Geography Reference
In-Depth Information
Table 2.2. Performance measures used in the comparative assessment and symbols
Value for
perfect per-
formance
How it relates to other
measures
Symbol
Name
Estimator
Meaning
X
ð
Q
i
−
Q
Þð
Q
i
−
Q
Þ
2
r²
Coefficient of
determination
(squared
correlation
coefficient)
Degree of linear
association. 1 for
perfect positive
association, 0 if no
linear correlation
1
Random error after
scaling with a linear
relationship
r
2
X
ð
Q
i
−
Q
Þ
2
X
ð
Q
i
−
Q
Þ
¼
2
X
R²
Coefficient of
determination
ð
Q
i
−
Q
i
Þ
2
1 for perfect prediction, 0
if prediction is no better
than the average of the
observed data, negative
value would be worse.
1
Composite measure of
bias and random
error
X
ð
Q
i
−
Q
Þ
R
2
¼
1
−
2
s
1
RMSNE
root mean
square
normalised
error
0 for perfect prediction,
larger for poorer
predictions.
0
Composite measure of
bias and random
error
2
n
X
Q
i
−
Q
i
RMSNE
¼
Q
i
RRMSE
relative root
mean square
error
0 for perfect prediction,
larger for poorer
predictions.
0
Composite measure of
bias and random
error
r
1
n
X
ð
Q
i
−
Q
i
Þ
2
RRMSE
¼
Q
Var
ð
NE
i
Þ¼
RMSNE
2
if prediction unbiased,
i.e.,
NE
normalised error
Difference between
prediction and
observation, scaled by
the observation. 0 for a
perfect prediction at one
location, larger or
smaller for poorer
predictions.
0
NE
i
¼
Q
i
−
Q
i
Q
i
¼
0
X
Q
i
−
Q
i
Q
i
ANE
absolute
normalised
error
Absolute difference
between prediction and
observation, scaled by
the observation. 0 for a
perfect prediction at one
location, larger for
poorer predictions.
0
Q
i
−
Q
i
Q
i
ANE
i
¼
X
NSE
Nash and
Sutcliffe
model
efficiency
1 for perfect prediction, 0
if prediction is no better
than the average of the
observed data, negative
for poorer predictions.
1
Composite measure of
bias and random
error
ð
Q
t
−
Q
t
Þ
2
X
ð
Q
t
−
Q
Þ
NSE
¼
1
−
2
Q
i
: estimated runoff signature at location i, Q
t
: estimated runoff signature at time t, Q: corresponding observed runoff, Q: average observed
runoff in time (or space).
geological processes. The interactions and feedbacks
between these components have contributed to the gen-
eration of the diversity of interesting patterns that we see
in natural catchments.
Comparing many catchments with contrasting characteris-
tics in a synoptic way, defined as
'
comparative hydrol-
ogy
, will help understand the controls of the behaviour of
catchments viewed as complex systems. The resulting idea
is to learn from the similarities and differences between
catchments in different places, and to interpret these in
terms of underlying climate
'
Hydrological response signatures are the outward
manifestation of the operation of these complex systems.
They thus provide a window into the dynamic catch-
ment behaviour at a range of time scales. They help us to
understand the catchment system holistically.
-
landscape
-
human controls.
Hydrological similarity can be defined in terms of cli-
mate, catchment characteristics or runoff signatures.
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