Geology Reference
In-Depth Information
2.5 Data-Based Modeling
Complexity, Uncertainty,
—
and Sensitivity
Two major modeling themes focusing on modeling errors are upward or mecha-
nistic approaches (associated issues are overparameterization, equi
nality) and
downward or data-driven approaches (associated issue is lack of a priori de
ned
model structure) with different complexities [
78
]. Are more complex models better?
Should the increasing complexity of the existing model add any bene
t to the
model users? These issues are not properly addressed in hydrology and data-based
modeling although in abundance in the many competing arti
cial intelligence
models in the literature. These questions can be answered by tackling the com-
plexity of a model
'
is structure and the uncertainty associated with its output. It is
often dif
cult in hydrology to decide which model should be used for a particular
purpose, and the decision is often made on the basis of familiarity rather than the
appropriateness and effectiveness of the model. Another major concern is overpa-
rameterization of the model to represent an uncertain process over limited and noisy
data. Comparing different models just in terms of their better accuracy in predicting
numerical values is often ludicrous; there are many other aspects which need to be
taken into account before declaring one model a success with entirely different
mathematical concepts over the other. The best model is not necessarily the most
complex, or the one which overtly re
ects the most sophisticated understanding of
the system [
11
]. There is a hypothesis that more complex models simulate the
processes better but with high variability in sensitivity and relatively less error [
68
].
However, a study by Oreskes et al. [
55
] argues that there is no strong evidence that
simple models are more likely to produce more accurate results than complex ones.
Case studies in this topic use a simple index of utility which evaluates in terms of
model complexity (we used training time as the indicator of complexity), model
sensitivity (response to changes in input), and model error (closeness of simulation
to measurement). Perrin et al. [
57
] performed an extensive comparative perfor-
mance assessment of the structures of 19 daily lumped models, carried out on 429
catchments, and suggested that the main reason why complex models lack stability
is that the structure, i.e., the way components are organized, is not suited to
extracting information available in hydrological time series. Complex models in
their study face considerable dif
culties in parameter estimation and structure
validation. Gregory et al. [
27
] have applied Akaike
s information criterion (AIC)
[
7
] and Bayes information criterion (BIC) (Schwartz [
63
] model selection model
complexity problems in rainfall time series modeling, and similar approaches were
applied in groundwater modeling [
42
]. Cherkassky and Mulier [
21
] have developed
structural risk minimization (SRM) as an alternative model complexity control
method. Schoups et al. [
62
] used the above-mentioned three models. We compare
three model complexity control methods for hydrologic prediction. Information
theory could be selected as the central framework to evaluate information content in
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