#
View of Ponte Vecchio in Florence before the 1966 flood.
The Arno River Flood The Arno River Flood Phenomena On the morning of November 4,1966, the residents of Study (1971-1976) Florence, Italy, awoke to find themselves the victims of a major flood. Thirty-six people were drowned in Florence, and replaceable real property damage has Lorenzo Panattoni been estimated at $640,000,000 (C. Pandolfi, personal communication, 1977). In addition, art treasures of IBM Scientific Center of Pisa, Pisa, Italy inestimable value were lost, and the cleanup operation attracted worldwide attention, sympathy, and help James R. Wallis [Judge, 1967]. As an illustration of the amount of damage caused by this catastrophic flood, we have IBM T. J. Watson Research Center, Yorktown reproduced a photograph of Ponte Vecchio (Figure 1) Heights, New York taken on the morning of November 5,1966. Engineering structures and land use zoning The Arno River in Italy intermittently inundates measures can usually be designed so as to prevent most downstream flood damages, but the protection is large areas of the Arno River basin. This paper rarely absolute and may become prohibitively expen investigates flood phenomena and evaluates sive as one designs to protect against ever larger and some of the proposals that have been made to rarer catastrophic events. For a rational evaluation of alleviate the flood hazard using procedures alternative flood control measures it is helpful to have developed at the IBM Pisa Scientific Center. an accurate flood frequency analysis that is an estimate of the probabilities of flood events of various mag nitudes. Customarily, these flood probabilities are expressed as recurrence interval Tfor floods of a given Cover The design on the cover is the new AGU logo. magnitude. To estimate Tfor a major flood, it is custom The logo is the culmination of the work of the staff art ary to consider only the highest annual flow recorded department, Dae Sung Kim, Pamela Thompson, and Ed for each year at a convenient stream-gaging station. A Pitts, supervisor. In the spirit of de gustibus non dispu- little upstream from Florence, at Nave di Rosano, there tandum, the logo was presented to the Council last is a stream-gaging station that was established in month in San Francisco, where it was not disapproved. 1920. The records are discontinuous during the war
0096-3941/79/0001/0001 $01.00
Copyright 1979 by the American Geophysical Union. years, but the instantaneous peak flow for each of 35 gaging program was initiated. Spurred by the 1966 years is known. These data were ranked and plotted on flood, the historical evidence for past major floods has Gumbel extreme value probability paper (Figure 2). The been the subject of extensive investigations [Losacco, data were fitted to a Gumbel extreme value distribution 1967; Cawna, 1969]. For the 1333 and 1557 flood using both the method of moments (line A, Figure 2) and events the water levels reached were marked on many the method of maximum likelihood (line B, Figure 2). By of the buildings of Florence. Some of these markers still the method of moments the 1966 flood is estimated at T exist (Figures 3 and 4). Villani, a prominent writer of the = 633, while the method of maximum likelihood yields T period, stated that the flood of 1333 was less than that = 3675. While Gumbel extreme value procedures are of 1269, although the damage in the city was reported commonly used in Europe, they are not favored by the to have been greater. No markers exist for the 1269 or U.S. Water Resources Council, which has recom 1171 inundation levels, but they are both believed to mended using a Pearson type III distribution with the have been at least comparable to those of 1333 and method of moments and the calculations conducted in 1557. logarithmic space [U.S. Water Resources Council, This exogenous information on the frequency of past 1976,1978]. large Arno River floods can be incorporated into the If this procedure is followed for the Nave di Rosano flood frequency analysis in the manner suggested by data, the third moment in logarithmic space is +0.1, the U.S. Water Resources Council (WRC). Their report, which leads to very high probabilities for extremely Bulletin 17A, contains additional procedural adjust large floods. As can be seen from line C in Figure 2, the ments that are recommended when it is known that a recurrence interval for the 1966 flood is estimated at T large flood in a short record has not been exceeded in a = 200 years, and several even more extreme floods longer historical period. For the Arno River it appears could be expected in a 1000-year interval, but as we certain beyond reasonable doubt that no flood since shall see, the historic information does not accord well 1 270 has exceeded the 1966 event. Using the WRC with such a supposition. procedures and assigning T = 700 for the 1966 event It is clear from the above analyses that the 1966 flood yield a negative third moment in log space (—0.1), was an extreme event, but there have been many other which assures that a maximum certain flood can be cal floods in Florence before the Nave di Rosano stream- culated from the data and that extreme events will be
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I
Fig. 1. View of Ponte Vecchio in Florence after the 1966 flood.This photograph was taken on the morning of Novem ber 5,1966. The boutiques that line both sides of the bridge were totally destroyed. Three bridges have occupied this site. The first, a Roman bridge, disappeared sometime before 1080. The second, built in 1080, withstood major floods in 1171 and 1269 and was destroyed by the flood of 1333. The present bridge was designed by Tad- deo Gaddi and completed in 1345; it has withstood major floods in 1557 as well as in 1966. CUMULATIVE PROBABILITY P
0.0I 0.2 0.6 0.8 0.9 0.99 0.995 0.999 ~i—i i i i i—i—i 1 1 1 1 1 r
Fig. 2. Plot of the available 24 years of o highest instantaneous peak flows for the Nave di Rosano Gaging Station. The graph paper is Gumbel extreme value type 1, and a ro Weibull plotting position was used. A, E Gumbel method of moments; B, Gumbel method of maximum likelihood; C, log Pear 5 son III, and D, log Pearson III 'adjusted' for O WRC historic procedures.
2 5 10 20 50 I00 200 500 I000
RECURRENCE INTERVAL T
assigned extremely low probability of occurrence (line The Arno River Basin D, Figure 2). In fact, by following the WRC Bulletin 1 7 A 2 procedures for historic floods, one is led to an The Arno River basin has an area of about 8229 km , erroneous and inconsistent estimate of T = 200,000 for with a main channel of approximately 245-km length the 1966 event. from its source on the slopes of Mount Falterona to the Tyrrhenian Sea below Pisa. Proceeding downstream, It is evident that the WRC procedures lead to either the Arno River receives several major tributaries as well ridiculously high or incredibly low estimates of the Arno as many minor ones (Figure 5). River flood hazard, and they should therefore be dis For the purpose of flood forecasting at Florence, the regarded. However, the Gumbel extreme value pro major contributors are the Sieve and Casentino regions, cedures and the historical evidence confirm that the both of which are steep mountainous regions that can flood hazard in the Arno River basin is severe and that experience heavy fall and winter rains and have shallow while floods of the 1 966 magnitude may be rare, others impermeable soils developed from calcarious marine of only slightly less severity have occurred on four sediments. In particular, the disastrous flood at occasions within the last 800 years. It was the flood of Florence on November 4,1966, was precipitated by the 1966, however, which initiated and gave impetus to the nearly contemporaneous arrival of major flood waves Arno River flood study which is to be described in the from both the Sieve and Casentino regions. The other following sections. subregions of the Arno River basin have a more rolling topography with verdant hills that are largely devoted to agriculture and gently sloping rivers that usually Overview of the Arno River Flood Study meander quietly on wide alluvial plains. To predict, control, and evaluate the Arno River flood hazard, it would be useful to have an accurate, easy to The Data Base use model of the flood phenomena. With this goal in mind a group of scientists at the IBM Scientific Center A hydrologic model is only as good as the data that of Pisa and the Istituto di Idraulica of the Universita di are available to calibrate and operate it, and for the Arno Pavia set up a joint research study that lasted 6 years River the data were far from optimal. In fact, model and took approximately 15 man-years of work. While choice was often restricted by the deficiencies in the the initial and the final goal always remained the con existing data base and by the prohibitive costs in time struction of a computer-based model of the Arno River and money associated with obtaining more and better flood phenomena, the study also included a critical machine readable data. examination of theory and experimental evaluation of The main channel from Levane (Figure 5) to the sea many numerical alternatives. Computer programs for was surveyed at intervals of —200 m in the period most of these alternative algorithms did not exist and 1952-1963 by the Ufficio Idrografico. The main chan had to be prepared, debugged, and evaluated as the nel from Levane (Figure 5) to the sea was surveyed at work Droceeded [Ciriani et a/., 1977]. intervals of —200 m in the period 1952-1963 by the Partial and intermediate results and findings of the Ufficio Idrografico deH'Arno. The availability of these study have been published in numerous journals and 900 preexisting cross sections allowed the main chan books written in both English and Italian, and a massive nel routine of the Arno model to use gradually varied three volume documentation of the whole model has nonuniform partial differential equations; the so-called been published in Italian [IBM, 1976]. This paper is an equations of Saint Venant. (Note: the mathematical attempt at an English language summary of the model; description of the model has been relegated to an much has been omitted, but it is hoped that sufficient appendix, available on microfiche, where the interested remains for the interested reader to understand the reader can obtain details about the Saint Venant equa model, its implementation, and its usefulness. tions and other matters.) There are eight continuous recording stream gages in times, the data were collected by more than one agency, the Arno River basin, three continuous stage recorders, and none of the measurements were available in and a few other staff gages that are only observed in machine readable form at the commencement of the times of high flow. Information about these gages is project. Obtaining usable weighted average storm rain contained in Table 1, and their locations are shown in falls for all the subbasins likewise proved to be a Figure 5. The records for all of these stations are dis tedious and time consuming process. continuous during the war years and also sometimes for other periods. More data are available for the postwar period than for the prewar period, and the postwar period was selected for the model calibration. The availability of data for the principal stream gages in the The Arno Model postwar period is shown in Figure 6. None of these As previously mentioned, the main channel flood rout hydrologic data were available in machine readable form at the start of the project, and preparing the data ing model is based upon the solution of a set of one- for computer processing was a major chore for the pro dimensional partial differential equations that were first ject staff. formulated by Barre de Saint Venant in 1871 and which Fifty recording rain gages were operational within the have become known as the Saint Venant equations. The Arno River basin during the postwar period (see Figure Saint Venant equations are derived from conservation 5 for locations). Not all gages were operational at all principles, the first from the conservation of mass and
Fig. 3. Plaques marking the depth of inundation for the 1333 and 1966 floods at the intersec tion of Via S. Remigio and Via dei Neri. the second from the conservation of momentum (details gave a very good approximation to the overall nonlinear are to be found in the appendix (on microfiche).1 catchment responses [Todiniand Wallis, 1977].The Various numerical solutions of the Saint Venant equa- basis for choosing between which of the two linear tidns are possible, and the these along with an explana systems to use was by reference to a threshold value tion of the calibration procedures for them are also con and the cumulative precipitation in a preceding time tained in the appendix. period (see appendix for further details). The other sub- The rainfall runoff procedures used for each con basins of the Arno River do not have stream gages near tributing subcatchment area were based upon a linear their confluences with the Arno River, and the extra systems approach. For the critical flood producing accuracy of using coupled linear systems could not be catchments, the Casentino and Sieve, and also the less justified. However, the other subbasins have historically critical Chiana, sufficient data were available to allow been of comparatively minor importance to the overall for the coupling of two parallel linear systems, which flood phenomena of the Arno River. Figure 7 is a schematic diagram of the overall model.
1 Computer Implementation of the Model Appendix is available with entire article on microfiche. Order from American Geophysical Union, 2000 Florida Avenue, N.W., Washington, D.C. 20009. Document E 79-001; $1.00. All of the computer programs for the Arno model were Payment must accompany order. written in Fortran IV and were designed to be used in an
Fig. 4. Plaques marking the depth of inundation for the 1557 and 1966 floods in Piazza di Santa Croce. interactive manner from a remote terminal. The model Tests of the Model has been extensively tested under the CP/CMS monitor system on an IBM 370-168 owned and operated by The completed model has been tested on three of the Centro Nazionale Universitario Calcolo Elettronico at larger historic floods that were not used for calibration Pisa. Some of the routines are also available in a batch of the model, the floods of 1951,1960, and 1968. The mode formulation. All the operational details needed to flows predicted by the model for three cross sections ol run the model are contained in volume 3 of the pre the Arno River, Nave di Rosano, Brucianesi, and San viously mentioned report [Cirianiera/., 1977], and the Giovanni, are shown with dotted lines in Figure 9a for necessary data to reproduce the calibration and tests of 1951, Figure 9bfor 1960, and Figure 9c for 1968. the model are given in volume 2. A simplified flowchart These predicted flood waves were made on the basis of for the main program of the Arno model is displayed in the precipitation data for the events and the previously Figure 8. calibrated model, that is, no on-line updating of model
SUBBIANO
PONTE FERROVIA 1 1
FORNACINA
NAVE DI ROSANO
BIFONICA
GAMBERAME —
BRUCIANESI 1
CASTELFIORENTINO
S. GIOVANNI
I946 I95I I956 I96I I966 I97I I976
Fig. 6. Postwar periods for which streamflow records are available. 0MBR0NE BISENZIO SIEVE
VALDARNO SUPERIORE
z I HUH
z • tttttt CASENTINO CO z UJ § si o UJ< >cn o <0 zrr I £ £ M ^ VALDARN0 SUPERIORE ERA ELSA PESA GREVE AMBRA CHI AN A
Flood routing models Rainfall-runoff models (CLS)
Based on saint With threshold Without threshold venant equations
Fig. 7. Schematic representation of the Arno model.
predictions was involved. For comparison purposes the flood events and much less good for the 1968 event. measured flood heights have been shown in the figures The channel cross-section surveys for the Arno River (when available), and it can be seen that the predicted were accumulated in the period 1952-1 963, and it is values are comparatively good for the 1951 and 1960 believed that time and the 1966 flood have caused
Table 1. Stream Gages in the Arno River Basin
Name of Station Area of Basin, km2 Beginning Year of Record Elevation Above Sea Level, m Type of R
Arno River at 738.0 1929 249.95 Mr Subbiano Chiana River at 1271.0 1926 229.80 Mr Ponte Ferrovia Sieve River at 830.6 1921 92.47 Mr Fornacina Arno River at 4082.8 1920 72.33 Mr Nave di Rosano Greve River at 124.1 1953 90.00 Mr Strette di Bifonica Bisenzio River at 150.0 1937 92.98 Mr Gamberame Arno River at 5469.0 1927 25.93 Ir Brucianesi Elsa River at 805.8 1950 46.00 Mr Castelfiorentino Arno River at 7007.00 1916 12.73 I Callone Arno River at 8181.2 1916 9.22 I Leoncini Arno River at 8186.8 1922 6.78 Mr S. Giovanni Arno River at 8212.0 1916 3.08 I Pettori Arno River at 8220.0 1916 0.02 I Politeama Arno River at 8224.7 1916 -0.06 Ir Sostegno Arno River at 8226.0 1916 0.31 Ir Cascine Nuove
Mr, continuous recording stream gage of volumes of flow, Ir, continuous recording stream gage of stage height. I, intermittent (high flow) stream gage of stage height. 5.60i
4.20 PREDICTED
2.80^ OBSERVED LU
S 1.40 -. NAVE DI R0SAN0 £ & 0 g 3 8.00
^ ^ 6.00 - /•' PREDICTED o OBSERVED
2.00 ^ CO BRUCIANESI LU o 0- o NO 7.20 - .OBSERVED 5.40 /•' PREDICTED
3.60 ./ /
SAN GIOVANNI 50 100 150 TIME (hrs) Fig. 9a. Observed and predicted flood waves for the 1951 flood event. Model pre dictions made without updating.
6.40
4.80 PREDICTED 3.20 l.6(H 0- OBSERVED NAVE DI R0SAN0 o many changes in channel geometry. New measure forecasts for later periods could be made more accur ments of the channel geometry are currently being ate by a recalibration of the roughness coefficients made, and recalibration with the newer measurements using post-1966 data for the calibration period. In should greatly increase the accuracy of subsequent essence, the roughness coefficient is a fitting para model predictions. meter that incorporates model errors as well as energy It should be noted that while waiting for these new losses, and this approach might obviate much of the cross-sectional surveys to be completed, model need for expensive resurveys of the channel. Uses of the Model Chiana-Arno confluence). For the 1966 flood event their conclusions were that the combination of both Catastrophic floods generate numerous committees dams with channel improvements to allow 3500 m3/s of and panels of experts who make plans and recommen flow within the banks would have totally prevented dations to avert similar damages in the future. The 1966 inundation in Florence. Lesser channel improvements, Arno flood has not proved an exception, and there is or the construction of only one of the dams would give now a plethora of proposals and counterproposals to lesser protection, the results being summarized in alleviate the flood hazards of the Arno River valley, It is Figure 10. By Monte Carlo simulation of numerous other not yet clear which of the many alternative proposals flood events it was determined that the frequencies of will emerge as the final choice. However, a model such possible future inundations of any given size would be as the one that has been presented in this paper can be reduced by these measures, as well as the ratios of used to help in the evaluation process. An example of inundation amounts to total flood flow. A further this type of use for the Arno model has been reported by interesting discovery of this use of the Arno model was Todiniand Buffoni [1976]. the finding that if the flood gages installed at the base of Todini and Buffoni used a simplified version of the ttie proposed reservoirs were made sufficiently large, Arno model to predict the individual and combined then the protection against inundation at Florence was effects of three proposed flood control measures. The not a function of whether the reservoirs were full or proposals which they studied were (1) channel empty at the commencement of the flood-producing improvements in the vicinity of Florence, (2) a dam on storms. This finding is important, as it appears to allow the Sieve River of 20,000 * 106 m3 capacity in the for the reservoirs to be managed for water supply, vicinity of Dicomano, and (3) a dam of 70,000 * 106 m3 recreation, or pollution abatement, without compromis capacity at Laterina (just above Levane and below the ing their flood reduction properties. 6.00 4.80 PREDICTED 3.60 2.40 CO m 1.20 o NAVE DI R0SAN0 I— 0- CJ> UJ CO CO 6.40- CO o cn o 4.80- PREDICTED 3.20- o CD I.60- BRUCIANESI 0- 6.40- /PREDICTED 4.80- 3.20- 1.60 SAN GIOVANNI 40 80 120 Fig. 9c. Observed and predicted flood waves for the 1968 flood event. Model pre dictions made without updating. IBM, Modello Matematico delle Piena dell'Arno, vol. 1, Studi e Ricerche per la Slmulazione dei Fenomeni di Formazione e Propagazione delle Onde di Piena nel Bacino dell'Arno, 210 pp., vol. 2, Dati Utilizzati per la Costruzione del Modello, 496 pp., vol. 3, Organizzazione dei Dati e Programmi di Calcolo, 79 pp., Pisa, Italy, 1976. Judge, J., Florence rises from the flood, Nat Geogr., 732(1), 1-43,1967. Losacco, U., Notizie e considerazioni sulle inondazioni d' Arno in Firenze, 140 pp., Coi tipi dell'lstituto Geografico Militare, Florence, Italy, 1967. Todini, E., and E. Buffoni; Studio su una possible difesa di Firenze dalle alluvioni mediante serbatoi, No. 6, Bollettino degli Ingegneri, Florence, Italy, 1976. Todini, E., and J. R. Wallis; Using CLS for daily or longer period rainfall modelling, in Mathematical Models for Surface Water Hydrology, edited by T. A. Ciriani, U. Maione, and J. R. Wallis, pp. 149-168, John Wiley, New York, 1977. Todini, E., and J. R. Wallis, A real time rainfall runoff model for an online flood warning system, paper pres 3 ented at the Chapman Conference on Applications of ADMISS IBLE IN BANK CHANNEL FLOW (m /s) Kalman Filters to Hydrology, Hydraulics, and Water Resources, AGU, Pittsburgh, Pa., May 1978. Fig. 10. Evaluation of proposed flood control measures for the Arno River at U. S. Water Resources Council, Guidelines for flood fre Florence with reference to the Novem quency analysis, Bull. 17, Washington, D. C, 1976. ber 4,1966, event for different admissi U.S. Water Resources Council, Guidelines for determin ble in-bank flows: (1) without reser ing flood flow frequency, Bull. 17A, Washington, D. C, voirs, (2) Sieve reservoir, (3) Arno 1978. reservoir at Laterina, and (4) both reservoirs. Lorenzo Panattoni, a native of Pisa, Italy, received his degree in physics from the University of Pisa in June Simulation models such as the Arno model are used 1968. He joined the IBM Scientific Center of Pisa in in many parts of the world for making real time forecasts 1969, where he is a researcher in the field of river modeling, with special emphasis on fluvial hydraulics. of flood events, although other techniques are likely to be superior for this purpose. An early warning flood forecasting system was not a politically or economically feasible application for the original Arno River modeling group to undertake. However, the relevant public authorities have expressed some interest in such an application, and the complete model has been made available to them. The final on-line flood forecast model when it emerges will hopefully be a highly modified ver sion of the Arno model with a Kalman filter updating capacity and telemeter to upstream sensors [Todini and IYa///s.1978]. References James R. Wallis received his B.S. from the University of New Brunswick, his M.S. from Oregon State University and his Ph.D. from the University of California at Cavina, G., Le Grandi Inondazioni dell'Arno Attraverso i Berkeley. He served as advisor for the Arno River Flood Secoli, 225 pp., Bonechi Editore, Firenze, Italy, 1969. Study Group at the IBM Scientific Center, Pisa. At pre Ciriani, T. A., U. Maione, and J. R. Wallis (Eds.), sent he is a research staff member with the IBM T. J. Mathematical Models for Surface Water Hydrology, Watson Research Center, Yorktown Heights, New York. John Wiley, New York, 1977. He is also president-elect of AGU's Hydrology Section.