Abstract
SummaryThe extraction, transformation, use, and disposal of materials can be represented by directed, weighted networks, known in the material flow analysis (MFA) community as Sankey or flow diagrams. However, the construction of such networks is dependent on data that are often scarce, conflicting, or do not directly map onto a Sankey diagram. By formalizing the forms of data entry, a nonlinear constrained optimization program for data estimation and reconciliation can be formulated for reconciling data sets for MFA problems where data are scarce, in conflict, do not directly map onto a Sankey diagram, and are of variable quality. This method is demonstrated by reanalyzing an existing MFA of global steel flows, and the resulting analytical solution measurably improves upon their manual solution.
Highlights
As noted by Brunner and Rechberger (2004), material flow analysis (MFA) data are normally aggregated from a range of different sources, including both direct and proxy measurements, using diverse methods of data collection and processing with a range of qualities
This review indicates that, there are many MFA data reconciliation procedures, those that can incorporate a wide selection of different forms of data, multiple data points per variable, as well as measures of data quality, are relatively underdeveloped
Results of the Global Steel Reanalysis. The effectiveness of this reconciliation method was tested against the “manual” MFA of global steel flows from Cullen and colleagues (2012a,b)
Summary
As noted by Brunner and Rechberger (2004), material flow analysis (MFA) data are normally aggregated from a range of different sources, including both direct and proxy measurements, using diverse methods of data collection and processing with a range of qualities. This is true when MFAs cross many industries and data collection entities. A number of techniques have been documented for data reconciliation of nonmatching data points, and estimation of the value of variables where no data exists, in MFA Such methods are generally restricted to the use of basic classifications of flow data and linear constraints in the reconciliation. This study extends current MFA data reconciliation and estimation methods by formulating: 1. A mathematical classification system for incorporating “unconventional” forms of data that do not directly map onto Sankey diagrams
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