P1: OTA/XYZ P2: ABC
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42 CH 3 MODELING UNCERTAINTY: CONCEPTS AND PHILOSOPHIES
In some cases, one may built a few 3D models (3–5), for example based on different
scenarios for the geological setting, or simply by running a stochastic method such as in
Chapters 5–8 a few times; in the Danish case, this could include modifying the buried
valley positions slightly to account for the difficulty in interpreting accurately the TEM
image in Figure 3.1. Such an approach is, however, not necessarily a rigorous exercise in
modeling uncertainty, the idea here is just to explore a few alternative models. In the case
of Figure 3.1, any rigorous uncertainty assessment would not only include uncertainty in
the contouring but also uncertainty in processing the raw TEM observations to create the
TEM image data set in Figure 3.1. The relationship between raw observations and data
sets is discussed later in this chapter.
A single deterministic model is often built simply because of time (CPU or man-hour)
constraints. Such a model may contain “all bells and whistles” that the model builder be-
lieves is representing those processes occurring in nature. An example of a deterministic
model is a process-based model; examples are discussed in Chapter 5. This model explic-
itly simulates the dynamic process that took place or will take place. Examples of such
process models are general circulation models (GCMs) for studying climate change, the
simulation of sedimentary deposition to represent an aquifer or oil reservoir, the mechan-
ical simulation of fracture growth and the simulation of carbonate reef growth. Determin-
istic models therefore aim, in the first place, to be physically realistic, that is, represent
realistically physical and dynamic processes as well as their mutual interaction. In this
sense, deterministic models are often deemed superior to models that are physically less
realistic (simpler models). If that is the case then one should define specifically what is
meant by “superior”. Also, even a fully theoretical model is often dependent on ad hoc or
arbitrary adjustments of physical parameters. This is certainly true for 3D gridded mod-
els, where the size of the grid cell may be large (km); therefore, any fine scale features
or processes may need to be aggregated (i.e., summed/integrated) into a large grid cell.
Indeed, a reservoir can never be represented by modeling every sand grain contained in
it or a climate model by including every single cloud formation. Hence, even a full de-
terministic physical model may heavily rely on empirical or ad hoc determined input
parameters, hence subject to a great deal of uncertainty in its physical representation,
which is supposed to be its strength.
In addition, physical models often require initial conditions, boundary conditions that
may be prone to large uncertainty. This is the case in modeling of the tectonic defor-
mation of a particular region. In modeling such deformation, one is interested in the
reconstruction over geological time of the deformation that took place, that is, the folding
and faulting of a rock formation within a particular region or basin. Many combinations
of initial conditions and deformation histories (which are basically space–time varying
boundary conditions) may lead to the same current structural geological setting. Since
the current geological setting is the only observation that can be made (one cannot go
back in time unfortunately), much uncertainty remains in the initial / boundary or defor-
mation histories.
Deterministic models are certainly useful as a good start to understand some of the
processes taking place, to perform some initial investigation of what is possible. However,
they have little “predictive” power, that is, they cannot be used to quantitatively forecast a