Nat. Hazards Earth Syst. Sci., 9, 135–144, 2009
www.nat-hazards-earth-syst-sci.net/9/135/2009/
© Author(s) 2009. This work is distributed under
the Creative Commons Attribution 3.0 License. Natural Hazards
and Earth
System Sciences
Rainfall thresholds and flood warning: an operative case study
V. Montesarchio, F. Lombardo, and F. Napolitano
Department of Hydraulics, Highways and Roads, “Sapienza” University of Rome, 00184 Rome, Italy
Received: 4 April 2008 – Revised: 8 January 2009 – Accepted: 19 January 2009 – Published: 16 February 2009
Abstract. An operative methodology for rainfall thresholds
definition is illustrated, in order to provide at critical river
section optimal flood warnings. Threshold overcoming could
produce a critical situation in river sites exposed to alluvial
risk and trigger the prevention and emergency system alert.
The procedure for the definition of critical rainfall thresh-
old values is based both on the quantitative precipitation ob-
served and the hydrological response of the basin. Thresh-
olds values specify the precipitation amount for a given dura-
tion that generates a critical discharge in a given cross section
and are estimated by hydrological modelling for several sce-
narios (e.g.: modifying the soil moisture conditions). Some
preliminary results, in terms of reliability analysis (presence
of false alarms and missed alarms, evaluated using indica-
tors like hit rate and false alarm rate) for the case study of
Mignone River are presented.
1
Introduction
Floods analysis aims to face residual risk, due to failure of
technical systems, or due to the rare flood which exceeds
the design flood. Forecasting catastrophic events with ad-
vance allows civil protection measures to restrain the socio-
economic impact.
Naturally, the flood forecasting methods are different in
relation to the basins size and time of concentration (Rosso,
2002). If a 12 h advance warning is needed, necessarily the
forecasting methods are based on different parameters. For
large basins (>10 000 km
2
) the concentration time is higher
then 10 h and the flood forecast warning in one section can
be made on the basis of the water levels recorded in upstream
sections. For intermediate basins (400–10 000 km
2
) the con-
Correspondence to: V. Montesarchio
(valeria.montesarchio@uniroma1.it)
centration time varies between 3 and 10 h and the flood fore-
casting can be made mainly on the basis of precipitation mea-
surements, eventually integrated with forecasted precipita-
tion. For small basins (<400 km
2
), the concentration time
is smaller than 3 h, and the flood forecasting warning can be
made only on the basis of precipitation forecasts.
Warning methods work in the precipitation domain and
provide rainfall thresholds (in terms of rainfall rate, duration
and space extent) for river system critical state. Threshold
overcoming could produce a critical situation in river sites
exposed to alluvial risk and trigger the prevention and emer-
gency system alert (Georgakakos, 1995).
In this work the critical rainfall thresholds for Mignone
River cross section are defined to set a warning for critical
flood events. This paper is developed as follows: firstly, an
overview of the methodology for rainfall thresholds estima-
tion is given. Secondly, the methodology is applied to the
case study of Mignone River. Finally, rainfall thresholds re-
liability is evaluated and results are discussed.
2
Flood rainfall thresholds
Generally, rainfall thresholds identify precipitation critical
values, that could be used both in the context of landslides
and debris flow hazard forecasting (Neary et al., 1987; An-
nunziati et al., 1996; Crosta and Frattini, 2000) and in the
flood forecasting or warning (Carpenter et al., 1999; Mancini
et al., 2002; Georgakakos, 2006; Martina et al., 2006).
In the flood warning context, when critical values are over-
came, effects of flooding are expected. Rainfall thresholds
specify the precipitation amount for a given duration that
generates a critical discharge in a given cross section.
2.1
Critical cross section identification
In this study critical cross sections are identified from the
available history data and hydraulic geometry. Given the
Published by Copernicus Publications on behalf of the European Geosciences Union.
136
V. Montesarchio et al.: Rainfall thresholds: an operative case study
hydraulic geometry, critical water stage is known and critical
discharge is estimated by the stage-discharge curve (Rosso,
2002).
When the basin is ungauged, neither hydraulic geometry
or hydraulic data are known, so is more difficult to establish
which is the critical cross section and relative discharge. For
choosing the critical cross section, the first element is how-
ever the historical one, with information about past floods
events. This knowledge allows to identify hydraulic risks ar-
eas. If there are no past events recorded, it does not mean that
in the future flood events will not occur. It is also possible
that in the past flood events occurred, but there is no informa-
tion available. A way to identify hydraulic risks section is to
refer to hydraulic risks planning (i.e. in Italy “Piani di Assetto
Idrogeologico” or “Piani Stralcio di Assetto Idrogeologico”,
in which possible flooding areas are identified), often based
on a methodology that allows to identify both critical cross
sections and critical discharge (or hydraulic stage), the hy-
draulic simulation. It requires, however, to know some cross
sections of the river, to perform at least one-dimensional flow
propagation.
However, in case of no available information, the most
critical section could be identified as the outlet of the basin,
as all the upstream contributions flow in this section, arriving
from the entire drainage area.
Assuming that the critical cross section was identified, the
next step is to evaluate the critical discharge. As it has been
told, it is more difficult when stream flow data (or stage
data and stage-discharge curve) are not available, and the hy-
draulic modelling is not possible. A feasible solution is to
use regional method to evaluate the critical discharge. For
example, the flood index method (Dalrymple, 1960) could
be used. This method, based on the statistical regionaliza-
tion, allows to replace the time with the space and to use the
set of hydrometric observations of a homogeneous area to fit
the lack of discharge data in the critical cross sections.
Given a return period T relative to the critical cross sec-
tions, the peak discharge is expressed as the product of two
terms: the scale factor of the examined site (the index flood)
and the dimensionless growth factor, which has regional va-
lidity. Naturally, the index flood of the site and the growth
factor of the homogeneous region need to be estimated. In
gauged sections it is clearly possible to estimate the index
flood directly, by calculating the arithmetic mean of the avail-
able observations, in ungauged sections indirect methods
have to be used (Brath et al., 2001). Using this approach,
the rainfall thresholds is not referred to a critical discharge
value, but to different return periods discharge (i.e. 2, 5, 10,
20, 50, 100 years).
2.2
Simulation model
The methodology is based on the hydrological simulation:
the river basin closed at the critical cross section is outlined
with a rainfall/runoff model, opportunely calibrated. The in-
verse hydrologic problem is iterative solved to identify, for
given duration d, the cumulative rainfall correspondent to the
critical discharge.
When the basin is ungauged, the calibration is more dif-
ficult, because of the lack of observed data.
The litera-
ture however contains numerous studies on the possibly ap-
proaches. First of all, it can be used a model including only
physically based parameter that can be measured, with no
calibration procedures. A second possibility is to extrapolate
the parameters of the ungauged sites from those of gauged
sites, using regression analysis: in this case could be dif-
ficult to relate all model parameters with proper catchment
characteristics (Nathan and McMahon, 1990; Servat and
Dezetter, 1993; Sefton and Boorman, 1997). Then, there is
the possibility of relating the response of the catchment to its
morphologic or topologic aspects, using a geomorphologic
approach: geomorphologic IUH (GIUH) (Rodriguez-Iturbe
and Valdes, 1979) or width function based IUH (WFIUH)
(Kirkby, 1976; Mesa and Mifflin, 1986; Naden, 1992). Fi-
nally, calibration is possible using synthetic flow duration
curves generated for ungauged sites based on regional anal-
ysis methods (Yu and Yang, 2000). Thus the methodology
could be applied also at ungauged sites, in a more general
framework of regional analysis methods, with a grater ef-
fort in the model calibration phase, not based on observed
data but on opportunely obtained synthetic values. Once the
model is calibrated, the inverse hydrologic problem is solved
for different return period discharge (cfr. Sect. 2.1).
In this study a semi-distributed rainfall/runoff model is
chosen, to consider spatial variability of physical processes.
In fact, even if the threshold will be expressed in terms of
cumulative precipitation, it seems important to evaluate the
variability of response with spatial variability of input, be-
cause critical situation could be triggered by local phenom-
ena, and a semi-distributed model allows to highlight these
effects.
2.3
Rainfall thresholds evaluation
The critical reference discharge could be reached and over-
came for different space-time configurations of rain fields.
One possible simplified solution is to evaluate globally the
cumulative precipitation (P ) over the basin, after a time (d)
from the beginning of the thunderstorm. Rainfall thresholds
are generally function of the critical cross section character-
istics, but also of the boundary conditions and the rain event
type, especially:
– soil imbibition condition at the beginning of thunder-
storm;
– temporal evolution of precipitation.
To evaluate their role, the first parameter was summarised us-
ing the AMC (Antecedent Moisture Condition) (SCS, 1971,
1986) index, while the second was simply outlined using four
standards hyetotypes (cfr. Sect. 4).
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V. Montesarchio et al.: Rainfall thresholds: an operative case study
137
PAST EVENTS
YES
NO
HYDRAULIC
GEOMETRY
Model Calibration on data
FLOOD RAINFALL TRESHOLDS
EVALUATION
Lack of informations
No past events
YES
Critical stage
CRITICAL DISCHARGE
Stage-discharge curve
INVERSE HYDROLOGICAL PROBLEM
NO
Regional analysis
Flood index methods
RAINFALL-RUNOFF MODEL
Model Calibration (regional approach
based on synthetic flow duration curves)
Physically based model (no
calibration)
Geomorphological model (WFIUH)
Qc
CRITICAL DISCHARGE
Q
T
(T=2,5,10,20,50,100 yrs)
RAINFALL-RUNOFF MODEL
Fig. 1. Flood rainfall thresholds evaluation.
Mignone SS n. 1 Aurelia
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
0
10
20
30
40
50
60
70
80
Progressive
ms
l
m
H
max
=3.80 m
Fig. 2. Critical section hydraulic configuration.
Figure 1 illustrated the steps of rainfall thresholds evalua-
tion procedure.
3
The case study: Mignone River
3.1
Basin characteristics
The Mignone River begins on the Sabatini Mounts
(633 m.s.l. m) and flows into the Tirreno Sea. The river to-
tal length is 62 km. The basin surface is about 560 km
2
, the
average elevation is 233 m a.s.l. The hydraulic behaviour is
very variable, typical of a torrential regimen.
Table 1. Initial conditions: API5 (SCS, 1986).
AMC Class
5-days antecedent rainfall API5(mm)
dormant season
growing season
I dry
<
12.7
<
35.5
II average
12.7÷28.0
35.5÷53.3
III saturated
>
28.0
>
53.3
Table 2. Rain gauges events AMC (SCS, 1986) classification.
AMCI
AMCII
AMCIII
16
5
7
The soil is constituted by the 25% of vulcanites, in cor-
rispondence of the reliefs. Coming down towards valley are
present sand and conglomerates (14%), clays (9%), antropiti
(2%), but above all Flysch (41%) and alluvial deposits along
the river (9%).
3.2
Mignone River: data sets
3.2.1
Critical cross section identification
In this work the critical hydraulic cross section is identi-
fied by a preliminary historical-documentary analysis of past
flood events.
From the information available on Sistema Informativo
Catastrofi Idrogeologiche (SICI) of CNR-GNDCI website
it was found that in the last century Mignone River over-
flowed 3 times (08/11/1934, 27/12/1959, 16/11/1962) in Tar-
quinia area along the S.S. Aurelia. In first approximation,
it has been considered the overflowed fluvial cross sections
coinciding with the monitored cross sections “S.S. Aurelia”
(drainage area 440 km
2
), therefore identified as critical cross
section. Given cross section geometry (Fig. 2) and stage-
discharge curve used by authorities, the critical reference dis-
charge, Qc was identified to be equal to 131.0 m
3
/s.
3.2.2
Hydrometric and pluviometric data
Hydrometric and pluviometric data (from 1999 to 2007) were
used both in rainfall/runoff model calibration and validation
and in reliability rainfall thresholds evaluation. To take in
account soil initial imbibition conditions, given the complex
time-space dynamics, a synthetic index, related to antecedent
precipitation (Table 1), was chosen. In Table 2 the events are
classified in the 3 AMC classes of Soil Conservation Ser-
vice (USDA, 1971, 1986): type I, dry soil; type II, average
conditions and type III saturated soil. In Table 3 are reported
date and peak discharge of the floods events interesting the
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Nat. Hazards Earth Syst. Sci., 9, 135–144, 2009 
138
V. Montesarchio et al.: Rainfall thresholds: an operative case study
Table 3. Flood events in Mignone River Basins.
date
Q
p
(m
3
/s)
15–20/04/1999
135.41
14–17/12/1999
69.57
31/03–02/04/2000
103.06
09–13/04/2000
422.09
28/01–01/02/2001
207.36
11–14/12/2002
160.33
05–08/01/2003
179.38
26–29/11/2003
235.17
04–08/05/2004
101.04
04–07/12/2004
498.03
25–31/12/2004
530.89
18–21/01/2005
88.24
02–06/03/2005
367.75
08–11/09/2005
63.96
05–07/11/2005
233.21
25–28/11/2005
333.66
02–05/12/2005
217.43
05–07/12/2005
210.72
08–11/12/2005
260.18
01–04/01/2006
68.18
19–24/02/2006
518.54
05–08/03/2006
399.52
15–18/03/2006
490.69
16–19/09/2006
110.81
20–23/10/2006
78.55
08–10/12/2006
171.69
08–11/02/2007
144.98
24–27/03/2007
248.63
Mignone River Basin from 1999 to 2007, for which pluvio-
metric data are available.
3.2.3
Radar data
The Polar 55C is located 15 km south-east of Rome,
in the Tor Vergata research area (lat. 41
◦
50 24 N,
lon. 12
◦
38 50 E, 102 m above sea level). Polar 55C is a C-
band (5.5 GHz, λ=5.4 cm). Doppler weather radar with po-
larization ability and with a 0.9
◦
beamwidth. The radar has
the capability to transmit and receive horizontally and verti-
cally polarized signals on alternate pulses, allowing not only
the measurement of the widely used horizontally reflectivity
factor (Zh), but also the differential reflectivity (Zdr) and the
differential phase shift ( dp). Radar measurements are ob-
tained by averaging 64 pulses with a range-bin resolution of
75 m, covering an area with a radius up to 120 km from the
radar site. The temporal resolution is five minutes.
To remove spurious returns from the data, a polarimetry-
based ground clutter removal algorithm was applied (Lom-
bardo et al., 2006).
Fig. 3. Study area and radar position.
Table 4. Radar events AMC (SCS, 1986) classification.
AMCI
AMCII
AMCIII
6
3
2
In order to convert the radar data into rainfall rates, was
used an algorithm based on a Z-R relation. For C-band by
means of a non-linear regression analysis, the following Z-R
relation was obtained (Russo et al., 2005):
R=
7.27×10
−
2
Z
0.62
h
(1)
where Z
h
is the reflectivity factor [mm
6
·
mm
−
3
] and R is
rainfall intensity [mm·h
−
1
].
After a transformation from Polar to Cartesian coordi-
nates, a regular grid (2 km×2 km) over the basin was built
(Fig. 3). From each time interval rain intensity values for
each pixel were obtained intensity and then total cumulative
rainfall Radar rainfall temporal resolution is 30 min.
Radar measurements are classified in AMC classes in Ta-
ble 4. It is to be underlined that the radar data not coincide
with the floods events summarized in Table 3. In fact, as
it is shown in Table 5, only the November 2003 events is
covered by both radar and raingauges. Other radar measure-
ments were taken in not flood periods.
3.3
Simulation model
A preliminary estimation of main hydrological parame-
ters was derived from the DEM, using the program HEC-
GeoHMS (HEC, 2003a). The obtained values have been used
as first attempt values in the calibration of rainfall/runoff
models implemented in program HEC-HMS (HEC, 2003b),
used in this work for modelling rainfall/runoff transforma-
tion.
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V. Montesarchio et al.: Rainfall thresholds: an operative case study
139
Table 5. Radar measurement intervals.
Measurement interval
Q
p
(m
3
/s)
22/10/2003
6.25.34
23/10/2003
7.31.34
0.25
26/11/2003
6.56.02
27/11/2003
18.46.46
235.17
26/02/2004
10.35.53
27/02/2004
7.00.53
30.01
01/03/2004
8.08.04
01/03/2004
15.20.53
55.43
11/03/2004
8.50.57
11/03/2004
16.40.54
14.73
24/03/2004
12.57.59
25/03/2004
14.30.34
7.16
07/05/2004
8.07.59
07/05/2004
16.36.34
37.69
12/05/2004
5.42.59
12/05/2004
16.41.35
5.71
14/05/2004
8.16.34
14/05/2004
18.16.35
3.28
05/08/2004
8.55.55
05/08/2004
17.31.35
0.09
The basin area was subdivided in two subbasins (Fig. 4):
the first closed to Rota and the second closed to the critical
cross section; for both subbasins, for rainfall/runoff transfor-
mation was used the modified Clark model (Kull and Feld-
man, 1998; Peters and Easton, 1996), that allows using a
semi-distributed approach and considering explicitly physi-
cal processes space variability. For hydrological losses was
used a gridded SCS-CN model (SCS, 1971, 1986), while for
flood wave propagation was used the Lag model (Pilgrim and
Cordery, 1993).
The Meteorologic model was a gridded precipitation, dis-
tributed from rain gauges data with isohyetes method every
30 min.
The hydrologic model calibration and verification are per-
formed for the following flood events:
– AMCI class: calibration event 05/11/2005,
control event 10/12/2006;
– AMCII class: calibration events 22/02/2006,
30/01/2001, control event 25/03/2007;
– AMCIII class: calibration events 04/12/2005,
06/12/2005, control event 10/12/2005.
In Fig. 5 calibration and validation of hydrologic model for
AMCIII class are shown. To evaluate model performance,
two indicators were considered (Table 6).
The Root Mean Squared Error (RMSE, Eq. 1) mea-
sures the overall agreement between observed and modelled
events. It has non-negative value and no upper bound. If the
model were perfect, RMSE would be zero.
RMSE=
n
i=
1
Q
i
− ˆ
Q
i
2
n
(2)
In Eq. (1), Q
i
and ˆ
Q
i
are the observed and the modelled
values at time i, with n total number of time intervals. Gen-
erally, for high flows this index can provide good measure of
model performance (Karunanithi et al., 1994)
Fig. 4. Mignone model in HMS.
Table 6. Hydrological model performance.
RMSE
CE
AMCI
calibration event (05/11/2005)
35.90
0.51
control event (10/12/2006)
31.50
0.31
AMCII
calibration event (22/02/2006)
61.70
0.78
calibration event (30/01/2001)
39.46
0.00
control event (25/03/2007)
28.87
0.66
AMCIII
calibration event (04/12/2005)
33.11
0.59
calibration event (06/12/2005)
23.51
0.84
control event (10/12/2005)
15.29
0.96
The other indicator used is the Coefficient of Efficiency
(CE; Nash and Sutcliff, 1970, Eq. 2), that is proportional to
variance of observed data. CE can range between minus in-
finity and one, which represents a perfect model. If CE is
zero, there is no difference between using the mean of ob-
served data or simulated values. If CE is negative, the mean
of observed data is better then the model.
CE=
1−
n
i=
1
Q
i
− ˆ
Q
i
n
i=
1
Q
i
−
Q
(3)
In Eq. (1), Q
i
and ˆ
Q
i
are the observed and the modelled
values at time i, with n total number of time intervals, and Q
is the mean of observed data.
The Table 6 shows that the model with best performance is
the AMCIII condition model. In fact, RMSE and mainly CE
tends to optimal values for control events. For AMCII condi-
tion model, the performance varies between the calibrations
events, for which there are a good CE but a bad RMSE, or a
good RMSE and a zero CE . Anyway, for the control event
the model shows an overall good performance. For AMCI
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140
V. Montesarchio et al.: Rainfall thresholds: an operative case study
S.S. Aurelia
Calibration
0.0
50.0
100.0
150.0
200.0
250.0
300.0
05/12/2005 10.30
06/12/2005 10.30
07/12/2005 10.30
date
Q(
m
3
/s
)
0.0
2.0
4.0
6.0
8.0
10.0
12.0
h(
m
m
)
Qobserved
Qsimulated
S.S. Aurelia
Validation
0.0
50.0
100.0
150.0
200.0
250.0
300.0
08/12/2005 15.30
09/12/2005 15.30
10/12/2005 15.30
date
Q(
m
3
/s
)
0.0
2.0
4.0
6.0
8.0
10.0
12.0
h
(
mm)
Qobserved
Qsimulated
Fig. 5. Calibration and control of class AMC III hydrologic model for the Mignone River basin on the base of the observed hydrographs at
“S.S. Aurelia” gauge station in December 2005.
Table 7. Hydrologic parameters values.
AMCI Class
Subbasin
Subbasin
S.S. Aurelia
Rota
Initial Abstraction Ratio
0.2
0.2
Potential Retention Scale Factor
0.35
0.35
Time of Concentration (h)
6.59
5.21
Storage Coefficient (h)
5.54
3.01
Lag (min)
312
–
AMCII Class
Subbasin
Subbasin
S.S. Aurelia
Rota
Initial Abstraction Ratio
0.10
0.20
Potential Retention Scale Factor
0.30
0.23
Time of Concentration (h)
6.09
6.11
Storage Coefficient (h)
4.72
2.14
Lag (min)
276
–
AMCIII Class
Subbasin
Subbasin
S.S. Aurelia
Rota
Initial Abstraction Ratio
1
1
Potential Retention Scale Factor
0.10
0.30
Time of Concentration (h)
4.65
3.84
Storage Coefficient (h)
3.94
3.50
Lag (min)
275
–
condition model there is the worst performance, mainly for
the low CE values.
In Table 7 are summarized all the numerical values of the
model parameters.
3.4
Rainfall thresholds evaluation
The inverse hydrologic problem was solved to identify the
rainfall fields configuration that implies the critical discharge
value overcoming. Several scenarios were simulated, analyz-
ing basin response to 4 hyetotypes (Rosso, 2002):
Hyeto_1
15
20
25
30
35
3
6
9
12
15
18
21
24
d(h)
AMCI
AMCII
AMCIII
AMCII
15.0
20.0
25.0
30.0
35.0
3
6
9
12
15
18
21
24
d(h)
h
cum
(
mm)
hyeto_1
hyeto_3
hyeto_2
hyeto_4
Fig. 6. Rainfall thresholds for different hyetotype, fixing class AMC
II, and for different AMC classes for the step hyetograph (Hyeto
1). In ordinate the cumulative rainfall amount (in millimeter), in
abscissa the duration (in hours).
– step hyetograph (Hyeto 1);
– triangular increasing rate hyetograph (Hyeto 2);
– triangular decreasing rate hyetograph (Hyeto 3);
– isosceles triangular hyetograph (Hyeto 4).
Given hyetotype, rain duration d and initial soil imbibition
condition based on AMC index, it was investigated the crit-
ical cumulative rainfall depth. Indipendent simulations were
performed for all the combination of duration (3, 6, 12 and
24 h), hyetotypes and AMC classes. The rainfall thresholds
are iterative identified, by trial and error until the critical dis-
charge value was reached. In Fig. 6 are shown AMC II rain-
fall thresholds for different hyetotypes and step hyetograph
rainfall thresholds for different AMC classes.
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V. Montesarchio et al.: Rainfall thresholds: an operative case study
141
Event-Hyetotypes
0
10
20
30
40
50
60
70
80
90
100
0
10
20
30
40
50
60
70
80
90
100
d/d
tot
(% )
h
cu
m
/h
cu
m
t
o
t
(%
)
Observation
10/12/2005
Hyeto_1
Hyeto_2
Hyeto_3
Hyeto_4
Fig. 7. Association to hyetotype: in ordinate % cumulative rainfall,
in abscissa % duration. Event 10/12/2005.
4
Preliminary results: reliability evaluation
In this work the reliable thresholds were tested following
these steps:
– identification of significative duration d
∗
and associa-
tion of observed pluviometric events with a standard
hyetotype;
– reliability evaluation in terms of right, false and missed
alarms.
Preliminary it was necessary to establish some criteria for de-
termining the beginning of actual runoff (d
∗
, from when cu-
mulative rainfall amounts were calculated) and for dividing
precipitation events. Two parameters have been fixed (Rosso,
2002):
– significant rain: value of cumulative rainfall, discrimi-
nating between state of rain and of not-rain, identified
with initial infiltration of the loss model;
– system relaxation time: time of concentration of the
river basin closed to the critical cross section.
To identify the reference hyetotype, given the irregularity of
real hyetographs, a “likelihood” approach is used. The hyeto-
type was estimated considering a differences minimization.
An example is shown in Fig. 7, for the event observed on
10/12/2005.
To estimate the rain thresholds reliability is necessary to
investigate on the presence of any missed alarms or false
alarms. It is defined:
– missing alarm (MA): the flood event exceeds the criti-
cal reference discharge in the critical cross section, but
the recorded precipitation does not exceed the rainfall
threshold.
– false alarm (FA): the rainfall threshold is overcame, but
the observed discharge is lower than critical reference
discharge.
Table 8. Two-by-two contingency table.
Forecasts
Observations
Warning W
No Warning W
Total
Event E
h
m
e
Non Event E
f
c
e
Total
w
w
n
Obviously presence of FA and above all of MA invalidate
rainfall thresholds reliability as warning tool. A possible way
to assess the performance of the proposed method is using a
two-by-two contingence table, as illustrated in Table 8. The
table is structured as follows: the n observations are divided
in Event E (critical discharge overcame) and Non Event E
(critical discharge not overcame). If an event occurred and
a warning was issued the outcome is an hit (with h the total
number of hits); if an event did not occur but a warning was
issued the outcome is a false alarm, (with f the total number
of false alarms); if an event occurred but warning was not
issued the outcome is a missed alarm, (with m the total num-
ber of misses); if an event did not occur and a warning was
not issued the outcome is a correct rejection, (with c the total
number if correct rejections). The total number of warning is
w
, of no warning w , the total number of event e and of non
event e .
The performance can be evaluated in terms of hit rate and
false alarm rate, defined as follows:
hit rate=
h
h+m
=
h
e
(4)
false alarm rate=
f
f +c
=
f
e
(5)
The threshold based forecasting system has a good perfor-
mance if the hit-rate exceeds the false-alarm rate.
4.1
Reliability evaluation performed on pluviometric data
In Figs. 7 and 8 show the steps for reliability evaluation for
the 10/12/2005 event. At first (Fig. 7) the actual hyetograph
was associated with the standard hyetotype by differences
minimization; the best adaptation was with triangular de-
creasing rate hydrograph (Hyeto 3). The event belongs to
AMCIII class, so the reference threshold is AMCIII-Hyeto
3, that is overcame (Fig. 8. left graph) after 5.5 h from the
beginning of significative rain. In the right graph (Fig. 8) is
shown the observed hydrograph, with the instant of threshold
and critical discharge overcoming. The lead time is 3.5 h.
The two-by-two contingency table is shown in Table 9. The
corresponding hit and false alarm rate are:
www.nat-hazards-earth-syst-sci.net/9/135/2009/
Nat. Hazards Earth Syst. Sci., 9, 135–144, 2009 
142
V. Montesarchio et al.: Rainfall thresholds: an operative case study
Reference Threshold
10
15
20
25
30
35
40
0
3
6
9
12
15
18
21
24
27
d(h)
h
cu
m
(m
m)
AMCIII-Hyeto3
threshold overcoming
Lead time
0.0
50.0
100.0
150.0
200.0
250.0
300.0
08/12/2005 15.30
09/12/2005 15.30
10/12/2005 15.30
date
Q(
m
3
/s
)
0.0
1.0
2.0
3.0
4.0
5.0
hc
um
(
m
m
)
threshold overcoming
9/12/2005 6.00
Qc overcoming
9/12/2005 9.30
3.5 h
Reference Threshold
10
15
20
25
30
35
40
0
3
6
9
12
15
18
21
24
27
d(h)
h
cu
m
(m
m)
AMCIII-Hyeto3
threshold overcoming
Lead time
0.0
50.0
100.0
150.0
200.0
250.0
300.0
08/12/2005 15.30
09/12/2005 15.30
10/12/2005 15.30
date
Q(
m
3
/s
)
0.0
1.0
2.0
3.0
4.0
5.0
hc
um
(
m
m
)
threshold overcoming
9/12/2005 6.00
Qc overcoming
9/12/2005 9.30
3.5 h
Fig. 8. Example of rainfall thresholds reliability evaluation.
Table 9. Rain gauges events: two-by-two contingency table.
Forecasts
Observations
Warning W
No Warning W
Total
Event E
19
1
20
Non Event E
6
2
8
Total
25
3
28
– hit rate=0.95
– false alarm rate=0.75
The mean lead time, when a warning is correctly issued, is
8.5 h, that allows to alert the emergency system. On the ba-
sis of this results, for pluviometric data the threshold based
forecasting system seems to have a good performance. On
the other hand, the false alarm rate is quite high. False alarm
were issued when there were long period of rain, but low in-
tensity. So there was the time for the basin to drain the runoff
without high peak discharge, even if the cumulated rainfall
overcame the reference threshold. Therefore, the false alarm
rate seems to depend from the infiltration dynamic, and it
would be probably lower identifying differently the signifi-
cant rain.
To sum up, the described threshold based forecasting sys-
tem using rain gauges data works well when the rain event is
short and intense, and gives problems in terms of false alarm
with long low intensity events.
4.2
Reliability evaluation performed on radar data
From radar data only the November 2003 event was criti-
cal for Mignone River (Fig. 9), for which a warning based
on calculated thresholds is obtained. The lead time is more
than 24 h. For the same event, also using rain gauges data
the warning is correctly issued, even if the lead time is only
of 8 h. It seems that using radar data, the warning system
November 2003
0.00
3.00
6.00
9.00
12.00
15.00
18.00
26/11 0.00
27/11 0.00
28/11 0.00
29/11 0.00
30/11 0.00
h(
m
m
)
0.00
50.00
100.00
150.00
200.00
250.00
300.00
Q(
m
3
/s
)
rain gauges
radar
Qobserved
26/11/03
6.56.02
27/11/03
18.46.46
Radar measurement interval
Fig. 9. November 2003: rain gauges and radar data.
works better, but to completely evaluate the performance also
the presence of false alarms was investigated, and results are
summarised in the two-by-two contingency table (Table 10).
The corresponding hit and false alarm rate are:
– hit rate=1
– false alarm rate=0.10
The results highlight a very good performance, but it is lim-
ited by the characteristics of the available data set. In fact,
as illustrated in par. 3.2.3, radar measurements were gen-
erally not taken during flood events, and the rainfall depth
estimated from radar reflectivity was generally very low, cor-
responding to ordinary discharge value for critical section.
Moreover, the presence of the false alarm seems due to an
overestimated rainfall depth from radar data, and this proba-
bly explain also the long lead time obtained. In conclusion,
the threshold based forecasting system gives encouraging re-
sults using radar measurements, but it is need to test the per-
formance on a more consistent radar data set.
4.3
Advantages of flood rainfall threshold approach
When the hydrologic model is calibrated, it is possible to per-
form directly rainfall-runoff simulation with observed data,
Nat. Hazards Earth Syst. Sci., 9, 135–144, 2009 www.nat-hazards-earth-syst-sci.net/9/135/2009/
V. Montesarchio et al.: Rainfall thresholds: an operative case study
143
Table 10. Radar events: two-by-two contingency table.
Forecasts
Observations
Warning W
No Warning W
Total
Event E
1
0
1
Non Event E
1
9
10
Total
2
8
11
0.0
1.0
2.0
3.0
4.0
5.0
0.0
50.0
100.0
150.0
200.0
250.0
300.0
hcum(
m
m)
Q(
m
3
/s
)
date
Threshold approach vs. Hydrologic simulation
threshold overcoming
9/12/2005 6.00
Qc overcoming
9/12/2005 9.30
3.5 h
simulated flow
Qc overcoming
in simulation:
no leading time
10/12/2008 15:30
09/12/2008 15:30
08/12/2008 15:30
Fig. 10. Comparison between threshold approach and simulation
model.
instead of comparing observed value with reference thresh-
olds. Nevertheless, the rainfall threshold approach is more
convenient in term of leading time. In fact, using observed
precipitation for forcing rainfall runoff model can reproduce
the actual situation, but not in advance: the critical discharge
is simulated in the same time it is actually reached, so hy-
drological simulation can not be used as forecasting system
(Fig. 10).
A possibility of using calibrated hydrologic model for
forecasting could be to force the model with forecasted
precipitation, for different leading time, in on-line mode.
Clearly, the uncertainty about the performance of the model
raises by increasing the leading time and there is the need
to refresh the model when new observed data are available.
Thus using the calibrated hydrologic model in off-line mode
as in the rainfall thresholds approach seems to be more useful
in a practical warning framework.
5
Conclusions
This work shown an operative case study of a rainfall thresh-
olds definition methodology. Threshold overcoming triggers
the prevention and emergency system alert. Thresholds were
identified by simulation from rain gauges data and then their
reliability was performed on both rainfall recorded data and
radar data. Using rain gauges data the thresholds hit-rate is
95%, using radar data is 100%. It follows that for Mignone
River basin flood warning based on rainfall thresholds seems
to be an effective and immediate tool. However, it must
be underlined that thresholds reliability was tested on few
events, especially for radar data and further validation are re-
quired.
Acknowledgements. The authors would like to thank Ufficio Idro-
grafico e Mareografico of Lazio Region for providing hydrometric
and pluviometric data, and Institute of Atmospheric Sciences
and Climate of the National Research Council for providing
radar data. The research has been partially supported by CNR-
GNDCI. In addition, authors would like to thank the reviewers
for their useful comments, which helped to improve the manuscript.
Edited by: G. Roth
Reviewed by: S. Manfreda and another anonymous referee
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