Uncertainty correlation and Monte Carlo sampling in LCA
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1 The world s most consistent and transparent Life Cycle Inventory database Uncertainty correlation and Monte Carlo sampling in LCA LCAXV, Vancouver, Canada 07 October 2015 Guillaume Bourgault, Ph.D Project Manager ecoinvent
2 Outline What is Monte Carlo and why we use it? What correlation are we tackling today? How beta and Dirichlet distributions can help? Ignoring correlation overestimates uncertainty Trust in Transparency! 2
3 What is Monte Carlo? y = x1 + x2 Trust in Transparency! 3
4 What is Monte Carlo? Trust in Transparency! 4
5 Why Monte Carlo? What is the uncertainty of the model output? All models are wrong, but some are useful. How useful is your model? Decision makers appreciate the information What parameter of the model drives the output uncertainty? Learn something about the model Recommendations on model use Guide data collection Restructure the model: more parameters necessary? Trust in Transparency! 5
6 Why Monte Carlo? Simpler models: analytical tools Cumbersome to impossible for large models Taylor series expansion: ill-adapted to large uncertainties in LCIA Advantage of Monte Carlo Variables are sampled on their entire domain All variables change at once: captures interactions between parameters Drawback of Monte Carlo Computationally expensive (time and memory) Requires coding skills Trust in Transparency! 6
7 Correlation in LCI Electricity consuming activity NG + C + H = 1 1 kwh Natural gas Coal Hydro 0.13 kwh ± X 0.68 kwh ± Y 0.19 kwh ± Z Trust in Transparency! 7
8 Correlation in LCI Trust in Transparency! 8
9 Correlation in LCIA Fate factor FF ij = mass transported from source cell (i) to all other cells (j). 1 FF ij j 0 1 n j=1 FF ij 0 Trust in Transparency! 9
10 Beta and Dirichlet distributions Lognormal 3 degrees of freedom: minimum (often zero), average, variance Only has a lower bound skewed to higher values VERY skewed for high variance Beta Upper and lower bound 4 degrees of freedom: min, max, α, β Choose min, max, average, percentile 97.5 α, β Skewed to the right, left, or symmetrical Trust in Transparency! 10
11 Beta and Dirichlet distributions α + β, σ Trust in Transparency! 11
12 Beta and Dirichlet distributions Trust in Transparency! 12
13 Beta and Dirichlet distributions Trust in Transparency! 13
14 Beta and Dirichlet distributions Dirichlet is a multi-variate beta Inputs of Dirichlet: Vector 1 x N. Example: [0.13, 0.68, 0.19] Scaling value. Example: 10 and 100 M iteration. Example: 1000 Output of Dirichlet: Parameters for N beta distributions N samples of M iterations Trust in Transparency! 14
15 Beta and Dirichlet distributions Each iteration sums to 1 Trust in Transparency! 15
16 Beta and Dirichlet distributions market share market share market share market share market share market share Trust in Transparency! 16
17 Beta and Dirichlet distributions Shuffled sample Trust in Transparency! 17
18 Beta and Dirichlet distributions Trust in Transparency! 18
19 Beta and Dirichlet distributions sum of market shares sum of market shares Trust in Transparency! 19
20 Beta and Dirichlet distributions Electricity production, ecoinvent v3.1, IPCC 2007 GWP 100 scores, Austria Natural gas : kg CO 2 -eq/kwh Hard coal : kg CO 2 -eq/kwh Hydro, run-of-river: kg CO 2 -eq/kwh Trust in Transparency! 20
21 Beta and Dirichlet distributions Trust in Transparency! 21
22 Take home message Ignoring correlation leads to uncertainty overestimation Larger the uncertainty of the parameters larger overestimation No rule of thumb to predict if the difference is noticeable Safer to test if the effect is significant in the setting at hand Ask your software provider the detail of the algorithm Ask a statistician friend! Trust in Transparency! 22
23 The world s most consistent and transparent Life Cycle Inventory database Thank you for your attention! Questions? Guillaume Bourgault Project Manager bourgault@ecoinvent.org
24 Why not divide by sum? Trust in Transparency! 24
25 Why not divide by sum? Trust in Transparency! 25
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