Safety of Italian dams in the face of ﬂood hazard

Abstract Most rivers in Italy are segmented by dams that need rehabilitation because of (1) safety requirements by increasingly risk-averse societies, (2) changes in the downstream river and riparian system after dams building, (3) poor initial design at the time of completion and (4) modified priorities of watershed management. Safe design of flood spillways is a major concern, and requires to cope with low frequency flood hazard. One must estimate flood figures with high return periods ( R  ⩾ 1000–10,000 years) but statistical methods involve large uncertainties because of the short length of the available records. This paper investigates the return period of the design flood of existing spillways R S of large dams in Italy. We used re-normalized flood frequency approach and regionalization using the Generalized Extreme Value distribution. The estimation of the site specific index flood is carried out by simple scaling with basin area at the regional level. The result show that 55% (245) of the 448 examined dams are equipped by spillway with R S  > 10,000; and 71% (315) of the dams have R S  > 1000. Conversely, 29% (130) of the dams display R S R S


Introduction
Dams have segmented most rivers with associated environmental impacts, sometimes disruptions.The interspacing of dammed, inundated, preserved and restored reaches has fragmented large watersheds by disconnecting once integrated free-flowing systems (e.g.[1]), and river impounding is often blamed for jeopardizing biodiversity downstream [2][3][4].However, dams provided support to economic and social development worldwide, and a large number of dams under construction and planned is a matter of significance in the world today.The safe operation of dams has significant social, economic, and environmental relevance, and appropriate management procedures are necessary (e.g.[5,6]).Dams will continue to provide valuable services, but rehabilitation is needed because of (1) the new hydrological safety requirements posed by increasingly risk-averse societies, (2) the changes in the downstream river and riparian system after the dam were built, and (3) the modified priorities of watershed management.
A large number of dams was built in Italy during the XX century under different engineering, social, economic, and possibly climate conditions from those nowadays.As a consequence large uncertainties affect the policies for mitigation of flood hazard in regulated rivers.Uncertainties descend from the complexity of both physical and man-controlled processes, including scale problems in observation and modeling, management strategies and operational practice.Additional uncertainty is given by the lack of knowledge of the effects of dams on floods downstream, let alone the unexplored evolution of social perception of flood risk after dams were built and operated for a long time.Lack of knowledge of worldwide dam accidents is a further factor of uncertainty, in spite of the role of incident reporting and data collection in enhancing reservoir safety [7].
Berga [8] reported that dam failures had been significantly reduced in the XX century.The percentage of failures before 1950 was 2.3%, while for dams constructed from 1951 to 1982 it reduced to 0.2%, and since 1982 it was 0.09%.Major advances are associated with ameliorated structural safety, but hydrological safety of dams, and safe design of flood spillways are also major concerns, and hydrologists worldwide continuously investigate new methods to approach spillway design under uncertainty (e.g.[9,10]).The Committee on Failures and Accidents to Large Dams [11] of USCOLD estimated that overtopping covered more than 40% of dam failures worldwide.Charles et al. [12] showed that most of the failures of embankment dams causing loss of life can be attributed to the embankment breaching due to either of two causes, namely: (1) overtopping during an extreme flood, and (2) internal erosion due to piping or hydraulic fracture.Study of overtopping is largely within the province of hydrology, and so is design flood assessment for the provision of appropriate spillway and freeboard, and guidelines emphasize the importance of design flood as a key factor to dam safety [13,14].For instance, in the United States, over 2000 dams (3% of the 75,000 US dams) were identified as potential hazards to people living in upstream or downstream areas, due to inadequate spillway capacity [15].The International Commission on Large Dams [16] suggested that the return period R of the spillway design flood should range from 1000 to 10,000 years, depending upon exposition and vulnerability of downstream riparian areas (e.g.[17], for a comparative study of regulatory frameworks for dam safety worldwide).One notes that the length of the available hydrological series (typically R 6 50-100 years), is too short for any site specific flood estimation based on local data, if available.
The American Society of Civil Engineers [18] reports that the average age of the 84000 dams in the country is 52 years.Many of these dams were built as low-hazard dams protecting undeveloped agricultural land.However, with an increasing population and greater development downstream, the overall number of high-hazard dams continues to increase, to nearly 14,000 in 2012.The number of deficient dams is estimated at more than 4000, which includes 2000 high-hazard dams.The Association of State Dam Safety Officials estimates that it will require an investment of $21 billion to repair these aging, yet critical, high-hazard dams.
In Italy there are 548 large dams, i.e. those displaying dam height higher than 15 m, or impounded storage larger than 10 6 m 3 (e.g.[19], and Fig. 1).Design and building records are available for 488 dams only, 83% of which (403 dams) were built before 1970, and roughly 41% (198 dams) before 1950.About 63% (332 dams) are concrete dams (arch, gravity, or both) and 31% (165 dams) are earth dams.Spillway design flood q S was generally evaluated using empirical formulas based on stream flow records available at the time of dam completion, without any probabilistic argument to support hydrologic hazard and dam safety.Governmental surveillance of dams was enforced after 1925, after a major dam's failure occurred at the Gleno reservoir, on December 1st 1923, causing at least 353 deaths.However, a national authority was established in 1989 only, called SND and further RID.It operated for about 20 years before being discontinued, and its mission included generic infrastructure management, with unclear liabilities by the National and Regional Administrations.RID recommended the rehabilitation of dam spillways in order to accommodate the 1000 years flood, regardless of dam's type.
To assess the capability of the existing dam spillways to accommodate the 1000 years flood one has to face large uncertainties.The assessment of low frequency flood flows is cumbersome in Italy, because the average length of Annual Flood Series (i.e. the largest observed annual peak flow, henceforth referred to as AFS) is about 28 years [20].After 1970, systematic stream flow records decreased countrywide, because of lacking responsiveness by both governmental and local agencies.Also, a few dam sites, if any, are equipped to measure hydrological flows continuously, so site specific data of (long term) dam operation are unavailable in practice.Notwithstanding so, one needs to achieve a first, approximate but comprehensive assessment of flood hazard in Italian large dams, hopefully before some catastrophic event will focus the social perception of risk.The estimation of low frequency flood figures plays an essential role in assessing current and future hazard.This paper provides an answer to this question using the regional approach to low frequency estimation of flood flows.

Flood frequency estimation and safety of dams in Italy
2.1.Regional approach Statistical prediction of floods with low frequency has been a major task of hydrology insofar (e.g.[21,22]).Manifold methods are available to predict flood frequency in poorly gauged basins, but large uncertainties still remain for floods with high return periods, e.g.larger than 100 years.Application of regional methods provides the state-of-the-art approach, also supported by scaling arguments [23].Extreme value theories (e.g.[24], for a comprehensive review) provide the mathematical core.The index flood method provides the operational framework [25][26][27][28].This is a two-step procedure.The first step is the identification of homogeneous regions, where a common extreme value probability distribution can be adopted to accommodate renormalized flow figures.Homogeneity of a region can be assessed using different criteria [23,29,30,31].In a homogenous region one can assume that the renormalized variable, say X, has the same frequency distribution, F X (x), for all river sites in the region, and the R-year flood can be estimated as q R = q i x R , where x R denotes the R-years quantile of X, and q i the renormalization parameter, i.e. the index flood, which is usually taken as the expected value or the median of the probability distribution of maximum annual flood.The regional cumulative distribution function F X (x) of X, henceforth referred to as cdf, is known as the growth curve, and it is generally understood to reduce uncertainty for increasing return period as compared with estimates achievable by fitting the cdf to single site data [32][33][34].If insufficient or no stream flow data are available, the regional flood frequency curve provides more accurate estimates than that achievable by deriving the cdf from precipitation and other climate statistics [20].
The estimation of index flood, q i , is the second step.The approach mainly depends on data availability, and the methods range from statistical regression of flood data versus catchment parameters and/or precipitation and other climate statistics [35], to conceptualization of rainfall runoff processes [36], and high resolution watershed modeling using a spatially distributed framework [37].
Data availability is the major concern.If local flood data are available, one can either use the observed AFS to get a direct statistical estimate of the mean or the median, or explore the observed Partial Duration (PDS) series, or the Peaks Over a Threshold (POT) series, to improve accuracy of estimation [32,38,39].PDS approach requires, a preliminary, not trivial, threshold estimation to assess statistical independence of peaks [40].When few or no stream flow data are available, the index flood may be estimated via rainfall-runoff simulation, using of either observed precipitation data [41][42][43], or generated data through stochastic simulation methods [44][45][46][47].These methods may provide accurate results, but involve time consuming data handling and processing, and 'business-as-usual' application is not straightforward.Alternatively, index flood value can be estimated by way of derived distribution approach based upon expected storm scaling [48,49], multiple regression and other regional empirical formulas, historical flood marks, paleohydrology or fluvial geomorphology of bank-full discharge figures [50].However, all these methods require site specific investigations, so application to large scale assessment is cumbersome.A straightforward method to achieve a countrywide assessment is power law scaling of floods against drainage area, based upon the finding that maximum annual flood peaks within homogeneous regions display statistical scale invariance as parameterized by drainage areas, A [51,52].

Regional flood assessment in Italy
Italy stretches for more than 1000 km from North to South, and displays tremendous relief from the coast to mountainous inland.Climate regimes of Italy range from Mediterranean hot, to continental with cold Winter and hot Summers, to Alpine with seasonal snow cover and permanent glaciers and permafrost (e.g.[53]).Hydrologic regime and flood generation processes strongly vary in space and time, so flood prediction must account for these factors.Also, most flood series are relatively short (about 28 years on average), so introducing large uncertainties in floods estimates with low frequency.A countrywide assessment of flood frequency figures was provided starting more than twenty years ago by the National research Council of Italy (henceforth referred to as CNR) after the completion of the National Flood Estimation Project (henceforth referred to as VAPI).The final report is a collection of regional reports delivered by major research institutions in this research area (see [54], where one retrieves the list of individual regional reports).VAPI project identified 23 homogeneous regions countrywide (see Fig. 2) and two different cdfs were adopted to accommodate F X (x) to regional observations.The General Exteme Value distribution (henceforth referred to as GEV) was selected to accomodate the variability of growth curve in North-Western Italy.Elsewhere, the two component estreme value (TCEV) cdf [55][56][57][58] was used based on the conjecture that floods are generated from two different mechanisms, or precipitation patterns, i.e. frontal and convective [59].
Bocchiola et al. [60] further tested the performance of GEV, TCEV, three parameters Log-Normal (Gibrat-Galton) and Generalized Logistic to accomodate renormalized regional flood data in these 23 regions.Statistical analysis using state-of-the-art hypothesis testing procedures showed that GEV predictions provide the most accurate estimates in most cases, and that these estimates display the lowest variance of estimation for regional samples.Therefore, they provided GEV estimates of renormalized maximum annual flood countrywide, and these estimates were suggested by RID based on parsimoniousness and reliability arguments.The GEV cdf is used here to represent renormalized regional flood, X, in Italy in order to estimate regional quantiles, x R .Regional power law scaling is then used to estimate index flood at each dam site.
The estimated index flood is then combined with the regional growth curve to assess the expected return period of spillway design capacity, q S .We further investigated the role of drainage area in determining the potential hazard, in order to assess safety of major dams.This helps in assessing the need of rehabilitation, also indicating the route towards ameliorated dam operation and river management.

Dam safety in Italy
In Italy governmental surveillance of dams was enforced after the Gleno dam failure in 1923.After three major accidents in year 1935 (Molare dam, more than 100 deaths), in year 1963 (Vajont dam, about 2,500 deaths) and in year 1985 (Stava reservoir, 268 deaths) the surveillance procedures by the national authorities were progressively enforced.Several accidents with minor or no losses of human lives occurred after year 1985, the last of which at Montedoglio dam in Central Italy, on December 2010.This dam was initiated in year 1978, and then completed in 1990, so it is a rather recent facility as compared with the average age of Italian dams.
Spillway capacity q S could be evaluated for 445 dams out of 584, based on the design reports and the periodical surveys made available by former RID.One notes that spillway facilities are complex structures in most cases, because they involve both open and submerged weirs, operating in parallel under both automatic and manually operated modes.In most cases, physical scale models were built at the time of dam construction or after its completion, to test the effective capability of the spillway system.

Regional growth curves GEV
We exploited the available data sets from the CNR VAPI reports for the 23 homogenous regions of Italy (Fig. 1(b)) to build normalized flood frequency quantiles using the GEV distribution, as with e, a, k, denoting the regional GEV position, scale and shape parameters, respectively, and y R = Àln[ln(R/(R À The definition of homogeneous regions flood wise was carried out in Italy based upon a TCEV distribution, and hierarchical approach [57] except for regions 2(a)-(c) in Fig. 1.Thus, we assumed that statistical homogeneity in a hierarchical TCEV analysis may translate into statistical homogeneity into a non-hierarchical GEV application, which is not proven as yet for Italy.However, hierarchical approach to regional flood assessment can be pursued successfully also when using GEV distribution [58], so there is no a priori limitation in this sense.Notice that the focus here is not to either discuss the potential drawbacks and limitation of the present regional framework of VAPI, or to develop a new regionalization method, which would require effort way beyond this paper, and building of credible motivation against use to the present one, but to use the presently available method to provide an assessment of dams' safety for Italy.As reported SND and RID enforced retrofitting of flood spillways with R S = 1000 years, based upon the VAPI regions, so use of such template seems warranted.According to a recent study from the authors, regionally estimated GEV distribution would provide better estimation of flood quantiles (within the same regions, and based upon the same pooled flood data), while providing a mathematically simpler way for quantile calculation, than the iterative approach required by TCEV.Also, using GEV, one may assess confidence limits for R years quantile [33], not available for TCEV that we know of.Given such purely data driven evidence, GEV distribution is tentatively used here.For each catchment within each homogenous region, we calculated index flood q i , as the average of the AFS series of maximum yearly flood, q.Then, the yearly maximum floods in each site were made dimensionless with respect to q i to obtain a growth factor, as x = q/q i .
For each region, all the growth factors x values in the pertaining catchments were pooled into one single sample, so obtaining 23 pooled samples (one for each homogeneous region).This sample, supposedly homogeneous, was used to estimate the regional GEV distribution of the (dimensionless) growth factors x R , using L-moments approach [61].To assess distribution fitting of the so obtained GEV distribution a number of statistical tests were then carried out (namely Pearson or v 2 , Anderson-Darling AD, Kolmogorov-Smirnov KS, and confidence limits for GEV quantiles CL [33]).

Regional index flood estimation
Flood flow records are not available at dam sites, usable to estimate the index flood based on site specific observations.A straightforward method is to apply the concept of scale invariance with basin area within a homogenous region, as introduced, among others by Gupta et al. [51], Robinson and Sivapalan [52] and Bocchiola et al. [28].Power laws of flood quantiles against drainage area stem from the (self-similar) structure of channel networks, climate and soil properties, and scaling theory gives reason of the physical implications of floods formation in streams [62,63].Scale invariance against area A in each homogeneous region was estimated here using q i at each dam site within the region as where m is a scaling exponent and q i (1) is the index flood associated to the unit area, both calculated by a multiple regression of the logarithmic transformed sample mean, Log (q i ), versus the logarithmic transformed values of drainage area Log (A), within a homogeneous region.Here, we assessed q i (1) and m by way of jack-knife linear regression.Although scale invariance usually holds over a limited range of scales (or areas), to be determined from observed data [23], scaling with catchment area is sometimes assumed as a reasonable working assumption over a wide range of scales for ruleof-thumb estimation [64].The estimation variance of q i depends upon the properties of the homogeneous region and can be assessed by the determination coefficient D of the regression.One has r 2 qi ¼ r 2 qi;s ð1 À D 2 Þ, where r 2 qi;s denotes the variance of the observed sample of q i in the homogeneous region, estimated from the observed data.
Eventually, to evaluate the return period associated with the spillways design discharge q S of a specific dam site j with known drainage area A j we carried out a three steps procedure, namely (i) estimate local index flood according to Eq. ( 2), (ii) associate an estimated growth factor corresponding to local spillways design discharge q Sj , and (iii) invert Eq. ( 1) as a function of that growth factor, to assess the frequency of exceedance of q Sj , as We then estimated the return period R S of the saturated capacity of the spillway as

Results
Tables 1 and 2 report the parameter estimates for flood evaluation.Table 2 also contains information on AFS data availability (N s number of gauged sites, N e number of equivalent years) for the 23 Italian homogeneous regions of the VAPI procedure.Also, Table 1 reports estimated scaling of index floods according to Eq. ( 2).In Basilicata and Calabria regions (see Fig. 2) a few gauged rivers were available, so homogeneity of index floods when scaled against area was obtained by grouping some sub regions.In Pescara region, flood scaling was observed to differ in gauged sites of the Pescara river from that observed elewhere in the region, so two different power laws were adopted.The scaling exponent m ranges from m = 0.24 for Palermo region (however based upon five sites only) to m = 1.04 for Calabria (a, b) region, but it is mostly clustered within a quite narrow range of variability, namely with E[m] = 0.75, and CV[m] = 0.18.Visual inspection did not display noticeable changes of scaling exponent with area, or scale breaks in either region.However, accurate investigation of scale breaks is beyond our current purpose, and it should be targeted by a specific analysis.Fig. 3 shows the countrywide growth curves x R against y R for Italy, the corresponding parameters are reported in Table 1, where a summary of statistical tests are also reported (v 2 , AD, KS, and CL), with significance level 5%.The chosen statistics for AD and KS tests are valid for an a priori known distribution (i.e. with parameters assumed a priori, and not estimated from data).Notice that a posteriori reference statistics for AD and KS tests, albeit possibly found for some distributions (e.g.GEV, Generalized Logistic, for AD test in [65]), are not available for both tests, and for all distributions (e.g.TCEV, Lognormal, etc.), that we know of.
Pearson v 2 , accounting for parameter estimation, also indicates good fitting using GEV.CL test indicates that mostly GEV distribution fits well the observed data.
Fig. 4 reports the share of dams displaying a given range of return period of spillway saturation, as per four area bins from 0.1 to 10,000 km 2 .Globally, 55% (245) of the dams display R S > 10,000, and R S > 1000 for 71% (315) of the investigated dams.There are 130 dams (29%) with spillway saturation occurring with a return period R S < 1000 years, this indicating a not negligible potential risk of failure.One also finds 62 dams (14% of the countrywide sample) with a spillway displaying a value of R S < 100 years, i.e. there might be a noteworthy potential risk of dam overtopping.The distribution of R S is independent of basin area, except for catchments with area A > 1000 km 2 .Focusing on the 37 dams (8.3% of the sample) within the largest contributing area, one finds that 27 display R S < 1000 years (and 23 have R S < 100).

Discussion
Our results provide some room for discussion.A number of simplifying hypothesis were made in our dams safety assessment, that may result in some over-simplifications of the application of state-of-the-art methods, to evaluate the multifaceted potential risk associated with old and often un-maintained Italian dams.
Flood routing was neglected in all cases.This has likely a negligible effect on safety assessment of dams impounding small mountain streams, but it can provide an essential contribution to safety of dams impounding large rivers.Therefore, the actual value of R S may increase for large catchments, and our approach may be distorted therein.This might be reflected in the anomalous number of potentially dangerous dams impounding large rivers as reported.However, one notes that the largest majority of Italian dams was built in rivers with small contributing areas (see Fig. 4).
Notice that the estimated return period R S refers to the event ''Exceeding of spillways design flood''.The latter does not mean per se overtopping of the dam for a number of reasons, including flood routing, pool level management, safety margins, semi-height of wind waves, length of fetch, wind direction, etc.A record of overtopping events for Italy is not available that we know of, so no comparison could be made in this sense.Also, overtopping does not imply per se the occurrence of any particular event, say if the dam's body is not breached, and if river conveyance downstream is large enough, so overtopping events may have occurred without any large consequences, and without having been recorded officially.
Clustering of hydrologically similar drainage basins, and extrapolation of regional growth curves relied upon the VAPI template of flood wise homogeneous regions.This approach was assumed to better fit the requirement of estimating flood figures with very low frequency, but the database available in Italy is still poor and there is no real hope of improving it in the next future.Pooled rescaled flood data from each homogeneous regions were used to estimate the growth curve, which was accommodated using the GEV model.Fig. 3 and Table 1 show that there is a large variability in Italy, as indicate by shape parameter k ranging from k = 0, i.e.Gumbel distribution for Calabria B region, to k = À0.32 for the Parma B region in Northern Italy.
Index flood estimates using simple scaling with basin area is widely accepted in diagnostic analysis of flood patterns, but using it to back estimate the index flood in ungauged rivers may entail Table 1 Estimated parameters, and goodness of fit test of GEV distribution for the 23 hydrologically homogenoeus regions of Italy according to VAPI procedure.Shape parameter k = 0 (-) implies use of Gumbel distribution.Goodnes of fit assessed using three different tests, Pearson or v 2 , Anderson-Darling AD, and Kolmogorov-Smirnov KS.Ref. is reference statistics (AD, KS, a priori distribution fitting, a = 5%).CL is test for confidence limits (a = 5%), passed (Y), or not passed (N).In italic we report cases when goodness of fit test is not passed.considerable uncertainty, and local conditions may provide different behavior with respect to the generally valid regional one.We could not collect systematically flow data from all the dams' sites, given that these are not publicly available.The estimated scale invariance parameters (Table 2) pertain to SIMN monitored stream sections, concerning relatively large rivers (i.e.A > 100 km 2 or so), while several of our dam sites drain relatively small catchments (A < 10 km 2 , see Fig. 1), and the issue arise whether scale invariance holds for these latter.Recently, we were able to collect AFS data from dam sites with small area (A % 1-600 km 2 ) in Region 2a (19 sites), and Region 2b (6 sites), covering 1932-2002 (on average 38 years of data for each basin).We found that for small catchments (down to 1 km 2 ) scale invariance as reported in Table 2 well fits the observed index floods (not shown for shortness).However, such assessment could not be done systematically country wise given the lack of data as reported.

GEV
Our analysis here displayed scaling exponents m generally coherent with those reported in scientific literature, where m values are found to depend upon physical properties of the catchment, including soil thickness, and texture, and hydrological network structure and response [62].
Eventually, the scaling approach seems a powerful method when no information is available locally, and a large scale assessment is needed, like here, to define sites at risk, where more refined studies need be carried out.
We found that almost one third of the investigated dam sites display R S < 1000 years.This apparently indicates that detailed analysis is needed to improve current safety of a large number of Italian dams, so dam rehabilitation should ameliorate spillway capacity when required.The dams in small rivers with spillway saturation for short return period (i.e.R S < 100 years) are the first candidates to re-analysis of dam safety.
In Fig. 4 we report the percentage distribution within the 23 homogeneous regions of those dam sites where R S < 1000 years.One third or so of these dams are located within regions Parma A and Parma C, i.e. central Italian Alps (21%), and Thyrrenian Liguria (12%).Also, Palermo C region (South Sicily, 9%), and Cagliari B (East Sardinia, 13%) have some hot spots for dam safety (see Fig. 5).
The estimation of R S by way of Eq. ( 3) and Eq. ( 4) may entail some inaccuracies, as given by uncertainty in flood quantile estimation, e.g.expressed using confidence limits [33].However, one may assume that estimation of low return periods is relatively accurate.In turn, sites with low return periods design flood q S are more likely to be at risk of exceedance, and accurate assessment is more important therein.We evaluated the confidence limits of R S , which we back calculated from the confidence limits of x RS  (a = 5%) for regional GEV estimation, as set out by De Michele and Rosso [33], for each of our homogeneous regions (not shown for shortness).The width of the confidence limits (upper value R S + minus lower value R S À) clearly increases with R S .For sites displaying R S 6 10 years, we found on average confidence limits (variation with respect to the estimated value) within the range ±0.5 years, with a largest value of ±2 years.For sites displaying 10 6 R S 6 100 years, we found on average ±6 years, with max ±22 years.For 100 6 R S 6 1000 years, we found on average ±57 years, with max ±245 years.For 1000 6 R S 6 10000 years, we found on average ±385 years, with max ±2200 years.Of the 130 sites with R S 6 1000 years, only 7 had an upper boundary R S + > 1000 years (but not larger than 1200 years), and of the 315 sites with R S > 1000 years, only 1 had R S À < 1000 (i.e.990 years).Therefore, the R S estimates we provided here seem to deliver an acceptably accurate indication as to whether a local assessment needs to be done, and the priority therein, independently of potential uncertainty.
To evaluate the return period of design flood q S bypassing the issue of choosing a parent (i.e.GEV here) distribution and of the uncertainty therein, we could have adopted e.g. a model-average approach, by simultaneously considering several different distributions, mirroring what done in some cases when dealing with design flood quantile assessment [66].Indeed, whenever a given distribution would provide a scarce performance in representing flood quantiles x RS (and assessment of the return period R S of a given quantile in backward estimation as we did here), clearly this would need be discarded, so less performing distribution would not be used anyway.On the other hand, if more than one distribution would provide a similar performance (i.e. a similar value of X RS, or return period R S ), the final estimated value will not be so much different, albeit the results may be significantly improved statistically.Notice further that return period here needs basically be assessed on a logarithmic scale, so averaging of different (acceptably performing) distributions would likely change our results marginally.Given the focus here is delivering a first order of magnitude of the frequency (or return period) of exceedance of q S for a large number of dams, while accurate assessment needs to be carried out locally with more complex studies, this seemed unnecessary here.GEV distribution is easily usable, depicts acceptably flood risk within our target regions, and it is capable of capturing rapidly (hyperbolically) increasing extreme floods, so its use here seemed appropriate.
Operation of Italian reservoirs dates back 60 years and more, sometimes to the end of the XIX century.Ever since then, changes of hydrological behavior of our streams may have occurred due to climate change, and modified hydrological response as per land use changes.Our analysis of flood hazard here implicitly rely upon an assumption of stationarity during the period of measurements , and further assumes that distribution fitting upon that period is representative now, which is debatable indeed.However, we have little way to investigate this facet with no recent data available.Even in the future flood safety of dams may be influenced by climate change, that is expected to enhance flood occurrence and severity in both Alpine and Mediterranean areas [67,68], and large impoundments may even feedback into modified climate conditions locally [69].However, our method can provide a statistical tool for hazard screening, and duly address investigation of critical cases, also including potential effect of recent, and prospective climate change.

Conclusions
We attempted here to perform a countrywide assessment of dam safety for Italy, where flood assessment dates back 60 years and more in some cases, and both hydrologic data and dam operation figures became quite unavailable in last 40 years.This required comprehensive flood evaluation for the peninsula, and neat, locally based assessment of flood quantiles at each and every one of our 450 dam sites.To tackle such large scale effort, we exploited the available state of the art regional approach as provided by VAPI of Italy and investigated i) site specific index flood assessment using scale invariance against area, and ii) assessment of the return period of spillway design flood at each dam site using a regionally valid extreme value distribution.
Our results showed that 55% (245) of the 448 examined dams are equipped by spillway with R S > 10000; and 71% (315) of the dams have R S > 1000.Conversely, 29% (130) of the dams display R S < 1000 years, lower than required.The spillway of 14% (62) of the dams has R S < 100 years, indicating unacceptably low frequency of exceedance, and potential overtopping, and witnessing that accurate local re-assessment is utmost needed therein.Uncertain as our results might be given the over simplified approach we adopted, the present work deliver evidences that Italian dams display non negligible hazard hydrologically, and intervention is needed to cope with the most critical cases, and in general to provide an updated assessment of flood risk.
Our results are therefore methodologically interesting for scientist in the field of hydro-geological hazard, and stake holders in the area of reservoirs management, and provide a quantitative, albeit preliminary highlighting of critical cases for hydropower companies in charge of dams' safety maintenance, as well as a potential, priority driven road map for dams' rehabilitation in Italy.

Fig. 1 .
Fig. 1.Investigated large dams of Italy.Color scale of dams sites displays the contributing area.(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 2 .
Fig. 2. Homogeneos regions of Italy for flood hazard assessment in Italy.

Fig. 4 .
Fig. 4. Class of return period RS os spillway saturation per class of contributing area A.
1)] the Gumbel variate.The data base we used here includes about 7300 AFS sampling values, i.e. the maximum annual flood figures observed in 264 gauged rivers, evenly spread countrywide.The period of observation is from 1921 to 1970 countrywide, and from 1921 to 1993 for North Western Italy.The data were collected and controlled by the former SIMN agency (Servizio Idrografico e Mareografico Nazionale) now discontinued.

Table 2
Data base of flood peaks for the 23 homogeneous hydrological regions of Italy, and estimated parameters of observed flood scaling.q i (1) is the index flood associated to an unit area, m scaling exponent, and D determination coefficient of the regression.