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Models and Scenarios

Models are mathematical representations of material cycles and their drivers which are used to simulate historical changes in material cycles or to make forecasts for future changes through the use of scenarios. Estimation of future material flows is important and finds use in several policies, for example environmental, raw material safeguarding, land use planning, but also in market analysis and economic studies.

The optimisation of material flow systems is typically done by comparing alternative management scenarios. Demand and/or supply of raw materials can be predicted by scenario analysis, which uses predefined assumptions in mathematical functions to provide prediction results. Various different scenario drivers are perceived in investigations of material systems. A driver is any natural or human-induced factor that directly or indirectly causes a change in a system. A direct driver unequivocally influences ecosystem processes. An indirect driver operates more diffusely by altering one or more direct drivers. Global driving forces include demographic, economic, socio-political, cultural and religious, scientific and technological, and physical and biological parameters. Drivers in categories other than physical and biological are considered indirect. Important direct, namely physical and biological drivers include changes in climate, plant nutrient use, land conversion, and diseases and invasive species. Scenarios represent plausible futures in terms of plausible developments for the material cycles that are consistent with the mass balance principle and the assumed drivers.

Strong models and scenarios depend on robust system definition and data. There are different approaches to model development.

Please note: The following text is taken from the existing MinFuture reports "A systems approach for the monitoring of the physical economy" and "Concise description of application fields for different MFA approaches and indicators". Please click on the afore-mentioned links to access and read the full publications.


Projections for demand and/or supply of raw materials are made based on scenarios, which allow transforming certain assumptions into mathematical functions, which then provide scenario results. Different MFA approaches and drivers will be analysed and listed. MFA approaches on different levels are available and will be evaluated:

  • Static and dynamic
  • Top-down and Bottom-Up
  • Flow and stock driven
  • Leaching and delay 


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Key principles of MFA models
A range of criteria is used to define MFA models. These are grouped in the four dimensions (i) stages, (ii) trade, (iii) layers, and (iv) time, as presented in Table 5 below. Additional criteria relevant to data and the overarching scope of the MFA model (general issues) are grouped together under the “transversal” attributes.

Table 5: Criteria to characterize MFA models

MFA models can have different spatial boundaries (stages and the trade flows). A fix or standardized system definition has the advantage of making different systems (or economies) comparable. A flexible system definition allows for a detailed analysis of critical parts of the system. The system definition is therefore problem- or case-oriented, but less suitable for making comparisons. A key challenge when developing refined system definitions is data availability and the compatibility between different datasets, for example production and trade data.

MFA models can address one or several properties of the stocks and flows of goods in a system. The selection of the layer dimension properties (e.g. total mass, substances, energy, monetary value, multi-layer approach) is a consequence of the problem description. MFA models can integrate the time dimension in different ways:

  • Static models are available on global and national scale. A static MFA is concerned with generating a better understanding of a material system based on simple accounting principles (i.e., mass-balance equations).
  • Dynamic models are primarily used to investigate the stock build-up of materials in society (i.e., secondary resources) and in the environment (i.e., dissipative losses) based on the investigation of material flows over time.
  • Stationary models also consider time, however in stationary models, things do not change over time – all system variables are invariant under time shift. Stationary models usually consist only of flows, while stocks are omitted or assumed not to be changing. Traditional input-output models are typical examples of stationary models.
  • Quasi-stationary models are similar to stationary models; however, the stocks may change linearly over time, while flows are assumed constant.

Stocks of materials can be measured by two different methods (see Figure 9):

  • The top-down approach usually derives the material stock from the net flow; the difference between inflows (consumption) and outflows (discard). The methods used in top-down studies are further differentiated in input-driven (driven by the input in the stock) and stock-driven (driven by service units provided by the in-use stock) approaches. Furthermore, the modelling approach can be either a delay approach (based on lifetime functions) or a leaching approach (based on fractions of the presented stock.
  • The bottom−up approach directly estimates the stock by summing up the material in question present within the system boundary at a certain time.

Figure 9: Top-down and bottom-up approach use in estimating material stocks (Laner and Rechberger 2016)

Figure 10: MFA Models and approaches used for estimating material stock

MFA and other related methods integrate the attributes of time (vertical axis) and space (horizontal axis) as shown in Figure 11. MFA and SFA models present substantial advantages when compared to other common methods, such as EW-MFA (Economy wide material flow analysis). Overall, they provide more detail, are more flexible as spatial and temporal boundaries can be varied and they can take into account both material flows and stocks.

Figure 11: Assessment of different MFA approaches and related tools, and the way they integrate time (vertical axis) and space (horizontal axis) in their analysis.

Figure 12: Estimating material stocks. The delay versus the leaching approach.

In order for MFA models to be widely applicable, it would be appropriate to establish standardised system definitions in all four dimensions of the physical monitoring framework proposed here. This implies, for instance, precise definitions of the life cycle stages, the required layers, as well as the methodology for estimating outflows in a prospective modelling approach. For the layer dimension in particular, a multi-level approach would be desirable, where environmental and economic aspects are included alongside the mass balance layer to provide different viewpoints and a holistic approach. At the “substance” layer it would be valuable to account the quality of the substance in addition to the quantity. This is especially relevant for critical raw materials, which otherwise would be negligible, and therefore dismissed, in a mass flow context. A more complete description of the diverse MFA approaches, models and related tools is included in the MinFuture report "Concise description of application fields for different MFA approaches and indicators" (Villalba, 2018).

  • MFA models are mathematical representations of material cycles.
  • MFA models are developed to address issues around resource management (e.g. monitoring material cycles, development of strategies to address resource utilisation concerns, investigation of environmental implications associated with material use).
  • Scenarios represent plausible futures.
  • Optimisation of material flow systems is typically done by comparing alternative management scenarios.
  • Demand and/or supply of raw materials can be predicted by scenario analysis, which uses predefined assumptions in mathematical functions to provide prediction results.
The figure shows the first page of the Framework 2-page document
The MinFuture framework

Robust strategies for sustainable resource management depend on a solid understanding of the physical economy – the anthropogenic stocks and flows of matter and energy.

This figure shows the cover page of the report "Report on pilot studies"
MinFuture Deliverable 4.1

MinFuture project aims to develop a common methodological framework for monitoring the physical economy and to deliver clarity on the different components of MFA needed for monitoring the physical economy.

The photo shows the participants of the MinFuture Final Conference

The intention of this conference "Monitoring the physical economy requires putting raw material data in a system context" was to present, reflect on and refine key recommendations from the MinFuture project on a monitoring system for the physical economy.

The presentations held and recommendations made will soon be available via this website.

The figure shows a snap shot of the report's cover page.
MinFuture Framework

This report aims to address existing challenges by developing a methodological framework for the monitoring of the physical economy that facilitates the users in reflecting more systematically about the problems mentioned above and in developing more effective strategies for addressing them. The framework proposed is based on Material Flow Analysis (MFA), a tool widely used for tracking materials and energy in the economy.

The figure shows a snap shot of the report's cover page.
MinFuture Deliverable D4.2

Six material-specific workshop were organised under the umbrella of MinFuture project, aiming to identify gaps that hamper a robust mapping of raw material cycles. In each material-specific workshop, stakeholders from academia, industry, and government were brought together to discuss and comment on the current status of each material cycle.

The picture shows a snap shot of the cover page of the report.
MinFuture Deliverable D3.3

Material flow analysis (MFA) in general, is a term used to summarize a wide range of approaches to describe material stocks and flows in systems defined in space and time.

The figure shows a snapshot of the cover page of the synthesis brief
MinFuture Workshop synthesis brief No. 3

In order to develop strategies as well as to define and reach goals concerning raw materials management, maps are needed to help navigate existing knowledge and data.


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