Hello to all,
I have some problems in combining the results of
conditional simulations of different variables. This is
my problem: With the help of a model I'm trying to
estimate the variance of remediation costs of
contaminated sites. The costs are calculated using an
estimation of the 3-D spatial distribution of the
contamination. The variance in the costs is due to the
uncertainty of the estimations of the concentrations
of the contaminants in unsampled points.
To estimate the distribution of the pollutant the
polluted area is devided in cubes of soil of a certain
area and depth and then the concentration of the
contaminant is estimated for each of these cubes.
This is done for several different contaminants.
For each cube the cost model determines the most
polluting contaminant and this determines the
contamination-class the cube is assigned to. This class
determines the further use/processing of the soil in the
cube, which is linked with certain known costs.
Furthermore for each column of soil the depth till
which the soil should be digged up is determined so all
contamination till a certain level will be removed. This
then determines the costs for digging; the deeper the
higher the costs.
To estimate the remediation costs and its variance I
want to use 3D- conditional simulations of the
distributions of the pollutants. For each pollutant
separately concentrations are simulated for all
cubes several times.
Now one of the problems is how to combine the
simulations of the different substances in the cost
model. When combining the simulations of e.g. five
pollutants, it's very likely that in every cube the
concentration of (at least) one of the substances
regarded will be estimated/simulated relatively high
and as the most polluting substance determines the
processing costs the estimated costs will be
relatively high. The more pollutants are regarded the
higher the estimated costs will be.
The same applies for the number of layers
distinguished. The more layers are distinguished in the
simulation the higher the risk that at greater depth the
simulated value will exceed a certain limit and the soil
should be digged up which results in higher costs, i.e.
the more layers the higher the estimated costs.
Who has been dealing with these problems before and
who has any suggestions on how to tackle
these problems? We have been thinking about using
Principal Component Analysis to reduce the
multivariate problem into a univariate problem
(simulating only the first Principal Component), but
we're afraid of loosing a lot of information.
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