Uncertainty characterization for emergy values
Introduction
Emergy, a measure of energy used in making a product extending back to the work of nature in generating the raw resources used (Odum, 1996), arises from general systems theory and has been applied to ecosystems as well as to human-dominated systems to address a scientific questions at many levels, from the understanding ecosystem dynamics (Brown et al., 2006) to studies of modern urban metabolism and sustainability (Zhang et al., 2009). Emergy, or one any the many indicators derived from it (Brown and Ulgiati, 1997), is not an empirical property of an object, but an estimation of embodied energy based on a relevant collection of empirical data from the systems underlying an object, as well as rules and theoretical assumptions, and therefore cannot be directly measured. In the process of emergy evaluation, especially due to its extensive and ambitious scope, the emergy in a object is estimated in the presence of numerical uncertainty, which arises in all steps and from all sources used in the evaluation process.
The proximate motivation for development of this model was for use of emergy as an indicator within a life cycle assessment (LCA) to provide information regarding the energy appropriated from the environment during the life cycle of a product. The advantages of using emergy in an LCA framework are delineated and demonstrated through an example of a gold mining (Ingwersen, under review). The incorporation of uncertainty in LCA results is commonplace and furthermore prerequisite to using results to make comparative assertions that are disclosed to the public (ISO 14044: 2006).
But the utility of uncertainty values for emergy is not only restricted to emergy used along with other environmental assessment methodologies; uncertainty characterization of emergy values has been of increasing interest and in some cases begun to be described by emergy practitioners (Bastianoni et al., 2009) for use in traditional emergy evaluations. Herein lies the ultimate motivation for this manuscript, which is to provide an initial framework for characterization of uncertainty of unit emergy values (UEVs), or inventory unit-to-emergy conversions, which can be applied or improved upon to characterize UEVs for any application, whether they be original emergy calculations or drawn upon from previous evaluations.
Uncertainty in UEVs may exist on numerous levels. Classification of uncertainty is helpful for identification of these sources of uncertainty, and for formal description of uncertainty in a replicable fashion. The classification scheme defined by the US EPA defines three uncertainty types: parameter, scenario, and model uncertainty (Lloyd and Ries, 2007). This scheme is co-opted here to represent the uncertainty types associated with UEVs. These uncertainty types are defined in Table 1 using the example of the UEV for lead in the ground.
There are additional elements of uncertainty in the adoption of UEVs from previous analyses. These occur due to the following:
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Incorporation of UEVs from sources without documented methods.
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Errors in use of significant figures.
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Inclusion of UEVs with different inventory items (e.g. with or without labor & services).
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Calculation errors in the evaluation.
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Conflicts in global baseline underlying UEVs, which may be propagated unwittingly.
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Use of a UEV for an inappropriate product or process.
These bulleted errors are due to random calculation error, human error, and methodological discrepancy, which is not well-suited to formal characterization, and can be better addressed with more transparent and uniform methodology and critical review. But uncertainty and variability in parameters, models, and scenarios can theoretically be quantified.
Different components of uncertainty in a model must be combined to estimate total uncertainty in the result. These component uncertainties may originate from uncertainty in model parameters. In multiple parameter models, such as emergy formula models, each parameter has its own characteristic uncertainty. Uncertainty in environmental variables is often assumed to be normal, although Limpert et al. (2001) presents evidence that lognormal distributions are more versatile in application and may be more appropriate for parameters in many environmental disciplines. This distribution is increasingly used to characterize data on process inputs used in life cycle assessments (Huijbregts et al., 2003, Frischknecht et al., 2007a, Frischknecht et al., 2007b).
A spread of lognormal variable can be described by a factor that relates the median value to the tails of its distribution. Slob (1994) defines this value as the dispersion factor, k, but it is also known as the geometric variance, :where for variable a is a function of ωa (Eq. (1)),1 which a simple transformation of the coefficient of variation (Eq. (2)),2 where σa is the sample standard deviation of variable a and μa is the sample mean. This can be applied to positive, normal variables with certain advantages, because parameters for describing lognormal distributions result in positive confidence intervals, and the lognormal distribution approximates the normal distribution with low dispersion factor values.
The geometric variance, , is a symmetrical measure of the spread between the median, also known as the geometric mean, μgeo, and the tails of the 95.5% (henceforth 95%) confidence interval (Eq. (3)).
The symbol ‘(x÷)’ represents ‘times or divided by’. The geometric mean for variable a may be defined as in the following expression (Eq. (4)):
The confidence interval describes the uncertainty surrounding a lognormal variable, but not for a formula model that is a combination of multiplication or division of each of these variables. The uncertainty of each model parameter has to be propagated to estimate a total parameter uncertainty. This can be done with Eq. (5):where a, b …z are references to parameters of a multiplicative model y of the form y = Πa …z. Note that parameter uncertainties are not simply summed together, which would overestimate uncertainty. This solution (Eq. (5)) is valid under the assumption that each model parameter is independent and lognormally distributed.
Describing the confidence interval requires the median, or geometric mean, as well as the geometric variance. The geometric mean of a model can be estimated first by estimating the model CV (Eq. (6)) and then with a variation of Eq. (4) (Eq. (7)).3
Section snippets
Models for uncertainty in UEVs
Numerous methods exist for computing unit emergy values,4 but for uncertainty estimation, it is import to distinguish between them according to a fundamental difference in the way UEVs are calculated: the formula vs. the table-form model. The formula model is used for estimation of emergy in raw materials,
Results
The details of the uncertainty calculations for lead are shown in Table 3. For lead, parameter and model uncertainty were estimated. The values (approximately the upper tail of the distribution divided by the median) for the five parameters range from 1.03 to 2.25. The total parameter uncertainty is larger than the largest individual parameter value, but less than the sum of these parameter values. The total uncertainty for lead, consisting of the combined model and
Discussion and conclusions
To fully characterize uncertainty for UEVs, the sources of uncertainty need to be identified and quantified. The classification scheme introduced by the EPA provides a useful framework which helps in identification of quantifiable aspects of uncertainty. However in practice, describing the uncertainty in parameters, scenarios and models requires significant effort and must draw from previous applications of various models and across various scenarios. In this manuscript, the data sufficient to
Acknowledgements
The author would like to acknowledge the intellectual support and encouragement of Dr. Mark Brown and his students and James Colee of UF-IFAS for statistical consultation. Financial support came from the UF Department of Environmental Engineering Sciences.
References (27)
- et al.
The solar transformity of petroleum fuels
Ecol. Model.
(2009) - et al.
The solar transformity of oil and petroleum natural gas
Ecol. Model.
(2005) - et al.
Emergy-based indices and ratios to evaluate sustainability: monitoring economies and technology toward environmentally sound innovation
Ecol. Eng.
(1997) - et al.
Emergy evaluations and environmental loading of electricity production systems
J. Cleaner Production
(2002) - et al.
Promise and problems of emergy analysis
Ecol. Model.
(2004) - et al.
Ecological network and emergy analysis of urban metabolic systems: model development, and a case study of four Chinese cities
Ecol. Model.
(2009) - et al.
The Lognormal Distribution with Special Reference to its Uses in Economics
(1957) - Australian Museum, 2007. Structure and composition of the Earth....
- et al.
Species diversity in the Florida Everglades USA: a systems approach to calculating biodiversity
Aquat. Sci.
(2006) - Buenfil, A., 2001. Emergy Evaluation of Water. Doctoral Thesis, University of Florida,...
Computing the unit emergy value of crustal elements
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