Monte Carlo uncertainty analysis in LCA: from the pedigree matrix to P10/P90

An EPD says "GWP-fossil: 245 kg CO₂eq". Could the true value be 200, or 300? A single-point result cannot answer that. Monte Carlo uncertainty analysis models the uncertainty of every inventory input as a probability distribution, runs the model thousands of times with random samples, and returns a distribution instead of a single number. ISO 14044 explicitly recommends uncertainty assessment for comparative assertions.

The pedigree matrix: turning data quality into numbers

The source of uncertainty is usually not measurement error but data representativeness. The pedigree approach scores every inventory line 1-5 on five criteria: reliability (measured or estimated), completeness (how many sites, which period), temporal correlation (how old is the data), geographical correlation and technological correlation. Each score combination maps to an empirically derived uncertainty factor; combined with the basic uncertainty, these yield the geometric standard deviation (GSD) of a lognormal distribution.

Why lognormal?

Environmental flows cannot be negative and are products of multiplicative processes (yield × intensity × distance...); these two properties make the lognormal the natural choice. The median of the lognormal is the value you entered in the inventory; the GSD² says "with 95% probability the true value lies between median/GSD² and median×GSD²". GSD² = 1.2 is a narrow band; 2.0 is wide — energy data is typically narrow, emission factors wide.

Reading the results: P10, P50, P90

• P50 (median) — the middle of the distribution; it can differ from the deterministic result, no panic needed
• P10-P90 band — "the result lies in this range with 80% probability"; the most honest range for EPD communication
• Coefficient of variation (CV) — spread / mean; if CV > 30%, revisit the most uncertain inventory lines
• Contribution analysis — which input drives total variance; sets the improvement priority

Comparative uncertainty: is A really better than B?

When comparing two products, the correct method is not to eyeball two separate distributions but to sample both within the same iteration and look at the distribution of the difference — background data is shared, so uncertainties are correlated and the difference distribution is far narrower than the overlap of separate bands. "A is lower than B in 94% of iterations" is a far more defensible claim than "A is 12% lower".

How many iterations are enough?

Practical rule: 1,000 iterations suffice for P10/P90 estimates in most models; if tail percentiles (P5, P95) will be reported, prefer 5,000-10,000. Test convergence directly: if P90 at 1,000 and 2,000 iterations differ by less than 1%, you have converged.