available interval probability is a key issue in its application. In this paper, a CN model based on Imprecise Dirichlet Model (IDM) is proposed to solve this problem, and a case study of hazardous material road transportation accidents (HMRTAs) is conducted. Firstly, based on the accident causation model, the CN topology is established by analyzing 30 investigation reports of HMRTAs in China. Secondly, the conditional probability table is calculated and then the CN model of HMRTAs is obtained by transforming the point probability into interval probability using IDM. Finally, causes and consequences of HMTRAs are analyzed. The results show that the method in this study can well represent the uncertainty propagation in the accident causal model and provide a new way for accident risk analysis.

Additional MRI for initial M-staging in pancreatic cancer: a cost-effectiveness analysis

ObjectivePancreatic cancer is portrayed to become the second leading cause of cancer-related death within the next years. Potentially complicating surgical resection emphasizes the importance of an accurate TNM classification. In particular, the failure to detect features for non-resectability has profound consequences on patient outcomes and economic costs due to incorrect indication for resection. In the detection of liver metastases, contrast-enhanced MRI showed high sensitivity and specificity; however, the cost-effectiveness compared to the standard of care imaging remains unclear. The aim of this study was to analyze whether additional MRI of the liver is a cost-effective approach compared to routinely acquired contrast-enhanced computed tomography (CE-CT) in the initial staging of pancreatic cancer.MethodsA decision model based on Markov simulation was developed to estimate the quality-adjusted life-years (QALYs) and lifetime costs of the diagnostic modalities. Model input parameters were assessed based on evidence from recent literature. The willingness-to-pay (WTP) was set to $100,000/QALY. To evaluate model uncertainty, deterministic and probabilistic sensitivity analyses were performed.ResultsIn the base-case analysis, the model yielded a total cost of $185,597 and an effectiveness of 2.347 QALYs for CE-MR/CT and $187,601 and 2.337 QALYs for CE-CT respectively. With a net monetary benefit (NMB) of $49,133, CE-MR/CT is shown to be dominant over CE-CT with a NMB of $46,117. Deterministic and probabilistic survival analysis showed model robustness for varying input parameters.ConclusionBased on our results, combined CE-MR/CT can be regarded as a cost-effective imaging strategy for the staging of pancreatic cancer.Key Points• Additional MRI of the liver for initial staging of pancreatic cancer results in lower total costs and higher effectiveness.• The economic model showed high robustness for varying input parameters.

Bayesian calibration and uncertainty analysis of an agroecosystem model under different N management practices

Process-based agroecosystem model provides a powerful tool to evaluate the effects of various field management practices on soil water balance, nitrogen (N) fates, and crop growth for cropland ecosystems. However, parameter calibration of those models is usually time-consuming and uncertain due to the involvement of complex soil and plant growth processes in models. In this study, the Different Evolution Adaptive Metropolis (DREAM) algorithm was successfully used to estimate model parameters and quantify uncertainties of the soil Water Heat Carbon Nitrogen Simulator (WHCNS) model. The calibration efficiency was further improved by identifying the sensitive parameters using global sensitivity analysis. The simulated soil water content, crop N uptake, and yield were in agreement with the measured values, with indices of NRMSE, IA, and NSE ranging from 6.4% to 22.1%, from 0.59 to 0.98, and from 0.43 to 0.92, respectively. The simulation of soil nitrate concentration showed a relatively large NRMSE that varied from 35.9% to 50.2% but was still within the acceptance range. This study suggested that the two-step method of global sensitivity analysis and DREAM algorithm is a robust way to estimate model parameters and quantify uncertainties of agroecosystem models.

Using a fugacity model to determine the degradation rate of typical polycyclic musks in the field: A case study in the North Canal River watershed of Beijing, China

To quantitate the degradation rate of 1,3,4,6,7,8-hexahydro-4,6,6,7,8,8-hexamethylcyclopenta-[g]-2-benzopyran (HHCB) and 7-acetyl-1,1,3,4,4,6-hexamethyl-1,2,3,4-tetrahydronaphthalene (AHTN) under field conditions, a level III fugacity model combined with a least-squares method was used to determine the degradation rate of HHCB and AHTN in the North Canal River watershed of Beijing, China. Model fitting, validation, sensitivity, and uncertainty analyses revealed that the established model was stable and robust. The degradation rates of HHCB and AHTN were 4.16 × 10−3 h−1 (t1/2 = 167 h) and 1.68 × 10−2 h−1 (t1/2 = 41.3 h), respectively. The calculated degradation rates were extrapolated to the Liangshui River, and indicated that the differences between the measured and predicted concentrations were less than 0.32 and 0.34 log units for HHCB and AHTN, respectively. The attenuation rates of HHCB and AHTN were calculated, and the results indicated that degradation was an important yet not the sole contributor to the degradation of the polycyclic musks. Results of uncertainty analyses indicated that the inflow and outflow concentrations of the polycyclic musks in the surface water of each segment strongly influenced the model outputs, followed by environmental factors (water depth and flow rate). It is essential to measure the degradation rate in the field because of the influence of the surrounding environment. The present study reveals the utility of fugacity models to quantify the degradation rate of organic micropollutants in the field.

Prediction of Grape Sap Flow in a Greenhouse Based on Random Forest and Partial Least Squares Models

Understanding variations in sap flow rates and the environmental factors that influence sap flow is important for exploring grape water consumption patterns and developing reasonable greenhouse irrigation schedules. Three irrigation levels were established in this study: adequate irrigation (W1), moderate deficit irrigation (W2) and deficit irrigation (W3). Grape sap flow estimation models were constructed using partial least squares (PLS) and random forest (RF) algorithms, and the simulation accuracy and stability of these models were evaluated. The results showed that the daily mean sap flow rates in the W2 and W3 treatments were 14.65 and 46.94% lower, respectively, than those in the W1 treatment, indicating that the average daily sap flow rate increased gradually with an increase in the irrigation amount within a certain range. Based on model error and uncertainty analyses, the RF model had better simulation results in the different grape growth stages than the PLS model did. The coefficient of determination and Willmott’s index of agreement for RF model exceeded 0.78 and 0.90, respectively, and this model had smaller root mean square error and d-factor (evaluation index of model uncertainty) values than the PLS model did, indicating that the RF model had higher prediction accuracy and was more stable. The relative importance of the model predictors was determined. Moreover, the RF model more comprehensively reflected the influence of meteorological factors and the moisture content in different soil layers on the sap flow rate than the PLS model did. In summary, the RF model accurately simulated sap flow rates, which is important for greenhouse grape irrigation.