Data Quality and Uncertainty Distribution for

6.5.2.1 Probability Distribution of an Individual Variable

Figure 6.8 illustrates three types of probability distributions used in the quantifica-tion of uncertainty on the parameters of a life cycle assessment. In LCA, uncertain-ties are often important and represented by lognormal distributions, thus avoiding the possibility of negative emissions. It is rare, however, to actually have sufficient measurements (over 30) to parameterize a lognormal (or Gaussian) distribution. In such a case, uncertainties are estimated based on qualitative indicators that are then transformed into semiquantitative distributions.

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6.5.2.2 Quality Indicators

Several quality indicators have been developed (Weidema and Wesnaes 1996;

Weidema 1998), including the following:

• The reliability of data is based on the measurement method used and the verification procedures.

• The completeness depends on the representativeness of the available data and the number of companies considered over a given time period.

• The temporal, geographical, and technological correlations indicate whether the place, time, and technology of the collected data correspond well to the process studied.

Each inventory data point is given a qualitative score between 1 (best) and 5 (worst) for each of these indicators. Table  6.4 presents the criteria for assigning scores.

To transform these qualitative indicator scores into a quantitative score, an uncertainty factor can be assigned to each of the pedigree matrix scores using Table 6.5.

A supplementary factor characterizes the base uncertainty (UB), which is spe-cific to certain demands of energy and resources and certain pollutant emissions (Table 6.6). This factor is low for CO2 emissions because they are mainly due to well-understood combustion processes, but it is relatively high for substances such as heavy metals whose emissions vary with multiple parameters.

The square of the geometric standard deviation (95% confidence interval) of the considered value is then calculated based on Equation 6.2 (as derived from the gen-eralized Equation 6.3 in Section 6.6.4):

GSD2=exp ln(UR)2+ln(UC)2+ln(UG)2+ln(UT)2+ln(UL)2+ln(US)2+ln((UB)2

(6.2) where U indicates the uncertainty factors based on reliability (UR), completeness (UC), geographic correlation (UG), temporal correlation (UT), technological correla-tion (UL), sample size (US), and the base uncertainty (UB).

Taking the example of a process requiring aluminum, let us assume that the data on the necessary quantity of aluminum required by this process have the following characteristics:

• Peer-reviewed and based on measurements (quality score of 1 for reliability)

• Representative of a small number of enterprises and for an adequate time period (quality score of 2 for completeness)

• Obtained less than 3 years prior to the current study (temporal correlation score of 1)

• Coming from a geographical area having similar conditions to the condi-tions of the case study (geographical correlation score of 4)

Interpretation 165

TABLE 6.4 Data Quality Indicators with Five Levels of Quality as Described in a Pedigree Matrix Quality Score12345 ReliabilityVerified data based on measurementsVerified data partially based on assumptions or nonverified data based on measurements Nonverified data partially based on qualified estimates

Qualified estimate (e.g., by industrial expert)Nonqualified estimate CompletenessRepresentative data from all sites relevant for the market considered, over an adequate period to even out normal fluctuations

Representative data from > 50% of the sites relevant for the market considered, over an adequate period to even out normal fluctuations Representative data from only some sites (< 50%) relevant for the market considered or from > 50% of sites but from shorter periods Representative data from only one site relevant for the market considered or from some sites but from shorter periods

Representativeness unknown or data from a small number of sites and from shorter periods Temporal correlationLess than 3 years of difference to the time period of the data set

Less than 6 years of difference to the time period of the data set Less than 10 years of difference to the time period of the data set Less than 15 years of difference to the time period of the data set

Age of data unknown or more than 15 years of difference to the time period of the data set Geographical correlationData from area under studied Average data from larger area in which the area under study is included

Data from area with similar production conditionsData from area with slightly similar production conditions

Data from unknown area or distinctly different area (North America instead of Middle East; OECD-Europe instead of Russia) Further technological correlation

Data from enterprises, processes. and materials under study Data from processes and materials under study (i.e., identical technology), but from different enterprises Data from processes and materials under study but from different technology

Data on related processes or materials Data on related processes on laboratory scale or from different technology Sample size>100, continuous measurements>20>10>=3Unknown Source:Ciroth, A. et al. 2013. International Journal of Life Cycle Assessment. With permission.

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• Exactly corresponding to the type of desired aluminum (technological cor-relation score of 1)

• Obtained from a sample of unknown size (quality score of 5 for sample size) For a demand of materials, the basic uncertainty factor is 1.05 (Table 6.6). Having determined the default uncertainty factors corresponding to the quality scores defined for each data characteristic (Table 6.5), the variance of the aluminum quan-tity is then

GSD²=exp ^{ln( . )1 002+ln( . )1 022+ln( . )1 002+ln( . )1 022+ln( . )1 002+lln( . )1 202+ln( . )1 052} =1 21.

Note that the final GSD² (dimensionless) does not depend on the required quantity of aluminum.

Once the uncertainty over each individual component is determined as above, these individual uncertainties are combined using Monte Carlo methods or a Taylor series expansion. This yields the overall uncertainty of the inventory flows or impacts per functional unit, as described further in Section  6.6, which also discusses the essential concept of comparative uncertainty based on which parameters are com-mon acom-mong scenarios.