One of the most widely used material accounting methods is the Material Flow Analysis (MFA). This method takes a systems-perspective and quantifies the relevant inputs and outputs for these systems. MFA relies on the principles of mass balancing as a way to verify that the model is complete and accurate. One of the reasons that MFA is so widespread is the versatility in its use. MFA can be used in any reference system, which can include global, national, regional, functional, or temporal reference systems. The time horizon can range from a contemporary point in time to a time series or even involve a long-range historical perspective. Finally, depending on the aim of the work, all physical material flows can be studied, or a specific subset that is of interest. Energy flows can also be subjected to an MFA. If only a single substance is studied, then this is called a substance flow analysis instead. Many of these main features as well as a historic perspective on MFA are discussed in a great reference paper by Fisher-Kowalski and Hüttler published just over two decades ago (Fischer‐Kowalski and Hüttler 1998).

One of the strengths of MFA is the relative straightforward procedure (at the core of this method is ‘counting numbers’) that does not require advanced operations or mathematical models, and the obtained results (expressed in total weight of materials or quantity of energy flows) can be easily communicated to and understood by a wide audience.

There are some difficulties that arise depending on the chosen scope and system reference. The line between the natural and the socio-economic system is not always clear, which can lead to double counting or reporting inconsistencies. Examples include accounting for livestock and domesticated animals (and their respective nutrient intake and waste flows), defining a water balance within a reference system, accounting for the use of oxygen for respiration, and quantifying all inputs and outputs that are required to properly balance the combustion of fuels.

The method has been thoroughly described in a practical handbook (Brunner and Rechberger 2004). This handbook discussed the following procedural steps:

• Selection of Substances
• System Definition in Space and Time
• Identification of Relevant Flows, Stocks and Processes
• Determination of Mass Flows, Stocks and Concentrations
• Assessment of Total Material Flows and Stocks
• Presentation of Results
• Materials Accounting

The authors also discuss data uncertainty, software to use for MFA, and relevant evaluation methods (which include a number of methods discussed further on in this report). All in all, this handbook has been a guiding reference for many MFA studies, and together with other books (e.g. Baccini and Brunner (2012)) this makes MFA one of the most strongly documented methods.

Despite the well-documented procedure and rationale behind the method, there is no single approach that is adopted across the board. Gerber and Scheidel (2018) highlight a very relevant paragraph from one of the leading books:

Baccini and Brunner (2012: 105, their emphasis) wrote that “there are no theories available to perform MFA/SFA. [...] There are many groups active in MFA/SFA using their individual techniques and accumulating their specific experience and data. [...] [However], despite the many approaches, there are only small differences between the methods of the individual schools of MFA/SFA. The main divergence is the focus.”

Specific frameworks also exist, for example for water (Kenway, Gregory, and McMahon 2011). However, within this report these were here classified as MFA with their respective material. Another related method is Material Flow Cost Accounting (MFCA). This method is seen as a management tool that has considerable uptake at a corporate level, and which has also been codified in an ISO standard (ISO 14051). This is a tool to improve economic and environmental performance (Christ and Burritt 2015). The focus of MFCA is to allocate all production costs to material flows. MFCA focuses on the costs for product and non product output (Jasch 2008)

Strengths:

• Extremely versatile in its use and can be catered to suit many specific needs.
• Plentiful documentation has helped define standard terms and procedures.
• Relatively straightforward procedure around ‘counting numbers’.
• Results can be easily communicated to and understood by a wide audience.

Weaknesses:

• Inconsistencies or double counting need to be carefully considered when defining the exact scope and system boundaries, especially where the natural and human systems directly interact.
• Lack of a single methodological framework has led to a multitude of specific approaches.
• Difficult to translate results to policy interventions.