Under human high-intensity activities and the rapidly changing global environment, ecosystem change has become one of the core issues about global environment and ecological sciences in the 21st century. Aspects of ecological economic problems include resources, environment, human society, economic activities, etc., and how to integrate special issues has been the key to solving them. Based on a common quantity like, emergy, Energy System Theory can unify and evaluate all kinds of knowledge on energy, material, information and money flows, which was not originally comparable. As the bridge between the environment and the economy, emergy network analysis has been developing into a mature theory and increasingly applied to integration study of ecological economic systems.

Since emergy synthesis has special rules for calculating emergy different from energy analysis, emergy network analysis can not directly exploit the existing methods from energy analysis or economics. Although the Track Summing Method can rightly calculate emergy and transformity, the calculating processes will be very complicated for complex systems. Therefore, a simpler and more understandable method for solving transformity will be necessary for the development of emergy theory. The Minimum Eigenvalue Model developed by Dr H.T. Odum, a well-known ecologist and the founder of Emergy Theory and Methods, and the Linear Optimization Model based on Newton Iterative Method, brought by Dr M.T. Brown, one of the current academic leader in emergy research area, has been widely applied to all kinds of emergy evaluation cases, but their results were very different from those calculated by the Track Summing Method and there were some errors between them.

Following his advisor Dr. LU Hongfang, the master candidate LI Linjun at vegetation and landscape ecology research group (SCBG) found that these errors were actually derived from doubt counting and missing a preconditioning step for complex flows. In this study, configurations of network energy flows were classified into seven types based on commonly occurring combinations of feedbacks, splits and co-products. Meanwhile, the corresponding preconditioning methods were developed to avoid double counting errors in determining the emergy basis for the complex flows. Furthermore, based on the existing models, a Matrix Model was introduced to simplify the calculation of transformity. 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.

The results of this study will contribute greatly to emergy network analysis and modeling, and the related paper was recently accepted for publication by the journal Ecological Modelling.