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40 CH 3 MODELING UNCERTAINTY: CONCEPTS AND PHILOSOPHIES
certainty can never be objectively measured, as a rock type or an elevation change could
be perfectly measured if perfect measurement devices were available. Any assessment of
uncertainty will need to be based on some sort of model. Any model, whether statisti-
cally or physically defined, requires implicit or explicit model assumptions, data choices,
model calibrations and so on, which are necessarily subjective. A preliminary conclusion
would therefore be that there is no true uncertainty; there are only models of uncertainty.
For example, the quantity “60%” in the statement: “given the meteorological data
available, the probability of raining tomorrow is 60%” can never be verified objectively
against a reference truth, because the unique event “it rains tomorrow” either happens
or does not happen. There exists no objective measure of the quality or “goodness” of
a choice or decision made prior to knowing the result or outcome of that decision. Nor
does acquiring more observations necessarily guarantee a reduction of uncertainty. The
acquisition of additional observations may result in a drastic change of our understanding
of the system, it changes our interpretation of what we don’t know (or in hindsight, didn’t
know). It just means that our initial model of uncertainty (prior to acquiring additional
observations) wasn’t realistic enough.
3.2 Sources of Uncertainty
Various taxonomies of sources of uncertainty exist. Those sources most relevant to the
applications in this book are discussed. At the highest level one can distinguish uncer-
tainty due to process randomness and uncertainty due to limited understanding of such
processes. Consider this in more detail:
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Process randomness: due to the inherent randomness of nature, a process can behave
in an unpredictable, chaotic way. Examples are the behavior of clouds, the turbulent
flow in a pipe or the creation of a hurricane in the Atlantic Ocean. Literally the wing
flap of a butterfly (termed the butterfly effect) off the coast of West Africa can create a
major hurricane hitting the USA. Also, this type of uncertainty is particularly relevant to
studying human behavior, societal and cultural tendencies and technological surprises.
This uncertainty is less relevant to this book, where we study mostly physical processes
that are considered deterministic (such as flow in a porous medium); however, many of
the techniques described in this book could account for such uncertainty.
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Limited understanding: this source is related to the limited knowledge of the person
performing the study or modeling task in question.
Limited understanding is therefore the main focus here. In this category, many subcat-
egories can be classified. Some, as will become clear, are more relevant to the topic of
this book.
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“We roughly know”: this uncertainty refers to the so-called “measurement error”.
Pretty much every physical quantity we measure is prone to some random error. Some-
times this error is negligible compared to other sources of uncertainty; for example, we