Addressing uncertainty in modelling material and energy flows

To discuss detailed C-THRU research updates, further the team’s knowledge, and promote collaboration, the C-THRU researchers have been holding regular seminars. Dr Rick Lupton (Data modelling and uncertainty) recently presented on uncertainty in modelling material and energy flows.

Uncertainty is inevitable in modelling material and energy flows due to the diversity of data sources and availability of data, etc. Quantifying the uncertainty is crucial as it could affect the reliable results obtained and conclusions made by using such a flows model.

In Dr Rick Lupton’s talk, first, he introduces the Bayesian approach under the background of material flow analysis. A simple one-process material flow analysis model is used to explain how the material flow analysis works in the Bayesian framework as shown in Figure 1.

Material flow analysis model depicting a) hypothesis space; b) Inference — Figure 1¹. (a) For a simple one-process MFA model, there is a range of possible hypotheses consistent with the mass-balance constraints and other assumptions. The small Sankey diagrams illustrate 9 possibilities drawn from the hypothesis space, arranged according to two model parameters, the input y0 and the efficiency η. (b) The inference process takes newly observed data and combines it with the predictions of the model to update knowledge about the model parameters. In this sketch, a measurement of y0 results in knowledge about parameters becoming more specific (i.e., the probability distribution becomes more peaked).

Secondly, he uses an example of a Sankey diagram resulting from a global material flow analysis of iron to demonstrate the feasibility of the above idea as shown in Figure 2. In this diagram, the line width indicates the flow magnitude, while the colour indicates the level of uncertainty in the flow.

Sankey diagram showing uncertainty in material flow values — Figure 2. Sankey diagram² shows uncertainty in flow values. The shading indicates the width of the 95% credible interval, with darker colours showing more certain flows.

Thirdly, Dr Lupton provides a further example of quantifying the uncertainty associated with final and useful energy balances based on the Bayesian approach as shown in Figure 3. Previously unpublished data about average end-use conversion device efficiency has been compiled and the useful energy balance of the UK has been calculated. The results show that the largest source of uncertainty is the allocation to energy end-uses, where the uncertainty of the energy flows goes from a median value of 5% to one of 34%. Useful energy consumption for transport and heating has low uncertainty (4–10%) and overall, 85% of consumption has uncertainties below an acceptable 25% threshold.

Sankey diagram showing energy flows — Figure 3. Sankey diagram² represents the energy data used in this study. The width of the lines represents the quantity of energy (in PJ, where 1 PJ = 109 MJ) while the intensity of the colour represents the uncertainty (in %) of each flow. The first four layers are loss-less because they show only allocations, losses are only incurred in the stage between conversion devices and Useful energy categories.

To apply the Bayesian approach to material and energy flow analysis, finally, Dr Rick Lupton pointed out that we need to (a) set up the model structure with hypotheses, (b) quantify initial knowledge about hypotheses, and (c) relate the observed data to the model. Dealing with uncertainty in modelling materials and energy can allow greater confidence in decision-making by highlighting how much uncertainty is there in the output of the flow and where further work/data is needed if a sensitivity analysis is conducted.

1. Lupton, R. C. & Allwood, J. M. Incremental Material Flow Analysis with Bayesian Inference. J. Ind. Ecol. 22, 1352–1364 (2018).

2. Paoli, L., Lupton, R. C. & Cullen, J. M. Useful energy balance for the UK: An uncertainty analysis. Appl. Energy 228, 176–188 (2018).

Photo credit: Robin Pierre

Addressing uncertainty in modelling material and energy flows

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