Protocol for the Derivation of Environmental and Human ... - CCME

Appendix G
Based on the results of the sensitivity analysis, the four most dominant parameters identified above
excluding building height detailed probabilistic analysis; other variables were assigned values
approximately equal to the means of their respective distributions.
As part of the sensitivity analysis, the effect of changing the form of the input probability distribution was
investigated by utilizing various types of distribution for the most critical parameter, crack spacing. The
influence of normal, lognormal, beta, and uniform distributions was assessed; the shape of the
distribution of dilution factor tended to reflect the shape of the distribution of crack spacing, although
mean, minimum, and maximum values were not significantly affected. It was concluded that in the
absence of more detailed statistical information on the input parameters, or site-specific data, the
triangular distribution was an appropriate assumption for the purposes of this study.
4.3 Probabilistic Analysis
The probabilistic analysis was carried out using a form of Monte Carlo simulation, whereby probability
distributions were generated for the dilution factor on the basis of 5 000 iterations of the vapour
transport analysis, using input parameters randomly sampled from their respective distributions. A Latin
hypercube sampling technique was used. Distributions of dilution factor were developed for each of the
two soil types for a number of depths to contamination. These were used to establish relationships
between dilution factor and depth for a number of points (percentiles) on the probability distribution.
Illustrative probability distribution, corresponding to a depth of 1 m, are presented in OAEI (1994) on
Table G.2 for sandy and clayey soils respectively. The respective relationships between dilution factor
and depth for sandy and clayey soils are presented in OAEI (1994) on Tables G.3 and G.4. Curves
are presented for the 0, 5th 10th, 25th, 50th, 75th, 90th, and 100th percentiles. At the 5th percentile
there is a 5% chance, based on variations in the key parameters, that the dilution factor will overpredict
the dilution and hence underpredict the indoor air concentration. The 5th percentile therefore
corresponds to a 95% level of conservatism.
The results of the analyses for sandy and clayey soils are presented in Tables G.3 and G.4. For sandy
soils, the mean dilution factor ranges from approximately 14 400 at zero depth to 48 500 at 10 m
depth. The corresponding range for clayey soils is 22 300 to 635 500. For the more conservative 5th
percentile values, the dilution factor for sandy soils ranges from approximately 9 500 at zero depth to
31 400 at 10 m depth. The 5th percentile range for clayey soils is 12 600 to 388 000.
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