Stochastic error propagation with independent probability distributions in LCA does not preserve mass balances and leads to unusable product compositions—a first quantification
Authors: Marsh Ellen , Hattam Laura , Allen Stephen 
Published: October 2024

Abstract

Purpose
To mitigate the effects of the triple planetary crisis of climate change, pollution and biodiversity loss, a system-based approach to estimating environmental impacts—such as life cycle assessment (LCA)—is critical. International standards recommend using uncertainty analysis to improve the reliability of LCA, but there has been debate about how to do this for many years. In particular, in order to characterise uncertainty in the inputs and outputs of each unit process in an LCA, a prevalent approach is to represent each one by an independent probability distribution. Thus, any physical relationships between inputs and outputs are ignored, which causes two potential errors during Monte Carlo simulation (a popular method for propagating uncertainty through an LCA model). First, the sum of the inputs to a unit process may not equal the sum of the outputs (i.e. there may be a mass imbalance), and second, the proportions of each input and output may be unrealistic (e.g. too much cement in a concrete production unit process). However, while some literature has discussed the problem, it has not yet been quantified.

Methods
Therefore, this paper investigates the extent to which existing uncertainty characterisation approaches, where there is a lack of parameterisation or correlations in databases, lead to mass imbalances and unrealistic variations in unit process compositions when performing uncertainty analysis. The matrix-based structure of LCA and the standard uncertainty analysis procedure using Monte Carlo (MC) simulation to propagate uncertainty are described. We apply the procedure to a concrete production process. Two uncertainty characterisation approaches are also explored to assess the effect of data quality scoring on mass imbalances and the mass contribution of each exchange (i.e. production compositions).

Results and discussion
For median data quality scores and using a typical (basic + additional uncertainty) uncertainty characterisation approach, the 1000-iteration MC simulation leads to mass imbalances ranging from − 49 to + 30% of the original mass and found that the mass imbalance exceeded existing prescribed plausibility limits on 62.7% of MC runs. On average across all exchanges, the exchange mass exceeded the 5% plausible variation limit on 77.7% of MC runs. This means that the final concrete product compositions are unlikely to be realistic or functionally equivalent to one another. We discuss the appropriateness of using universal variances for the underlying normal distribution for data quality scores (“additional uncertainty”) when input exchange quantities are of different scales. Additionally, we discuss potential solutions to the mass imbalance problem and their suitability for implementation at a database scale.

Conclusions
We have quantified, for the first time, the significant impact that uncertainty characterisation via independent probability distributions has on maintaining mass balances and plausible product compositions in unit processes. To overcome these challenges, databases would need to be parameterised and have the ability to sum quantities to perform mass balance checks during uncertainty analysis.