Modeling metal stocks and flows: a review of dynamic material flow analysis methods

Dynamic material flow analysis (MFA) is a frequently used method to assess past, present, and future stocks and flows of metals in the anthroposphere. Over the past fifteen years, dynamic MFA has contributed to increased knowledge about the quantities, qualities, and locations of metal-containing goods. This article presents a literature review of the methodologies applied in 60 dynamic MFAs of metals. The review is based on a standardized model description format, the ODD (overview, design concepts, details) protocol. We focus on giving a comprehensive overview of modeling approaches and structure them according to essential aspects, such as their treatment of material dissipation, spatial dimension of flows, or data uncertainty. The reviewed literature features similar basic modeling principles but very diverse extrapolation methods. Basic principles include the calculation of outflows of the in-use stock based on inflow or stock data and a lifetime distribution function. For extrapolating stocks and flows, authors apply constant, linear, exponential, and logistic models or approaches based on socioeconomic variables, such as regression models or the intensity-of-use hypothesis. The consideration and treatment of further aspects, such as dissipation, spatial distribution, and data uncertainty, vary significantly and highly depends on the objectives of each study.