Uncertainty Bands Research Articles

Metoda dopasowania funkcji nieliniowej do danych punktów pomiarowych i jej pasmo niepewności

The paper presents a method of determining parameters and uncertainty bands of a specific non-linear function fitted to given measured data of examined points. One or both of the variables of this non-linear function are changed so as to linearize it. Using the linear regression method, fined are the most favorable parameters of this straight line for its adjustment to the measured values of the coordinates of points tested according to the weighted total mean square WTLS criterion. Their autocorrelation and cross-correlation coefficients as well as uncertainties estimated according to the rules of the GUM guide are considered. The parameters and the uncertainty band of the non-linear function result from the parameters of this straight line and its uncertainty band. Numerical examples of determining the parameters and uncertainty bands for the branch of a 2nd degree parabola (two methods) and for the complex exponential function are given.

A resilience-based framework for evaluating the carrying capacity of water and environmental resources under the climate change

This paper proposes a new framework for evaluating water and environmental resources carrying capacity (WERCC) based on the concept of resilience under uncertainty. First, several quantitative and qualitative criteria based on the seven principles of resilience and the Pressure-Support-State (PSS) framework are defined to incorporate the positive and negative impacts of human interventions and natural factors on water resources and the environment. The resilience principles include redundancy and diversity, managing connectivity, managing slow variables and their feedbacks, fostering complex adaptive system (CAS) thinking, encouraging learning, broadening participation, and promoting polycentric governance. After evaluating the values of the criteria and sub-criteria using a two-point evidential reasoning (TPER) approach and considering the existing uncertainties, the monthly time series of WERCC with uncertainty bands are calculated. The proposed methodology is then used to evaluate the WERCC in the Zarrinehrud river basin in Iran for a given historical period (1991–2012), and the period of 2020 to 2049 under different climate change scenarios. The results of this analysis demonstrate the inadequacy of the WERCC during the historical period and indicate that the continuation of the existing trend (base scenario, MSC0) will cause many environmental issues. Hence, several water and environmental resources management (WERM) scenarios are proposed to enhance the WERCC. These scenarios are evaluated using a multi-agent-multi-criteria decision-making method to identify the preferable WERM scenario (MSC12356). This scenario, which encompasses various projects (e.g., development and enhancement of water transfer networks and upgrading cultivation methods), improves the average value of the WERCC by 26 %. The results of the proposed methodology are compared with those of a traditional decision-making method, which considers three criteria of average WERCC, the pressure-support index, and the implementation cost. The results demonstrate that the multi-agent-multi-criteria decision-making approach provides a more cost-effective management scenario, with 30 % less cost, leading to only 3 % less carrying capacity.

Reducing uncertainties in hydromechanical modeling with a recently developed Rosetta 3 podeotransfer function

Stability analysis of unsaturated landslide deposits requires reliable estimates of soil moisture and pore water pressure. However, modeled soil moisture and pore water pressure contain substantial uncertainties due to imperfect information on soil hydraulic properties. Due to the relatively high dimensionality, commonly used parameter optimization strategies can be significantly affected by equifinality problems. This study investigates the effectiveness of reducing parameter estimation dimensionality using soil pedo-transfer functions. Specifically, we first estimated soil hydraulic parameters using the traditional Generalized Likelihood Uncertainty Estimation (GLUE) method, with parameters randomly drawn from the entire space (refer to as GLUE-random). In a second strategy, we use the Rosetta 3 pedotransfer function to constrain soil hydraulic parameters (refer to as GLUE-Rosetta). The two methods were tested in a typical landslide deposit with in-situ measured soil moisture dynamics for inverse modeling. The GLUE-random estimated soil hydraulic parameters contained substantial uncertainties –resulting in poorly constrained soil water retention curves (SWCC) and hydraulic conductivity functions (HCF). As a result, the uncertainty bands of pore water pressure and slope stability can cross values with several orders of magnitudes. In contrast, GLUE-Rosetta provided well-constrained SWCC and HCF, which significantly reduce the uncertainties in pore water pressure and slope stability estimates. These results suggest that the Rosetta 3 pedotransfer function can significantly improve the reliability of soil hydraulic parameters by reducing the dimensionality of the optimization problem and high-quality prior information of soil hydraulic properties. In conclusion, Rosetta 3 can enhance the reliability of soil parameters estimates and the reliability of subsurface hydrology, which may benefit the development of landslide early-warning systems.

An ensemble data-driven approach for incorporating uncertainty in the forecasting of stormwater sewer surcharge

ABSTRACT Stormwater surcharge events are unavoidable above a certain rainfall intensity. Thus, for protection and damage mitigation, forecast systems are of outstanding importance. This study develops an ensemble forecast system (EFS) to predict the beginning and end of sewer surcharge events. It applies a nonlinear autoregressive with exogenous inputs (NARX) network to each member of the ensemble, making it suitable for real-time predictions. The fundamental idea is the forecast of water depth time series within manholes based on the given rainfall. The novelty lies in the consideration of uncertainty through the ensemble structure for which the numbers of neurons in the hidden layer, the weights, and biases are considered to be uncertain. The results are evaluated based on observed values captured within the uncertainty band ), and the width of the band ). The varied between 74% and 94% and the between 1.36 and 10.68.

The large-break LOCA uncertainty analysis in a VVER-1000 reactor using TRACE and DAKOTA

An uncertainty analysis is inevitable in simulating reactor performance, particularly in the accident analysis for the estimation of safety borders. In this paper, the application of the uncertainty analysis of a Large Break Loss of Coolant Accident (LBLOCA) from main coolant pipeline at the reactor inlet and outlet, and also pressurizer (PRZ) connecting pipe are presented. First, the model developed in TRACE is verified in steady-state conditions and LBLOCA using the Final Safety Analysis Report (FSAR) of Bushehr nuclear power plant. By the verified model, the uncertainty analysis is made respecting uncertainty in boundary conditions. Finally, the analysis is achieved using the surrogate models and Wilks’ method in DAKOTA. The 95/95 uncertainty band of the peak cladding temperature (PCT) and main reactor parameters are obtained and analyzed. The results indicate that the PCT uncertainty in LBLOCA at the reactor inlet is large, the PCT varies in the range of 910 to 970 °C. The drop temperature time of fuel cladding is in the range of 270 to 600 s for LBLOCA at the reactor inlet. The PCT uncertainty in LBLOCA at the reactor outlet and PRZ connecting pipe is low.

Long-lead streamflow forecasting using computational intelligence methods while considering uncertainty issue.

While some robust artificial intelligence (AI) techniques such as Gene-Expression Programming (GEP), Model Tree (MT), and Multivariate Adaptive Regression Spline (MARS) have been frequently employed in the field of water resources, documents aimed to explore their uncertainty levels are few and far between. Meanwhile, uncertainty determination of these AI models in practical applications is highly important especially when we aimed to use the AI models for streamflow forecast due to the repercussions of poorly managed water resources. With the aid of a global daily streamflow dataset, understanding the uncertainty of GEP, MT, and MARS for forecasting streamflow of natural rivers was studied. The efficiency of uncertainty analysis was quantified by two statistical indicators: 95% Percent Prediction Uncertainty (95%PPU) and R-factor. The results demonstrated that MT had lower uncertainty (95%PPU=0.59 and R-factor=1.67) in comparison with MARS (95%PPU=0.61 and R-factor=1.92) and GEP (95%PPU=0.64 and R-factor=2.03). Overall, although the confidence interval bands of uncertainty for the AI models almost captured the mean streamflow measurements, wide bands of uncertainty were obtained and consequently remarkable uncertainty in the calculation of monthly streamflow values was met.

Proximate analysis of waste-to-energy potential of municipal solid waste for sustainable renewable energy generation

Over-dependence on virgin resources has been a major topic of social and political debates as the world's population and urbanization continue to rise. The high rate of rural–urban migration and changes in standard of living habits give rise to rapid economic activities that have an enormous impact on the gradual increase in waste generation and continued demand for electricity in urban centres. The solutions to these concerns can be achieved through efficient waste management options by waste resource utilization for energy and nutrient recovery and reduced solid waste pollution footprint. This research examined the viability of present and projected municipal solid waste streams to generate green energy through field surveys by physical characterization of the waste composition, projected waste quantity based on available population and waste data for the period 2000 – 2014, modelled methane gas generated by IPCC method, and the energy value was determined respectively. The findings indicated a high organic content of 54.1% of MSW and a per capita waste generation rate of 0.49–0.57 kg/capita/day. The waste was projected to increase from 353717.41 to 2,223497 tonnes between 2014 and 2035 at a population growth rate of 9.15%. This accounted for methane gas generated estimated to be 9.85Gg/year with an energy value of 15 MW/day in 2014 and projected to increase to 33.4 MW/day by 2035. The energy value estimated represented an increase from 6.14% to 212.74% of the allocated power supply from the national grid within the projected period. However, it is worth noting that, there are some limitations associated with the research due in part to inadequate field data which was supplemented by default model values as recommended by IPCC, although within an acceptable uncertainty band of result sensitivity. Therefore, the WTE management option can serve as a pathway for green energy integration for sustainable development.

Machine learning approach for impedance locus uncertainties

Abstract This work deals with the determination of the uncertainty of measurement data, determined by electrical impedance spectroscopy. Four different types of sand were measured impedimetrically in a measuring cell designed as a plate capacitor in a frequency range from 20 Hz to 1 MHz. The measuring cell was filled ten times with each sand and 20 impedance spectra were recorded for each filling. The uncertainty at each frequency was determined from the measurement data. It was found that the measurement data variance with a given measuring-cell filling was negligibly small. However, it increased by a factor of up to 100 when the measuring cell was repeatedly emptied and re-filled with the same material. We propose a way to estimate a continuous approximation of the uncertainty band of the impedance locus in the complex plane from the discrete uncertainties at each frequency. It uses a Support Vector Machine (SVM) to generate a regression curve using the discrete uncertainties. The result of the regression was used to estimate the uncertainties of an average impedance locus. The said machine learning tool can handle large amounts of data, classes, and influencing variables. In this manner, it can help to identify cause-effect relationships. Furthermore, at the end of this work a possibility to estimate a continuous uncertainty band along the impedance locus curve via SVM regression is shown. This is an extension to the common methodology in literature, where the uncertainty is only determined at selected individual points of the impedance spectrum.

Calibration and prediction uncertainty analysis of a hydraulic-water quality coupling model using a modified moth-flame optimizer

Abstract There is a lag between the latest development of the heuristic algorithm and its application in environmental model calibration. Besides, heuristic algorithms are usually thought to be deterministic and can hardly account for the equifinality of different parameters. To fix these limitations, we proposed a novel elite opposition-modified moth-flame optimizer (EOMFO) and presented a scheme combining it with the frequency statistical method for auto-calibration and prediction uncertainty estimation. A case study of a hydraulic-water quality coupling model was provided, in which the urban non-point source ammonia nitrogen (NH3-N) and total phosphorus (TP) were simulated. Compared with the benchmark particle swarm optimizer (PSO) and MFO, EOMFO has better global optimization ability and can obtain behavioral samples with higher quality for sensitive parameters. Regarding the calibration performance, EOMFO performed well in both the NH3-N and TP simulations (Nash–Sutcliffe efficiency around or greater than 0.5 and R greater than 0.7) and outperformed benchmark algorithms for both the deterministic prediction and uncertainty band prediction. The generated uncertainty band bracketed the majority of TP observation points, although it is not in good agreement with NH3-N observations due to several potential reasons. With this scheme, a more efficient and robust calibration process is expected.

Best estimate plus uncertainty analysis of metal-water reaction transient experiment

Uncertainty analysis is applied in the licensing process for nuclear installations to complement best estimate analysis and to verify that the upper bound value is less than the threshold corresponding to the safety parameter of interest. Metal-water reaction is a critical safety phenomenon of water-cooled nuclear reactors at accident conditions, e.g. Loss-Of-Coolant Accidents (LOCA). AISI 348 cladding is able to increase the accident tolerance comparing to Zr-based alloys and differently from other accident tolerant fuel cladding options, there is operational experience of nuclear power plants with stainless steel. In this study, a transient oxidation experiment of AISI 348 by steam was conducted and the major sources of uncertainty were addressed. An evaluation model was developed to calculate the evolution of mass gain during the experiment. Meanwhile, uncertainty propagation of experimental data was performed. The results show that the mass gain predicted by the transient metal-water reaction model lays within the experimental data uncertainty band. Furthermore, the selection of the oxidation kinetics model seems to be important whether the analysis wills to provide conservative results.

Assessing CFSR climate data for rainfall-runoff modeling over an ungauged basin between Iraq and Iran

In most developing countries, networks of gauge observations are frequently sparse and may have significant spatial and temporal gaps in the meteorological records. Reanalysis products are extensively used as alternative climate inputs for watershed modeling that provide continuous data worldwide. However, the direct utilization of such products is highly doubtful at different basin scales. This article aims to evaluate the accuracy of the Climate Forecast System Reanalysis (CFSR) product for streamflow simulation using the Soil and Water Assessment Tool (SWAT) model in the northeastern part of the Little Zab River Basin (LZRB), a mountainous basin between Iraq and Iran. The quality of CFSR was assessed from two viewpoints: (1) the precipitation aspect, an analysis of the CFSR precipitation compared to observational meteorological data (OMD) from 2004 to 2013 on a daily time scale, and (2) the hydrology aspect, a comparison of the SWAT model performance based on OMD (scenario I) and the CFSR product (scenario II) for monthly streamflow simulations. Results showed that the CFSR precipitation had a satisfactory correlation with rain gauge data ranging from 0.55 to 0.81. The performance of OMD in SWAT-based streamflow simulation achieved a ‘very good’ rating in calibration (2006–2010) and validation (2011–2013). Meanwhile, the CFSR-based model demonstrated a ‘very good’ hydrologic prediction skill in calibration. In contrast, CFSR revealed a lower performance in the validation period as it considerably overestimated base and peak flows in LZRB. Nevertheless, model uncertainty analysis after calibration showed that more than 88% of measured streamflow values at the basin outlet were bracketed within the 95 percent prediction uncertainty (95PPU) band for OMD and CFSR. These findings revealed that the CFSR product, after proper bias correction, could be a reliable alternative climate input for hydrologic modeling and climatological studies in semi-arid basins where gauge data is limited.

Using Macrofinancial Models to Simulate Macroeconomic Developments During the COVID-19 Pandemic: The Case of Albania

ABSTRACT The COVID-19 pandemic, and its impact on the economy tested the capacity of current macroeconomic models to forecast economic developments in turbulent times. In this article, we develop a linear macrofinancial model for Albania and examine whether it can predict the developments of key macroeconomic and financial variables during 2020–2021. To address increased uncertainty in the forecasts, we construct uncertainty bands with quantile regressions. The results indicate that, in general, a linear model is flexible enough to analyze non-linear events and may thus be used in abnormal times.

Flood hazard attribution and uncertainty analysis with climate changes in data scarce watersheds of southeastern Ethiopia

Abstract The interaction of the atmosphere and the land surface is vital in hydrological processes. In this paper, climate change impacts on streamflow are explored using soil and water assessment tool (SWAT) in one of the tropical watersheds, Wabi Shebele River Basin of Ethiopia. Regional climate model (RCM) from CORDEX-Africa region is used to analyze the basin's hydrological responses to climate forcing in the projected period. The result indicates that the watershed is likely to experience an increase in flood hazard with an increase in precipitation in the future as temperatures increase less than 2 °C. Flood hazard indices showed a larger value downstream of the river station (i.e., Gode) and a smaller value at the upper and middle stations with no change in climate variables (i.e., the baseline scenario, T + 0 °C, P + 0%). Based on separation method analysis, climate change has a greater impact on the streamflow and flood hazards in the region during the last four decades. Model uncertainty analysis reveals that simulated seasonal streamflow using RCMs has similar oscillation patterns to streamflow using observed climate data within uncertainty bands (UBs) in the study area with NSE and R2 values greater than 0.75 and 0.92, respectively.

A robust approach for the derivation of rating curves using minimum gauging data

Rating curves are robust tools for continuously evaluating streamflows by gauging water levels. This paper introduces a procedure to derive rating curves by combining a stage-discharge relationship proposed by Maghrebi et al. and the inverse-distance weighting (IDW) method. In order to determine the appropriate value of the α parameter in IDW, a trial-and-error procedure using different values of α from 0 to 5 is implemented. To this end, 2000 subsamples in different sizes selected randomly from the observed data of four cross-sections are generated, and the corresponding rating curves are delivered. The mean absolute percentage error (MAPE) and the root mean square error (RMSE) are used to evaluate the results. The results from four cross-sections demonstrated that α = 0 corresponds to the least favorable results, while α = 1 is the most appropriate value. The Maximum MAPE and RMSE, observed in the Trent River section, were 22.5 % and 13.1 m3/s using Maghrebi’s relation, respectively. These values decreased to 13.5 % and 8.6 m3/s when applying the proposed method using 7 points. Additional cross-sections from the Tiber River are used to validate the method and to compare it with the classical model. The results demonstrated that MAPE and RMSE values are reduced with increasing sample size, and the proposed model outperforms the classical one for small sample sizes. RMSE values declined from 62, 27.4, 46, 76.7 m3/s to 32.8, 14.4, 23.5, 33.9 m3/s using seven observed points in Ponte Nuovo, Santa Lucia, Ponte Felcino, and Ponte Rosciano cross-sections, respectively. The proposed model illustrated a notable decline in the uncertainty bands, which diminished significantly with increasing sample sizes. The proposed method is advantageous in constructing rating curves in new sites, specifically in the case of limited funding, and building more reliable rating curves in gauged sites.

Addressing effective real-time forecasting inflows to dams through predictive uncertainty estimate

The effect of flood waves entering into artificial reservoirs has to be carefully considered for properly addressing dam management to warrant water resources utilization and to provide flood control within a context of safety for the upstream and downstream territories. The optimization of the dam management has to be mainly based on the forecast of the water volume entering the reservoir and of the planning releases from the bottom outlets and the spillways. The flood forecasting models are able to provide discharge predictions at sections of particular interest, i.e. upstream of artificial reservoirs, with forecast horizons appropriate to support the civil protection activities for the mitigation of flooding effects. In 2019, Nanda et al. developed five deterministic forecasts of inflows to the Indian dam of Hirakud, in the Mahanadi River basin, by using the semi-distributed Variable Infiltration Capacity (VIC) model and four error correction models for updating the streamflow predictions by VIC. These models only provide deterministic forecasts for the future events and do not deal with the uncertainty on decisions. With the aim to shed light on the benefits for appropriately using probabilistic forecasts and uncertainty estimate, the deterministic forecasts provided in Nanda et al. (2019) are here used to feed the Model Conditional Processor (MCP) that allows to estimate the predictive uncertainty through the analytical treatment of multivariate probability densities, enabling a decision based on multiple forecasts of different models at the same time.The study is performed considering the monsoon periods of the years 2008–2011: the results achieved for the calibration and validation analysis show that MCP application involving a larger number of deterministic models, up to five, improves the probabilistic forecast accuracy in terms of the expected value accuracy and 90% uncertainty band width. Moreover, when only the two best deterministic models are considered as inputs for MCP, the results are similar to the ones achieved by using all the available deterministic forecasts.The results indicate that MCP is able to provide effective probabilistic real-time inflow forecasting into the reservoir to be used as an appropriate support for the artificial reservoir management during significant flood events.

EnConVis: A Unified Framework for Ensemble Contour Visualization.

Ensemble simulation is a crucial method to handle potential uncertainty in modern simulation and has been widely applied in many disciplines. Many ensemble contour visualization methods have been introduced to facilitate ensemble data analysis. On the basis of deep exploration and summarization of existing techniques and domain requirements, we propose a unified framework of ensemble contour visualization, EnConVis (Ensemble Contour Visualization), which systematically combines state-of-the-art methods. We model ensemble contour visualization as a four-step pipeline consisting of four essential procedures: member filtering, point-wise modeling, uncertainty band extraction, and visual mapping. For each of the four essential procedures, we compare different methods they use, analyze their pros and cons, highlight research gaps, and attempt to fill them. Specifically, we add Kernel Density Estimation in the point-wise modeling procedure and multi-layer extraction in the uncertainty band extraction procedure. This step shows the ensemble datas details accurately and provides abstract levels. We also analyze existing methods from a global perspective. We investigate their mechanisms and compare their effects, on the basis of which, we offer selection guidelines for them. From the overall perspective of this framework, we find choices and combinations that have not been tried before, which can be well compensated by our method. Synthetic data and real-world data are leveraged to verify the efficacy of our method. Domain experts feedback suggests that our approach helps them better understand ensemble data analysis.

Prediction and uncertainty quantification of SAFARI-1 axial neutron flux profiles with neural networks

In this study, Deep Neural Networks (DNNs) are used to predict the assembly axial neutron flux profiles in the SAFARI-1 research reactor, with quantified uncertainties in the DNN predictions and testing using data from cycles that are unseen in the training process. The training dataset consists of copper-wire activation measurements from the reactor’s historical cycles. Uncertainty Quantification of the regular DNN models’ predictions is performed using Monte Carlo Dropout (MCD) and Bayesian Neural Networks solved by Variational Inference (BNN VI). The regular DNNs, DNNs solved with MCD and BNN VI results agree very well with each other and with the new measured dataset not used in the training process, thus indicating good prediction and generalization capability. The uncertainty bands produced by MCD and BNN VI agree very well and fully envelop the noisy measurement data points.

Consistent assessment of neutron-induced activation of 93Nb

A concurrent assessment of all measured excitation functions for various reactions induced by neutrons on 93Nb, in addition to the results of TENDL-2021 and default parameters in TALYS-1.96, is given in this work. We use consistent parameter sets that were formerly obtained or validated by the analysis of other independent data, while no empirical rescaling factors of γ and/or neutron widths have been used. The correlation between the measured error bars of the primary data providing the consistent input parameters and the final uncertainty bands of the calculated results have been pointed out. At the same time, a proper account in this work of all available data for competitive reaction channels prevented compensation effects of less accurate model parameters. Remaining questions and the need for additional measurements are emphasized.

Ggdist: Visualizations of Distributions and Uncertainty in the Grammar of Graphics.

The grammar of graphics is ubiquitous, providing the foundation for a variety of popular visualization tools and toolkits. Yet support for uncertainty visualization in the grammar graphics-beyond simple variations of error bars, uncertainty bands, and density plots-remains rudimentary. Research in uncertainty visualization has developed a rich variety of improved uncertainty visualizations, most of which are difficult to create in existing grammar of graphics implementations. ggdist, an extension to the popular ggplot2 grammar of graphics toolkit, is an attempt to rectify this situation. ggdist unifies a variety of uncertainty visualization types through the lens of distributional visualization, allowing functions of distributions to be mapped to directly to visual channels (aesthetics), making it straightforward to express a variety of (sometimes weird!) uncertainty visualization types. This distributional lens also offers a way to unify Bayesian and frequentist uncertainty visualization by formalizing the latter with the help of confidence distributions. In this paper, I offer a description of this uncertainty visualization paradigm and lessons learned from its development and adoption: ggdist has existed in some form for about six years (originally as part of the tidybayes R package for post-processing Bayesian models), and it has evolved substantially over that time, with several rewrites and API re-organizations as it changed in response to user feedback and expanded to cover increasing varieties of uncertainty visualization types. Ultimately, given the huge expressive power of the grammar of graphics and the popularity of tools built on it, I hope a catalog of my experience with ggdist will provide a catalyst for further improvements to formalizations and implementations of uncertainty visualization in grammar of graphics ecosystems. A free copy of this paper is available at https://osf.io/2gsz6. All supplemental materials are available at https://github.com/mjskay/ggdist-paper and are archived on Zenodo at doi:10.5281/zenodo.7770984.

Estimation of the uncertainty bands of regression line for correlated data of variable Y using the GUM rules

The estimation of the accuracy of the linear regression method used for measurements based on the GUM recommendations is considered. The impact of correlation and autocorrelation of the variable Y data together with type A and type B uncertainties, not provided in statistical literature about regression methods, is discussed. The theoretical backgrounds are given. The simulated examples of determining the uncertainty bands of the regression line fitted to the measured points with different cases of correlated values and absolute and relative uncertainties of type A and type B of the dependent variable Y are considered.