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Evaluation of matrix algebra methods for calculating transformities from ecological and economic network data

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  • Patterson, Murray

Abstract

This paper describes and characterises matrix algebra methods for calculating transformities from ecological and economic network data. Particular attention is given to those characteristics of complicated energy-flow and mass-flow networks that lead to the following methodological problems: joint production (co-products), non-square matrices (unequal number of processes and quantities), matrix singularity, problematic occurrence of negative transformities in the solution vector, and unequal emergy efficiencies which frequently occur in non-square matrices. Each of these problems is discussed and the means of resolving these problems are consequently presented. In addressing these problems, besides covering the use of the previously reported matrix inversion, regression, eigenvalue–eigenvector and singular value decomposition methods; a new method – the reflexive method – is introduced.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ecomod:v:271:y:2014:i:c:p:72-82
    DOI: 10.1016/j.ecolmodel.2013.03.011
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    References listed on IDEAS

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    1. Patterson, Murray G. & Wake, Graeme C. & McKibbin, Robert & Cole, Anthony O., 2006. "Ecological pricing and transformity: A solution method for systems rarely at general equilibrium," Ecological Economics, Elsevier, vol. 56(3), pages 412-423, March.
    2. Michael Lahr & Louis de Mesnard, 2004. "Biproportional Techniques in Input-Output Analysis: Table Updating and Structural Analysis," Economic Systems Research, Taylor & Francis Journals, vol. 16(2), pages 115-134.
    3. Patterson, Murray G., 2002. "Ecological production based pricing of biosphere processes," Ecological Economics, Elsevier, vol. 41(3), pages 457-478, June.
    4. Brown, M. T. & Herendeen, R. A., 1996. "Embodied energy analysis and EMERGY analysis: a comparative view," Ecological Economics, Elsevier, vol. 19(3), pages 219-235, December.
    5. Hannon, Bruce & Costanza, Robert & Herendeen, Robert A., 1986. "Measures of energy cost and value in ecosystems," Journal of Environmental Economics and Management, Elsevier, vol. 13(4), pages 391-401, December.
    6. 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.
    7. Patterson, M. G., 1983. "Estimation of the quality of energy sources and uses," Energy Policy, Elsevier, vol. 11(4), pages 346-359, December.
    8. Patterson, Murray G., 2012. "Are all processes equally efficient from an emergy perspective?," Ecological Modelling, Elsevier, vol. 226(C), pages 77-91.
    9. 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.
    10. Patterson, Murray G, 1996. "What is energy efficiency? : Concepts, indicators and methodological issues," Energy Policy, Elsevier, vol. 24(5), pages 377-390, May.
    11. Sciubba, Enrico, 2010. "On the Second-Law inconsistency of Emergy Analysis," Energy, Elsevier, vol. 35(9), pages 3696-3706.
    12. Patterson, Murray, 1998. "Commensuration and theories of value in ecological economics," Ecological Economics, Elsevier, vol. 25(1), pages 105-126, April.
    13. Stefan Baumgärtner & Malte Faber & Johannes Schiller, 2006. "Joint Production and Responsibility in Ecological Economics," Books, Edward Elgar Publishing, number 2598.
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    Cited by:

    1. 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.
    2. Oleksandr Galychyn & B.D. Fath & D. Wiedenhofer & E. Buonocore & P.P. Franzese, 2024. "An urban emergy footprint: Comparing supply- and use-extended input-output models for the case of Vienna, Austria," Post-Print hal-04507173, HAL.
    3. Galychyn, Oleksandr, 2022. "Towards sustainable cities: A multi-criteria assessment framework for studying urban metabolism," MPRA Paper 121584, University Library of Munich, Germany, revised 11 May 2022.

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