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68 CH 4 ENGINEERING THE EARTH: MAKING DECISIONS UNDER UNCERTAINTY
the output response could be the decision made or the value of a payoff. The relationship
between input and output is modeled through a deterministic function, that is, once the
input is known, the output is also uniquely known. Note that even a “stochastic simula-
tor” such as Monte Carlo simulation falls in this category, in that case the deterministic
function is the probability distribution, the inputs are the parameters of the probability
distribution and the random number generated for a given random seed.
In modeling uncertainty as well as in decision analysis, the exact numbers obtained
through the analysis and modeling, such as payoffs, probabilities or scores, are often less
important than the impact a change in these values have on either the decision made
or the model of uncertainty. Indeed, why care about being obsessed with determining
a payoff exactly when even a large change of such payoff will not affect the ultimate
decision? A sensitivity analysis, even a simple one, allows what matters and what does
not to be figured out and can lead to a more focused modeling of the uncertainty about the
Earth. This is important, since any modeling of uncertainty requires a context, as such,
the actual modeling becomes much simpler when targeted than just modeling uncertainty
for the sake of uncertainty.
4.2.4.4.1 Tornado Charts Tornado charts are used for assessing the sensitivity of a
single output variable to each input variable. This entails varying one input variable while
leaving all other input variables constant. Varying one input variable one at a time is
called “one-way sensitivity.” We will cover “multi-way sensitivity” where multiple input
variables are varied simultaneously in later chapters.
Tornado charts are visual tools for ranking input parameters based on their sensitivity
to a certain response or decision. The input variables are changed one at a time (the others
remain fixed) by a given amount on the plus and minus side and the change in response,
such as a payoff, are recorded. Often a change of +/− 10% is used; alternatively, the
change is made in terms of quantiles, such as given by the interquartile range of the
variable. Next, the input variables are ranked in order of decreasing impact on response,
in terms of absolute value difference in response for the +/−. Using the initial (prior to
sensitivity analysis) value of the payoff as a center point, the changes are plotted on a bar
chart in descending order of impact, forming a tornado-like shape. An example is shown
in Figure 4.10. Note how the length of the bars need not be symmetric on either side. The
color indicates positive or negative correlation; a blue bar on the left and red bar on the
right indicates that an increase of the input parameter leads to an increase in response.
The opposite color bar combination indicates a decrease in response to an increase in the
input parameter.
4.2.4.4.2 Sensitivity Analysis in the Presence of Multiple Objectives In the case
of multiple, possibly competing, objectives it may be important to assess the impact
of changing the weights, such as in Figure 4.11, on the decision made. Again one can
change one weight at a time, possibly starting with the largest weight. However, in doing
so, one must also change the other weights such that the sum equals unity. This can be
done as follows, consider as largest weight, in our case w
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given to objective “minimize