Analytical Propagation of Uncertainty in Life Cycle Assessment Using Matrix Formulation

Inventory data and characterization factors in life cycle assessment (LCA) contain considerable uncertainty. The most common method of parameter uncertainty propagation to the impact scores is Monte Carlo simulation, which remains a resource‐intensive option—probably one of the reasons why uncertainty assessment is not a regular step in LCA. An analytical approach based on Taylor series expansion constitutes an effective means to overcome the drawbacks of the Monte Carlo method. This project aimed to test the approach on a real case study, and the resulting analytical uncertainty was compared with Monte Carlo results. The sensitivity and contribution of input parameters to output uncertainty were also analytically calculated. This article outlines an uncertainty analysis of the comparison between two case study scenarios. We conclude that the analytical method provides a good approximation of the output uncertainty. Moreover, the sensitivity analysis reveals that the uncertainty of the most sensitive input parameters was not initially considered in the case study. The uncertainty analysis of the comparison of two scenarios is a useful means of highlighting the effects of correlation on uncertainty calculation. This article shows the importance of the analytical method in uncertainty calculation, which could lead to a more complete uncertainty analysis in LCA practice.     

Extrapolation in Risk Assessment: Improving the Quantification of Uncertainty,and Improving Information to Reduce the Uncertainty

Risk assessments inevitably extrapolate from the known to the unknown. The resulting calculation of risk involves two fundamental kinds of uncertainty: uncertainty owing to intrinsically unpredictable (random) components of the future events, and uncertainty owing to imperfect prediction formulas (parameter uncertainty and error in model structure) that are used to predict the component that we think is predictable. Both types of uncertainty weigh heavily both in health and ecological risk assessments. Our first responsibility in conducting risk assessments is to ensure that the reported risks correctly reflect our actual level of uncertainty (of both types). The statistical methods that lend themselves to correct quantification of the uncertainty are also effective for combining different sources of information. One way to reduce uncertainty is to use all the available data. To further sharpen future risk assessments, it is useful to partition the uncertainty between the random component and the component due to parameter uncertainty, so that we can quantify the expected reduction in uncertainty that can be achieved by investing in a given amount of future data. An example is developed to illustrate the potential for use of comparative data, from toxicity testing on other species or other chemicals, to improve the estimates of low-effect concentration in a particular case with sparse case-specific data.     

Probabilistic accounting of uncertainty in forecasts of species distributions under climate change

Forecasts of species distributions under future climates are inherently uncertain, but there have been few attempts to describe this uncertainty comprehensively in a probabilistic manner. We developed a Monte Carlo approach that accounts for uncertainty within generalized linear regression models (parameter uncertainty and residual error), uncertainty among competing models (model uncertainty), and uncertainty in future climate conditions (climate uncertainty) to produce site‐specific frequency distributions of occurrence probabilities across a species' range. We illustrated the method by forecasting suitable habitat for bull trout (Salvelinus confluentus) in the Interior Columbia River Basin, USA, under recent and projected 2040s and 2080s climate conditions. The 95% interval of total suitable habitat under recent conditions was estimated at 30.1–42.5 thousand km; this was predicted to decline to 0.5–7.9 thousand km by the 2080s. Projections for the 2080s showed that the great majority of stream segments would be unsuitable with high certainty, regardless of the climate data set or bull trout model employed. The largest contributor to uncertainty in total suitable habitat was climate uncertainty, followed by parameter uncertainty and model uncertainty. Our approach makes it possible to calculate a full distribution of possible outcomes for a species, and permits ready graphical display of uncertainty for individual locations and of total habitat.     

Estimating Uncertainty in Ecosystem Budget Calculations

Ecosystem nutrient budgets often report values for pools and fluxes without any indication of uncertainty, which makes it difficult to evaluate the significance of findings or make comparisons across systems. We present an example, implemented in Excel, of a Monte Carlo approach to estimating error in calculating the N content of vegetation at the Hubbard Brook Experimental Forest in New Hampshire. The total N content of trees was estimated at 847 kg ha⁻¹ with an uncertainty of 8%, expressed as the standard deviation divided by the mean (the coefficient of variation). The individual sources of uncertainty were as follows: uncertainty in allometric equations (5%), uncertainty in tissue N concentrations (3%), uncertainty due to plot variability (6%, based on a sample of 15 plots of 0.05 ha), and uncertainty due to tree diameter measurement error (0.02%). In addition to allowing estimation of uncertainty in budget estimates, this approach can be used to assess which measurements should be improved to reduce uncertainty in the calculated values. This exercise was possible because the uncertainty in the parameters and equations that we used was made available by previous researchers. It is important to provide the error statistics with regression results if they are to be used in later calculations; archiving the data makes resampling analyses possible for future researchers. When conducted using a Monte Carlo framework, the analysis of uncertainty in complex calculations does not have to be difficult and should be standard practice when constructing ecosystem budgets.     

森林生物量估算中模型不确定性分析

单木生物量估算是区域森林生物量估算的基础。量化单木生物量模型中各种不确定性来源,分析各不确定性来源对森林生物量估算的影响,可为提高森林生物量估算精度提供理论依据。基于52株杉木地上部分生物量实测数据,建立杉木单木地上部分生物量一元与二元模型。在两种模型形式下,根据临安市2009年森林资源连续清查数据中杉木实测数据,分析单木生物量模型中所包含的2种不确定性,即模型参数不确定性和模型残差变异引起的不确定性。最后利用误差传播定律计算单木生物量模型总不确定性。结果表明,基于一元生物量模型的临安市杉木生物量估计均值为6.94 Mg/hm~2,由一元模型残差变异引起的生物量不确定性约为11.1%,模型参数误差引起的生物量不确定性约为14.4%,一元生物量模型估算合成不确定性为18.18%。基于二元生物量模型的临安市杉木生物量估计均值为7.71 Mg/hm~2,模型残差变异引起的不确定性约为7.0%,模型参数误差引起的不确定性约为8.53%,二元生物量模型估算合成不确定性为11.03%。研究表明模型参数不确定性随建模样本的增加逐渐降低,当建模样本由30增加到40再增加到52时,一元生物量模型模型参数不确定性分别为20.26%、16.19%、14.4%,二元生物量模型分别为13.09%、9.4%、8.53%。此外,建模样本的增加对残差变异不确定性也有一定影响,当建模样本由30增加到42再增加到48时,一元模型残差变异不确定性分别为15.2%,12.3%和11.7%;二元模型残差变异不确定性分别为13.3%,9.4%和8.3%。在2种不确定性来源中模型参数不确定性对估计结果影响最大,其次为模型残差变异。由于模型残差变异、参数不确定性与建模样本有关,因此可以通过增加建模样本来减小模型参数不确定性。二元生物量模型总的不确定性要低于一元生物量模型。     

Optimal compensation for temporal uncertainty in movement planning

Motor control requires the generation of a precise temporal sequence of control signals sent to the skeletal musculature. We describe an experiment that, for good performance, requires human subjects to plan movements taking into account uncertainty in their movement duration and the increase in that uncertainty with increasing movement duration. We do this by rewarding movements performed within a specified time window, and penalizing slower movements in some conditions and faster movements in others. Our results indicate that subjects compensated for their natural duration-dependent temporal uncertainty as well as an overall increase in temporal uncertainty that was imposed experimentally. Their compensation for temporal uncertainty, both the natural duration-dependent and imposed overall components, was nearly optimal in the sense of maximizing expected gain in the task. The motor system is able to model its temporal uncertainty and compensate for that uncertainty so as to optimize the consequences of movement.     

Risk, unexpected uncertainty, and estimation uncertainty: Bayesian learning in unstable settings

Recently, evidence has emerged that humans approach learning using Bayesian updating rather than (model-free) reinforcement algorithms in a six-arm restless bandit problem. Here, we investigate what this implies for human appreciation of uncertainty. In our task, a Bayesian learner distinguishes three equally salient levels of uncertainty. First, the Bayesian perceives irreducible uncertainty or risk: even knowing the payoff probabilities of a given arm, the outcome remains uncertain. Second, there is (parameter) estimation uncertainty or ambiguity: payoff probabilities are unknown and need to be estimated. Third, the outcome probabilities of the arms change: the sudden jumps are referred to as unexpected uncertainty. We document how the three levels of uncertainty evolved during the course of our experiment and how it affected the learning rate. We then zoom in on estimation uncertainty, which has been suggested to be a driving force in exploration, in spite of evidence of widespread aversion to ambiguity. Our data corroborate the latter. We discuss neural evidence that foreshadowed the ability of humans to distinguish between the three levels of uncertainty. Finally, we investigate the boundaries of human capacity to implement Bayesian learning. We repeat the experiment with different instructions, reflecting varying levels of structural uncertainty. Under this fourth notion of uncertainty, choices were no better explained by Bayesian updating than by (model-free) reinforcement learning. Exit questionnaires revealed that participants remained unaware of the presence of unexpected uncertainty and failed to acquire the right model with which to implement Bayesian updating.     

物种谱系不确定性对群落谱系格局指标的影响

物种谱系关系常被用于衡量群落谱系格局及推断格局背后的生态过程,但多数研究往往忽视谱系关系的不确定性及其可能对群落谱系格局造成的影响.为此,本文以浙江天童20 hm^2样地内150个树种为研究对象,采用这些物种叶绿体DNA的rbcL和matK碱基序列构建1棵一致系统发育树和反映谱系不确定性的999棵系统发育树,然后结合样地物种分布数据计算标准化净亲缘指数(NRI)和最近亲缘指数(NTI),最后运用独立置换零模型衡量样地群落谱系格局.结果表明:物种系统发育树在拓扑结构和物种谱系分支节点年龄上均存在较大的不确定性,谱系不确定性随着谱系分支节点年龄的减小而增大,也随物种间平均谱系距离的增加而增加;在样方尺度上,物种谱系的不确定性增加了标准化NRI和NTI指数的变异,但对两个指数的影响几乎独立;其对两指数的空间分布影响不同,且程度不一,其中标准化NRI受到的影响相对更大;在群落尺度上,物种谱系的不确定性增加了标准化NRI和NTI的变异,平均变异系数分别为0.37和0.077,表明群落水平的标准化NRI更易受到谱系不确定性的影响.这说明物种谱系不确定性会传递到常用的群落谱系格局指标中,且不同指标受影响的程度不同,进而影响对群落谱系格局的衡量及相关生态过程的推断.该结论也暗示以往不考虑谱系不确定性的研究中,非随机的群落谱系格局比例可能被高估.     

Uncertainty Analysis in Biofuel Systems

This article evaluates the implications of uncertainty in the life cycle (LC) energy efficiency and greenhouse gas (GHG) emissions of rapeseed oil (RO) as an energy carrier displacing fossil diesel (FD). Uncertainties addressed include parameter uncertainty as well as scenario uncertainty concerning how RO coproduct credits are accounted for (uncertainty due to modeling choices). We have carried out an extensive data collection to build an LC inventory accounting for parameter uncertainty. Different approaches for carbon stock changes associated with converting set‐aside land to rapeseed cultivation have been considered, which result in different values: from ?0.25 t C/ha.yr (carbon uptake by the soil in tonnes per hectare year) to 0.60 t C/ha.yr (carbon emission). Energy renewability efficiency and GHG emissions of RO are presented, which show the influence of parameter versus scenario uncertainty. Primary energy savings and avoided GHG emissions when RO displaces FD have also been calculated: Avoided GHG emissions show considerably higher uncertainty than energy savings, mainly due to land use (nitrous oxide emissions from soil) and land use conversion (carbon stock changes). Results demonstrate the relevance of applying uncertainty approaches; emphasize the need to reduce uncertainty in the environmental life cycle modeling, particularly GHG emissions calculation; and show the importance of integrating uncertainty into the interpretation of results.     

Confronting Uncertainty in Wildlife Management: Performance of Grizzly Bear Management

Scientific management of wildlife requires confronting the complexities of natural and social systems. Uncertainty poses a central problem. Whereas the importance of considering uncertainty has been widely discussed, studies of the effects of unaddressed uncertainty on real management systems have been rare. We examined the effects of outcome uncertainty and components of biological uncertainty on hunt management performance, illustrated with grizzly bears (Ursus arctos horribilis) in British Columbia, Canada. We found that both forms of uncertainty can have serious impacts on management performance. Outcome uncertainty alone – discrepancy between expected and realized mortality levels – led to excess mortality in 19% of cases (population-years) examined. Accounting for uncertainty around estimated biological parameters (i.e., biological uncertainty) revealed that excess mortality might have occurred in up to 70% of cases. We offer a general method for identifying targets for exploited species that incorporates uncertainty and maintains the probability of exceeding mortality limits below specified thresholds. Setting targets in our focal system using this method at thresholds of 25% and 5% probability of overmortality would require average target mortality reductions of 47% and 81%, respectively. Application of our transparent and generalizable framework to this or other systems could improve management performance in the presence of uncertainty.     

Uncertainty propagation of phase contrast-MRI derived inlet boundary conditions in computational hemodynamics models of thoracic aorta

This study investigates the impact that uncertainty in phase contrast-MRI derived inlet boundary conditions has on patient-specific computational hemodynamics models of the healthy human thoracic aorta. By means of Monte Carlo simulations, we provide advice on where, when and how, it is important to account for this source of uncertainty. The study shows that the uncertainty propagates not only to the intravascular flow, but also to the shear stress distribution at the vessel wall. More specifically, the results show an increase in the uncertainty of the predicted output variables, with respect to the input uncertainty, more marked for blood pressure and wall shear stress. The methodological approach proposed here can be easily extended to study uncertainty propagation in both healthy and pathological computational hemodynamic models.     

Uncertainty Is Part of Making Decisions

Advances in computer technology and applied statistics have provided the opportunity for the non-statistician to investigate uncertainty in a quantitative manner. The following discussion argues, notwithstanding the possible misuse of uncertainty analysis, that uncertainty is always present and that decisions based on human or ecological risk assessment would benefit from disclosure of uncertainty in the estimated risks.     

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

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Accounting for uncertainty in marine reserve design

Ecosystems and the species and communities within them are highly complex systems that defy predictions with any degree of certainty. Managing and conserving these systems in the face of uncertainty remains a daunting challenge, particularly with respect to developing networks of marine reserves. Here we review several modelling frameworks that explicitly acknowledge and incorporate uncertainty, and then use these methods to evaluate reserve spacing rules given increasing levels of uncertainty about larval dispersal distances. Our approach finds similar spacing rules as have been proposed elsewhere – roughly 20–200 km – but highlights several advantages provided by uncertainty modelling over more traditional approaches to developing these estimates. In particular, we argue that uncertainty modelling can allow for (1) an evaluation of the risk associated with any decision based on the assumed uncertainty; (2) a method for quantifying the costs and benefits of reducing uncertainty; and (3) a useful tool for communicating to stakeholders the challenges in managing highly uncertain systems. We also argue that incorporating rather than avoiding uncertainty will increase the chances of successfully achieving conservation and management goals.     

The Long and Winding Road to Uncertainty: The Link between Spatial Distance and Feelings of Uncertainty

Construal Level Theory (CLT) [1] defines psychological distance as any object, event, or person that cannot be experienced by the self in the here and now. The goal of the present research was to demonstrate that feelings of uncertainty are closely linked to the concept of psychological distance. Two experiments tested the assumption that spatial distance and uncertainty are bidirectionally related. In the first experiment, we show that perceived spatial distance leads to a feeling of uncertainty. The second experiment revealed that a feeling of uncertainty leads to a perception of greater distance. By demonstrating that distance is closely tied to uncertainty, the present research extends previous research on both distance and uncertainty by incorporating previously unexplained findings within CLT. Implications of these findings such as the role of uncertainty within CLT are discussed.     

Survey of approaches to improve reliability in lca

Limitations of data quality and difficulties to assess uncertainty are long since acknowledged problems in LCA. During recent years a range of tools for improvement of reliability in LCA have been presented, but despite this there is still a lack of consensus about how these issues should be handled. To give basic understanding of data quality and uncertainty in LCA, key concepts of data quality and uncertainty in the context of LCA are explained. A comprehensive survey of methods and approaches for data quality management, sensitivity analysis, and uncertainty analysis published in the LCA literature is presented. It should serve as a guide to further reading for LCA practitioners interested in improving data quality management and uncertainty assessment in LCA projects. The suitability of different tools for addressing different types of uncertainty and future needs in this field is discussed.     

The human toxicity potential and a Strategy for Evaluating Model Performance in Life Cycle Impact Assessment

The Human Toxicity Potential (HTP) is a quantita tive toxic equivalency potential (TEP) that has been introduced previously to express the potential harm of a unit of chemical released into the environment. HTP includes both inherent toxicity and generic source-to-dose relationships for pollutant emissions. Three issues associated with the use of HTP in Life Cycle Impact Assessment (LCIA) are evaluated here. First is the use of regional multimedia models to define source-to-dose relationships for the HTP. Second is uncertainty and variability in sourceto-dose calculations. And third is model performance evaluation for TEP models. Using the HTP as a case study, we consider important sources of uncertainty/variability in the development of source-to-dose models — including parameter variability/uncertainty, model uncertainty, and decision rule uncertainty. Once sources of uncertainty are made explicit, a model performance evaluation is appropriate and useful and thus introduced. Model performance evaluation can illustrate the relative value of increasing model complexity, assembling more data, and/or providing a more explicit representation of uncertainty. This work reveals that an understanding of the uncertainty in TEPs as well as a model performance evaluation are needed to a) refine and target the assessment process and b) improve decision making.     

Metacognition and mentalizing are associated with distinct neural representations of decision uncertainty

Metacognition and mentalizing are both associated with meta-level mental state representations. Conventionally, metacognition refers to monitoring one’s own cognitive processes, while mentalizing refers to monitoring others’ cognitive processes. However, this self-other dichotomy is insufficient to delineate the 2 high-level mental processes. We here used functional magnetic resonance imaging (fMRI) to systematically investigate the neural representations of different levels of decision uncertainty in monitoring different targets (the current self, the past self [PS], and others) performing a perceptual decision-making task. Our results reveal diverse formats of internal mental state representations of decision uncertainty in mentalizing, separate from the associations with external cue information. External cue information was commonly represented in the right inferior parietal lobe (IPL) across the mentalizing tasks. However, the internal mental states of decision uncertainty attributed to others were uniquely represented in the dorsomedial prefrontal cortex (dmPFC), rather than the temporoparietal junction (TPJ) that also represented the object-level mental states of decision inaccuracy attributed to others. Further, the object-level and meta-level mental states of decision uncertainty, when attributed to the PS, were represented in the precuneus and the lateral frontopolar cortex (lFPC), respectively. In contrast, the dorsal anterior cingulate cortex (dACC) represented currently experienced decision uncertainty in metacognition, and also uncertainty about the estimated decision uncertainty (estimate uncertainty), but not the estimated decision uncertainty per se in mentalizing. Hence, our findings identify neural signatures to clearly delineate metacognition and mentalizing and further imply distinct neural computations on internal mental states of decision uncertainty during metacognition and mentalizing.

The relationship between metacognition and mentalizing is still a matter of debate, as both are associated with meta-representations. This study adapts a task paradigm used in metacognition to apply in mentalizing and compares the neural representations of decision uncertainty in metacognition and mentalizing.     

Giving a scientific basis for uncertainty factors used in global life cycle inventory databases: an algorithm to update factors using new information

Purpose

Life cycle inventory (LCI) databases provide generic data on exchange values associated with unit processes. The “ecoinvent” LCI database estimates the uncertainty of all exchange values through the application of the so-called pedigree approach. In the first release of the database, the used uncertainty factors were based on experts’ judgments. In 2013, Ciroth et al. derived empirically based factors. These, however, assumed that the same uncertainty factors could be used for all industrial sectors and fell short of providing basic uncertainty factors. The work presented here aims to overcome these limitations.

Methods

The proposed methodological framework is based on the assessment of more than 60 data sources (23,200 data points) and the use of Bayesian inference. Using Bayesian inference allows an update of uncertainty factors by systematically combining experts’ judgments and other information we already have about the uncertainty factors with new data.

Results and discussion

The implementation of the methodology over the data sources results in the definition of new uncertainty factors for all additional uncertainty indicators and for some specific industrial sectors. It also results in the definition of some basic uncertainty factors. In general, the factors obtained are higher than the ones obtained in previous work, which suggests that the experts had initially underestimated uncertainty. Furthermore, the presented methodology can be applied to update uncertainty factors as new data become available.

Conclusions

In practice, these uncertainty factors can systematically be incorporated in LCI databases as estimates of exchange value uncertainty where more formal uncertainty information is not available. The use of Bayesian inference is applied here to update uncertainty factors but can also be used in other life cycle assessment developments in order to improve experts’ judgments or to update parameter values when new data can be accessed.