il modello mg per la stima delle portate di piena per elevati tempi di ritorno
TRANSCRIPT
-
8/3/2019 Il modello MG per la stima delle portate di piena per elevati tempi di ritorno
1/21
A PROBABILISTIC MODEL
FOR FLOOD FREQUENCY ANALYSIS
BASED ON A LARGE SPACE
EARTH: OUR CHANGING PLANET
U. Majone
DIIAR Polytechnic of Milan
M. TomirottiDICATA University of Brescia
G. Galimberti
Studio Maione Ingegneri Associati
-
8/3/2019 Il modello MG per la stima delle portate di piena per elevati tempi di ritorno
2/21
Introduction
The estimation of peak discharges to be assumed for flood
protection planning is usually performed on the basis of return
periods much longer with respect to the historical series that are
usually available.
For instance, in Italy the above mentioned return periods range
Another typical example is the design of dam spillways, that in
Italy but also in other countries is usually performed on the basis
of a 1000 year return period flood.
To make more significant the estimates of high return period
quantiles of peak flows and also to handle the case of ungauged
sites, regional estimation methods are commonly used.
-
8/3/2019 Il modello MG per la stima delle portate di piena per elevati tempi di ritorno
3/21
The hydrological data (1)
Geographical distribution of the gauged sites considered in the analysis
State Continent Stations Aver. size CVmin CVavr CVmax
Italy Europe 249 36 0.23 0.62 1.81Switzerland Europe 143 45 0.11 0.36 0.79
Austria Europe 83 34 0.19 0.79 1.91
Portugal Europe 63 35 0.25 0.77 1.53
. . .
Others Europe 101 56 0.14 0.49 1.49
USA North America 6326 40 0.12 0.78 5.14
Canada North America 674 29 0.11 0.44 1.67
Australia Oceania 227 28 0.22 1.08 5.33
Others South America 14 30 0.17 0.33 0.55Others Asia 42 36 0.16 0.64 1.55
Others Africa 24 46 0.19 1.12 1.61
ALL 8551 38 0.08 0.71 5.33
-
8/3/2019 Il modello MG per la stima delle portate di piena per elevati tempi di ritorno
4/21
-
8/3/2019 Il modello MG per la stima delle portate di piena per elevati tempi di ritorno
5/21
The MG model (1)
Scattering ofQmax/ data in (CV(Q), Q/)
plane and interpolating functions
33.161.31 CV
Q+=
33.1Q=
For the new probabilistic
model the followingexpression is assumed:
.
,133.033.1
CVQ
CVQY
==
It follows that a standardized
variable can be introduced:
whose probability distribution
is constant for all sites.
-
8/3/2019 Il modello MG per la stima delle portate di piena per elevati tempi di ritorno
6/21
The MG model (2)
33.1
1
CV
QY
=
the following equation is
obtained for Q / quantiles:
TY ln80.037.0 +=
From the definition of the
standardized variable
Frequency distribution of the Y values
and interpolating function
.)ln80.037.0(133.1
CVTQ
++=
The above equation yields
the analytical expression ofthe MG model, that can be
applied for return periods
ranging from 30-50 years up
to about 4000 years.
-
8/3/2019 Il modello MG per la stima delle portate di piena per elevati tempi di ritorno
7/21
The MG model (3)
Scattering ofQmax/data for
different geographical areas
and interpolating curves
Empirical frequency
distributions of the
standardized variables
-
8/3/2019 Il modello MG per la stima delle portate di piena per elevati tempi di ritorno
8/21
The MG model (4)
Empirical frequency distributions of Q/ for different values of
CV and Q/ quantiles deriving from the MG model and from
other probability distributions
-
8/3/2019 Il modello MG per la stima delle portate di piena per elevati tempi di ritorno
9/21
The MG model (5)
Empirical frequency distributions of Q/ for different values of
CV and Q/ quantiles deriving from the MG model and from
other probability distributions
-
8/3/2019 Il modello MG per la stima delle portate di piena per elevati tempi di ritorno
10/21
Some remarks about the estimation of design flood (1)
The values
Maximum observedvalue of the
standardized variable:
9
133.1 =
YCV
Q
Frequency distribution of the Yvalues
and interpolating function
define the upper bound Qbof flood discharge beyond
which the statistical
estimates loose their
significance.
or
.
+=
)91(33.1
CVQ +=
-
8/3/2019 Il modello MG per la stima delle portate di piena per elevati tempi di ritorno
11/21
Some remarks about the estimation of design flood (2)
Q/ quantiles deriving from the MG model and Qb curve in (CV(Q),
Q/) plane
-
8/3/2019 Il modello MG per la stima delle portate di piena per elevati tempi di ritorno
12/21
Some remarks about the estimation of design flood (3)
Variability of the ratios Qb/QTwith respect to CV(Q)
1.6
1.7
1.8
1.9
2
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2CV(Q)
1
1.1
1.2
1.3
1.4
1.5Q
b/Q
T
T=200 yearsT=500 years
T=1000 years
-
8/3/2019 Il modello MG per la stima delle portate di piena per elevati tempi di ritorno
13/21
Some remarks about the estimation of design flood (4)
1.5
1.6
1.7
1.8
1.9
2
Qb
/QT
Supposing for instance that
CV=1 for the selected river
site, it turns out:
Qb/Q1000=1.45.
Since the discharge equation
of the spillway is
proportional to h3/2, it
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2CV(Q)
1
1.1
1.2
1.3
1.4
T=200 years
T=500 years
T=1000 years
follows that hb/h1000=1.28.
h
Definition of design freeboard
-
8/3/2019 Il modello MG per la stima delle portate di piena per elevati tempi di ritorno
14/21
Conclusions (1)
The calibration of the MG model is based on the definition of a
dimensionless standardized variable Ywhose probability distribution
can be assumed constant for all the considered sites.
The MG model, obtained by interpolation of the empirical nonexceedance frequencies of the maximum observed values ofYgives the
probability distribution of peak discharges for 30-50
-
8/3/2019 Il modello MG per la stima delle portate di piena per elevati tempi di ritorno
15/21
Conclusions (2)
The value Y=9 is the absolute maximum of the empirical values of
the standardized variable. The corresponding peak discharges can
be assumed both to define the predictability bound of flood events
and to estimate the design peak discharges in cases of particularly
high risk levels (e. g. in the presence of nuclear sites).
The application of the MG model requires the estimation of the
maximum peak discharge. The major difficulties arise in the lattercase, due to the limited length of the historical series that are usually
available.
The most part of the data were obtained from digital archivesfurnished by hydrological services and from free internet sites. It is
hoped that the increasing availability and accessibility of these kinds
of data will promote their use for the formulation of reliable
estimation models of flood flows.
-
8/3/2019 Il modello MG per la stima delle portate di piena per elevati tempi di ritorno
16/21
-
8/3/2019 Il modello MG per la stima delle portate di piena per elevati tempi di ritorno
17/21
Regional estimation ofCV(Q) (1)
Scattering of the sample values ofCVversus catchment areas
-
8/3/2019 Il modello MG per la stima delle portate di piena per elevati tempi di ritorno
18/21
Regional estimation ofCV(Q) (2)
Comparison between local and regional estimates of CV for some
regions of the Italian territory
-
8/3/2019 Il modello MG per la stima delle portate di piena per elevati tempi di ritorno
19/21
Some remarks about the MG model (1)
Scattering ofQmax/ data in (CV(Q), Q/)
plane and interpolating functions
The distribution function
of the maximum
33.1
max, 1
j
jj
CV
Q
Y
=
Yis the annual maximum ofthe standardized variable and
is the maximum of the series
aN
YYyPyP )()( =)
aNY yF
yT/1 )(1
1)(
=
is provided by theapproximate expression
Na=38 is the average size
of the historical series
Return period T(y) in years
-
8/3/2019 Il modello MG per la stima delle portate di piena per elevati tempi di ritorno
20/21
Some remarks about the MG model (2)
Relation between sample values
ofCV(Q) and (Q)
Behaviour ofQ/quantiles
furnished by GEV distribution in
(CV(Q), Q/) plane (T=200 years)
-
8/3/2019 Il modello MG per la stima delle portate di piena per elevati tempi di ritorno
21/21
Scattering of three different
random samples ofQmax/
data and interpolating curves
Empirical frequency
distributions of the
standardized variables
Some remarks about the MG model (3)
8
10
Y=0.37+0.80lnT
OsservatoEmpirical
15
20
Q/=1+3.65CV1.33
OsservatoEmpirical
1+3.61CV1.33
1 10 100 1000 10000
T(anni)
0
2
4
6
Y
n erpo a o
T(years)0 0.5 1 1.5 2 2.5 3 3.5 4
CV(Q)
0
5
10Q/
1
nterpo aton erpo a e