Geology Reference
In-Depth Information
higher than that of the real system. One can
find discussions of hydrological model
identi
ability from the late 1980s [
12
,
40
] in the hydrological literature.
ning modeling uncertainty as a function of the model properties above
(particularly model sensitivity and modeling error), it is important to investigate the
relationship between modeling uncertainty and model complexity.
De
2.6 Index of Model Utility (U)
This topic adopts an index of model utility to make a decision about which is the
'
model for any hydrological modeling exercise. The adopted
approach is a somewhat modi
best and right
'
ed version of Snowling and Kramer [
68
] for suit-
ability in data-based modeling. Statistically, the proposed
'
index of model utility
'
of
a model can be de
ned as a scaled distance from the origin on a graph of sensitivity
versus modeling error of different models to the point corresponding to that model
in the graph. Mathematically it can be written as
s
K
s
S
i
þ
K
e
E
i
U
i
¼
1
ð
2
:
6
Þ
ð
K
s
þ
K
e
Þ
where
U
i
is the utility index for model I,
S
i
is the sensitivity value for model i (relative to the maximum
sensitivity), in this study the value obtained from the mean value of
slope of all sensitivity curves obtained from all inputs,
E
i
is the error value for model i (relative to the maximum error; in this
study we have adopted root mean squared error as the indicator of
model error), and
K
s
and K
e
are weighting constants for sensitivity and error, respectively.
The value of U varies between 0 and 1 and if the value of U is larger, the model
has higher utility. The values of S and E for each model should be normalized to
satisfy the equation, which is the reason for dividing all values by the maximum
sensitivity and error value. The values of K
s
and K
e
depend on how the model
values error and sensitivity. If error and sensitivity are valued equally, then K
s
and
K
e
should both be set to 1. In this study, both values were set to 1. In this topic, the
model utility indexes (U) were calculated for the three case studies and are illus-
trated in Chaps.
5
several statistical models, considering their complexity and sensitivity in hydrologic
prediction in a simpler way. Further research can be accomplished by considering
varying proportions of K
s
and K
e
values.
-
