Flood risk assessment using an integrated hydrological and hydraulic modelling approach: a case study

Journal

ELSEVIER

Journal of Hydrology 175 (1996) 533-554

Flood risk assessment using an integrated hydrological and hydraulic modelling approach: a case study V. Anselmoa,

G. Galeatib,

S. Palmieri”,

U. Rossid, E. Todinie,*

“Rural Engineering Institute, Tuscia University, Viterbo, Italy bENEL S.p.A., DSR CRIS Hydrogeological Unit, Mestre Venice, Venice, Italy ‘Physics Department, ‘Lo Sapienza’ University, Rome, Italy ‘ENEL S.p.A., Direction of Construction, Rome, Italy eInstitutefor Hydraulic Construction, University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy

Received 2 March 1995;accepted 30 March 1995

Abstract This paper describes an integrated hydrological and hydraulic modelling approach for the risk assessment of a flood-prone area and its application to analysing the effects of extreme flood events on the Montalto di Castro thermoelectric power plant. The approach is based on four major steps. The first step entails a detailed analysis of available critical events as well the collection of hydro-meteorological and cartographic data to perform a statistical evaluation of extreme rainfall events and an estimation of the probable maximum precipitation (PMP). The second step involves the calibration of a rainfall-runoff model for the upper catchment area based on the data observed during a recent flood event. The third step involves the calibration of a two-dimensional hydraulic model for simulating the flood plain inundation using the previously reconstructed runoff and a comparison of the results with the maximum flood levels observed during the same event. The fourth and final step concerns the simulation by the twodimensional hydraulic model of the flood wave obtained via the rainfall-runoff model using the extreme and PMP values of rain defined in the first step. The results of this approach appear to be extremely useful and easily transferable to other areas.

1. Introduction

The growing interest of the public in environmental issues and in the interaction between anthropogenic activity and the environment calls for a close assessment of all the issues connected with the location of new civil engineering structures, with a view * Corresponding author. 0022-1694/96/$15.000 1996 - Elsevier Science B.V. All rights reserved SSDI 0022-1694(95)02844-7

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to correctly evaluating their environmental impact and to thoroughly examining the flood risk associated with these structures. The location of thermoelectric power plants in particular demands a careful analysis of the hydrological and hydraulic characteristics of the geographical area in question: the reconstruction of critical hydro-meteorological events, the simulation of flood formation resulting from an extreme rainfall event, and the estimation of the process and scale of area1 development of flood inundation make possible an objective assessment of the safety conditions in which the plant operates, with regard both to electricity generation and to the interaction with surrounding economic and environmental activities. This paper describes the technique adopted for flood risk assessment for the Montalto di Castro site, on the Tyrrhenian coast in central Italy, where a thermoelectric plant is actually under construction (Fig. l), and where an exceptional meteorological event that affected the strip of coastline between Tuscany and Latium on 29 October 1987 caused partial flooding of the site area. To conduct a comprehensive analysis of the flood risk that would satisfy the above-mentioned requirements, the following plan of action was designed: (1) collection of hydrological and cartographic data and rainfall characterization of the site area, including the calculation of extreme rainfall and the estimation of the probable maximum precipitation (PMP); (2) detailed analysis of the event of the 29 October 1987; (3) identification and calibration, on the basis of the 29 October experimental data, of a rainfall-runoff model of the upper hydrographical catchments that caused the flood plain inundation; (4) calibration, using the data on extent and scale of flooded area collected during the same event, of a two-dimensional hydraulic model; (5) simulation of critical meteorological events with generation of the corresponding runoff by means of the hydrological model and analysis of possible resulting flood plain inundation using the hydraulic model. After a description of the site and of the methodological approach, the aforementioned points are developed below, particular attention being paid to the engineering application aspect; the theoretical development of the different models used within the frame of the proposed technique has been described by Di Giammarco et al. (1996) and Todini (1996).

2. Characteristics of the Tafone and Ponte Rotto basins The Montalto di Castro power plant is located in the catchment area of the Tafone and Ponte Rotto, rivers which originate in the hills of the Tyrrhenian hinterland and, after running along the whole of the central-upper portion of the basin in a direction virtually perpendicular to the line of the coast, then flow directly into the sea (Fig. 1). The soil is covered by woodland only in the upper reaches of the basins; the rest of the land is devoted to grazing, with large tracts given over to wheat growing in the lower areas. The land in the upper reaches has slopes with an average gradient of 40%, which drop swiftly to 15% in the middle areas and all but disappear near the sea. A short distance upstream of the Via Aurelia, the Tafone river receives the Acqua Bianca river, a left-hand tributary. The basins, at the road crossing level, have areas of

V. Anselmo et al. / Journal of Hydrology 175 (1996) 533-5.54

Fig. 1. Map of focus area with location of ENEL thermoelectric power plant.

535

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V. Anselmo et al. 1 Journal of Hydrology 175 (1996) 533-554

47.2 km* and 12.5 km* with average slopes of 8.9% and 3.4% and average heights of 175 m and 78 m above sea-level, respectively. The Ponte Rotto river drains an area with a gentler slope between the Tafone and the Fiora rivers (Fig. 1); it consists of two branches, one particularly extensive and the other symmetrical, into which the river Violetta, a right-hand tributary, feeds a short distance downstream of the Via Aurelia. The catchment areas of the two rivers are 27.6 km* and 4.1 km*, respectively. Unfortunately, no level gauging stations are available on the Tafone and Ponte Rotto catchments. After crossing the Rome-Florence railway line, the Tafone and Ponte Rotto rivers flow into a single channel (which keeps the name Tafone); at the point of the confluence the Tafone basin has an area of about 61 km* with a maximum stream length of 22.5 km, and the Ponte Rotto basin has an area of about 36 km* with a stream length of 13.2 km. Before flowing into the sea the resulting river also receives the S. Agostino and Rio Platino canals (with partial areas of about 2.1 km* and 3.3 km*, respectively), so that the total area at the mouth is approximately 102.5 km* with a maximum river length of 24.5 km. Moreover, under a hydraulic reorganization project implemented by the Organization for Development of Tuscany and Latium, the courses of the end portions of the Pian dei Cangani, Margherita and Paglieto Grande rivers, which previously ran into the Tafone immediately upstream of the sea outlet, were altered so that now the outflow of the water conveyed by the respective catchment basins flows directly into the Tyrrhenian Sea.

3. Rainfall characterization of the site area 3.1. Regional analysis of short duration rainfall As rainfall-recording stations with sufficiently extensive historical series are not available in the basins under consideration, it is not possible to determine directly extreme rainfall events of assigned risk. Moreover, as pointed out in a recent report by ICOLD (International Commission on Large Dams, 1990), extrapolation to high return periods requires long, homogeneous data series if only at-site data are utilized. To reduce the influence of local data errors and outliers, and to systematically utilize information from other sites, regional analysis has to be preferred. Accordingly, recourse was made to a regional analysis of series of annual maximum rainfall events, to assess the depth of rainfall of a given duration that may occur with a return period T; this information will constitute the input data for the subsequent calculation of maximum flood flows (Moisello, 1976; Penta et al., 1972). In this context, the approach suggested by Rossi (1980) was adopted, which is based on the assumption that the annual maximum rainfall depth h is a random variable distributed according to Gumbel’s law, an assumption verified in numerous studies on Italian basins (Penta et al., 1972; Cao, 1974; Caligione and Fiorentino, 1979; Butera and Sordo, 1988). Inverting the Gumbel distribution, and according to the notation given by Penta et al. (1980), the annual maximum rainfall h,,, of given return period T and duration

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V. Anselmo et al. / Journal of Hydrology 175 (1996) 533-554 d

is defined by the relation

h,d =

cd{ l-O+(~)]}

(1)

where & = ~/(E~Q) is expressed as a function of the Gumbel position and scale parameters 6 and ad and is linked to the average number of independent rainfall events per year, which may be taken as constant in an area of homogeneous rainfall. In fact, the area covered by the stations reveals substantial homogeneity from a climatic standpoint in that, taken as a whole, this area is affected by fronts of the same type (Anselmo, 1990). The catchments in the area are mostly arranged perpendicularly to the line of the coast and there are no divides that would justify the assumption of different meteorological conditions from one catchment to another. The rainfall value at any point can be evaluated by linking Edto the morphological factors deemed significant, such as the altitude or the distance from the sea. Lastly, Eq. (1) can be used for any given duration by altering ed as a function of duration d with a law of the type cd = adb, whose validity for Italian rainfalls has been widely verified in the cited references. For the purpose of characterizing extreme rainfall at the site, maximum annual rainfall data of 1, 3, 6, 12 and 24 h durations were collected for 18 rainfall-recording stations owned by the Italian National Servizio Idrografico e Mareografico (see Fig. 2). The list of stations used, the historical period and the number of years available, together with a variety of geographical information are shown in Table 1. The 90 series corresponding to the five different durations have been described by means of

CASlEL DEL PIANO .

s mn?A . 0

POW0

10

30km

PEROT70

ALLIJMIEUE. BRACCMNO

Fig. 2. Location of the rainfall-recording stations used for regional analysis of extreme rainfall events.

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538

Table 1 List of stations used for the regional analysis of extreme rainfall events, measurement years available and orographic features Station

Historical period

No. of years

Height (m above sea-level)

Distance from sea (km)

Alberese Bolsena Bracciano Caste1 de1 Piano Civitavecchia S. Fiora Manciano Orbetello Orte Orvieto Pitigliano P. Perotto Pomonte Pontetura S. Donato Triana Tuscania Viterbo

1937-1915 1939-1982 1933-1983 1928-1975 1958-1982 1929-1983 1955-1975 1935-1975 1934-1967 1929-1983 1928-1976 1940-1975 1952-1975 1936-1975 1946-1975 1935-1975 1939-1983 1928-1983

28 22 17 41 17 27 19 31 21 32 25 24 21 31 23 22 18 44

20 348 288 639 6 687 443 1 51 315 313 82 193 15 19 761 166 327

5 39 20 46 1 52 24 1 65 65 40 12 25 11 8 45 25 40

(l), with the parameters CQand Edestimated graphically (with the Gringorten plotting position). The fit of (1) to the experimental rainfall distributions was verified by means of the Kolmogorov-Smirnov test, which consistently gave a positive result at the 5% level. It should, however, be pointed out that the small sample size, with an average value of 27.5 years of data for each station, deprives this test of much of its power. The ki,d values were calculated for each station i and each duration d, and finally a weighted regional average value was obtained as KA = 2 nik,,le i=l

12,

(2)

t=l

where N = 18 is the number of stations and n, is the size of the ith sample. As point position ed values showed a significant dependence on altitude, prior to calculating the weighted regional average value Ed, the values for each station were related to zero sea-level by means of the expression %,O,d =

6r.d -

&Hi

where Ki is a precipitation gradient, Hi indicates the height in metres above sea-level and e,,o,dthe value 0; Edfor station i, reduced to the zero sea-level. The values of the coefficients Kd and Kd, the latter being statistically different from zero only in the case of d >, 12 h, are shown in Table 2. The regional _!?o,d zero sea-level reduced values were then calculated using weighted

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539

Table 2 Values of coefficients K& and Ki for estimating rainfall depths of duration d d=3h

d=lh

d=6h

d=

1.41 0.0126

K&

1.06

1.28

1.32

K(d’

0.00

0.00

0.00

12h

d=24h 1.49 0.0227

averages similar to (2): Eo,d =

2

5 ni

%.o.d/

i=l

(4)

i=l

These regionalized values were then used to determine the regional precipitationduration relation, which resulted in Eo,d = adb = 27.1de’215

(5)

At any pointj in the area in question, the precipitation of duration d with return period T can be estimated, once its height above sea-level has been assigned, by entering Eq. (1) with the regional & and with the ‘at-site’ E,,d, computed from the regional zero sea-level reduced value as ij,T,d

I,

(6)

Ej,d= EO,d + KdH, to give

ij,T,d= E,,,{ 1- KLh[In(~)]} 3.2. Calculation of probable maximum precipitation (PMP)

in Upper Latium

The PMP is based on the assumption that there is a physical limit to the amount of precipitation that can occur in a given area over a given period of time. The PMP can therefore be defined as the precipitation height that can be reached but not exceeded in known meteorological conditions (Taylor, 1954; World Meteorological Organisation, 1986). Although the references cited should be consulted for further details, it is sufficient here to recall that the maximization process entails the following steps: (1) by means of a retrospective study into a representative number of fronts that have affected the area under consideration, the front characterized by the maximum dynamic efficiency (relation between precipitation intensity and the air’s humidity content) is determined. It is assumed that out of a congruent number of events considered at least one will be representative of the maximum dynamic efficiency that is effectively possible. (2) On the basis of a long-term climatological investigation, a maximum possible humidity value in the area in question is derived, expressed in precipitable water units. (3) It is assumed that the PMP derives from a hypothetical meteorological front in which maximum humidity and maximum dynamic efficiency converge.

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Table 3 Values of the PMP (mm) in Upper Latium, for various areas and durations Area (km’)

25 250 500 1000

Duration (h) 2

6

12

24

180 140 117 97

270 210 176 146

360 281 234 194

490 377 318 266

To calculate the PMP, meteorological data were obtained from the Air Force Weather Authority for the decade 1967-1976 relative to continuous rainfall events characterized by precipitation depth equal to or greater than 20 mm at the Viterbo weather station (Palmieri, 1989). The application of the above process to the available data permitted the values shown in Table 3 to be estimated. From Table 3, for the example of the Tafone basin upstream of the Via Aurelia (50 km2), PMP values of 300 mm and 400 mm can be inferred for durations of 12 h and 24 h, respectively. Although the use of the PMP and the derived probable maximum flood (PMF) have recently given rise to numerous controversies (see, e.g. Dawdy and Lettenmaier (1987) or Lave et al. (1990)) its application to this specific case should be viewed from the perspective of assessing the power plant’s ability to withstand hydro-meteorological events with a probability close to zero and thus its safety under extreme meteorological conditions.

4. The flood simulation models Within the frame of the proposed approach, there is the need to apply a mathematical rainfall-runoff model, to convert precipitation into runoff which will then be used as the input to the hydraulic two-dimensional model of the flood-prone area. As is well known, a plethora of rainfall-runoffmodels exists (Todini, 1988) and therefore a choice had to be made for this study. Recent studies (Franchini and Pacciani, 1991; Todini, 1996) have shown the qualities of the ARNO rainfall-runoff model, which performs reasonably well, although needing the estimation of a limited number of parameters. The ARNO model employs a distribution function approach to runoff production and a parabolic approach to overland and channel flow routing. A full description has been given by Todini (1996). Next, to assess the effects of the extreme events in the flood-prone area where the power plant is located, a two-dimensional hydraulic model was required. The mathematical model which was implemented solves the problem of gradually varied unsteady flow in an open channel network (Cunge, 1975; Abbott, 1979) following the simplified scheme proposed by Xanthopoulos and Koutitas (1976), Hromadka et al. (1985) or DeVries et al. (1986): the use of a diffusive approximation, in which the

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541

inertial terms are ignored over the gravitational terms, friction and pressure heads, permits the salient aspects of the phenomenon under study to be reproduced with sufficient accuracy for the engineering application aspect. The numerical solution is based on the integrated finite difference scheme (Lai, 1986; Narasimhan and Witherspoon, 1976) and simulates the area of investigation as a set of flow tubes along which the water movement takes place and whose width is based on the distance between the ortho-centres of the two triangles which define each connection (Todini and Venutelli, 1991). In addition, to each node is assigned an area which acts as a storage (or discharge) basin for the water volume. A more extensive description of the mathematical derivation of the model equations and of the implemented computational method has been given by Di Giammarco et al. (1996).

5. The meteorological event of 29 October 1987

The storm event that took place on 29 October 1987 attracted a great deal of attention nation-wide as a result of the enormous damage caused by the extensive flooding of farmland and conurbations occasioned by the inability of the rivers to contain the outflow. These phenomena involved not just the basins of the Tafone and Ponte Rotto but also the river areas of the southern Fiora and Marta basins; water flowed over road embankments of the Via Aurelia, cutting traffic circulation, and eroding and damaging road structures. The rainfall event, described by means of isohyets at 6, 12 and 24 h as inferred from the rainfall recorders owned by various bodies (ENEL, 1988; Anselmo, 1990) was particularly intense on the Montalto di Castro-Bolsena Lake line, with special regard to the Ponte Rotto basin; the meteorological station installed in the ENEL power plant area recorded 324 mm in 24 h (between 07:OOh on 29 October and 07:OOh on 30 October) with a maximum hourly intensity of 55.2 mm in the late evening (between 19:00 h and 20:00 h). Furthermore, the event of 29 October was preceded by a heavy downpour on 22 October (with a maximum intensity of 3 1.4 mm in 1 h). This event, which caused minor flooding, is nevertheless important in that it presumably saturated most of the area of the two basins; thus, when the subsequent precipitation occurred on 29 October, the process of infiltration through the soil was presumably minimal and the two basins responded rapidly to the heavy storm. Less certain is the reconstruction of the evolution of the flood event, given the total absence of direct flow measurements and the low population density in the area, which severely limited the possibility of acquiring eye-witness accounts, especially during the most critical phase that occurred late in the evening. On the basis of the information gathered, it may, however, be stated that the Tafone basin was not able to ensure the outflow of water in the main channel from the early afternoon. The water probably started to run parallel to the channel from 16:30 h, and at 18:30 h the area upstream of the road embankment was extensively flooded. The flood reached its peak at 20:00-20:30 h, and began to decline after 21:00 h. In fact, at 23:00 h, transit on the Via Aurelia was once again possible. The crossing of the Via Aurelia by the water flowing in the Tafone presumably took

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place in normal conditions, in view of the absence of obstacles downstream of the bridge, where the flood overflowed into the open countryside. Traces of the flood on the piers of the bridge allow a generally reliable overall estimate to be made of maximum flood, namely 425 m3 s-l (Anselmo, 1990). Information on the development of the flood in the Ponte Rotto basin is unfortunately still too scant and uncertain, given the total lack of direct eye-witness accounts. In the absence of this information, the only feasible assumption, which is moreover warranted by the relatively contained surface extension of the overall Tafone-Ponte Rotto basin, is that the event evolved with the same time scale in the two rivers. In addition, the runoff in the Ponte Rotto basin at the Via Aurelia crossing came about virtually entirely as a result of overflowing, as, on the basis of experimental evidence and of previous flood event experiences, it is fair to consider the bridge to have been completely obstructed. Any estimation of the flood flow is consequently highly uncertain, given the di&culty in assessing with a sufficient degree of reliability the length and the average depth of the overflowing front, as well the obstruction effect posed by the road’s guard-rail. Making allowances for these factors, a maximum flow of the same order of magnitude as the one evaluated for the Tafone basin (about 420 m3 s-i), was roughly estimated, although the catchment size is much smaller in this case (Anselmo, 1990). Downstream of the Via Aurelia, the riverbeds were similarly found to be incapable of conveying the water, which created an initial reservoir upstream of the RomeGrosset0 railway line and, downstream of this, flooded the underlying reclamation area of Pian dei Cangani and extended towards the west, beyond the Margherita river. Fig. 3 shows the extent of the area flooded as evaluated by means of a field investigation conducted 1 week after the event by ENEL’s technicians (with the simultaneous measurement of the maximum water level reached at a number of specific points), and supplemented by a series of aerial photographs, dated 6 November 1987, of the Montalto di Castro area and the basins of the Tafone, Ponte Rotto, Pian dei Cangani and Margherita rivers. Further information on the way in which the flood event occurred downstream of the railway line and the development of the flooding that took place between the power plant and the line of the dunes, as well as the value of the maximum water level reached by the Tafone river close to the ENEL’s erecting yard area, were obtained directly from personnel present in the yard during the event (D. Golfi, personal communication, 1988). The previous description of the event of 29 October constituted the basic data on which the study was based. These data were used to identify and calibrate both the rainfall-runoff model for the reconstruction of the runoff and the hydraulic model for the simulation of the flood plain inundation. Lastly, a general overview of the point rainfall in the area was obtained by means of a bibliographical investigation into analyses conducted by other researchers (Batini and Gazzolo, 1963; Siniscalchi, 1966; Lotti, 1971). Of particular interest is the fact that over the period 1921- 196524 events with daily rainfall between 200 and 300 mm and nine events with daily rainfall in excess of 300 mm were detected, most of the

V. Anselmo et al. / Journal of Hydrology I75 (1996) 533-554

543

Fig. 3. Map of end portion of the Tafone and Ponte Rotto basin with assessment of the areas flooded during the 29 October 1987 event (shaded area).

centres of rainfall (seven out of nine) being less than 40 km from the coast. The event of 29 October 1987, in which 324 mm of precipitation in 24 h were measured at the ENEL power plant, does not therefore appear to be an exceptional event in the region, as the Tyrrhenian coast is subject to localized and intense cloudbursts, but may have a high return period when viewed as a point event.

6. The application of the technique to the study area Following the determination of the extreme rainfall events to be used in the flood risk assessment, the hydrological and hydraulic models were identified, calibrated and used on the area to reproduce the effects of the 29 October event. The first of these, the hydrological rainfall-runoff model, was used to reconstruct the flood wave flowing in the Tafone and Ponte Rotto rivers at the Via Aurelia crossing, the model being calibrated with the rainfall data and the estimates of the river flow rates previously described. The generated runoff represents the flow input into the two-dimensional hydraulic model which was then used to simulate the flood plain inundation downstream of the Via Aurelia. This model was calibrated by making a comparison between the extent of the flooded area as calculated and measured experimentally, as well as by comparing the maximum water levels at those points where specific information was available.

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544

6.1. Calibration of the rainfall-runoff model

The calibration of the hydrological model was carried out on the basis of the following assumptions: (1) average hourly precipitation over the Tafone basin is equal to the precipitation recorded at the Montalto power plant multiplied by a reduction factor of 0.6, a coefficient calculated to meet the volumes estimated on the basis of the 6, 12 and 24 h isohyets. (2) Average hourly precipitation over the Ponte Rotto basin is equal to the precipitation recorded at the power plant. (3) The ground is presumed to be saturated at the onset of the event. This assumption is validated by the previous rainfall event of 22 October and, in any case, its effect on the generation of the flood condition is extremely limited; the downpours that occurred between 07:OOand 11:OOh undoubtedly completed the total saturation of the soil. (4) Evapotranspiration from the soil is zero. This assumption has virtually no effect on a short duration simulation such as the one of concern here, especially in the presence of a meteorological event of considerable intensity. (5) In assessing the parameters that define the model, greater weight is given to the estimate of the flow at the river Tafone crossover point in view of its greater reliability (see the above description of the event). For this last reason, the parameters of the model describing the generation of the flood condition in the Tafone basin were calibrated first by comparing the ‘measured’ values with the calculated values. In the case of the Ponte Rotto river, the results obtained with the parameters calibrated for the Tafone basin were much less than the rough estimate of 420 m3 s-l . Therefore a small adjustment of the parameters, as one can see from the values in Table 4, was needed, which gave a maximum estimate of 373 m3 s-i; the substantial homogeneity of the area does not warrant the adoption of significantly different parameters between the two basins. As was previously noted, the estimate of peak flood in the Ponte Rotto basin is only indicative and extremely rough. On the other hand, the uncertainties in the model calibration, which is performed using only two peak values, is greatly reduced by the extremely high saturation condition of the soil, which in practice directly converts all the precipitation into runoff. Table 4 Identified parameter values for the hydrological model Basin

Tafone P. Rotto

0 0

150 150

150 150

120 120

0 0

6

D,, (mm)

&, (mm)

a W)

0.4 0.3

2.0 1.5

0.0125 0 0.0094 0

c

1.5 1.5

0 0

Base, baseflow; W,, maximum field capacity; W,, initial soil moisture; W,, drainage threshold value; WI, deep tiltration threshold; b, saturation curve exponent; D,,,, maximum drainage; D,,, minimum drainage percentage; a, percolation curve parameter; c, drainage curve exponent; Ts, snow formation threshold.

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533-554

Table 5 Hydrological model diffusivity and convectivity coefficients Basin Tafone Length (km) Channel 20 Diffusivity (m* s-‘) Slope 200 Channel 1800 Convectivity (m s-‘) Slope 3.5 Channel 3.5 Area (km*) 59.7 Height (m above sea-level) Basin 150 Section 12

1000

Ponte Rotto

10.5 200 800 2.5 2.2 31.7 60 12

100.0,

TAFONE BASIN

P ROTTO BASIN

1 _

000 i

1 ; -.o 6 .g

00.0

i

60.0-

400-

29110 TA FONE BASIN

500.0

1

2 t

30110

P ROTTO BASIN

.. 400.0-

200.0-

29/10

301

IO

(b)

Fig. 4. Event of 29 October 1987. Reconstruction of runoff and comparison with estimated peak flow values for the Tafone (a) and Ponte Rotto (b) basins.

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Tables 4 and 5 show the parameters identifying the two models, and Fig. 4 shows the reconstructed flow values at the two sections under consideration. The Tafone basin reconstruction appears very good; the flood peak is accurately estimated in terms both of extent and its timing. By contrast, the simulated maximum flood flow at the Ponte Rotto basin, amounting to 373 m3 s-‘, seems to indicate that the experimental estimate of 420 m3 s-t is slightly conservative. As pointed out above, because of the numerous uncertainties surrounding this latter value, the assumption of geomorphological continuity of the basins was adopted in preference to allowing variations in the specific Ponte Rotto area parameters. 6.2. Calibration of the two-dimensional hydraulic model The two-dimensional hydraulic model for the simulation of the flood plain inundation was created using a 1:5000 scale relief map (for the year 1976) encompassing most of the area of the Tafone and Ponte Rotto basins downstream of the Via Aurelia, supplemented in the area furthest from the power plant by a 1:25 000 scale map. Fig. 5 shows the triangular element discretization used to simulate the transport and propagation of the runoff, the most significant boundary conditions and the location of Tafone

river

Sea outlet

Fig. 5. Triangular element grid used in the two-dimensional model. Shown on the grid are the boundary conditions, the most significant geometrical elements and the points (A-F) at which measurements of the maximum level reached were available.

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541

oL--!J=J 0

0.5

1.0

1.5

2.0

2.5 (km)

3.0

3.5

4.0

4.5

5.0

Fig. 6. Event of 29 October 1987. Comparison of observed (dashed line) and computed (continuous line) flood plain area at 21:00 h.

the points at which it was possible to make a comparison between calculated and measured water levels. The boundary conditions are represented by the runoffs at the Via Aurelia crossing, by the water level at the sea outlet and by the evolution of the water overflow depth from the Tafone basin into the Margherita basin, evaluated on the basis of observed measurements (ENEL, 1988). Along all the other grid boundaries, characterized by high topographic levels, no flow conditions were set. It should be noted also that the power plant area, set at a level in excess of + 7.80 m above sea-level, was schematized by means of an impervious boundary. The direct runoff contributed by the portion of the basin downstream of the Via Amelia was ignored in that its surface extent is negligible compared with that of the Tafone and Ponte Rotto basins upstream of the road. The roughness coefficients were calibrated by a comparison with the observed measurements of the water level and extent of the flood plain, giving a Manning coefficient n of 0.080 (s rn-‘j3) over the whole area except on the river bottoms, for which the roughness coefficient was varied from 0.040 in the vicinity of the mouth (with a partially regularized bed) to 0.080 in the portion further upstream. Fig. 6 shows a comparison between the maximum flood plain inundation as measured experimentally and calculated numerically. The model is highly satisfactory, given that: (1) the differences between the maximum water levels as measured and calculated are between approximately 0.1 and 0.4 m; (2) the runoff values used as input data are obtained from a mathematical model based on runoff in the upstream

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basins and not directly measured; (3) the 1:5000 scale map (and 1:25 000 scale in part) does not allow a very reliable representation of the available storage volumes; (4) discretization always involves some degree of approximation; (5) the Manning friction coefficients estimated both for the channels and the flood plain closely agree with the physical description of the site. Moreover, the main points of discrepancy seem to be ascribable to local phenomena that do not involve the area around the power plant; for example, at the node corresponding to the input of the runoff originating in the Ponte Rotto basin the model’s response refers to a concentrated load whereas experimentally a distributed overflow along the Via Aurelia was actually observed. It should be noted also that Fig. 6 does not show any inundation over the area between the power plant and the coastline of the sand dunes where some flooding took place; flooding was here due to localized runoff conveyed by the Rio Platino and not spilled over from the Tafone river. 6.3. Flood risk assessment In a way similar to the procedure described in previous sections, the flood risk assessment for the power plant area was carried out in two successive stages. The first entailed the generation, by the previously calibrated rainfall-runoff model, of the flood waves at the Via Aurelia crossing as a result of meteorological events of particular intensity. In the second step, the simulated runoff was transported and distributed downstream of the road by means of the two-dimensional hydraulic model, using the roughness coefficients defined during calibration. 4.4. Simulation of runoff generated by particular intense meteorological events

The rainfall-runoff hydrological model was used to generate the runoff deriving from two ‘critical events’, the first based on an assessment of the extreme rainfall with a return period of 1000 years and the second based on the evaluated PMP. Even though the limited amount of historical rainfall data employed to evaluate the extreme events gives the extrapolations with a return period of T = 1000 years scant practical significance, the adoption of this return period derives from the need to generate runoff that is significantly different from the event of 29 October, the precipitation for which is comparable to that with T = 100 years. As both of the above approaches allow the quantity of precipitable rainfall to be assessed in a given time interval (e.g. 1, 3,6, 12,24 h), though without providing any indication relative to the rainfall evolution in time, it was decided to define the rainfall hyetograph by dividing the estimated quantities according to a time sequence similar to that recorded during the event of 29 October. The reasons underlying this decision are basically as follows: (1) the simulation of all the possible hyetographs over the 24 h period would have generated an enormous computational load; at the same time, scant significance from a physical point of view would have been associated with most of the simulations. (2) The 29 October event proved to be particularly important in hydrological terms,

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60.0

301 IO

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given the considerable impact that the observed rainfall distribution had on runoff production. On the other hand, this impact can easily be justified when it is noted that the event reveals a particularly intense downpour of 5-6 h duration (between 18:00 and 22:00 h), comparable with the basin’s concentration time, and it follows a precipitation (between 07:OOand 18:00 h) which, though lighter, nevertheless caused the total saturation of the soil. (3) Very similar characteristics were found in another critical event involving the coastal area of Upper Latium on 5 September 1960 (Anselmo, 1990). The recorded cumulative curve of this event reveals interesting similarities, pointing to a substantial homogeneity in the distribution over time of extreme rainfall events in the area. (4) The event of 29 October 1987 reflects fairly faithfully the evolution resulting from the meteorological investigation and adopted in the assessment of PMP, characterized by the passage of a warm front (light or moderate rainfall of prolonged duration, e.g. from 4 to 8 h), followed by the transit of a cold front (heavy rainfall of short duration, e.g. 2 h), and lastly by the influence of a cell of convective clouds in the unstable post-frontal air (heavy rainfall of short duration). The point rainfall estimates relative to T = 1000 years were further reduced, according to the method advanced by Eagleson (1970) and on the basis of Table 3, to transfer the assessment from point to area1 values, assuming for the Tafone basin an area of 60 km2 and an area of 32 km2 for the Ponte Rotto basin. It should be noted that this assessment is extremely prudent: the geographical size of the area would, in fact, permit the assumption of an average area1 precipitation calculated on the overall

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basin of approximately 92 km2, to which a higher attenuation factor would apply. In all the simulated cases it was assumed that the basin was totally saturated at 0O:OOh on the hypothetical day on which the meteorological event took place and that the volume of evapotranspiration was negligible. The simulations were therefore carried out in the most conservative situation for the purpose of the flood generation. Fig. 7 shows the hyetographs used as input data for the model and the corresponding runoff for the two basins. The reference to 29 October obviously has no specific value, but merely graph-related meaning. 6.5. Simulation of thefloodplain inundation downstream of the Via Aurelia andanalysis of possible errors

The hydraulic model was used to simulate the flood plain inundation downstream of the Via Aurelia associated with the runoff obtained in the previous section, keeping the other boundary conditions the same as those implemented in the simulation of the calibration event. The assumption of the same hydraulic load at the Margherita river is warranted by the extremely slight probability that extreme rainfall events occur simultaneously over the two basins, the Tafone and the Margherita. The vast and, on average, topographically lower area located between the Margherita basin and the sea also offers abundant possibilities for water storage; a flood of the Margherita towards the Tafone accordingly appears most improbable. In the light of this, the assumption of the overflow conditions towards the Margherita as recorded on 29 October, with the Tafone presumably in a still greater flow condition, appears a conservative supposition; a greater water height at this boundary would, in fact, ensure greater overflow towards the Margherita basin and therefore a lower storage volume in the area around the power plant. Fig. 8 shows the maximum extent of the inundation downstream of the Via Aurelia embankment as obtained on the assumption of intense precipitation with T = 1000 years and on the PMP, respectively. The area affected by the ENEL structures is prudently extended compared with the previous case, and is again treated as an impervious boundary. The maximum water level along the power plant boundary is approximately + 4.70 m above sea level in the case of rainfall with T = 1000 years and approximately + 5.00 m above sea-level in the case of the PMP. It should be noted that the power plant is located at a height equal to or greater than 7.80 m above sea-level. These estimates are obviously affected by a series of uncertainties, and hence by the possibility of unrelated errors of different kind, which may in some way influence the final result. These possible errors lie in: (1) the estimation of the extreme rainfall values (point and/or surface); (2) the representation of the rainfall-runoff process; (3) the representativeness of the equations chosen for the hydraulic model (parabolic as opposed to hyperbolic); (4) the state-space discretization of the hydraulic phenomenon. In view of the short lengths of the samples at the individual stations, the uncertainty occasioned by the estimation of the extreme rainfall values (1) is considerable, though

V. Anselmo et al, / Journal of Hydrology 175 (1996) 533-554

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V. Anselmo et al. / Journal of Hydrology 175 (1996) 533-554

limited both by the regionalization of the data and by the fact that the area1 averaging reduces the importance of these errors. The rainfall-runoff transformation estimate (2) also has some weight, although in saturated soil conditions such as those assumed the variations are of less importance. The effect of the chosen schematization (3) is negligible, in view of the modest dynamic and kinetic components in two-dimensional phenomena. The spatial discretization (4) has greater significance, as the time discretization is sufficiently fine to follow the dynamic behaviour of the event, whereas spatial discretization, based on the 15000 map, does not allow representativeness below half a metre. Nevertheless, the resulting safety margin, which is greater than 2.5 m in the worst case flood, consequent upon the PMP, combined with the extremely conservative assumptions adopted in the simulations, make these uncertainties negligible and point to the safety level of the power plant.

7. Conclusions The problem of verifying the adequacy of a civil structure and of assessing the risk of flooding is not always a simple problem. In particular, there is a substantial difference when dealing with floods in rivers or in narrow gorges, where the knowledge of the flood peak is generally sufficient for planning and design purposes, as opposed to flood-prone areas, where the estimation of both the total volume and the shape of the flood hydrograph is also essential. The approach presented in this study deals with the latter problem and tends to follow, as much as possible, a physically based representation of the hydrological phenomena involved, so as to overcome the lack of available information, a situation all too frequently encountered in practice. In particular, the use of the physically plausible ARNO model to transform the reconstructed precipitation volume into flood discharges entering the flood plain has a number of advantages over the use of classical methods such as the combination of loss functions and regionalized unit hydrographs. The parameters of the runoff production function in any rainfall-runoff model, and in particular in the ARNO model, which is based upon a dynamical storage concept (Todini, 1996) do play a limited role when the soil reaches saturation, as in the case of very large precipitation events. But still, as opposed to what happens with a mere loss function, the model is capable of better reproducing the event pattern from the dynamical interaction of the surface runoff and the drainage components. In addition, in the ARNO model, the routing is obtained by convoluting the resulting runoff with parabolic linear unit hydrographs whose parameters are essentially based upon the actual catchment characteristics (such as length of the channel, width of slopes, size of the contributing area) and values of average velocity of water which can be reasonably established within a very close range. This approach seems to the authors to be particularly suited when, as in the presented case study, very few and mostly uncertain data are available for checking the validity of the resulting discharges. The models in the suite were checked at each stage with the limited available information and this, together with the mostly physical

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interpretation of their parameters, reduced the inherent uncertainty of calibration. For this reason, all the available information was interpreted and used, such as the overall precipitation pattern, the maximum discharges entering the plain, which were estimated from the marks observed under the bridges, and the highest levels reached by water in the flood plain, determined from aerial photographs. In addition to model calibration, the assumptions on the extreme event also play an important role in the uncertainty of the resulting design levels. Without entering into discussion on the use of regional flood frequency curves or of the PMP, it seems extremely important to assume a physically meaningful shape for the rare event hyetograph, or in the absence of information, to generate a set of possible realizations. Finally, one should be aware of the size of errors made along the cascade of models: errors in the extreme precipitation events may easily be larger than 20%-30%; moreover, the time distribution may be a cause of additional errors. Equivalent or smaller errors will also be made in the rainfall-runoff transformation under soil saturation conditions. When all these errors are introduced in the flood plain model, they will be partly smoothed out, but still the time of the incoming flood peak and the succession of flows may result in additional error sources. All these sources of uncertainty will bring about final errors of an order of magnitude of 0.5-l m, which is comparable with the safety margin generally added by Italian designers to the design levels produced by hydrologists when it is important to prevent the submersion of structures, such as, for instance, in the case of levees or dykes. Lastly, as a concluding remark, the authors would like to stress again the opportunity created by the use of the two models in cascade, which permits an indirect check of the validity of calibration from all the available information and the physical interpretation of the results obtained.

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DeVries, J.D., Hromadka, T.V. and Nestlinger, A.J., 1986. Applications of a two-dimensional diffusion hydrodynamic model. Hydrosoft 86-Hydraulic Eng. Software, Proc. 2nd Int. Conf., Southampton, UK. Di Giammarco, P., Todini, E. and Lamberti, P., 1996. A conservative finite elements aproach to overland flow: the control volume finite element formulation. J. Hydrol., 175: 267-291. Eagleson, P.S., 1970. Dynamic Hydrology. McGraw-Hill, New York. ENEL S.p.A., 1988. Evento meteorologico di carattere eccezionale de1 29/10/1987 per la fascia costiera e valliva della provincia di Viterbo da1 bacino de1 fiume Fiora al Marta e Mignone. Tech. Rep., ENELCRIS Hydrol. Service, SI-859/88. Franchini, M. and Pacciani, M., 1991. Comparative analysis of several conceptual rainfall-runoff models. J. Hydrol., 122: 161-219. Hromadka, T.V., Berenbrock, C.E., Freckleton, J.R. and Guymon, G.L., 1985. A two-dimensional dambreak flood plain model. Adv. Water Resour., 8: 7-14. International Commission on Large Dams (ICOLD), 1990. The Design Flood. Guidelines. Committee on Design Flood, Paris. Lai, C., 1986. Numerical modelling of unsteady open-channel flow. Adv. Hydrosci., 14: 161-333. Lave, L.B., Resendiz-Carrillo, D. and McMichael, F.C., 1990. Safety goals for high-hazard dams: are dams too safe? Water Resour. Res., 26(7): 1383-1391. Lotti, C., 1971. Rapport0 regionale: Toscana, Marche, Umbria, Abruzzo, Molise, Lazio. Proc. National Conf. on Hydrology and the Organization of Small Basins, Rome. Moisello, U., 1976. Curve segnalatrici di possibilitl climatica e calcolo delle massime portate di piena. Publ. 38, Hydraulic Institute, University of Pavia, Pavia. Narasimhan, T.N. and Witherspoon, P.A., 1976. An integrated finite difference method for analysing fluid flow in porous media. Water Resour. Res., 12(l): 57-64. Palmieri, S., 1989. Studio sulla massima precipitazione probabile nell’Alto Lazio. Tech. Rep., ENEL-CRIS Hydrol. Service, Prot. 23605. Penta, A., Rasulo, G. and Rossi, F., 1972. Criteri di similitudine idrologica per l’analisi dei massimi annuali di pioggia. Proc. CIGR Conf., Florence. Penta, A., Rossi, F., Silvagni, G., Veltri, M. and Versace, P., 1980. Analisi regionale dei massimi annuali delle piogge giornaliere nell’Italia Meridionale. Seminar on Soil Conservation, National Research Council, Perugia. Rossi, F., 1980. Legami di connessione tra le distribuzioni di probabilita delle massime piogge e delle massime piene in una regione. Proc. Seminar: Extreme Hydrological Events: Floods and Droughts, Erice, Italy. Siniscalchi, C., 1966. Una analisi regionale delle maggiori piogge di un giomo. Acqua, 5: 34-41. Taylor, G.F., 1954. Elementary Meteorology. Prentice-Hall, Englewood Cliffs, NJ. Todini, E., 1988. Rainfall runoff modelling. Past, present and future. J. Hydrol., 100: 341-352. Todini, E., 1996. The ARNO rainfall-runoff model. J. Hydrol., 175: 339-382. Todini, E. and Venutelli, M., 1991 Overland flow: a two-dimensional modelling approach. In: D.S. Bowles and P.E. O’Connell (Editors), Recent Advances in the Modelling of Hydrological Systems, NATO-AS1 Series, Kluwer, Dordrecht. World Meteorological Organisation (WMO), 1986. Manual for Estimation of Probable Maximum Precipitation. Tech. Rep. 332, WMO, Geneva. Xanthopoulos, Th. and Koutitas, Ch., 1976. Numerical simulation of two-dimensional flood wave propagation due to dam failures. J. Hydraul. Res., 14(4): 321-331.