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Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
567
DOI: 10.4408/IJEGE.2013-06.B-54
THE HYDROLOGICAL CHARACTERISTICS OF THE VAJONT VALLEY
M
aria
r
osaria
MARGIOTTA & B
eniaMino
ONORATI
Università degli Studi della Basilicata - Scuola di Ingegneria - Potenza, Italy
century. But it was in 1948 that a modern plan was de-
veloped to integrate Vajont water resources with those
flowing in Piave river and in Boite as well as Maè
and Val Gallina creeks. In 1957, this plan was called
“Grande Vajont”, literally in English: big Vajont. The
plan was mainly aimed to hydropower purpose and it
included the design of the now well famous dam, with
a height of 266 m and a effective storage of 175 Mcm.
The entire water supply scheme was supposed to ex-
ploit once an a half times the amount of water with-
drawn by the plants of the entire upper Piave valley.
Unfortunately, due to the dramatic event, the
scheme has never been completed and operated.
Also for that, the history of Vajont dam has been
very widely discussed with respect to causes, respon-
sibility, legal conflicts, etc., related to the disaster, but
a very little has been told about the hydrological po-
tential which has not been used because of the impos-
sibility of exploiting water stored in the reservoir.
In this paper, a hydrological analysis was car-
ried out to evaluate the amount of water which
could have been used in presence of an active res-
ervoir behind the Vajont dam.
In particular, in order to understand what has
been really lost in terms of water supply, annual runoff
yields were estimated based on the theory of storage-
yield curve, and then, as a comparison, the amount of
water which can be used nowadays was analyzed by a
stochastic method proposed by (C
laps
et alii, 1996).
Hydrological data used for this study ware daily,
ABSTRACT
In this paper a study on the hydrology of Vajont
creek, in northern Italy, is presented. The Vajont creek
is dramatically known because of the disaster which
occurred in 1963, when, before the dam located on the
creek between the towns Erto and Casso started its op-
eration, a huge landslide detached from the Toc moun-
tain, falling in the reservoir during the filling stage.
Consequently, a water wave overtopped the dam. Al-
though the dam is still there, the damage caused by the
wave was so high that this disaster is remembered as
one the most dramatic in a very long time.
As just a little has been said about the hydrology
of the water resources system planned at the time of
the dam design, the volume of water, which could
have been used if the system were realized, is here
estimated by use of a storage-yield curve theory and it
is compared to the amount of water that can really be
nowadays exploited, that has been in turn estimated
by a hydrological model proposed in 1996.
INTRODUCTION
The history of the Vajont dam dates back to years
‘20s and it is dramatically known because of disas-
ter occurred on October 9
th
, 1963, at 10:39 pm, which
caused nearly 2000 deaths and derangement of entire
towns as Longarone, Erto and Casso.
Actually, waters flowing through the Vajont creek
had been used for centuries well before the dam con-
struction. Official documents are found since the 14th
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M.R. MARGIOTTA & B. ONORATI
568
International Conference Vajont 1963-2013. Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013
(or the average) of k normal variables is still normal-
ly-distributed, so that parameters of the transformed
variable (D
k
)
μ
can be derived from these of D (=D1)
using the relations:
(2)
with μ and σ as the mean and the standard devia-
tion, respectively.
In a subsequent work (r
asulo
& r
ossi
, 1984) the
additional storage required to cover within-year deficits
with the same probability of failure was determined
with reference to the probability distribution of the defi-
cit in the dry season. This part of the storage-yield curve
is significant for low and medium regulations, and is
decisive for reservoirs in semi-arid regions.
In the Mediterranean climate there is only one wet
and one dry seasons, clearly separated. This means
that in the carryover storage-yield curve it is possible
to take into account the average deficit of the dry sea-
son preceding the critical period. This deficit is noth-
ing but the quantity
(3)
where E
S
is the yield in the dry season and µ(d) is the
mean seasonal runoff. In this way,the precedent equation
is representative of the deficit of a generic dry season.
The deficit of the critical dry seasons is, on the
other hand, given by the relation
(4)
where d
s,Φ
is the minimum runoff with non-ex-
ceedance probability Φ in s consecutive months out of
the S months of the dry season, with d
s,Φ
= d,
Φ
.
Given that the irrigation yield is not constant in the
dry season, the length S of the critical season essentially
depends on the within year diagram of the draft. It is to
say, however, that volumes required for irrigation share
about the same pattern in a given climatic region, so
that the deficit season is the same in large areas.
The probability distribution of the seasonal runoff
(r
asulo
& r
ossi
, 1984; C
laps
et alii, 1998) substan-
tially coinciding with that of the annual runoff, which
is a cube-root normal, at least in the regions of South-
ern Italy. In short, the global storage-yield curve, ac-
counting for both the seasonal and the carryover ca-
pacity, is determined as
(5)
monthly, and annual flow recorded on the Vajont creek
at Erto Caldaia and at Erto Bindi, two different hydro-
metric stations very close each other, which operated
in different periods. Incidentally, it may be useful to
know that the average mean annual flow provided by
both the recorded data series, is about 2.15 m
3
s
-1
.
THE STORAGE-YIELD CURVE. THEORY
The analytical approach in storage design is based
on the derivation of the probability distribution of
storage capacity that, when the target draft is smaller
than the mean inflow (partial regulation) is equal to
the maximum accumulated deficit of the inflow partial
sums ( M
CMahon
& M
ein
, 1986). The design problem
is then essentially constituted by the derivation of the
stochastic model of the runoff process. The family of
random variables to handle in order to build carryover
storage-yield curves (r
asulo
& r
ossi
, 1980), is D
k,Φ
as
the mean annual runoff over k consecutive years with
non-exceedance probability Φ.
Once these variables are determined, the carryo-
ver storage volume required to cover deficits up to a
frequency Φ for the annual yield E is:
(1)
The period k varies from 1 and K, the latter being a
number of the order of 10. This requirement is needed
to ensure that the autocorrelation implied in the over-
lapping sequence of mean runoff in k years remains in-
significant. Limitations on K usually do not practically
affect the design, unless one gets very close to the full
regulation region of the storage-yield curve.
The storage V
C,Φ
refers to a generic sequence of
years that presents initially full reservoir, and this af-
fects with some underestimation the curve in the re-
gion of the full regulation. The probabilistic method
discussed also relies on the assumption of uncor-
related annual runoff series, which is often realistic,
particularly when considering runoff data aggregated
over the water-year. Anyhow, even in presence of au-
tocorrelation it is possible to adjust the probability
distribution so that the reproduction of the observed
minima is ensured (M
CMahon
& M
ein
, 1986).
Using the Box-Cox Normal distribution to fit D
k,Φ
allows on to derive analytically the distribution of the
k-dependent stochastic process D
k
, because the sum
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THE HYDROLOGICAL CHARACTERISTICS OF THE VAJONT VALLEY
Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
569
third was assumed as a mixing of the first two by as-
suming a fifty-fifty partition between them.
The relation E-V
s,Φ
is shown in Fig. 3 and whereas
the global storage-yield curve, as given by equation (5)
is shown in Fig. 4.
As a result we could conclude that, according to
our estimation, given that the effective storage volume
in the Vajont reservoir would have been of 175 Mm
3
,
THE STORAGE-YIELD CURVE FOR THE
VAJONT WATER SUPPLY SCHEME
The flow records registered from 1926 through
1951 on the Vajont creek, before the construction of
the dam, were used for estimation purpose.
The goodness of fit of the cube-root normal dis-
tribution to the annual runoff series is shown in Fig. 1
the normal cumulative probability distribution of D
1/3
is fitted to data in a normal plot.
Following the procedure descripted in the section
above, the global storage-yield curve for the examined
scheme was derived.
The carryover storage volume required to cover
deficits up to a frequency Φ for the annual yield E was
first derived, and the curves obtained by the use of Eq.1
were consequently calculated. They are shown in Fig.
2 for k varying from 1 through 10. In the figure, both E
and V are measured in millions of cubic meters.
In order to estimate the deficit of the critical dry
seasons it was assumed as dry the period from May to
October. Three different water uses ware considered.
In particular, one case was referred to agricultural pur-
poses, for which water demand is entirely concentrat-
ed in the dry season; another one was considered for
civil purpose, where the water consumption is taken
as homogenously distributed within the year, and the
Fig . 1 - Cube – i9root normal distribution of annual runoff
Fig. 2 - Annual Curve E-V
k,Φ
Fig. 3 - Dry Seasons Curve E-V
S,Φ
Fig. 4 - Totally STORAGE-YIELD Curve E-V
Φ
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M.R. MARGIOTTA & B. ONORATI
570
International Conference Vajont 1963-2013. Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013
with u
Φ
as the normal reduced variate.
It is acknowledged that best performances of
this procedure are obtained in semi-arid situations,
in which coefficients of variation of daily flows
are significantly greater than 1. The reason is that
for lower C
v
the mean of qrd approaches 1 for rd
slightly greater than 1, whereas relation (7) is not
upper-bounded. Nevertheless, this procedure has
been applied to the Vajont case in order to provide a
first approximation result.
In order to estimate equation (7) parameters for
the case here considered, daily flow data recorded on
the Vajont at Erto Caldaia in the periods 1941-1946
and 1948-1953 and at Erto Bindi between 1954 and
1958 were used.
Mean, standard deviation and coefficient of varia-
tion of available series are reported in Tab. 1.
With regard to return periods T= 5 and 10 years,
and consequently to Φ=1/T equal to 0.20 and 0.10 re-
spectively, qrd values have been calculated for rd rang-
ing from 0.5 to 5. They are summarized in Tab. 2.
The relations qrd-rd are also plotted in Fig. 5
and 6 for the Erto Caldaia and Erto Bindi stations,
respectively.
As an overall comment, we could point out that
if the maximum derivable discharge is of the order of
the mean annual flow, that is about 2.15 m
3
s
-1
, an an-
nual volume of about 60% of the annual runoff could
be used. Whereas, this last percentage increases to
about 70% if the design discharge is doubled. On
the other hand, no further significant advantage is
achieved even if the maximum derivable discharge
is consistently increased. Therefore, in absence of
water storage in the reservoir, the amount of water
which can be used is nearly 40-50 million of cubic
meters, much less than 350 Mm
3
, which would have
been exploited by the use of the reservoir in case of
withdrawal for civil purposes.
CONCLUSIONS
In this paper a study on the hydrology of Vajont
creek is presented. In particular, attention was given to
estimate the amount of water which has not been used
because of the fact that the reservoir ended its opera-
tion after the well known disaster occurred in 1963.
This has been done by using a storage-yield curve
the annual regulated yield would have varied from
160 Mm
3
for agricultural water supply to 320 Mcm
for a civil water use.
It is noteworthy to mention that this result deals
with flows of Vajont creek only, while in the so called
“grande Vajont” plan, the reservoir was supposed to
collect runoff from the Piave river and from the Boite,
Maè and Val Gallina creeks, so increasing significantly
the amount of water to use.
THE DIVERSION CHANNEL DESIGN
METHOD BY CLAPS ET ALII (1996)
As the Vajont dam reservoir has never been used
for water storage purposes, it is interesting to evaluate
the annual yield which can be achieved by simple wa-
ter withdrawal at its site.
To this aim, let us consider that traditional meth-
ods to select the optimal maximum discharge of a di-
version channel are based on the use of flow duration
curves, that involve a deterministic approach to the
design task. In an effort to overcome the deterministic
connotation in this approach, they suggested a specific
methodology for the selection of the design discharge
in such channels, based on the estimation of volumes
transferred annually with assigned non-exceedance
probability (C
laps
et alii, 1996).
The problem was defined in terms of the process
of the annual volumes (or average annual discharge)
Qrd transferred with a 'diversion ratio' rd , which is the
ratio between the channel design discharge Dq and the
river average discharge q.
The analysis made led to the estimation of the
quantile q
rd,Φ
=Q
rd,Φ
/q for given diversion ratio rd and
non-exceedance probability Φ, considering the time
series of 11 different rivers in southern Italy, with co-
efficient of variation C
v
of the daily data ranging be-
tween 1.1 and 6. The outcome was that at the annual
scale the variable qrd is Gaussian, regardless of the
values of rd and of the river considered.
Therefore, to obtain q
rd,Φ
from rd it was sufficient to
estimate relations between mean and variance of the dis-
tributions of qrd and rd itself. The relations found were
shown to depend uniquely on the coefficient of variation
of the daily data, as reported in the following formulas:
(6)
After minor simplifications, the relation obtained
between q
rd,Φ
and rd was
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THE HYDROLOGICAL CHARACTERISTICS OF THE VAJONT VALLEY
Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
571
The study was also devoted to estimate the an-
nual amount of water that nowadays can actually be
withdrawn. To this aim, a method proposed by C
laps
et alii (1996) was used. As a result, we demonstrated
that, in this case, no more than about 60 Mm
3
can be
exploited.
theory, which allowed us to estimate in a range be-
tween 160 and 320 Mm
3
the amount of water usable
after reservoir regulation, in the very conservative
case of a water supply scheme including the Vajont
creek only, and excluding the other creeks which
should have been connected to the reservoir.
Fig. 5 - Curves of qrd vs. rd for the Vajont river at Erto
Caldaia with different non exceedance probabilities
Fig .6 - Curves of qrd vs. rd for the Vajont river at Erto
Bindi with different non exceedance proba
bilities
REFERENCES
a
lexander
G.n. (1962) - The use of Gamma distribution in estimating regulated output from storages. Civil Engineering
Transactions, The Institution of Engineers, Australia, CE4(1): 29-34.
C
laps
p., F
iorentino
M. & s
ilvaGni
G. (1996) - Curve probabilistiche di possibilità di derivazione dei deflussi. Proc. XXV Conv.
Idraulica e Costruzioni Idrauliche, Torino, III: 95-106.
C
laps
p., F
iorentino
M. & s
ilvaGni
G. (1998) - Studio per la valorizzazione e la salvaguardia delle risorse idriche in Basilicata.
Regione Basilicata.
d
atei
C. (2003) - Vajont La storia idraulica. Libreria Internazionale Cortina, Padova. ISBN 88-7784-2385.
e
vanGelisti
G. (1964, e
ds
.) - Impianti Idroelettrici, Vol. I., II edizione, Patron, Bologna.
G
ould
B.W. (1964) - Discussion of paper by Alexander, 1962. Water Resources Use and Management. Melbourne Univ. Press.
l
vovitCh
M.i. (1972) - Hydrologic budget of continents and estimate of the balance of global fresh water resources. Soviet
Hydrology, 4: 349-360.
Tab. 1 - Statistical parameters of daily flow data series
Tab. 2 - qrd-rd values as estimated from equation (7) by daily flow data recorded at Erto Caldaia and Erto Bindi
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M.R. MARGIOTTA & B. ONORATI
572
International Conference Vajont 1963-2013. Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013
M
C
M
ahon
t.a. & M
ein
r.G.(1986) - River and Reservoir Yield. Water Resources Publication, Littleton Co.
r
asulo
G. & r
ossi
F. (1980) - Deficit analysis by extreme value theory. Proc. 3
rd
Intl.IAHR Symp. on Stochastic Hydraulics,
Tokyo, A-17-1, A-17-11.
r
asulo
G. & r
ossi
F. (1984) - Possibilità di regolazione dei deflussi con il metodo dei periodi critici. Proc. XIX Conv. di
Idraulica e Costruzioni Idrauliche, Pavia.
t
onini
M. (1956) - Bacino del Piave. Note idrologiche con particolare riguardo all’impianto idroelettrico Piave-Boite-Maè-
Vajont. L’Energia Elettrica: 773-782
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