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Methods for Estimating the Uncertainty in Emergy Table-Form Models
Citation:
LI, L., H. LU, AND D. E. CAMPBELL. Methods for Estimating the Uncertainty in Emergy Table-Form Models . ECOLOGICAL MODELLING. Elsevier Science BV, Amsterdam, Netherlands, 222(15):2615-2622, (2011).
Impact/Purpose:
This paper makes a contribution to the calculation of uncertainties in emergy analyses, especially the uncertainty in transformities determined through the table-form calculation. This paper and a preceding paper (Ingwersen 2010) together make a substantial contribution to the use of emergy analyses in decision-making by developing and applying accepted methods of determining uncertainty to the types of calculations used in emergy evaluations. This paper should have a substantial impact as an aid to decision-makers whenever uncertainty is incorporated into emergy evaluations. Ingwersen, W.W., 2010. Uncertainty characterization for emergy values. Ecological Modelling 221, 445-452.
Description:
Emergy studies have suffered criticism due to the lack of uncertainty analysis and this shortcoming may have directly hindered the wider application and acceptance of this methodology. Recently, to fill this gap, the sources of uncertainty in emergy analysis were described and analytical and stochastic methods were put forward to estimate the uncertainty in unit emergy values (UEVs). However, the most common method used to determine UEVs is the emergy table-form model, and only a stochastic method (i.e., the Monte Carlo method) was provided to estimate the uncertainty of values calculated in this way. To simplify the determination of uncertainties in emergy analysis using table-form calculations, we introduced two analytical methods provided by the Guide to the Expression of Uncertainty in Measurement (GUM), i.e., the Variance method and the Taylor method, to estimate the uncertainty of emergy table-form calculations for two different types of data, and compared them with the stochastic method in two case studies. The results showed that, when replicate data are available at the system level, i.e., the same data on inputs and output are measured repeatedly in several independent systems, the Variance method is the simplest and most reliable method for determining the uncertainty of the model output, since it considers the underlying covariance of the inputs and requires no assumptions about the probability distributions of the inputs. However, when replicate data are only available at the subsystem level, i.e., repeat samples are measured on subsystems without specific correspondence between an output and a certain suite of inputs, the Taylor method will be a better option for calculating uncertainty, since it requires less information and is easier to understand and perform than the Monte Carlo method.