Emergy evaluation using the calculation software scale: case study, added value and potential improvements

Supplementary Information

SI1: Influence of the minflow threshold value in EME_SCALE

The backtracking algorithm employed in SCALE considers the studied system as a network of interlinked processes and performs a graph search; the emergy content of each node of the graph is tracked along the different paths from the inputs (resources) to the output (studied product). When a path (i.e., in emergy terms, an emergy flow) splits, and the emergy value assigned to a branch is lower than the threshold value set beforehand, then the algorithm stops propagating the emergy flow downstream and starts exploring a different path, visiting a new node (the order in which the nodes are visited is established by the search algorithm used, which is a depth-first search in SCALE). We refer to the flow that is not accounted for due to this circumstance (that we call minflow violation) as “flow lost due to minflow violation”. This threshold level must be optimized by the user to balance calculation time with the emergy value of flow lost due to minflow violation. The other halt condition for the flow propagation (i.e. the “loss” of a part of the emergy flow accounted for) in SCALE is the case of a feedback loop occurring: we refer to this portion of the flow as “flow lost due to loop violation”.

Figure S1 shows the portion of flows ‘lost’ due to minflow violation and due to loop violation. An optimal threshold is sought to balance result’s precision with calculation time. The numbers in brackets (next to the WTP’s name) indicate the negative log of the threshold value; e.g. ‘Site A (5)’ refers to the application of SCALE on Site A, with threshold = 1E-5 Msej. The calculation time increases exponentially with this value (Marvuglia et al., 2013): in our case studies, typical calculation times for a threshold of 1E-3, 1E-4, 1E-5 and 1E-6 Msej (using a 2.67GHz Intel Core i7 laptop, running with MS Windows 7) were respectively 1, 3, 24 and 240 minutes. Figure S1 shows that a rigorous application of emergy algebra affects the results by as little as 3% (flow lost due to loop violation), meaning that the ratio between the emergy value of the inputs and the emergy value of the output(s) is 97%. The choice of the threshold influences the amount of flow lost due to sheer algorithmic constraints (flow lost due to minflow), while increasing (to a lesser extent) the amount of flow lost due to loop violation. From Figure S1, one can conclude that threshold values of 1E-4 or 1E-5 Msej are the best tradeoffs.