Geography Reference
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Figure 5.16. Homogeneous regions
and estimated growth curves for
annual runoff in north-western Italy.
(a) Result of cluster analysis in the
space of catchment characteristics
(H
m
: average catchment elevation
(m a.s.l.); Y
bar
: longitude of the
centre of mass of the basin (deg)),
where H is the homogeneity measure
of Hosking and Wallis (
1997
); (b)
catchment groups in the geographic
space; (c) Pearson type III growth
curves associated to the four regions
(F: non-exceedance probability); and
(d) allocation rule for ungauged
catchments in the space of catchment
characteristics (
(a)
(b)
1
2
4
Region 2
H = 1.91
Region 1
46.0
H = 1.90
45.5
45.0
Region 4
H = -0.19
44.5
Region 3
H = 0.49
1000
1500
2000
2500
H
m
47.0
0.999
Region 2
a
2
= 10.60
46.4
are the
parameters of the Pearson type III
distribution). Adapted from Viglione
(
2007a
).
α
,
β
and
ξ
b
2
= 8.508. 10
-2
Region 1
0.95
x
2
= 9.843. 10
-2
a
2
= 4.764
b
2
= 9.543·10
-2
x
2
= 0.5458
0.75
45.8
0.25
45.2
Region 4
Region 3
a
2
= 5.817
b
2
= 0.1237
x
2
= 0.2801
0.05
a
2
= 3.107
44.6
b
2
= 0.2093
x
2
= 0.3496
0.001
44.0
0.5
1.0
1.5
2.0 2.5 3.0
100
680
1260
1840
2420
3000
Q
/
Q
A
H
m
is based on the hypothesis that while the mean annual
runoff may vary between different sites within a statistic-
ally homogeneous distribution, the remainder of the
probability distribution is identical. The regionalisation of
the mean annual runoff is usually performed with one of
the statistical methods addressed in
Section 5.3.1
, while
pooling of data in homogeneous regions is used to estimate
the regional growth curves (i.e., probability distributions
rescaled by the mean). Vogel and Wilson (
1996
) present
some applications related to the USA, while in Italy some
previous works can be traced back to Ferraresi et al.(
1988
)
and Claps and Mancino (
2002
).
A case study of regional frequency analysis is pro-
vided by the study of Viglione (
2007a
), who performed
an index flow regional frequency analysis in north-
western Italy. The mean annual runoff was obtained
throughregression(see
Figure 5.12
), and the between-
year variability of the annual runoff divided by the
mean was considered fixed in homogeneous regions
obtained through cluster analysis.
Figure 5.16a
shows
the results of the cluster analysis (Ward algorithm and
reallocation) in the space of the similarity indices, in
this case the mean catchment elevation and the latitude
of the centre of mass of the catchment. These two
attributes have the following hydrological interpretation:
mean elevation is a surrogate for temperature and sea-
sonality of snow processes; while latitude in the study
area correlates to the climatic gradient from the drier
south to the rainiest part of the region in the north.
These two catchment attributes are related to slope and
shape of the growth curve (Ganora et al.,
2009
). The
number of clusters was selected using a homogeneity
test (Hosking and Wallis,
1997
), and the homogeneous
regions are shown graphically in
Figure 5.16b
.
Figure
5.16c
showstheestimatedgrowthcurvesforthefour
regions. The Pearson type III distribution was used to
model the growth curves.
Figure 5.16d
shows how
ungauged catchments in the region were allocated to
the groups. The parameters of the Pearson type III
distribution to be used as growth curves of the ungauged
catchment were chosen by selecting the appropriate
region based on its mean elevation and latitude. Regions
1 and 4 present the largest difference in the shape of the
growth curves and are at the extremes in the attributes
space. Region 1, corresponding to the Valle d
Aosta
region in the north-west, is characterised by very high
elevation and a cold-alpine climate. The between-year
variability of annual runoff was less pronounced than in
other parts of the study area, and in particular than in
Region 4, located in the south and characterised by low
elevation and a temperate climate. This higher runoff
variability is attributed to higher mean annual evapor-
ation and a more non-linear relationship between pre-
cipitation and runoff.
'
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