Are all processes equally efficient from an emergy perspective? Analysis of ecological and economic networks using matrix algebra methods

Matrix algebra methods have been developed in recent years to calculate transformities (energy quality indicators) from matrices of energy and mass flows in ecological and economic networks. This paper argues that the application of these methods by Emergy Analysts have unfortunately ignored the likelihood that in complex ecological and economic networks with many nodes and interconnecting pathways, that emergy efficiencies of all processes are expected in most cases to be different. Accordingly, this paper illustrates by a new method of emergy analysis that the emergy-based efficiency of most processes in the 1987 New Zealand energy system are not the same, and this is because we are dealing with a rectangular matrix of inconsistent equations. On the other hand, with square matrices (which usually represent consistent equations), the emergy-based efficiencies of the constituent processes are all the same, which is arguably no more than just an artefact of the aggregation required for the construction of these square matrices. This point is illustrated by the application of the Singular Value Decomposition (SVD) method to energy and mass flows for the Schlei Fjord ecosystem in Germany. The paper concludes by suggesting that differing emergy efficiencies of processes in ecological and economic systems are indicative of the system being in a non-equilibrium state which has some important implications in terms of its future application and contribution to Emergy Analysis theory. Of more practical importance, it is suggested in the paper, that the application of this SVD method provides a rigorous basis for pinpointing those processes that are most efficient from an Emergy perspective, which is important in terms of informing environmental management and the analysis of public policy options.