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Emergy algebra: Improving matrix methods for calculating transformities

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  • Li, Linjun
  • Lu, Hongfang
  • Campbell, Daniel E.
  • Ren, Hai

Abstract

Transformity is one of the core concepts in Energy Systems Theory and it is fundamental to the calculation of emergy. Accurate evaluation of transformities and other emergy per unit values is essential for the broad acceptance, application and further development of emergy methods. Since the rules for the calculation of emergy are different from those for energy, particular calculation methods and models have been developed for use in the emergy analysis of networks, but double counting errors still occur because of errors in applying these rules when estimating the emergies of feedbacks and co-products. In this paper, configurations of network energy flows were classified into seven types based on commonly occurring combinations of feedbacks, splits, and co-products. A method of structuring the network equations for each type using the rules of emergy algebra, which we called “preconditioning” prior to calculating transformities, was developed to avoid double counting errors in determining the emergy basis for energy flows in the network. The results obtained from previous approaches, the Track Summing Method, the Minimum Eigenvalue Model and the Linear Optimization Model, were reviewed in detail by evaluating a hypothetical system, which included several types of interactions and two inputs. A Matrix Model was introduced to simplify the calculation of transformities and it was also tested using the same hypothetical system. In addition, the Matrix Model was applied to two real case studies, which previously had been analyzed using the existing method and models. Comparison of the three case studies showed that if the preconditioning step to structure the equations was missing, double counting would lead to large errors in the transformity estimates, up to 275 percent for complex flows with feedback and co-product interactions. After preconditioning, the same results were obtained from all methods and models. The Matrix Model reduces the complexity of the Track Summing Method for the analysis of complex systems, and offers a more direct and understandable link between the network diagram and the matrix algebra, compared with the Minimum Eigenvalue Model or the Linear Optimization Model.

Suggested Citation

  • Li, Linjun & Lu, Hongfang & Campbell, Daniel E. & Ren, Hai, 2010. "Emergy algebra: Improving matrix methods for calculating transformities," Ecological Modelling, Elsevier, vol. 221(3), pages 411-422.
    • Handle: RePEc:eee:ecomod:v:221:y:2010:i:3:p:411-422
    DOI: 10.1016/j.ecolmodel.2009.10.015
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    References listed on IDEAS

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    Cited by:

    1. Campbell, Elliott T. & Tilley, David R., 2016. "Relationships between renewable emergy storage or flow and biodiversity: A modeling investigation," Ecological Modelling, Elsevier, vol. 340(C), pages 134-148.
    2. Baral, Anil & Bakshi, Bhavik R., 2010. "Emergy analysis using US economic input–output models with applications to life cycles of gasoline and corn ethanol," Ecological Modelling, Elsevier, vol. 221(15), pages 1807-1818.
    3. Patterson, Murray G., 2012. "Are all processes equally efficient from an emergy perspective?," Ecological Modelling, Elsevier, vol. 226(C), pages 77-91.
    4. Le Corre, O. & Truffet, L. & Lahlou, C., 2015. "Odum–Tennenbaum–Brown calculus vs emergy and co-emergy analysis," Ecological Modelling, Elsevier, vol. 302(C), pages 9-12.
    5. Patterson, Murray & McDonald, Garry & Hardy, Derrylea, 2017. "Is there more in common than we think? Convergence of ecological footprinting, emergy analysis, life cycle assessment and other methods of environmental accounting," Ecological Modelling, Elsevier, vol. 362(C), pages 19-36.
    6. Cho, Cheol-Joo, 2013. "An exploration of reliable methods of estimating emergy requirements at the regional scale: Traditional emergy analysis, regional thermodynamic input–output analysis, or the conservation rule-implicit," Ecological Modelling, Elsevier, vol. 251(C), pages 288-296.
    7. Marvuglia, Antonino & Benetto, Enrico & Rios, Gordon & Rugani, Benedetto, 2013. "SCALE: Software for CALculating Emergy based on life cycle inventories," Ecological Modelling, Elsevier, vol. 248(C), pages 80-91.
    8. Le Corre, O. & Truffet, L., 2012. "Exact computation of emergy based on a mathematical reinterpretation of the rules of emergy algebra," Ecological Modelling, Elsevier, vol. 230(C), pages 101-113.
    9. Campbell, Daniel E., 2016. "Emergy baseline for the Earth: A historical review of the science and a new calculation," Ecological Modelling, Elsevier, vol. 339(C), pages 96-125.
    10. Bastianoni, Simone & Morandi, Fabiana & Flaminio, Tommaso & Pulselli, Riccardo M. & Tiezzi, Elisa B.P., 2011. "Emergy and emergy algebra explained by means of ingenuous set theory," Ecological Modelling, Elsevier, vol. 222(16), pages 2903-2907.
    11. Berrios, Fernando & Campbell, Daniel E. & Ortiz, Marco, 2017. "Emergy evaluation of benthic ecosystems influenced by upwelling in northern Chile: Contributions of the ecosystems to the regional economy," Ecological Modelling, Elsevier, vol. 359(C), pages 146-164.
    12. Patterson, Murray, 2014. "Evaluation of matrix algebra methods for calculating transformities from ecological and economic network data," Ecological Modelling, Elsevier, vol. 271(C), pages 72-82.
    13. Zarbá, Lucía & Brown, Mark T., 2015. "Cycling emergy: computing emergy in trophic networks," Ecological Modelling, Elsevier, vol. 315(C), pages 37-45.

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