P1: OTA/XYZ P2: ABC
JWST061-10 JWST061-Caers March 29, 2011 12:55 Printer Name: Yet to Come
172 CH 10 MODELING RESPONSE UNCERTAINTY
a high response. We can make such a selection more statistically motivated by picking
the Earth model whose response is such that 10% of the model responses are lower than
the model response of this so-called P10 model (lowest decile). In similar ways we can
then define the median model as the Earth model such that 50% of models have smaller
response and 50% have higher response, namely the P50 model. The P90 model is then
the antipode of the P10 model. For example, if the goal were to calculate the P10, P50
and P90 of the cumulative oil production of an oil field, then one would ideally only need
to pick the correct three reservoir models and perform flow simulation on them.
Picking the “correct” Earth models would be easy if the relationship between Earth
model and response function output was linear. Since in reality this relationship is highly
nonlinear, selecting which model to evaluate the response function is not a trivial task.
Some techniques for selecting representative models are discussed in this chapter. In line
with the philosophy of this book, the selection of models should be decision or application
driven. Indeed, one would not select the same three climate models to explore different
hypotheses about the detailed, regional nature of the global climate dynamics, the causes
of observed patterns of climate change, the generation of regional forecasts, or just to
predict the global mean temperature change.
Modeling response uncertainty should not be considered as an afterthought, for exam-
ple as a simple sensitivity analysis performed on the parameters of a single (determin-
istic) Earth model from which a single prediction (for example a temperature change)
was made. Instead, a full exploration of the range of uncertainty of responses based on
multiple alternative Earth models, keeping the intended application always in perspec-
tive, is desired. This does not mean that sensitivity analysis is useless. On the contrary,
a sensitivity analysis, as an integral part of modeling uncertainty, will make the compu-
tational burden bearable, in the sense that one can focus on the most important parame-
ters immediately and eliminate studying those scenarios that have no consequence to the
application or decision question. Additionally, such sensitivity analysis can reveal to the
modeler what kind of additional data should be gathered to reduce the uncertainty on these
parameters, if such reduction is relevant to the decision goal or application (Chapter 11).
Another way to relieve computational burden is to use surrogate models (also termed
proxy models or simple models), which is discussed first.
10.2 Surrogate Models and Ranking
If evaluating the response function or simulation model on an Earth model is too expen-
sive, then one option is simply to use a less expensive (less CPU demanding) function
that approximates the original or “full” response function. Such an approximating func-
tion is called a “proxy” function, “surrogate model” or “simple model”. The surrogate
or proxy model mimics the behavior of the full simulation model. A simply analogy
would be to approximate sin(x)byx which is easy to evaluate but is only a valid ap-
proximation when x is small. In similar ways, surrogate models will approximate the full
model well for certain types of conditions or ranges of physical and spatial parameters
or even for certain types of applications. The surrogate model can be a simpler physical
model, an analytical approximation of a more complex partial differential equation, but
can also be an interpolation model that interpolates between points evaluated on the full