GWP20 is a very precise and probably accurate indicator for the cumulative radiative forcing (i.e. the capacity to absorb energy, which can be measured in the lab) of a molecule during 20 years, but it neglects that this molecule may still be active long after. It is thus a very inaccurate indicator for the total potential contribution of the molecule to global warming, which is what we are usually interested in for an LCA study (unless the goal and scope definition requires a focus on short-term impacts). Therefore, implicitly assuming that GWP20 quantifies the (total) potential contribution of an emission to global warming bears a risk of interpreting LCA results wrongly in spite of using an indicator that is very precise, as it is inaccurate for the objective at hand (Fig. 11.3). This example may seem somewhat obvious, but there are many other instances of exactly this type of confusion that can be found in current LCA practice


11.3). This example may seem somewhat obvious, but there are many other instances of exactly this type of confusion that can be found in current LCA practice. Another example is the comparison of the uncertainty of indicator results from different impact categories. The GWP is generally perceived as a fairly certain midpoint indicator whereas human toxicity is seen as a very uncertain midpoint indicator, an argument that is sometimes used to justify the omission of toxicity characterisation from an LCA study. It is worth reflecting whether this direct comparison of uncertainties makes sense by looking at the environmental relevance of what both indicators are actually quantifying. We discussed in Chap. 10 that GWP is the time-integrated radiative forcing of a substance per unit mass emitted. The input data required to calculate it are relatively Fig. 11.3 GWP20 more precise but less accurate from an LCA perspective than GWP100 R.K. Rosenbaum et al.

11 Uncertainty Management and Sensitivity Analysis

Hauschild et al., LCA: Theory and Practice


straightforward to measure and well reproducible in a laboratory, or in other words it is a precise indicator. It indicates the potential absorption of energy in molecules in the atmosphere, but it does not inform us on its impact on the environment or human health, or in other words it is not accurate regarding the goal of quantifying potential environmental impacts. Most toxicity midpoint indicators, however, quantify statistically how many disease cases (or affected species) may potentially occur in a human (or ecosystem) population per mass emitted. Therefore, toxicity indicators are much more representative regarding the consequences of a potential impact than GWP, or in other words a toxicity midpoint indicator has a higher environmental relevance than GWP and may thus actually be more accurate than GWP, while being less precise


Only the inherent, and most likely often unconscious, assumption of causal links between radiative forcing––increased temperature––melting polar caps––rising sea levels––more extreme weather events––loss of agricultural yield––increased competition for food––starvation and possibly even war––and thus effects on human health makes this indicator useful for LCA, but does it make it actually less uncertain for indicating a potential environmental or human health impact? The argument of too high uncertainty of toxicity indicators thus refers to their precision (reproducibility), but not necessarily to their accuracy (in representing environmental impacts) and may hence be misleading. In addition, the spread between the highest and the lowest values for an indicator may differ widely between impact categories. Given that the toxicity-related impact categories cover several thousand elementary flows (i.e


Given that the toxicity-related impact categories cover several thousand elementary flows (i.e. chemical emissions) with different environmental mechanisms, related variability is higher by several orders of magnitude than for impact categories only covering a handful of elementary flows (e.g. climate change including *50 chemicals). An example of the relationship between uncertainty around results for a single chemical and spread of results across chemicals is given in Chap. 31, Fig. 31.7. In LCA, uncertainty should always be referring to what a study aims to quantify. The environmental relevance of indicators varies greatly among impact categories and is also a source of uncertainty towards the conclusions of a study. Just because this uncertainty is not quantified or even somewhat unconscious, that does not mean that it is not present


Just because this uncertainty is not quantified or even somewhat unconscious, that does not mean that it is not present. Hence, a direct comparison of purely precision-related uncertainty among midpoint indicators is not meaningful unless the compared indicators have a similar level of accuracy (i.e. environmental relevance). This brings us to another common misconception about the uncertainty of LCA indicators, namely the choice of using midpoint or endpoint indicators. The typical trade-off between both options is that a midpoint indicator result will be more precise but less environmentally relevant, while it will be the opposite for an endpoint indicator (i.e. less precise but more environmentally relevant). Therefore, endpoint indicators are typically perceived as more uncertain based on their usually lower precision (due to a larger number of choices and hypotheses involved in their modelling compared to midpoint indicators)


When considering environmental relevance as a measure of accuracy and a type of uncertainty (as discussed further below), it is important to keep in mind that midpoint indicators have a large portion Uncertainty Management and Sensitivity Analysis


of (unquantified or unperceived/unconscious) uncertainty due to their lower environmental relevance compared to endpoint indicators. As depicted in Fig. 11.4, overall uncertainty may increase or decrease from a midpoint to an endpoint indicator of a given impact category, depending on the uncertainty of models and parameters used for endpoint modelling. However, Weidema (2009) pointed out that this “figure implies that it is possible to make a trade-off between relevance and uncertainty, in which the overall error is minimised ... [and] ... that the consequences of the decision will be less uncertain if the decision is taken at the point where the overall error is minimised—that is, at a midpoint [...] (e.g., at the level of CO2-equivalents)”, which is a common perception among LCA practitioners and clients


Weidema then rightfully argues that “When the decision is implemented, however, the consequences occur not only at the level of the midpoint but also at the level of the endpoint (the decision will result in lost species and lost lives). This implies that the apparently low uncertainty of the decision at midpoint does not reduce the uncertainty of the consequences of the decision at endpoint level, which are still as uncertain as indicated at the bottom of [the] figure [...]. If the consequences at endpoint level (e.g., lost species and lost lives) are what we really are interested in (as implied by the maximum relevance), then taking the decision at the midpoint level (e.g., CO2-equivalents) is simply the same as ignoring the true uncertainty of the consequences of the decision.” In other words, if minimal or avoided environmental consequences are the objective of a Fig


11.4 Conceptual representation of how overall uncertainty may decrease (middle) or increase (right) from midpoint to endpoint (damage) in an impact pathway (left); uncertainty of interpretation and uncertainty of models and parameters contribute to different extents to overall uncertainty on midpoint (early in the impact pathway) and on endpoint/damage level (end of the impact pathway) while environmental relevance increases [taken from Hauschild and Potting (2005)] R.K. Rosenbaum et al.


decision, choosing midpoint indicators because they can be quantified with higher precision will still not avoid the uncertainty of that decision’s environmental consequences since a midpoint indicator is less relevant (representative) for the environmental consequences to be avoided. Weidema (2009) entertainingly compares this flawed logic as being “representative of the situation of the drunk who, when asked why he was searching for his keys under the streetlight although he had lost them in the dark alley, responded that it was easier to see under the light”. In consequence, the overall uncertainty of endpoint indicators may not (always) be much different to that of midpoint indicators from a decision-support perspective as indicated in Fig


In consequence, the overall uncertainty of endpoint indicators may not (always) be much different to that of midpoint indicators from a decision-support perspective as indicated in Fig. 11.4 where the development in the “overall uncertainty” accompanying the decision may sometimes be lowest at the damage level, when the reduction in interpretation uncertainty, going from midpoint to damage, more than compensates the increase in model and parameter uncertainty of the applied characterisation model. Hopefully, these examples illustrate that when discussing uncertainties between LCA indicators (of different impact categories or between midpoint and endpoint level), all types of uncertainty combined with the related concepts of precision and accuracy need to be considered or else the risk of oversimplifying and comparing apples and oranges is imminent, which may lead to unjustified and wrong conclusions


The very purpose of any model is to represent a simplification of reality, but what is the right level of simplification? In order to establish a useful model, a meaningful level of complexity is required. As illustrated in Fig. 11.5 adapted from Ciroth (2004), the overall error (of representing reality) of a model is, among other, a function of the error due to an inaccurate representation of reality (too complex model with, e.g. too many input parameters and algorithms that introduce each their own uncertainty) and the error due to ignoring too much of the complexity of reality (too simplistic model). Accordingly, balancing both will yield the lowest overall model-related error. This is known as the parsimony principle, i.e. as simple as possible and as complex as necessary, and intuitively is a suitable leitmotif for LCA. Fig


This is known as the parsimony principle, i.e. as simple as possible and as complex as necessary, and intuitively is a suitable leitmotif for LCA. Fig. 11.5 Too complex modelling can have a similar error of representing reality as too simplistic modelling [modified from Ciroth (2004)] Uncertainty Management and Sensitivity Analysis


Simplicity is often perceived as a desirable quality of a model making it easy to understand and less data demanding. Complexity on the other hand is frequently perceived as cumbersome, non-transparent and data intensive. However, rejecting complexity as such, without regarding its relevance and influence on the decision at hand, will of course be simpler and also lead to a decision, but it may not be a decision fulfilling the LCA objective of choosing an environmentally preferable option. In other words, it may be a more precise but less accurate and thus a potentially misleading decision. Given the inherent (i.e


In other words, it may be a more precise but less accurate and thus a potentially misleading decision. Given the inherent (i.e. unavoidable) complexity of environmental processes and our still limited knowledge of them, the principle of “It is better to be vaguely right than exactly wrong” (Read 1920) is a much cited and useful angle when discussing uncertainties in LCA, thereby also acknowledging that we should never design our models more complex than necessary to avoid “paralysis by analysis” potentially leading to no operational model at all and, hence, to no decision (support). 11.2.3 Representing Uncertainty The probabilistic nature of uncertainty of the studied process or object is conceptualised by a probability distribution. The probability distribution of a continuous variable is described by a distribution function, usually the probability density function (PDF—not to be confused with the abbreviation PDF for Potentially Disappeared Fraction of species as used in Chap. 10)


10). In practice, the PDF of an input parameter x is estimated by the values xi measured over a sample, ranging from a minimum to a maximum value. Hence, the probability is approximated by the relative frequency when enough values are sampled. For example, when measuring the body weight of individuals in a human population of several thousand people, we will always find a range of values with a minimum value given by the lightest and a maximum value given by the heaviest individual(s) among those measured. Drawing the full range of measured values on the x axis and how often each of these values occurs (=their relative frequency) on the y axis results in a distribution function (a PDF) as illustrated in Fig. 11.6. The shape of this function varies substantially depending on the frequency of the values of a variable


11.6. The shape of this function varies substantially depending on the frequency of the values of a variable. Many shape patterns have been clearly defined and termed, distinguishing continuous distributions such as normal, log-normal, or beta, and discrete ones such as binomial, Poisson, or hypergeometric, the latter being characterised by a probability mass function (PMF). When representing uncertainties, these names are used to describe the type of distribution and are an essential element when addressing the uncertainty of a (measured or estimated) parameter or the model output. Various methods exist to fit a continuous or a discrete distribution over a set of values. Generally, important measures to describe uncertainties of an input parameter x or the model output are the standard deviation for the spread of a distribution, and for the central tendency of a distribution the arithmetic mean (or average), the R.K. Rosenbaum et al.


median, and (more rarely) the mode. The arithmetic mean or average of a sample is calculated as the sum of all values divided by the total count of all values. The mode is the most frequent (i.e. most probable) value within the dataset, and the median is the value separating the upper 50% and the lower 50% of all values when ranked in order of their magnitude. In a perfectly normally distributed dataset, the average, median, and mode are identical, whereas in any skewed distribution (e.g. a log-normal distribution) these central tendency measures have different values. However, the mean has the disadvantage to be very susceptible to outliers (unusually small or large values within a dataset) and skewed data. Therefore, the mean does not represent the best central value in skewed distributions (e.g. log-normal), whereas the median is less affected by the skewness of a dataset. The variation of the sample values is most commonly described by the (sample) standard deviation


log-normal), whereas the median is less affected by the skewness of a dataset. The variation of the sample values is most commonly described by the (sample) standard deviation. The PDF or PMF are sufficient to fully characterise the distribution of an input parameter, but it is not always evident to derive these functions. Then the combined knowledge of the average (or median) and the (sample) standard deviation can provide a useful description of the behaviour of a parameter. In-between the minimum and the maximum values of the range, we will find all sampled values and measures of central tendency for a probability distribution, like the average and the median body weight in the previous example. For the quantification of uncertainty, we usually do not use the entire range between these two extrema, but rather a sub-set of (more representative) values. Figure 11.7a represents a normal distribution for an input parameter x with known parameters l (=mean) and r (=standard deviation)


Figure 11.7a represents a normal distribution for an input parameter x with known parameters l (=mean) and r (=standard deviation). Integrating under the curve of the normal distribution from negative to positive infinity, the area is 1 (i.e. 100%). Consequently, the probability for a value drawn from this distribution to fall in the range 1 is 100%. Obviously, this is not useful in terms of describing the uncertainty of a parameter. In the context of environmental modelling (including LCA) the typically used uncertainty range is the 95% interval as given in Fig. 11.7a as shaded area for a Fig. 11.6 Fitting of a distribution to a set of values for a variable Uncertainty Management and Sensitivity Analysis


normally distributed input parameter. This 95% uncertainty interval can be interpreted as the range of values within which (approximately) 95% of all randomly measured values can be found. When the distribution function is known, we can also say that any sampled (or measured) value one may take in the future will fall within this range with 95% chances. Assuming a normal distribution for our example on body weight, this means that 95% of all measured weights from our population will fall within this range and that if picking randomly a person from that population, one will have 95% chances that this person has a body weight within this range of values and only 5% chances to pick a person lighter or heavier than that. The limits of the uncertainty interval are referred to via various names such as upper and lower bounds or 2.5th (lower bound) and 97.5th (upper bound) percentiles. Other used uncertainty intervals for normally distributed variables are the 68 and the 99.7% intervals


Other used uncertainty intervals for normally distributed variables are the 68 and the 99.7% intervals. The link between measures of central tendency (especially the mean and median) and dispersion (standard deviation) of an input parameter x with the upper and lower uncertainty bounds is detailed in the following. Going back to the normal distribution in Fig. 11.7a with mean value l and standard deviation r, the 95% uncertainty interval (approximately) corresponds to the interval range between l  2r and l þ 2r. The limits of this interval are the 2.5th percentile (2.5th %ile) as the lower bound at l  2r and the 97.5th %ile as the upper bound at l þ 2r. Integrating over a range within r from the mean value l, the resulting value is 0.6826; hence, the probability for a value to fall within the range r around the mean is approximately 68%. This range is called the 68% (sometimes 65%) uncertainty interval


This range is called the 68% (sometimes 65%) uncertainty interval. You may have guessed it by now, the 99.7% uncertainty interval is then bounded by l  3r on the lower and l þ 3r on the upper end of the distribution. If an input parameter x is log-normally distributed with population parameters l and r, it means that the natural logarithm of the parameter follows a normal distribution. This distribution is often observed for measurements of environmental input parameters and hence frequently used in environmental modelling. The median value m of the log-normal distribution is identical to the geometric mean el, while the mean of the distribution is el þ r2=2. The mean is larger than the median as Fig. 11.7 a Normal distribution and b log-normal distribution with 95% uncertainty interval ranges shaded in grey R.K. Rosenbaum et al.


this distribution is right skewed. For a log-normally distributed input parameter, the corresponding distribution and the 95% uncertainty interval are depicted in Fig. 11.7b. The 95% uncertainty interval (approximately) corresponds to the integration over the range m=e2r to m  e2r. The exponential term is thereby defined as the squared geometric standard deviation: GSD2 , e2r: ð11:1Þ With that, the GSD2 is used to define the 2.5th and 97.5th %iles, i.e. the 95% uncertainty interval bounds, of a log-normal probability distribution around the median m of x as Probability m GSD2 \x\m  GSD2    0:95: ð11:2Þ The uncertainty intervals as discussed above should be distinguished from the confidence intervals. In practice, a population parameter (mean, median or standard deviation) is often unknown


In practice, a population parameter (mean, median or standard deviation) is often unknown. In statistical data analysis, confidence intervals are usually calculated, that is the estimated range of values that frequently contains the “true” value of the unknown population parameter, if the sampling procedure is repeated. We need here to clarify some common misconceptions around the interpretation of confidence intervals. For our example on body weight, suppose a 95% confidence interval for the unknown true mean weight that ranges from a to b (a < b). The statements “95% of the population weighs between a and b kilograms” or “There is a 95% chance that the mean weight of the population lies between a and b kilograms” are false


The statements “95% of the population weighs between a and b kilograms” or “There is a 95% chance that the mean weight of the population lies between a and b kilograms” are false. The correct interpretation is “If we were to repeat the weight measurement over and over, then 95% of the time, on average, the confidence intervals contain the true mean weight.” The latter does not refer directly to a property of the population parameter, but a property of the procedure itself. Two useful further readings on common misconceptions and misinterpretations of confidence intervals and other statistical methods and parameters are the papers from Greenland et al. (2016) and Hoekstra et al. (2014). For a further study of confidence intervals, and all the concepts presented in this section as well, the reader can refer to bibliography in probability and statistics, e.g. Walpole et al. (2012). The type of distribution is an important element to precisely describe the uncertainty of a parameter


Walpole et al. (2012). The type of distribution is an important element to precisely describe the uncertainty of a parameter. The simplifying assumption of a certain type of distribution (in LCA typically log-normal), instead of attempting to identify the exact distribution, is very useful when little or no information is available about a parameter or when using simplified, approximate analytical uncertainty propagation methods. However, this is sometimes met with criticism by practitioners who would like to integrate uncertainty information into their LCA studies using the exact distribution type. While from a purely statistical point of view this is the ideal, the very large number of variables and their distributions for individual inventory data and characterisation factors used to quantify the uncertainty of an impact score, will Uncertainty Management and Sensitivity Analysis


often result in a normal distribution of the impact score. This phenomenon is called the “central limit theorem” which states that the arithmetic mean of a sufficiently large number of independent values will be approximately normally distributed, regardless of the underlying input distributions (Pólya 1920). Although, this theorem requires certain conditions to be fulfilled (e.g. independence of the included parameters, existence of a finite expected value and standard deviation for each parameter), it is reasonable to assume these conditions to be fulfilled by most unit processes in LCI. This practical assumption offers several ways to significantly and parsimoniously simplify uncertainty quantification in the LCA context with a likely acceptable loss of precision when assuming one or only a few distribution types for LCA input parameters


11.3 Addressing Uncertainty in LCA 11.3.1 Types and Sources of Uncertainty and Variability in LCA There is no shortage of classifications of uncertainty types in literature, ranging from only two or three classes up to ten or more different types. A very useful classification for LCA was published by Huijbregts (1998) and comprises the following classes: 1. Temporal variability (e.g. seasons), 2. Spatial variability (e.g. population density, climate conditions), 3. Variability between objects (e.g. between different individuals), 4. Parameter uncertainty (e.g. inaccuracy, lack or non-representativeness of input data and model parameters), 5. Model (structure) uncertainty (e.g. algorithms in process and characterisation models), 6. Uncertainty due to choices (e.g. definition of functional unit and system boundaries, selection of LCIA method), to which Björklund (2002) added: 7. Epistemological uncertainty (e.g. lack of relevant knowledge), 8. Mistakes (e.g


definition of functional unit and system boundaries, selection of LCIA method), to which Björklund (2002) added: 7. Epistemological uncertainty (e.g. lack of relevant knowledge), 8. Mistakes (e.g. choosing the wrong substance or process due to similar names as references, unit conversions or unclear units like tons vs. metric tons/tonnes), and to which we add: 9. Relevance uncertainty (e.g. environmental relevance, accuracy or representativeness of an indicator towards an area of protection). Huijbregts (1998) also provided an illustrative list of examples of sources of uncertainty for each type and per LCA phase, which was slightly modified by R.K. Rosenbaum et al.


Björklund (2002) and by the authors of the present chapter and which is shown in Table 11.1. A classification of uncertainty types widely used in many fields of application distinguishes only three different types: parameter, model, and scenario uncertainty. Most of the nine uncertainty types listed above are essentially sub-classes of these three types as indicated in Table 11.1. Parameter uncertainty comprises variability and uncertainty in model input parameters. Model uncertainty indicates the uncertainty of the model itself via setup, initial and boundary conditions defined, variables/indicators taken into account, and equations used. Scenario uncertainty can be interpreted as uncertainty in the application and use of the model and its results under predefined conditions and assumptions


Scenario uncertainty can be interpreted as uncertainty in the application and use of the model and its results under predefined conditions and assumptions. Whereas parameter and model uncertainty only contribute to the uncertainty of the numerical model results, scenario uncertainty may also contribute to uncertainty in the interpretation of the model results and, hence, that of a consequent decision as illustrated in Fig. 11.9. For a number of reasons, parameter uncertainty and variability is the uncertainty type that is best considered in current LCA practice and it is what most people refer to when discussing uncertainty in LCA. With occasional, rare exceptions, the few published LCA studies that include uncertainty, essentially consider parameter uncertainty and variability


With occasional, rare exceptions, the few published LCA studies that include uncertainty, essentially consider parameter uncertainty and variability. This kind of uncertainty is estimated in LCI databases such as ecoinvent and in some LCIA methods such as Impact World+ or LC-Impact, and LCA software allows to include the respective calculations in an LCA study. It is also a source of uncertainty that practitioners can address by improving data quality and representativeness, e.g. using primary data for foreground processes, or via spatialised LCA. This can be illustrated using three axes of data representativeness as discussed by Weidema et al. (2003), which constitute a three-dimensional space as shown in Fig. 11.8. LCI data may thus be too detailed, too un-specific, or too non-representative along one, two, or all three axes. Their distance on each axis to the range of data needed thereby represents their uncertainty


Their distance on each axis to the range of data needed thereby represents their uncertainty. It is important to keep in mind that most types of uncertainty and variability listed in Table 11.1 will contribute, to varying degrees, to the overall uncertainty of a quantitative LCA result (i.e. impact score). Just because parameter uncertainty is essentially the most accessible one and therefore the most frequently assessed or discussed type of uncertainty, it does not mean that it is always the most important (i.e. most contributing) one. The ninth type in the list above (uncertainty related to environmental relevance, accuracy or representativeness) refers to how completely all relevant processes are included in a model, notably to how completely an environmental mechanism is represented in a given characterisation model for a given category midpoint or endpoint (as illustrated in Fig. 11.4)


11.4). Note that completeness and representativeness relate directly to the goal and scope of an LCA, e.g. the GWP model may be perfectly representative and complete if the goal of a study is to calculate a carbon footprint, while it may be incomplete and of low (environmental) relevance if the goal is to quantify the contribution of an activity to climate change-related human health impacts. For this reason, uncertainty related to environmental relevance or representativeness (i.e. termed here as relevance uncertainty in line with Paparella et al. 2013) cannot be part of the model Uncertainty Management and Sensitivity Analysis


Table 11.1 Examples of sources of uncertainty and variability for each type of uncertainty per LCA phase Uncertainty type LCA phase Goal and scope definition Inventory analysis Choice of impact categories and classification Characterisation Weighting and normalisation Variability Temporal variability Inherent variations in the studied system Differences in yearly emission factors Inconsistent time horizons between impact categories Time horizon or change in environmental characteristics over time Change of social preference over time Spatial variability Regional differences in emission factors Regional differences in relevance of an impact category Regional differences in environmental, ecological sensitivity or characteristics Regional differences in distance to (political) targets Variability between objects Differences in technology between factories which produce the same product Differences among technologies in relevance of an impact category Differences in environmental,


Variability between objects Differences in technology between factories which produce the same product Differences among technologies in relevance of an impact category Differences in environmental, ecological and human characteristics Differences in individual preferences when using a panel method Parameter uncertainty Inaccurate, non-representative or no inventory data Uncertainty in lifetimes of substances Inaccurate normalisation data (continued) R.K


Rosenbaum et al.


Table 11.1 (continued) Uncertainty type LCA phase Goal and scope definition Inventory analysis Choice of impact categories and classification Characterisation Weighting and normalisation Model uncertainty Model structure uncertainty Linear instead of nonlinear modelling, assuming continuous emissions Impact categories are not known; Contribution of impact category is not known Linear instead of nonlinear modelling, assuming steady-state conditions Weighting criteria are not operational Uncertainty due to choices Choice of system boundaries Choice of allocation methods Scenario uncertainty Choice of functional unit Choice of technology level Leaving out known impact categories Choice of the characterisation method(s) Choice of normalisation reference system or weighting method Relevance uncertainty Environmental relevance and representativeness required for decision Completeness of (relevant) impact categories covered Representativeness of an indicator regarding a given area of


uncertainty Environmental relevance and representativeness required for decision Completeness of (relevant) impact categories covered Representativeness of an indicator regarding a given area of protection Neglecting the influence of normalisation or weighting factors on results when interpreting them Epistemological uncertainty Ignorance about relevant aspects of studied system Ignorance about modelled processes Ignorance about relevant impact mechanisms Ignorance about relevant environmental processes Ignorance about relevant priorities Mistakes Any Any Any Any Any Extended from Huijbregts (1998) and Björklund (2002) Uncertainty Management and Sensitivity Analysis


uncertainty, which is an intrinsic property of a model result and does not depend on how it is used or interpreted. Uncertainties and variabilities are typically discussed regarding their importance for the uncertainty of a numerical model output or result, i.e. a number with its standard deviation and eventually a distribution function, which describes the uncertainty of the underlying tool and its result. This does however not consider what this result is being used for, which decision it supports and how it is being interpreted in the context of this decision. In order to also be able to represent and discuss additional sources of uncertainty related to results interpretation and the decision context, the concept of relevance uncertainty may be helpful. The more representative an indicator is for a given environmental (or social or economic) problem or damage, the lower the uncertainty on its interpretation, as discussed before. As shown in Fig


The more representative an indicator is for a given environmental (or social or economic) problem or damage, the lower the uncertainty on its interpretation, as discussed before. As shown in Fig. 11.9, this may be called the relevance uncertainty, which essentially contributes to the uncertainty of a conclusion or decision, but not to that of the numerical model result. Weidema (2009) pointed this out by stating that “Perhaps the cause of the logical error in the interpretation of (Fig. 11.4) ... is that it requires that relevance (or uncertainty of interpretation) can be measured in the same unit as uncertainty of measurement, which is, in fact, not possible. Relevance is what we look for; uncertainty addresses the reliability of our measurement. When we are deciding how to measure what we look for, it is irrelevant how precisely we can measure what we do not look for”. Fig. 11.8 Three aspects of data representativeness in LCA based on Weidema et al. (2003) R.K. Rosenbaum et al.


This can be illustrated via a simple example on the use of indicators. Before leaving the house in the morning, many people check the outdoor temperature. What will be the uncertainty of this information? We can probably assume it to be low, so it is a very certain indicator value. However, the real question behind may not be what the value of the current temperature is, but what would be the adequate way to dress for the day. This decision requires a number of indicators, among other temperature, but also wind speed (or chill factor), rainfall and the predictions of those parameters for the rest of the day. Now the uncertainty of these indicator values is probably already a bit higher than that of the current temperature, but that’s not all, since the decision at hand is the choice of clothes


Now the uncertainty of these indicator values is probably already a bit higher than that of the current temperature, but that’s not all, since the decision at hand is the choice of clothes. This however comes with its own uncertainty on the interpretation of the link between preferable clothes and the available indicator values for temperature, wind speed, precipitation, all with their respective predictions and related uncertainties. The overall uncertainty of the decision is therefore dependent not only on the contributions from the indicator values but also on their interpretation and on how to conclude from them to choosing among a range of options for pants, jumpers, shoes, and jackets. To translate this example into the world of LCA, one could ask “What is the GWP100 of 1 litre biodiesel?” and most practitioners will be able to answer this question (using a number of assumptions and choices) with reasonable certainty


However, a typical LCA goal is not the quantification of a given indicator, but the support of a decision like “Is biodiesel environmentally preferable to fossil diesel?”. To answer that question, multiple indicators besides GWP100 such as land use, (pesticide-related) toxicity, eutrophication and others will have to be calculated. The resulting midpoint or endpoint indicator values, respectively, have their uncertainties and comparing them among both diesel types also adds uncertainty. However, the overall uncertainty of the answer to the question of preference is also Fig. 11.9 Types of uncertainty and their contribution to result and decision uncertainty Uncertainty Management and Sensitivity Analysis


affected by how the link between the differences of the indicator values and their representation of environmental consequences is interpreted. Completeness refers to a parsimonious balance between simplicity and complexity (as discussed above in relation to Fig. 11.5), not to the need to include everything. The same parsimony principle also applies to the related balance between parameter and model uncertainty. In essence, a too simple model will be missing important processes and thus have high scenario and relevance uncertainty due to low environmental relevance, but will have low parameter and model uncertainty. A too complex model, in contrast, may need many (uncertain or unknown) parameters and may imprecisely represent some processes (high model uncertainty), but will also be more (environmentally) relevant, i.e. low uncertainty on representativeness. Similar to Fig


low uncertainty on representativeness. Similar to Fig. 11.5, overall uncertainty will thus, again, be lowest when both extremes are well balanced, the model being as simple as possible and as complex as necessary (i.e. following the parsimony principle), representing well all significantly influential processes (van Zelm and Huijbregts 2013). This is another example why the assumption of low uncertainty for a simple model, just because it needs few parameters, is incorrect and misleading. When discussing uncertainty or error in LCA, it is also important to be aware of the implications of random versus systematic errors. In most fields where uncertainty assessment is addressed, the goal is to be precise on an absolute indicator, like temperature or weight for example, which aims to respectively indicate how hot or cold or how light or heavy something or someone is


With some exceptions, the goal in LCA is usually to compare (even a hotspot analysis is essentially a comparison between all processes within a product system) and provide a relative indicator of how much better or worse an option is compared to another, as opposed to indicating how good or how bad something is in absolute terms. In such a comparative context, a systematic error—affecting all compared objects in the same way—may have little importance for the interpretation of results and drawing conclusions. It will just shift all results up or down systematically. It thus affects the result in absolute terms (i.e. the numbers are all higher or lower), but not in relative terms (i.e. the quantitative difference between compared objects remains largely the same)


the numbers are all higher or lower), but not in relative terms (i.e. the quantitative difference between compared objects remains largely the same). This is frequently ignored when LCA is being criticised as too uncertain, essentially because people tend to interpret its uncertainty in absolute terms and compare it with the absolute uncertainty of other methods like quantitative risk assessment for example, whereas much of the absolute uncertainty does not contribute to the uncertainty of the difference between compared alternatives, which will be further discussed in Sect. 11.4.2. This is also related to why LCA results represent potential impacts and (usually) not predictions of observable impacts (see discussion and definition in Chap. 10). R.K. Rosenbaum et al.


11.3.2 Uncertainty Quantification and Propagation Methods A quantitative uncertainty management is still a rare sight in LCA practice. If integrated, the most commonly considered types of uncertainty are parameter uncertainty and variability. Parameter uncertainty for example is captured in uncertainty estimates for inventory data such as given in the ecoinvent database. The quantification of uncertainty refers to the task of establishing a quantitative measure of uncertainty for (1) a specific source of uncertainty in an LCA (e.g. a mean value, standard deviation, and distribution type for a variable or an other uncertain aspect), and (2) the overall uncertainty of an LCA as a result of the combination of specific sources of uncertainty. The latter is achieved using uncertainty propagation methods


The latter is achieved using uncertainty propagation methods. Having discussed the types and sources of uncertainty and variability that are relevant for LCA, the question arises how to quantify them in order to consider and manage them during the assessment process. Some uncertainty types may be more straightforward to quantify statistically than others (e.g. variability of measurable parameters, uncertainty due to some choices), some can be estimated but may be very difficult to quantify (e.g. model uncertainty) and those that relate to the unknown cannot be quantified at all (e.g. mistakes, epistemological uncertainty, and environmental relevance). The latter can (and should) be considered qualitatively during the interpretation of LCA results (see Chap. 12). In consequence, the quantitative overall estimated uncertainty of a model result is both incomplete and uncertain in itself


12). In consequence, the quantitative overall estimated uncertainty of a model result is both incomplete and uncertain in itself. This however does not make this information useless, but it is essential to consider when interpreting results including their uncertainty. Several methods to quantify the (quantifiable) uncertainty elements of an LCA have been proposed and implemented to some extent into LCA. Among these methods are reporting uncertainty intervals, analysing parameter variability and/or different scenarios, translating qualitative data quality ‘pedigree criteria’ into a numerical pedigree matrix, using fuzzy data sets, applying analytical uncertainty propagation, conducting numerical, probabilistic simulations based on e.g. Monte Carlo analysis, using Bayesian statistics, or a combination of some of these methods


Monte Carlo analysis, using Bayesian statistics, or a combination of some of these methods. The following sections describe three methods that are already used in LCA: (1) the semi-quantitative pedigree matrix approach used for example by ecoinvent for the quantification of variability and uncertainty of LCI data; (2) Monte Carlo simulation used in LCA software like SimaPro, GaBi, openLCA, and the more explorative/educational LCA tools CMLCA and Brightway 2; and (3) Taylor series expansion used in CMLCA. A broader overview of selected quantitative uncertainty propagation methods in the context of LCA or the comparison of specific methods can be found in Lloyd and Ries (2007), Heijungs and Huijbregts (2004), or Groen et al. (2014). Uncertainty Management and Sensitivity Analysis


Pedigree Matrix Approach Information about the uncertainty associated with elementary flows is often not available or difficult to quantify for the hundreds to thousands of flows in a typical LCI. To nevertheless address uncertainty related to LCI results, a simplified semi-quantitative procedure can be used and is implemented into the ecoinvent database and also used by ILCD (EC-JRC 2010). It quantifies (exclusively) parameter uncertainty via combining two different kinds of uncertainty: (1) Basic uncertainty due to variation and stochastic error of the values for elementary flows, from measurement uncertainties, activity specific variations, temporal variations, etc. This is quantified either using statistical methods when sufficient data are available, or via a simplified approach assuming a lognormal distribution, establishing an approximation that reflects the lack of sufficient information to calculate a more precise estimate


(2) Additional uncertainty based on data quality indicators using a qualitative assessment of “reliability”, “completeness” and representativeness in terms of “temporal correlation”, “geographical correlation”, and “further technological correlation”. These quality indicators are assigned different scores expressing for each value different degrees of data quality and uncertainty and are represented by a numerical value (1, 2, 3, etc.) for each data quality and uncertainty degree. The lower a score for any quality indicator, the higher is the data quality and/or the lower the data-related uncertainty. As illustrated in Fig. 11.10, combining data indicators in rows with the scores for each indicator in columns gives the so-called “pedigree matrix” considering additional uncertainty (uncertainty due to using imperfect data)


Originally, the semi-quantitative pedigree matrix approach was proposed by Funtowicz and Ravetz (1990) in a framework for managing “all sorts of uncertainty” and later adapted to LCI modelling by Weidema and Wesnæs (1996) as being integrated into ecoinvent. The concept of the pedigree matrix is shown for the data quality indicator “reliability” of the data sources in Fig. 11.10. Combining data quality indicators with their respective scores gives a set of uncertainty factors aggregated into (geometric) standard deviations based on assuming log-normally distributed data in ecoinvent 2. These uncertainty factors are based on expert judgment, without (documented) empirical foundation and have been updated with a more empirical approach by Ciroth et al. (2016) based on analysing LCA studies and data with focus on industrial processes separately for each data quality indicator


(2016) based on analysing LCA studies and data with focus on industrial processes separately for each data quality indicator. Furthermore, in ecoinvent 3 the mathematical framework has been developed to also calculate uncertainty factors for distributions other than log-normal from the coefficient of variation chosen as a universal measure of variability and defined as the ratio between the arithmetic standard deviation and mean for all distributions (Muller et al. 2016). The pedigree matrix based approach was also applied in LCIA for estimating input data uncertainty for toxicity characterisation by Fantke et al. (2012). In this context, the matrix columns represent data-related base uncertainty and the matrix rows represent spatiotemporal data variability. This application and the framework R.K. Rosenbaum et al.


laid out by Muller et al. (2016) demonstrate that the semi-quantitative pedigree approach can be flexibly applied to different aspects of an LCA study based on a diversity of different data lacking fully quantifiable uncertainty information. Numerical Uncertainty Propagation The most widely used uncertainty propagation method is a numerical approach called Monte Carlo simulation (sometimes also referred to as Monte Carlo analysis). It is available in all major LCA software (although not in all respective versions). Its basic principle is the repetition of model calculations (i.e. iterations) using values for each input parameter sampled from its defined probability distribution. A Monte Carlo simulation is outlined as follows: Step 1: generate samples of random values for all input variables; Step 2: apply the model on the generated values to calculate the model output in terms of LCA results; Step 3: analyse statistically the model output


The model output can therefore be represented by a probability distribution instead of a single value. An insufficient number of iterations will result in an unreliable empirical distribution of the output variable that may neither consider the Fig. 11.10 Excerpt from the ecoinvent 3 pedigree matrix showing scores for the data quality indicator “reliability” of the data source [adapted from Ciroth et al. (2016)] and how the scores are translated into numerical uncertainty factors based on expert judgement (for ecoinvent 2) or based on empirical data (for ecoinvent 3). The full matrices contain scores for five different indicators Uncertainty Management and Sensitivity Analysis


full (or at least sufficiently representative) range of output values possible, nor represent the true shape of the distribution. In consequence, the distribution type will not be stable and the uncertainty will therefore be imprecisely estimated. The accuracy of a Monte Carlo analysis increases as the number of iterations becomes larger. However, there is no generic approach to determine when the number of iterations is ‘large enough’. Consequently, the number of iterations may vary among practitioners and also among studies performed by the same practitioner. The number of simulations does not dependent on the number of input parameters, but, in practice, the more complex a (LCI) model is, the more time-consuming a Monte Carlo simulation becomes, which may affect the total number of iterations


Instead of pre-defining the necessary number of iterations, it may be more efficient to run a few tests using an increasing number of simulations until the uncertainty measures (mean, standard deviation or eventually the distribution shape) does not change above an ‘acceptable’ difference, when further increasing the number of iterations. With enough experience, the number of required iterations can be identified based on the type or complexity of a study. While the basic, iterative principle is the same for any implementation of Monte Carlo simulation, the sampling method (i.e. how the values from the distribution of an input parameter are sampled) can vary. The simplest sampling method is called “simple random sampling” (SRS), sometimes also “Monte Carlo sampling”, and it randomly samples a value from the entire distribution of a parameter, as many times as the number of iterations set


Another, more optimised sampling approach is “Latin hypercube sampling” (LHS), which is a stratified sampling method that first divides a distribution into segments of equal probability and randomly samples one value from each segment. Subsequently, for each iteration, one of these pre-sampled values is randomly selected and used as input parameter value. If correctly set up, this allows a better representation of extreme values (close to upper and lower bounds of the distribution) and can significantly reduce the amount of iterations required as it needs less iterations in order to create a sufficiently representative amount of combinations of the different input parameter values. There are several specialised, further optimised variants of this sampling technique, including for example Median Latin Hypercube sampling, which samples the median of each segment instead of a random value


For most LCA applications with its many distributions and multiple sources of variance contributing to the result’s overall uncertainty, there will often be no difference or particular advantage in using LHS compared to SRS. Only when a small amount (typically less than five) of input parameters contributes most to the overall output uncertainty, the advantage of LHS may be tangible. For an overview on simulation and sampling approaches, see e.g. Ross (2012). Since all inputs are assumed to vary independently and thus in principle any combination of input values is possible, Monte Carlo simulation as described above implies mutual independence of all input parameters. In LCA however, many input parameters are correlated, i.e. if one parameter has an increased value any correlated parameter will consequently have a value that is higher or lower by a specific factor. This dependency of two or more parameters can be expressed using covariance or a R.K. Rosenbaum et al.


correlation coefficient, which can be incorporated into a Monte Carlo simulation so that no impossible combinations of input values are sampled. This will typically lead to a reduction (sometimes an increase) in output uncertainty that can be very large compared to assuming input parameter independence and it is therefore essential to consider. Note that, when correlations exist, appropriate conditional distributions are required. The difficulty in LCA practice is to identify and, even more so, to quantify input parameter correlations, which may be numerous and not typically provided in LCI databases. For a single scenario, Groen and Heijungs (2017) analysed the importance of correlation in uncertainty and sensitivity analysis in LCA. They compared two approaches to include correlation of input parameters and demonstrated that the risk of ignoring correlation can be quantified


They compared two approaches to include correlation of input parameters and demonstrated that the risk of ignoring correlation can be quantified. They found that in some cases it may not be necessary to quantify and consider correlation and that the risk of ignoring it can be included in the uncertainty analysis and thus be considered for the quantification of the robustness of the results and the consequent decision. One possible way of identifying and managing input parameter correlation is described in the Supporting Information of Fantke et al. (2012). A note to avoid confusion: LCA (and other) literature sometimes refers to Monte Carlo and Latin Hypercube (with or without further specification whether simulation, analysis or sampling is meant) as if they were two distinct alternative sampling methods. As described above however, both belong to the family of Monte Carlo simulations and the difference is the sampling method


As described above however, both belong to the family of Monte Carlo simulations and the difference is the sampling method. Analytical Uncertainty Propagation The most classic, simple and well-established analytical approach to uncertainty analysis, which is widely used in physical sciences and engineering, is the first-order approximation or Gaussian approximation, named after its famous developer Carl Friedrich Gauss. Morgan and Henrion (1990) described how a first-order approximation can be derived from the Taylor series (i.e. the representation of a function as an infinite sum of terms calculated from its derivatives at a given point), a technique based on a Taylor series expansion of the function relating model input parameters to model results (output). They extended this to a number of special cases, essentially allowing a wider application


They extended this to a number of special cases, essentially allowing a wider application. This method uses linear first-order equations within a fully multiplicative set of parameters assuming independence of all relevant inputs. In this method, relative (normalised local) sensitivity coefficients S^x are defined for each input variable x, calculated from the change of model output y (@ output) per relative change of input variable x (@ input) and evaluated at the point x 1⁄4 ^x: S^x , @ output=output @ input=input 1⁄4 @y=y @x=x  x1⁄4^x ð11:3Þ Model output uncertainty, represented by the corresponding squared geometric standard deviation of model output, GSD2 y, can be described by its variance, var ln y ð Þ 1⁄2 , i.e. the variation around its mean value. Output variance depends on the Uncertainty Management and Sensitivity Analysis


variance of all model input variables, var ln xi ð Þ 1⁄2  (Morgan and Henrion 1990). If we use the fact that the variance of any input variable is related to its GSD2 xi by var1⁄2lnðxiÞ 1⁄4 1⁄2lnðGSDxiÞ2, we can express model output uncertainty via its GSD2 y as a function of GSD2 xi of model input: GSD2 y 1⁄4 exp 2  ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X i1⁄41 var ln xi ð Þ 1⁄2  r ! 1⁄4 exp ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X i1⁄41 ln GSD2 xi   h i2 s ! ð11:4Þ The GSD2 xi for the different input variables need to be known or can be approximated e.g. for log-normally distributed data from the 95% uncertainty interval by GSD2 1⁄4 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 97:5th%ile=2:5th%ile p (see also Fig. 11.7b and Eqs


11.7b and Eqs. 11.1 and 11.2) to ultimately arrive at an overall model output uncertainty using this analytical uncertainty quantification approach. In the LCA context, this method was first proposed for use in LCI (Heijungs 1996, 2002, 2010; Heijungs et al. 2005). Based on this, application to LCA was demonstrated by Ciroth et al. (2004) for a virtual case and by Hong et al. (2010) for the real case of the carbon footprint of a car part comparing several scenarios and considering the dependency of many LCI and LCIA parameters shared by the considered scenarios, which is essential when comparing them. Imbeault-Tétreault et al. (2013) applied it to a complete LCA comprising 881 unit processes with 689 elementary flows comparing two scenarios and considering their dependencies


Imbeault-Tétreault et al. (2013) applied it to a complete LCA comprising 881 unit processes with 689 elementary flows comparing two scenarios and considering their dependencies. Different implementations of this method are possible, dealing in different ways with the limitations of this approach based on different underlying assumptions as compared and critically discussed by Heijungs and Lenzen (2014). Comparisons with the results from Monte Carlo simulation which is considered to be the reference method for uncertainty propagation in LCA, consistently found good accordance between both methods applied to LCA (Ciroth et al. 2004; Hong et al. 2010; Imbeault-Tetreault et al. 2013; Heijungs and Lenzen 2014). The main advantages of the analytical approach are its relative simplicity and calculation speed


2004; Hong et al. 2010; Imbeault-Tetreault et al. 2013; Heijungs and Lenzen 2014). The main advantages of the analytical approach are its relative simplicity and calculation speed. The uncertainty is instantly calculated, whereas Monte Carlo simulation may take several minutes for small systems and few iterations to hours or even days of calculation time for complex systems and many iterations. For a typical LCA and a reasonable number of iterations, half an hour up to several hours on a modern computer can be expected. This is a major drawback towards routine uncertainty assessment in LCA and a central motivation for the authors mentioned above to explore analytical approaches for use in LCA. On the other hand, analytical methods are limited to predominantly simple (i.e. linear and continuous) models. An overview of strengths and weaknesses of analytical versus numerical methods in LCA was derived by Heijungs and Lenzen (2014) and is summarised in Table 11.2


linear and continuous) models. An overview of strengths and weaknesses of analytical versus numerical methods in LCA was derived by Heijungs and Lenzen (2014) and is summarised in Table 11.2. It is worth mentioning that the analytical approach does not provide information about the distribution type of its result, only the standard deviation, but in LCA, a log-normal distribution is often assumed for the output similarly to the R.K. Rosenbaum et al.


input parameters. Heijungs and Lenzen (2014) concluded that both methods should be implemented in LCA software and used complementarily in LCA, in order to profit from their respective advantages. Quantification of Sensitivity Sensitivity can be quantified using perturbation analysis (although often also referred to as sensitivity analysis, a term which is not clearly defined and used in different ways in literature, including or excluding uncertainty). Perturbation analysis can be performed numerically by varying an input parameter (e.g. by a fixed amount, a percentage, a standard deviation, or between a minimum and a maximum) and observing the resulting change in model output relative to the result using the unchanged input parameter (Heijungs 1994). The sensitivity S is then the ratio of the relative change in output divided by the relative change in input as given in Eq. 11.3. There are also analytical approaches available to provide this analysis (Heijungs 1994, 2002, 2010)


11.3. There are also analytical approaches available to provide this analysis (Heijungs 1994, 2002, 2010). The illustrative case study of an LCA on window frames in Chap. 39) identifies sensitive parameters calculating sensitivity ratios Table 11.2 Comparison of main strengths and weaknesses of analytical and numerical uncertainty propagation methods Analytical: Taylor series expansion Numerical: Monte Carlo simulation Uncertainty information required per parameter Standard deviation Standard deviation, distribution type, parameter(s) describing the distribution Uncertainty information obtained for model result Standard deviation Standard deviation, distribution type, further statistical analysis (e.g


median, interquartile range, etc.) Applicability Linear (almost), continuous functions; small uncertainties; no covariance (unless considered in additional term) Linear and nonlinear, continuous and discrete functions; small and large uncertainties; no covariance (unless considered in additional term) Calculation time Instantly Several minutes to hours Capturing correlation of input parameters Possible Possible Advantages • Fast calculation time (i.e. seconds) • Distribution type and parameters of inputs not required • Useful screening approach • Distribution type and parameters or outputs determined • Flexible and widely applicable including to complex models Disadvantages • Distribution type and parameters or outputs not determined • Fairly rigid and limited to simple linear models • Less widely applicable than Monte Carlo • Long (sometimes very long) calculation time (i.e. hours to days) • More input information required Uncertainty Management and Sensitivity Analysis


using Eq. 11.3 and also runs two sensitivity scenarios to test the influence of central assumptions in the study concerning the choice of geographical location (Danish vs. average European residence) and the decision whether to go for a design with a two-layered or a three-layered window pane. If the input is not a parameter but a discrete choice (e.g. system boundaries, allocation rules, functional unit, LCIA method), a so-called scenario analysis evaluates the change in the result for each alternative considered (or meaningful) for a given choice. In this case Eq. 11.3 cannot be applied and a change in a choice may entail a change in several (correlated or mutually independent) input parameters, such as the case for the choice of LCIA method, which will usually change all characterisation factors. The analysis of the influence of a choice on the result is therefore referred to as scenario analysis, with each choice representing a possible scenario


The analysis of the influence of a choice on the result is therefore referred to as scenario analysis, with each choice representing a possible scenario. Although they are formally two different types of analysis, a scenario analysis can be seen as a sort of sensitivity analysis, but for discrete changes in (often multiple) inputs instead of variation of one continuous parameter value at a time. A scenario analysis is also often used to represent different possibilities, e.g. future developments or best-case/worst-case scenarios, of how a number of parameters may change. 11.4 Interpretation and Use of Uncertainty Information Once the uncertainties of input parameters, models, choices, etc., have been quantified and propagated, so that the results are not calculated deterministically but probabilistically (i.e. accompanied with a standard deviation and eventually a distribution of output values), the obtained information on uncertainty in the result can be used to improve (i.e


accompanied with a standard deviation and eventually a distribution of output values), the obtained information on uncertainty in the result can be used to improve (i.e. reduce) the uncertainty of important inputs and to enhance the interpretation and the robustness of conclusions drawn. This can be done in several, mostly complementary ways discussed in the following sections. We first discuss how to interpret uncertainty, variability, and sensitivity information, respectively, as the results of an uncertainty assessment in the LCA context. Then, we discuss the combined use of them and how to use the information obtained to reduce the uncertainty of an LCA study and the robustness of its conclusions


Then, we discuss the combined use of them and how to use the information obtained to reduce the uncertainty of an LCA study and the robustness of its conclusions. 11.4.1 Interpreting Uncertainty, Variability, and Sensitivity As discussed, the sensitivity analysis points out those input parameters that have an important influence on the result, while the uncertainty analysis (including variability) provides information on the spread of the result due to the spread in input data and other sources of uncertainty. An input parameter may be very uncertain, but if the model output is insensitive to this parameter, the uncertainty of the input parameter will not contribute to that of the result (since no change in its value R.K. Rosenbaum et al.


changes the model result) and improving the certainty of this parameter with better input data will bring no improvement to the robustness of the result and would thus be wasted effort. On the other hand, the model result may be very sensitive to an input parameter that is very certain, in which case it would depend on their degree of certainty and sensitivity whether or not better data would still improve the result’s robustness. From this illustration it is clear that neither the sensitivity nor the uncertainty of a parameter should be interpreted on their own, whereas the combination of both allows a meaningful judgement of the importance of a parameter regarding the model output. This can be illustrated plotting both aspects as illustrated in Fig


This can be illustrated plotting both aspects as illustrated in Fig. 11.11, which shows both cases described above plus the two cases of (1) complete insensitivity combined with complete certainty of a parameter, which makes it negligible regarding its importance for the output uncertainty, and (2) high sensitivity combined with high uncertainty of a parameter, which will identify the primary parameters to focus data collection and improvement (i.e. reducing parameter uncertainty) on in order to obtain the largest gains in result certainty. This basic concept is useful to keep in mind when identifying dominant sources of uncertainty for any model result. The concept of identifying and ranking sources of uncertainty, like input parameters, unit processes, or characterisation factors, in terms of their contribution to uncertainty in LCA results is called ‘identification of significant issues in the Interpretation phase (see Chap


12) but also referred to as key issue analysis, importance analysis or uncertainty contribution analysis, which is not to be confused with the impact contribution analysis or dominance analysis frequently used in LCA that identifies the unit processes most contributing to an impact score. It is useful for identification of important sources of uncertainty, where better information or data would directly improve the certainty of the result and hence the robustness of the conclusion. It can be applied to focus data acquisition and model refinement, ensuring that additional effort in getting better data or improving models actually contributes to more robust results. This also relates back to the discussion above on precision and accuracy, confirming that improving precision Sensitivity Uncertainty Very important parameters Negligible parameters Possibly important parameters Possibly important parameters Fig


11.11 Combining uncertainty of and sensitivity toward an input parameter to identify its importance in terms of contribution to overall uncertainty of the model result [based on Heijungs (1996)]; instead of parameters, any source of uncertainty in LCA could be identified, including for example characterisation factors Uncertainty Management and Sensitivity Analysis


by finding more precise data does not automatically result in lower uncertainty if those data are not central to the impact score they are used to model. Combining the information gathered via key issue analysis with that from impact contribution analysis, helps identifying unit processes that contribute significantly to (1) the impact score of a highly local or regional impact category (e.g. eutrophication, toxicity, land use, or water use, see Chap. 10) and (2) the uncertainty of that impact score. This can be used to apply a smart, partial regionalisation of the LCI model and its LCIA characterisation. Instead of using spatially resolved LCI and LCIA data for the entire LCA (which is resource intensive and thus usually prohibitive for both the practitioner and the LCA software used), only the identified unit processes and elementary flows are regionalised using primary input data and regionalised LCIA characterisation factors (or derived, representative archetypes of them)


If the uncertainty and variability information of the underlying elementary flows and characterisation factors has been kept separate (i.e. not been combined into a single uncertainty distribution), this will result in a (substantially) lower overall uncertainty of the impact score, since the contribution from spatial variability will be eliminated (or at least reduced) by using spatially resolved data and characterisation factors for these processes. This method allows a parsimonious consideration of complexity due to spatial variability and rewards the practitioner’s additional effort directly by a lower overall uncertainty and hence a more robust result and conclusion. The same approach can also be applied to temporal variability, i.e. using temporally explicit data instead of annual averages when it sufficiently influences the result’s uncertainty, e.g. for water consumption


using temporally explicit data instead of annual averages when it sufficiently influences the result’s uncertainty, e.g. for water consumption. 11.4.2 Relevance of Uncertainty When Comparing Scenarios So far we have discussed various aspects related to assessing the uncertainty of a single scenario, i.e. the environmental profile of one option, without comparing two or more alternative options, the latter being one of the most frequent applications of LCA. In the case of a comparative LCA however, there is an additional aspect to consider: the correlation of numerous input parameters between the compared scenarios, where many processes (i.e. electricity, fuel, transport, etc.) and almost all characterisation factors will be the same in several or all compared scenarios. When comparing two scenarios, the focal point is thus not on how large the value of an impact score is but what the difference (or the ratio) between two impact scores (i.e


When comparing two scenarios, the focal point is thus not on how large the value of an impact score is but what the difference (or the ratio) between two impact scores (i.e. between two scenarios or compared systems) is. Consequently, instead of the absolute uncertainty of a single impact score, the uncertainty of the difference (or ratio) between two impact scores needs to be assessed, because the uncertainty of correlated parameters will be the same in both scenarios and thus not contribute to the uncertainty of the difference between the scenarios. In other words, comparing two scenarios and their respective uncertainties (e.g. by simply overlaying both R.K. Rosenbaum et al.


distributions) without considering correlation, the uncertainty will be (strongly) overestimated, which may be misleading and result in the wrong conclusion. Note that in the illustrative case study presented in Chap. 39, it was not possible to consider the correlations between the compared scenarios, due to software limitations. The technical possibilities for uncertainty analysis vary between available LCA software and may also evolve (i.e. improve) from older to newer versions. Choosing LCA software that supports the requirements of a proposer uncertainty analysis is therefore essential. The uncertainty analysis presented in the illustrative case study is a screening level analysis and considers in its interpretation that uncertainty in the comparison of scenarios is overestimated due to lacking consideration of correlations. There are two frequently used ways to compare the impact scores of two scenarios A and B, calculating the difference A −B, or the ratio A/B


There are two frequently used ways to compare the impact scores of two scenarios A and B, calculating the difference A −B, or the ratio A/B. When using the difference, the result can be A – B < 0 when A has a lower impact score than B (A < B), it can be A – B = 0 when A = B, or it can be A – B > 0 when A > B. The second way works similarly, with A/B < 1 when A < B, A/B = 1 when A = B, or A/B > 1 when A > B. In both cases the environmentally preferable option for a given impact category (i.e. compared impact scores) is easily identified. The uncertainty of the difference or ratio can be quantified using covariance or correlation coefficients, which can be assessed with both numerical and analytical uncertainty propagation methods. When using Monte Carlo simulation, it is also straightforward to calculate the above difference or ratio pairing the results from the iterations from each scenario


When using Monte Carlo simulation, it is also straightforward to calculate the above difference or ratio pairing the results from the iterations from each scenario. This will result in a number of iterations where A > B and some where A < B unless one scenario is always better than the alternative over its entire range of uncertainty. This can then be interpreted as the frequencies of each case, i.e. x% of iterations where A > B and y% of iterations where A < B, with x and y representing the respective probability given that enough iterations where calculated. This means that it is possible to calculate the probability of A being environmentally preferable over B and vice versa as illustrated in Fig. 11.12. For example, if A is better than B in 25% of the simulated cases, there will be 75% where B is better than A. The conclusion may thus be that B is better than A with 75% likelihood, or in other words with a 25% probability to be wrong


The conclusion may thus be that B is better than A with 75% likelihood, or in other words with a 25% probability to be wrong. In a decision support context, the probability of one alternative being preferable over another is an essential measure of robustness of a recommendation and eventually an information that only uncertainty assessment can provide. If the decision is to choose one option over all other alternatives, there is a substantial added value for the decision maker if the probability for this to be wrong can be quantified. It helps, among other, to provide perspective on the robustness of an environmental gain of a certain option relative to other measures such as costs for example. If a higher investment is required but the probability that this really is an environmentally preferable option is very high, the investment may be easier to justify. Several authors demonstrated how to apply this in LCA (Hong et al. 2010; Wei et al


Several authors demonstrated how to apply this in LCA (Hong et al. 2010; Wei et al. 2016) and the following section provides an example where this approach was also used to enhance the interpretation of results and express the robustness of the conclusions. Uncertainty Management and Sensitivity Analysis


The example is a real case comparing different, functionally equivalent solutions for hand dryers in public restrooms (Quantis 2009). The study compared the (1) XLERATOR Hand Dryer (high-speed air flow) to (2) conventional hand dryers (low-speed air flow), (3) paper towels with virgin paper, and (4) paper towels with 100% recycled paper. The functional unit was to dry 260,000 pairs of hands. The study was performed by Quantis’ Boston office, commissioned by Excel Dryer Inc., underwent critical review according to ISO 14040/14044 and has been published (available via exceldryer.com). It is in many ways a classical LCA study, but what makes it stand out as an interesting example is that for climate change impacts, an uncertainty assessment was performed in order to determine the confidence in the conclusions regarding the preferable solution. Using the analytical propagation method, output uncertainty was calculated for the climate change results of all four scenarios as shown in Fig


Using the analytical propagation method, output uncertainty was calculated for the climate change results of all four scenarios as shown in Fig. 11.13. Even though it may be tempting to compare the distributions directly, the latter do not consider dependency and thus overestimate the uncertainty of the difference between scenarios when comparing them. They do, however, indicate the uncertainty of each scenario individually with the XLERATOR showing the lowest spread, which is due to the fact that many primary data are used that the commissioner has direct access to, whereas the input data for alternative scenarios are estimated or taken from other sources and secondary data, thus increasing their uncertainty. The XLERATOR shows the lowest impact score and very little overlap with the uncertainty range of the alternative scenarios. This allows a first conclusion that it is very certain that this is the preferable alternative among the compared options, Fig


This allows a first conclusion that it is very certain that this is the preferable alternative among the compared options, Fig. 11.12 Uncertainty of the difference between two scenarios A and B R.K. Rosenbaum et al.


because the uncertainty range can only be smaller when considering the dependency of parameters between the alternatives. In order to gain deeper insights into the uncertainty when comparing these alternatives, a paired comparison between two scenarios at a time was performed. A selection of the results is shown in Fig. 11.14. As discussed above, the ratio of two study results can be used to compare them and determine whether or not one of the two alternatives is environmentally preferable. It is clearly demonstrated that the XLERATOR consistently has the lowest impact score and that the probability that this is the wrong conclusion is virtually zero. In other words, according to the uncertainty analysis, it is 100% certain that the XLERATOR is the most preferable among all considered options regarding climate change impacts. It is an important question to ask which aspects of uncertainty have been considered and how completely the uncertainty has been captured


It is an important question to ask which aspects of uncertainty have been considered and how completely the uncertainty has been captured. If important sources of uncertainty that are independent between scenarios have been omitted, the uncertainty of the ratio between two scenarios may well be larger and the conclusion would be less robust. Assuring a complete consideration of important sources of uncertainty contributing to the difference between two scenarios is essential in order to fully trust the resulting measure of confidence in concluding the preference of one scenario over another. The comparison of other scenarios provides examples of less certain outcomes. The comparison of standard dryer and virgin paper towels shows that a part of the resulting distribution of the ratio between both scenarios is larger than 1. According to the numerical results provided in the report, there is a 24% chance that virgin paper towels have a lower climate change impact than standard dryers


According to the numerical results provided in the report, there is a 24% chance that virgin paper towels have a lower climate change impact than standard dryers. Consequently, there is a 76% chance that standard dryers are less impacting than virgin paper towels. When comparing standard dryer and recycled paper towels, the uncertainty distribution of the ratio between both is almost equally spread around 1, which means that there are about 50% chance for both possible conclusions. In that Fig. 11.13 Probability distributions (probability density functions) for the climate change impact scores of four compared alternatives to dry hands (Quantis 2009) Uncertainty Management and Sensitivity Analysis


case, both scenarios have to be considered essentially equal and no conclusion regarding their (difference in) climate change impact can be drawn. Comparing the two paper towel options, it appears that recycled paper towels are the less impacting alternative, but the distribution of the ratio between both is close to 1. Additionally, the report states that a number of potentially important and independent uncertainties have not been quantified, such as “the methodological issues relating to allocating for recycled content and that the data used do not include impacts for the processing of the recycled paper”. Hence, the range of the uncertainty distribution of the ratio between both scenarios may be larger and the conclusion of preference for the 100% recycled paper towels may be less robust. In order to derive concrete conclusions if one option is better than (preferable to) another one, the observed differences need to be examined in statistical terms


In order to derive concrete conclusions if one option is better than (preferable to) another one, the observed differences need to be examined in statistical terms. The two most used statistical tools to examine if their difference is statistically significant are confidence intervals and hypothesis testing. Fig. 11.14 Paired comparison of the climate change impact score ratio of alternative scenarios including uncertainty (Quantis 2009) R.K. Rosenbaum et al.


There is still room for improvement, but this study is an excellent example of how uncertainty analysis strengthens the robustness and the trust in the conclusions of an LCA. Besides showing the added value of uncertainty assessment and interpretation, it also illustrates the feasibility of quantifying and managing uncertainty in LCA. 11.5 Communication of Uncertainty Besides quantifying and improving the robustness of an LCA and its conclusions, the question of how to communicate this beyond the practitioners directly involved in the study is fundamentally important and may often be more complex than anticipated. Like any communication it needs to be adapted to the target audience and will have to look very differently if targeting the general public, high-level decision/policy makers, or fellow practitioners and it will depend on the goal and scope of the LCA itself and, thus, differ if the goal was, e.g


to support the eco-design of a product or the overall environmental performance of a company. The following set of questions is useful to address in order to identify a meaningful uncertainty communication strategy: 1. Who is the target audience and how familiar is this audience with LCA and its aspects of uncertainty? 2. What exactly should be communicated in relation to uncertainty? 3. How should uncertainty results be represented? 11.5.1 Who? Identifying the Target Audience Before choosing which uncertainty information should be conveyed, with how much detail and how exactly, it is essential to identify the target audience(s) of this information and adapt the communication strategy accordingly. Each potential target audience will understand and interpret uncertainty information differently in function of how familiar they are with underlying methodology, sources, types and meaning of uncertainty


There are many ways of classifying target audiences, but several main target groups (not necessarily always applying to all LCA reporting situations) may be: – LCA experts, e.g. other practitioners, scientists, etc., who are very familiar with the subject. This may well be the easiest case, since little or no selection of uncertainty information, or a particularly adapted presentation will be required in most cases. – Informed stakeholders with expertise regarding the LCA, the studied subject or the indicators considered (e.g. environmental, social, or economic), such as Uncertainty Management and Sensitivity Analysis


NGOs, competitors, governmental agencies, etc. This target group will be able to access the core issues of an LCA and its uncertainty as long as some guidance and transparency regarding uncertainty are provided and the information is presented in a way that does not require in-depth expertise and routine. – The general public, like NGOs, consumers, workers, or neighbours of a production site, will usually need as much pre-selection, pre-digestion and simplification of uncertainty information as possible. – High-level decision makers in a company or national/international policy-context will not be familiar with technical details around the LCA study and uncertainty analysis. They have little time to spend on understanding any details and need to know quickly what the implications of the underlying uncertainties are for their decision(s). They may want to know which uncertainties are considered and how certain they can be regarding the robustness of the LCA results


They may want to know which uncertainties are considered and how certain they can be regarding the robustness of the LCA results. – Medium-level decision-makers such as regional or local policy-makers, or industrial production managers may require to be presented with uncertainty information somewhere in-between high-level decision-makers and the general public, depending on the context. – The commissioner(s) of an LCA may fall into any of these groups and will have a particular interest in the uncertainty of its results. It may well be that an LCA study needs to address several of these target groups and that a meaningful compromise needs to be found. A good way to deal with multiple target groups’ needs is to prepare an adapted presentation for each target group, e.g. via an executive summary (for high-level) and a technical summary (for medium-level and informed stakeholders), or via dedicated reports or at least interpretation and discussion chapters for a given target group


The LCA report on window frames provided as an illustrative case study in Chap. 39 provides both an executive summary and a technical summary addressing different target groups for the report. 11.5.2 What? Selecting Which Information Is Relevant to Communicate There are many aspects related to uncertainty that could be communicated but need to be selected depending on the target group of the information and what they can and need to do with it, but also considering the importance of transparency: 1. Assumptions and hypotheses underlying a study, including simplifications and generalisations; 2. Representativeness of information, models, and data used; 3. General level of scientific knowledge and understanding about important aspects of a study, particularly for new issues or approaches used; R.K. Rosenbaum et al.


4. Subjective, ethical or moral values and choices implicitly or explicitly included in the study; 5. Aspects that have not been considered (for whatever reason) but that may be important; 6. Types and sources of uncertainty that have been quantified; 7. Types and sources of uncertainty that have not been quantified but that are expected to be important contributors to overall uncertainty of results and/or conclusions; 8. How exactly uncertainties have been quantified and propagated; 9. Types of analyses that have been performed to consider uncertainty (e.g. sensitivity, uncertainty, uncertainty contribution, scenario analysis, etc.); 10. Uncertainty management and reduction strategies applied; 11. Robustness of the numerical results eventually including the quantitative uncertainty of some or all of them and a list of the most sensitive underlying assumptions and data; 12


Robustness of the numerical results eventually including the quantitative uncertainty of some or all of them and a list of the most sensitive underlying assumptions and data; 12. Robustness of the conclusions and recommendations, eventually including quantitative measures and a list of the most sensitive underlying assumptions, data and choices; 13. Implications and consequences of the uncertainty underlying the results and/or conclusions. It is important to keep in mind that communication of uncertainty does not necessarily imply its quantification using sophisticated methodology and substantial resources. The absolute minimum of a qualitative discussion of some or all aspects listed above can and should always be provided by a practitioner. 11.5.3 How? Representing Uncertainty Effectively This section is largely inspired by a report from Wardekker et al. (2013), which nicely summarises the essential aspects around representing uncertainty


(2013), which nicely summarises the essential aspects around representing uncertainty. Although not specifically adapted to LCA, further details and insights beyond the selection in this chapter may be found there. When communicating LCA results, in which ever way, it is important to be aware that it is the responsibility of the author(s) (i.e. the practitioner, sometimes also the commissioner) to consider and adapt to the target audience. It is clearly insufficient to focus on a scientifically correct and complete presentation of results and related uncertainty, leaving the responsibility of their correct interpretation solely to the (target) audience. When choosing a way to express and represent uncertainty, it is thus important to keep in mind that the target audience may interpret it very differently than intended. Only using point estimates or deterministic results and conclusions, without mentioning any uncertainty, already bears the risk of unintentional interpretations


Only using point estimates or deterministic results and conclusions, without mentioning any uncertainty, already bears the risk of unintentional interpretations. This will be even more the case when including uncertainty information, where it is well possible that referring to a low probability of an environmental consequence to occur may result in Uncertainty Management and Sensitivity Analysis


unintentional focus and unrest about this unexpected risk. It is also possible that evoking a high probability of adverse effects may not be noticed as an issue of concern, just because it was presented as something of a certain probability and not as the (almost) certain environmental consequence of an act or decision. In other words, the same uncertainty information may result in opposite interpretations by different readers. While this is difficult to fully foresee and avoid, paying attention to such details when preparing a presentation or report can help avoiding unintentional or wrong interpretation when considering the target audience’s context and interpretation capacity. Wording and phrasing are essential elements in this context. For example, a non-technical audience may not be familiar with the meaning and implication of terms like risk, probability or likelihood. The expression of uncertainty in a positive way versus a negative way can make an important difference


The expression of uncertainty in a positive way versus a negative way can make an important difference. To illustrate this, the following two phrases express the same uncertainty information in an LCA comparing two alternatives A and B, but in a very different way: (1) “there is a 10% risk that choosing option B may be the wrong decision” versus “there is a chance of 90% that option B is the best option”. Besides paying attention to how an information is phrased (sent), it also plays an important role how the information is received, which Wardekker et al. (2013) describe via three effects of distortion: – “Availability: matters that easily come to mind are generally regarded as occurring more frequently or more likely to occur than matters that are more obscure. A strong focus on a specific issue (in the media) may result in people regarding it as more likely to occur. – Confirmation: once a view has been adopted, new information will be interpreted on the basis of this view


– Confirmation: once a view has been adopted, new information will be interpreted on the basis of this view. It is difficult to change people’s views. – Overconfidence: people are often too certain of their own judgement. This applies to the general public as well as to scientists.” The exact place in a report or presentation where uncertainty information is included is worth some consideration. Numerous options exist, but each solution may bear its particular risk of failure to communicate uncertainty, like a dedicated chapter stating all there is to state, may be easily ignored because it is little inviting to read, or an annex containing all relevant information may never be read, as it is not part of the main body of the report and therefore may not be considered relevant by some readers


It may be a good idea to spread uncertainty information meaningfully in different parts of the report, a concept referred to as progressive disclosure of information (PDI) which employs the concept of layers of information, distinguishing “outer layers (e.g. press release, summary, [oral presentations]) [that] refer to non-technical information, uncertainties integrated into the message, emphasis on context, implications and consequences” and “inner layers (e.g., appendices, background report, [or specific section like introduction, conclusion, recommendations]) [containing] detailed technical information, uncertainties discussed separately, emphasis on types, sources and the extent of uncertainty)” R.K. Rosenbaum et al.


(Wardekker et al. 2013). Different layers can be used that are adapted to specific target groups and uncertainty information to communicate. In any case, conclusions and recommendations should always directly include relevant and central information regarding uncertainty. There are different, often complementary ways to present uncertainty information: • Qualitatively (e.g. reporting sources of uncertainty and their potential influence on results); • Descriptively (e.g. reporting central tendencies like mean and variability around the mean); • Graphically (e.g. visualising uncertainty information in graphs); • Numerically (e.g. reporting ranges, probability distributions of results values or statistical results). Presenting uncertainty information in a verbal or descriptive way is useful, as it allows direct integration with the results and conclusions, especially for non-quantitative information and may be retained more easily than numerical information by most readers


It is particularly well suited for inclusion with outer layers (e.g. report summary). Such a description of uncertainties may be based on a quantified evaluation or even just on a qualitative appreciation of uncertainty. In any case, it is important to keep in mind that many terms typically used to describe uncertainty are quite imprecise and prone to vary in perception and interpretation among individuals, e.g. large, small, important, significant, etc. It is essential to use these terms consistently with the same meaning throughout a report and that they match numerical results, if available. They may even be explicitly defined, e.g. very likely = 90–99% probability, likely = 80–89% and so on. If quantified, uncertainty information can also be communicated numerically, e.g. in tables, as standard deviations, minimum and maximum bounds, ranges, uncertainty and confidence intervals, probabilities, comparison with other studies or measurements, etc


in tables, as standard deviations, minimum and maximum bounds, ranges, uncertainty and confidence intervals, probabilities, comparison with other studies or measurements, etc. This is useful especially for application in inner layers of information, such as a report appendix. A frequent mistake in this case is the communication of results and quantified uncertainties with a “false precision” showing too many digits. This practice suggests a very precise quantification of uncertainty that is most likely not defendable in an LCA context. For example, considering a typical standard deviation of a global warming impact score, a value of 2.49678 is essentially the same as 2.5 and in fact even the same as 3. The opposite may also exist, when a “false imprecision” is used to express numerical results so vaguely that they could mean anything, or are immune to criticism, but not very helpful for decision support


Graphical representation of uncertainty can be provided in many different ways, e.g. using error (or uncertainty) bars or bands, box plots, probability distributions, coefficients of variation, confidence intervals, etc. This has the advantage that a lot of information can be aggregated and shown in a concise and structured way, allowing to capture a lot of uncertainty information in a short time and single graph. Uncertainty Management and Sensitivity Analysis


This is illustrated in Fig. 11.15 which shows an example of a box plot (or whisker plot) of the spread of freshwater ecotoxicity characterisation factors for 2499 organic chemicals and 4 emission compartments from USEtox 2.02 (see Chap. 10 for further information regarding freshwater ecotoxicity characterisation factors). The boxes efficiently illustrate that 90% of the characterisation factors fall within the range of five to six orders of magnitude, whereas the difference between the lowest and highest characterisation factors (grey dots) is in the range of 16–19 orders of magnitude. Although the actual shape of the uncertainty distribution cannot the seen, it is visible that the distribution is skewed towards higher values with the median (the value at 50%) being in the upper range of values and not in the centre. However, graphical representation of uncertainty also bears the risk of being suggestive, easily misinterpreted, or too complex