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. In MFA, the consideration of uncertainty should enable the use of all available information about the system, reflecting the purpose of the MFA and the data quality. The uncertainty of the basic data and the accuracy of the results are fundamental pieces of information for the evaluation process. As MFA concerns gathering, harmonizing and analysing data from various different sources with varying quality, limitations of data are unavoidable in material flow studies. The majority of data in MFA are empirical quantities with uncertainty arising from different sources:

Causes of uncertainty

• Non-deterministic behaviour of a system
• Uncertainty of model parameter values
• Uncertainty of model structure
• Uncertainty due to external influence factors
• Uncertainty due to numerical solutions of model equations

Sources of uncertainty

• Statistical variation
• Variability
• Inherent randomness and unpredictability
• Subjective judgment
• Disagreement
• Linguistic imprecision
• Approximation

Types of uncertainty

• Parameter Uncertainty
• Scenario Uncertainty
• Model Uncertainty
• Output Variable

If sufficient data are available, unknown flows including their uncertainties can be determined by mass balancing and error propagation. It is also important to convince data providers to include data uncertainty in their publications. In some situations, however, problems will occur with statistical methods, if only limited data are available. Therefore, different approaches to quantify and treat uncertain data are available:

Data classification

• Asymmetric uncertainty intervals
• Symmetric intervals
• PEDIGREE Matrix
• Information defects

Uncertainty analysis

• Gauss’s law of error propagation
• Data reconciliation
• STAN Software
• Mathematical material flow analysis
• Probabilistic material flow analysis
• Monte Carlo simulation
• Fuzzy set theory

Sensitivity analysis

Comparison of model structures

Based on Laner et al. (2014) a step-wise iterative procedure for handling uncertainty in MFA is suggested. This schematic framework for considering uncertainty in MFA facilitates transparent uncertainty analysis in MFA and is suitable to accommodate any of the approaches presented here. Some studies may not warrant full uncertainty analysis because of different foci of the MFAs. Therefore, only parts of the scheme can be applied. In addition to providing a systematic way to consider uncertainty in MFA, the suggested procedure forms a basis for consistently communicating the approach used to consider uncertainty in a specific MFA study.
In conclusion, it can be said that there are a handful of applicable approaches to consider data uncertainty in MFA. The employment of MFA software would facilitate the implementation of these approaches and reduce the additional workload because of automation to acceptable levels. However, such software support is not yet on the market (with the exemption of STAN1, which is limited to normally distributed values) and there is a strong necessity to fund such software development. Only then, MFA could enter into an era where reporting uncertainty ranges of stocks and flows is mandatory and state-of-the-art. This would help to judge or gauge the reliability of MFA studies and also allow comparative studies for different regions with respect to quality and quantity of data generation.