Framework for risk-informed decisions beyond point estimates: statistically rigorous Monte Carlo methods for heavy-gas dispersion uncertainty analysis

Accurate modelling of toxic dispersion for denser-than-air gases is inherently complex, where atmospheric variability intersects with dense-gas dynamics. The SLAB model offers an optimal balance of physical fidelity, coupling mass, momentum, energy, and species conservation equations, with computational efficiency. Prior uncertainty analyses within Quantitative Risk Analysis often rely on simpler dispersion models or lack rigorous statistical validation tests for Monte Carlo-based uncertainty propagation, sacrificing accuracy and reliability in high-stakes assessments. This contribution presents a computationally robust Uncertainty Analysis (UA) framework tailored to Quantitative Risk Analysis for a catastrophic ammonia tank rupture scenario, emphasizing input uncertainties rising from practitioner assumptions and site-specific variability. Leveraging Monte Carlo methods for nonlinear, highuncertainty propagation, our approach addresses a key gap in dispersion risk modelling UA: the rare application of rigorous convergence tests. We implement the Law of Large Numbers-guided Maximum-to-Sum plots to verify stability of output moments, namely the mean and the variance, ensuring dependable estimates even under fat-tailed distributions, adding essential scientific rigor to Monte Carlo applications in risk analysis and mitigating samplingdriven variability that can lead to unreliable results. The methodology features a sampling and uncertainty propagation scheme that integrates several stability classes, capturing atmospheric variability beyond discrete scenarios. The resulting analysis guarantees consistency of Monte Carlo outputs and delivers statistically robust toxic concentration uncertainty estimates. This framework enables insightful interpretation for risk thresholds and regulatory decisions, reinforcing risk-informed decisions beyond the traditional single-point estimates.

Keywords: Dense-gas Dispersion, Quantitative Risk Analysis (QRA), Monte Carlo, Uncertainty, Convergence Analysis.