Dealing with uncertainty in material flow analysis

Abstract

Material flow analysis (MFA) is a tool to investigate material flows and stocks in defined systems as a basis for resource management or environmental pollution control. Due to the lack of general information on data and model structure, and the diverse nature of data sources, MFA results are inherently uncertain (e.g. recycling rates, flow quantities). In this work, the treatment of uncertainty in material flow modeling is analyzed. Possible causes of uncertainty, such as uncertainty of model parameters or uncertainty of model structure, and the according treatment methods, such as uncertainty analysis, sensitivity analysis and uncertainty treatment of model structure, are presented. In order to address the typical drawbacks of uncertainty treatment in MFA in already existing approaches, three studies with three methods, differing in problem set-ups and objectives, are proposed in this work. As various MFA studies rely on data about flows and stocks from different sources with varying quality, in the first study, an uncertainty analysis method, which expresses the belief that the available data are representative for the value of interest via fuzzy sets, is presented, specifying the possible range of values of the data. A possibilistic framework for data reconciliation in MFA was developed and applied to a case study on wood flows in Austria. The framework consists of a data characterization and a reconciliation step. Membership functions are defined based on the collected data and data quality assessment. Possible ranges and consistency levels (quantifying the agreement between input data and balance constraints) are determined. The framework allows for identifying problematic data and model weaknesses, and can be used to illustrate the trade-off between confidence in the data and the consistency levels of resulting material flows. While reconciliation is useful in static MFA systems, the focus in dynamic MFA system is rather on robustness of the material flow models, by defining variation ranges for parameters rather than to capture the true range of variation. Therefore, the use of sensitivity analysis in dynamic MFA studies has been on the increase. Variance based global sensitivity analysis decomposes the variance of the model output into fractions caused by the uncertainty or variability of input parameters. The second study investigates interaction and time-delay effects of uncertain parameters on the output of an archetypal input-driven dynamic material flow model using variance based global sensitivity analysis. The results show that determining the main (first order) effects of parameter variations is often sufficient in dynamic MFA because substantial effects due to the simultaneous variation of several parameters (higher order effects) do not appear for classical set ups of dynamic material flow models. For models with time-varying parameters, time-delay effects of parameter variation on model outputs need to be considered, potentially boosting the computational cost of global sensitivity analysis. Finally, the implications of exploring the sensitivities of model outputs with respect to parameter variations in the archetypal model are used to derive model- and goal-specific recommendations on choosing appropriate sensitivity analysis methods in dynamic MFA. When it comes to dynamic studies of uncertain model structure, sensitivity analysis may not be sufficient. Principal examples are analyses of waste streams of building stock, which are uncertain with respect to data and model structure. Wood constructions in Viennese buildings serve as a case for the third study to compare different modeling approaches for determining end-of-life (EOL) wood and corresponding contaminant flows (lead, chlorine and PAH). A delayed input and a leaching stock modeling approach are used to determine wood stocks and flows from 1950 until 2100. Cross-checking with independent estimates and sensitivity analyses are used to evaluate the results¿ plausibility. Under the given data situation in the case study, the delay approach is a better choice for historical observations of EOL wood, and for analyses on a substance level. It has some major drawbacks for future predictions on the goods level, though, as the durability of the high amount of historical buildings with considerably higher wood content is not reflected in the model. The wood content parameter differs strongly for the building periods, and has therefore the highest influence on the results.