Journal of Hydrology 385 (2010) 150–164

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Journal of Hydrology

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A method for estimating flash flood peak discharge in a poorly gauged basin:Case study for the 13–14 January 1994 flood, Giofiros basin, Crete, Greece

Aristeidis G. Koutroulis, Ioannis K. Tsanis *

Department of Environmental Engineering, Technical University of Crete, Chania, Greece

a r t i c l e i n f o s u m m a r y

Article history:Received 24 June 2009Received in revised form 11 January 2010Accepted 6 February 2010

This manuscript was handled byK. Georgakakos, Editor-in-Chief, with theassistance of Marco Borga, Associate Editor

Keywords:Flash floodPoorly gauged basinStage gauge failurePeak discharge estimationHydrological simulationFlood volume

0022-1694/$ - see front matter � 2010 Elsevier B.V. Adoi:10.1016/j.jhydrol.2010.02.012

* Corresponding author.E-mail address: tsanis@hydromech.gr (I.K. Tsanis).

A method for estimating flash flood peak discharge, hydrograph, and volume in poorly gauged basins,where the hydrological characteristics of the flood are partially known, due to stage gauge failure, is pre-sented. An empirical index is used to generate missing hourly rainfall data and hydrologic and hydraulicmodels performs the basin delineation, flood simulation, and flood inundation. The peak discharge, hyd-rograph, and volume, derived from the analysis of measured hydrographs in a number of non-flood caus-ing rainfall events with operating stage gauge, were used for calibration and verification of the simulatedstage-discharge hydrographs. An empirical equation was developed in order to provide the peak dis-charge as a function of the total precipitation, its standard deviation, and storm duration. The peak dis-charge for a flash flood case based on the empirical equation was in close agreement with the results froma number of consolidated methods. These methods involved hydrological and hydraulic modeling andpeak flow estimates based on Manning’s equation and post flash flood measurements of the maximumwater level observed at the control cross-section, for the 13–14 January 1994 flash flood in the Giofirosbasin on the island of Crete, Greece. This method can be applied to other poorly gauged basins for floodswith a stage higher than that defined by the rating curve.

� 2010 Elsevier B.V. All rights reserved.

Introduction

Flash floods are those floods that follow the causative storms ina short period of time, with water levels in the drainage networkreaching a crest within minutes to a few hours resulting in a verylimited opportunity for warnings to be prepared and issued (Borgaet al., 2007; Collier, 2007). The severity of flash flood generatingstorms is poorly captured by using conventional rain-gauge net-works (Norbiato et al., 2007). Poor knowledge of this phenomenoncomes from the fact that, in most flash-flood cases, the rain accu-mulations and the discharges are unknown over most of the water-sheds of concern (Creutin and Borga, 2003). The number of rainfallstations in poorly gauged basins is not sufficient to fully describethe spatiotemporal hydrometeorologic characteristics of the stormevents. In addition during the flash flooding process, the streamgauges usually fail. This renders each methodology almost uniqueand coupled with some special catchment characteristics difficultto generalize and apply at a different location.

Various methods have been developed in order to study ex-treme floods in ungauged or poorly gauged basins. An ungaugedbasin is one with inadequate records of hydrological observationsto enable computation of hydrological variables of interest at the

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appropriate spatial and temporal scales, and to the accuracyacceptable for practical applications. There are a number of meth-ods that can be applied to study extreme floods on ungaugedwatersheds including the so-called ‘‘indirect” peak discharge esti-mates, rainfall–runoff modeling through hydrological models andempirical methods.

Gaume (2006), refers to the peak discharge as a key issue of postflood studies and further hydrological analysis and makes anextensive reference to a number of indirect estimation methods,discussing the estimates accuracy. The methods presented, varyamong those based on the Manning–Strickler formula like slope–area and slope–conveyance methods, non-parametric methods likecritical depth and ‘‘super-elevation” in bends and in front of obsta-cles, water surface velocity evaluation on films and rainfall–runoffchecking through the ‘‘rational-method” or rainfall–runoff simula-tion. Gaume et al. (2009), enumerates the various methods of peakdischarge estimation used for 550 documented flash flood eventsacross seven European hydrometeorological regions. This categori-zation includes Manning–Strickler formula estimation, extrapola-tion of calibrated stage–discharge relation, hydraulic 1D and 2Dsimulation, reconstruction from reservoir operation and direct cur-rent-meter measurement, with the first two being more popular.Webb and Jarrett (2002), provide a particularly concise review ofthe mathematic and hydrologic assumptions that underlie thecommonly used slope–area, step-backwater, and critical-depth

Nomenclature

A index that correlates the daily precipitation of eachstation with the daily precipitation of the gauge withhourly data

Px0j total daily precipitation of gauge x0 on day j

VT total event runoff volume, m3

PT total event precipitation, mmD event duration, hrP standard deviation of precipitation over a rainfall–run-

off event, mmQpeak peak discharge, m3/sa, b, c, d coefficients related to the characteristics of the basin

and the precipitation time seriesQ total flow rate, m3/sS bed slope, m/mAij area of cross-section i for water level j

Rij hydraulic radius of cross-section i for water level j, mni roughness coefficient of area i (river channel or flood-

plain)fc maximum potential rate of precipitation loss, mm/hpt storm mean areal precipitation depth during a time

interval t to t + Dt, mmpet excess during a time interval t to t + Dt, mmId initial deficit, mmtc basin time of concentration, hR Clark coefficient for storage, hCR constant rate (percolation rate), mm/hAPI average precipitation intensity over the basin, mm/hL basin’s travel length in the Kirpich formula, ftr correlation coefficientD = R2 coefficient of determination

A.G. Koutroulis, I.K. Tsanis / Journal of Hydrology 385 (2010) 150–164 151

methods. Bathurst (1990), tested three discharge gauging tech-niques in mountain rivers and concluded that flood flow can beestimated, with limited accuracy, by the slope–area and critical-depth methods. Costa (1987), combined the maximum rainfall–runoff floods in basins from 0.39 to 370 km2 in the conterminousUSA where the slope–area indirect method primarily was used toestimate the peak discharge. The slope–area method computes dis-charge based on an adaptation of a uniform-flow equation (theBernoulli energy equation) using channel-geometry characteris-tics, water-surface profiles, and Manning roughness coefficients.The uniform-flow assumption and Manning’s equation were usedby Gaume et al. (2004) for the estimation of the peak dischargeof several cross-sections during the 12 and 13 November 1999flash flood of the River Aude in France. Wohl (1995), used step-backwater method in order to convert peak stage estimates fromscour lines to discharge estimates in ungauged mountain channels.Hydrological models of varying complexity approaches are appliedto provide detailed estimates of flow processes for ungauged sites(Sangati et al., 2009; Bonnifait et al., 2009; Bloschl et al., 2008;Reed et al., 2007; Bohorquez and Darby, 2008).

However, empirical methods have also been developed and ap-plied at ungauged sites. Empirical methods can be of great value inview of constrains of application effort when compared to alterna-tive traditional methods. Wharton (1992) and Wharton et al.(1989) applied an alternative indirect peak discharge technique atungauged sites, first developed by the US Geological Survey. Thechannel-geometry method is based on the assumption that channelcross-section size and geometry at specific location reflects thedrainage process during a storm. The method can be applied whenestimating relations have been defined for a region and channelwidth or cross-sectional area, are the only available information.Specific procedures have to be followed for accurate and consistentmeasurements during field survey. Nasri et al. (2004), presented ageomorphological model methodology to predict shape and volumeof hydrographs for floods in small hillside semiarid catchments.Their model was built around a production function that definesthe net storm rainfall (portion of rainfall during a storm whichreaches a stream channel as direct runoff) from the total rainfall (ob-served rainfall in the catchment) and a transfer function based on themost complete possible definition of the surface drainage system.Very high resolution (5 min) observations of rainfall were used inthe model. The model runoff generation was based on surface drain-age characteristics, which can be easily extracted from maps and ob-served runoff, was satisfactory reproduced.

Detailed and well organized post flash flood surveys providevaluable information for the understanding of the event processes.

Guidance for flash floods surveys is provided by Marchi et al.(2009), describing the investigation process of a flash flood in Wes-tern Slovenia. Peak discharges and associated uncertainty wereestimated for 22 cross-sections using the slope–conveyance meth-od that proved to be practically useful and simple. Pruess et al.(1998), presented the methodology and implications of 15 fieldreconnaissance surveys for estimation peak discharges of extremeflash floods along mountain channels of southwestern Colorado,using step-backwater flow modeling. Thirty selected major floodsin the US were analyzed by Costa and Jarrett (2008) aiming tothe most possible accurate estimate of the peak discharges usingthe best available practices. The dominant method used was theslope–area method for 21 of the events. For the rest of the events,direct current-meter measurements, culvert measurement, rating-curve extension, and interpolation and rating-curve extension wasused, as well as combination of the above. The study makes anextensive report to the errors and uncertainty embedded to thepeak flow estimation.

The estimation of peak discharges without direct current-metermeasurements is, above all, a question of sound engineering judg-ment (Gaume et al., 2004; Gaume, 2006). Empirical relations mustbe used with caution and estimates should be made at a minimumof two or three cross-sections for the same river reach to reduceuncertainties (Gaume et al., 2004; Gaume, 2006). Errors in the esti-mation of peak discharges can be controlled by careful hydraulicand laboratory analysis (NRC, 1999). The estimation accuracy ofpeak discharge based on slope–area method in small steep water-sheds in the US was evaluated by Jarrett (1987) by examining theeffect of various parameters such as the roughness coefficient, thegeometry of the cross-section, and the unsteady nature of largedischarges, leading to overestimation of peak discharge by up to100% or over. Dottori et al. (2009), presented a dynamic ratingcurve approach for indirect discharge estimation, based on simul-taneous stage measurements at two adjacent cross-section. Theauthors compared various approaches described in the literature,examined the significant uncertainty produced in the extrapola-tion beyond the range of measurements of the rating curve, andpresented the improvement in the discharge estimation using theirproposed approach. In order to avoid significant errors and reducethe uncertainties, it is necessary to use various sources of informa-tion to enable cross-checking using different approaches (Gaumeand Borga, 2008).

The purpose of the paper was the comparison between a num-ber of consolidated methods for estimating peak discharge under astage gauge failure, or, in general, when limited information areavailable. The Giofiros basin (158 km2) located in the central-north

Fig. 1. Location and available hydrometeorological data for Giofiros basin.

152 A.G. Koutroulis, I.K. Tsanis / Journal of Hydrology 385 (2010) 150–164

part of the island of Crete (Fig. 1) was used as case study and, inparticular, the flash flood occurred on 13th January 1994 wasanalyzed.

Methodology

Reconstruction of precipitation realizations of variable spatiotemporaldistribution

The precipitation reconstruction approach combines the Thies-sen polygons method, the extrapolation of the hourly rainfallintensity variations to the daily rain-gauges and the generationof gridded realizations using the assumption of multiplicativespace-time separability as presented by Woods and Sivapalan(1999). In the case of the Giofiros basin the hourly rainfall datawas available from the station with the higher elevation that re-corded at least four times higher rainfall than the other stationsin the lower elevations in the valley with daily rainfall data. There-fore the hourly distribution of the rainfall in the stations with low-er rainfall will not significantly alter the hydrograph. Thetransformation is done with the introduction of index A for eachof the daily recording stations. Index A correlates the daily precip-itation of each station with the daily precipitation of the gaugewith hourly data. Index A is introduced as:

Axkj ¼

Pxkj

Px0j

ð1Þ

where Pxkj is the total daily precipitation at gauge xk (k = 1–n for n

daily precipitation gauges) on day j and Px0j is the total daily precip-

itation of gauge x0 on day j. Index A reflects the correlation of thetotal amount of precipitation between gauges x0 and xk, within aperiod of 1 day. The hourly estimations for gauge xk is producedby multiplying the index Axk

j for each daily recording gauge xk with

the hourly precipitation of gauge x0. At a second step, the methodby Woods and Sivapalan (1999) can be applied by splitting the spa-tial and temporal variability into two separate terms. Different real-izations of stationary hourly rainfall of different intensity andtiming reproduce the spatiotemporal variability. The average hourlyor distributed precipitation, over the basin is then estimated by theThiessen method (Thiessen, 1911) or by other interpolation meth-ods such as inverse distance weighted – IDW (Shepard, 1968), Kri-ging (Matheron, 1965). The proposed methodology takes intoaccount the spatial distribution of precipitation due to topography(e.g., orographic precipitation) or locality of the meteorological phe-nomena. There are limitations of the size of the basin that can beapplied since the spatial structure of convective rainstorms dependson the local meteorology and topography, but generally the dis-tance of decorrelation between measured rainfall intensities lies be-tween 10 and 20 km at an hourly time step (Lebel et al., 1987).

Empirical peak discharge estimation

In order to fill in missing data for runoff, an attempt was madeto correlate the total event runoff volume with precipitation char-acteristics and peak discharges. The suggested method does notuse directly soil properties and infiltration processes during runoffbut rather compares the total runoff volume VT (m3) occurring dur-ing a single event with the total precipitation PT (mm) that causesit, the standard deviation of the precipitation time series (rP inmm) and the rainfall event duration D (h). When the total runoffvolume VT (m3) for a sufficient number of gauged floods are plottedagainst the product of the square of total precipitation PT and thestandard deviation of precipitation rP their relation can be repre-sented via a linear regression equation:

VT ¼ aP2TrP ð2Þ

A.G. Koutroulis, I.K. Tsanis / Journal of Hydrology 385 (2010) 150–164 153

where a is a coefficient for the basin. Eq. (2) expresses that the aver-age flow rate during the rainstorm is proportional to the product ofthe total precipitation, its intensity and its standard deviation whilethe coefficient of proportionality a is related to the characteristics ofthe basin. The nonlinearity of the peak discharge Qpeak with the totalvolume is expressed as:

Q peakD ¼ bVcT ð3Þ

where D is the event duration in seconds, and b and c are coeffi-cients related to the characteristics of the basin. Due to limited dataavailability a number of non-flood causing rainfall events with anoperating stage gauge meter are used to evaluate the coefficientsin Eq. (3). Peak discharges of selected rainfall–runoff events, covera wide range of discharge conditions for optimal method validation.Combining Eqs. (2) and (3) results in the elimination of VT:

Q peak ¼1D

dðP2rPÞc ð4Þ

where d ¼ bac. Given the coefficients related to the characteristicsof the basin and the precipitation time series, the peak dischargeof a flood can be determined via Eq. (4).

Flood peak flow estimation from cross-sectional geometry andparameters

In the absence of field flow data, the evaluation of the resultscan be based on the estimation of the observed peak flow from aspecific cross-section if the geometric and hydraulic characteristicsof the cross-section along with the water level are available. Thecross-section can be divided in two parts, the first of which is con-sidered as the main channel and the second is the floodplain. UsingEq. (5) (Streeter and Benjamin, 1988) the total flow between twocross-sections can be estimated as:

Q ¼ ðK1 þ K2ÞffiffiffiSp

ð5Þ

where Q is the total flow rate in m3/s, Ki ¼ 1ni

AijR2=3ij , S is the energy

slope along flow, Aij is the area of cross-section i for water level j, Rij

is the hydraulic radius, and ni is the roughness coefficient (i = 1 forthe main channel and i = 2 for the floodplain).

Hydrological and hydraulic modeling

The US Army Corps of Engineers Models, developed at theHydrologic Engineering Center (HEC) in Davis, California, were ap-plied for flood simulation and mapping. The hydrological analysiswas divided in four main steps according to the HEC modules:(a) the extraction of basin’s characteristics (HEC-GeoHMS), (b)the distributed rainfall–runoff simulation (HEC-HMS), (c) the sim-ulation of the flood wave (HEC-RAS) and (d) the mapping and rep-resentation of flood extend (HEC-GeoRAS). In HEC-HMS model, thedeficit and constant was used as the loss method, the ModClarkwas selected as the transform method and the recession methodfor sub-basin baseflow (HEC, 2001). For the precipitation represen-tation, the generated hourly precipitation data were interpolatedto hourly gridded precipitation datasets over the study area usingthe IDW method.

Deficit and constant loss method

Deficit and constant is a quasi-continuous model of precipitationlosses (HEC, 2000). The concept of the deficit and constant rate lossmodel is that the maximum potential rate of precipitation loss, fc

(in mm/h), is constant throughout an event and the initial loss can‘‘recover” after a prolonged period of no rainfall. An initial deficit,Id (in mm), represents interception and depression storage. Intercep-

tion storage is a consequence of absorption of precipitation by sur-face cover, including plants in the watershed. Depression storage isa consequence of depressions in the watershed topography; wateris stored in these and eventually infiltrates or evaporates. This lossoccurs prior to the onset of runoff. Until the accumulated precipita-tion on the pervious area exceeds the ‘‘recovered” initial loss volume,no runoff occurs. Thus, if pt is the storm mean areal precipitationdepth (mm/h) during a time interval t to t + Dt, the excess, pet (inmm/h), during the interval is given by:

pet ¼0 if

Ppi < Id

pt � fc ifP

pi > Id and pt > fc

0 ifP

pi > Id and pt < fc

8><>: ð6Þ

ModClark transformation and recession methods

The modified Clark (ModClark) model in HEC-HMS is a distrib-uted parameter model in which spatial variability of characteristicsand processes are considered explicitly (Kull and Feldman, 1998;Peters and Easton, 1996). This model accounts explicitly for varia-tions in travel time to the watershed outlet from all locations of awatershed. The ModClark algorithm is a version of the Clark unithydrograph transformation modified to accommodate spatiallydistributed precipitation (Clark, 1945). Runoff computations withthe ModClark model explicitly account for translation and storage.Storage is accounted for within the same linear reservoir modelincorporated in the Clark model. Translation is accounted for with-in a grid-based travel-time model tcell ¼ tcðdcell=dmaxÞ (HEC, 2000),where tc is the time of concentration for the subwatershed and isa function of basin’s length and slope, dcell is the travel distancefrom the cell to the outlet, and dmax is the travel distance fromthe cell furthest from the outlet. The method requires an inputcoefficient for storage, R, where R accounts for both translationand attenuation of excess precipitation as it moves over the basintoward the outlet. Storage coefficient R is estimated as the dis-charge at the inflection point on the recession limb of the hydro-graph divided by the slope at the inflection point. The translationhydrograph is routed using the equation:

QðtÞ ¼ ½ðDt=ðRþ 0:5DtÞÞIðtÞ� þ ½1� ðDt=ðRþ 0:5DtÞÞQðt � 1Þ� ð7Þ

where Q(t) is the outflow from storage at time t, Dt is the timeincrement, R is the storage coefficient, I(t) is the average inflow tostorage at time t and Q(t � 1) is the outflow from storage at previ-ous time (t � 1).

The exponential recession baseflow method, used in HEC-HMS(Chow et al., 1988), approximates the watershed drainage behaviorwhen channel flow recedes exponentially after an event (Linsleyet al., 1982). This recession model defines the relationship Qt, thebaseflow at anytime t, to an initial value as:

Qt ¼ Q 0kt ð8Þ

where Q0 is the initial baseflow and k is an exponential decay constantdefined as the ratio of the baseflow at time t to the baseflow 1 day ear-lier. In HEC-HMS the parameters of this model include the initial flow,the recession ratio, and the threshold flow. The parameters can beeasily estimated if gauged flow data are available.

Calibration of the model

Various indices of evaluation were used in order to calibrate themodel. They are divided in two categories depending on time scaleissues. The first group of indices that evaluate the model is in thescale of entire rainfall events

154 A.G. Koutroulis, I.K. Tsanis / Journal of Hydrology 385 (2010) 150–164

peak flow error % ðPFEÞ diff ðQÞ½%� ¼ Qobsmax � Q simmax

Qobsmax

� 100 ð9Þ

phase errorðPEÞ diff ðsÞ½h� ¼ sobs � ssim ð10Þ

volume error % ðVEÞ diff ðVÞ½%� ¼ jVobs � VsimjVobs

� 100 ð11Þ

where Qobsmax Qsimmax are the maximum observed and simulated flowvalues for each rainfall–runoff event, sobs, ssim the peak times for theobserved and simulated process, and Vobs, Vsim the total runoff vol-ume for the observed and simulated process, respectively.

The second group of indices is related to the time step of therainfall–runoff simulation.

Nash and Sutcliffe (1970):

E ¼ 1�Pn

i¼1ðQ obsðiÞ � Q simðiÞÞ2Pni¼1ðQ obsðiÞ � Q obsÞ2

ð12Þ

Coefficient of correlation:

r ¼Pn

i¼1 ðQ obsðiÞ � Q obsðiÞÞðQ simðiÞ � Q simÞh i

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPni¼1ðQ obsðiÞ � Q obsÞ2

q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPni¼1ðQ simðiÞ � Q simÞ2

q264

375

0:5

ð13Þ

Explained variance:

EV ¼ 1�Pn

i¼1 ðQ simðiÞ � Q obsðiÞÞ � 1=NPn

i¼1ðQ simðiÞ � Q obsðiÞÞ� �2

Pni¼1ðQ obsðiÞ � Q obsÞ2

ð14Þ

Root mean square error:

RMSE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPni¼1ðQ simðiÞ � Q obsðiÞÞ2

N

sð15Þ

Average absolute percent errors:

AAPE ¼ 1N

Xn

i¼1

ðQ simðiÞ � Q obsðiÞÞQobsðiÞ

�������� ð16Þ

where Qobs(i), Qsim(i) the observed and simulated flow values for timestep i, Qobs, Qsim the mean observed and simulated flow values foreach event (Marsigli et al., 2002) and N the number of observations.

Case study of Giofiros basin

Description of the study area

Giofiros basin is located in the central-north part of the island ofCrete, Greece (Fig. 1) and has a drainage area of 186 km2 at the out-let to the Aegean Sea, while the drainage area at the river gauge is158 km2 (about 6 km upstream). The southern upstream part ofthe basin is rugged mountainous terrain, whereas, the northernpart has milder rolling hillslopes. Geologically, the basin is com-posed of extensive strata of marly limestone, flysch and sandstone,gypsum and alluvial deposits. The watershed has a Mediterraneanclimate, thus, the Giofiros basin has seasonal flow during the wetfall-winter period (typically from October to March), when themajority of the mean annual rainfall of 827 mm occurs (Ganoulis,2003).

Land use in Giofiros basin is mainly vineyards, olive trees andfarmlands, which are also present along the stream banks. Never-theless, tourism has caused a rapid development increase in thenorthern part of the stream, along the riverbanks and the shore-lines of the Mediterranean Sea. Due to the absence of planning,natural passages of water gradually give their place to constructionand infiltration rates are declining continuously (Ganoulis, 2003).This allows flash floods induced by heavy winter rainstorms thatcause damages at the outlet areas.

On 13th January 1994 and around 15:00, the intensity of thelight precipitation that had saturated Giofiros soils during the pre-vious days started to increase. Reaching a maximum 5 h accumu-lated precipitation of 123 mm at 21:00 this extreme rainfalleventually stopped at 24:00 lasting almost 9 h. By that time theresulting flash flood had catastrophic impacts on Giofiros basin.Many houses located near the coast were flooded leaving 49 peoplehomeless. In terms of precipitation severity, the 100-years recur-rence interval of 5 h accumulated precipitation of a nearby meteo-rological station (Heraklio EMY in Fig. 1) is 98 mm according toGumbel distribution (Ganoulis, 2003). The maximum 5 h accumu-lated storm rainfall of 123 mm that was observed at the south partof the basin (Ag. Varvara station in Fig. 1), far exceed the 100-yearsrecurrence interval of 98 mm of the nearby, lowland, Heraklio EMYstation. The single most adverse effect of the flood was the damagecaused to the city’s wastewater treatment plan which was still un-der construction at the time of the flood. Many of the concretetanks were rendered unserviceable or were completely destroyedby the force of the oncoming flood wave (Ganoulis, 2003). The ex-act flood characteristics cannot be known since the only stagegauge was destroyed at 20:00 during the flash flood.

During a recent flash flood data compilation effort in the frameof the EC funded research project HYDRATE (CN: 037024), aninventory – first step towards an atlas of extreme flash floods inEurope was developed containing over 550 documented events(Gaume et al., 2009). The 1994 Giofiros flash flood event was oneamong the 22 Greek floods that enriched this flood inventory. Interms of flash flood magnitude and under a pan-European andinternational perspective (Gaume et al., 2009), the 1994 Giofirosstorm had a moderate unit peak discharge of 1.85 m3/s/km2

(300 m3/s/158 km2). Due to lack of high resolution precipitationdata both spatially and temporally it is possible that the unit peakdischarge could be much higher, i.e., (a) assuming that the majorityof flood was produced in the upper 1/5th of the basin (186/5 = 37.2 km2) due to orographic effect the unit peak dischargecould be 8.1 m3/s/km2, (b) simulations with the peak hourly pre-cipitation occurring in 15 min instead of an hour reveal an increasein velocity from 3.62 m/s to 4.08 m/s, in water depth from 5.1 m to5.4 m and in peak discharge from 300 m3/s to 375 m3/s, thatbrings the unit peak discharge as high as 9.67 m3/s/km2.

Since 1994, several studies have been conducted on Giofiros ba-sin, related to that flash flood. Most of them focused on the estima-tion of the hydrological parameters of the basin, so thatappropriate flood prevention measures could be taken, and the restaimed at simulating the 1994 flood. Due to lack of flood recordingdata these studies could not verify the simulation results but ratherempirically estimated the total flood volume. It should be notedthat flood researchers have come up with peak discharge estimatesthat vary significantly from 300 m3/s up to 600 m3/s (Ganoulis,2003; Barboudakis, 1998).

Field data

Flash-flood monitoring requires rainfall estimates at small spa-tial scales (1 km or finer) and short-time scales (15–30 min, andeven less in rugged mountainous areas and urban areas) (Borgaet al., 2008; McCain and Shroba, 1979). Floods research at hydro-logical basin scale requires high resolution data, particularly forusing the most robust hydrologic models that have been recentlydeveloped. Existing data usually does not included all the data re-quired for newer models. From the three rain-gauges of Giofirosbasin, one has hourly records and two stations providing daily pre-cipitation measurements (Fig. 1). The stations that provided thedaily precipitation records and the station with the hourlymeasurements are located along the south–north direction, whichis the main orientation axis of Giofiros basin. Along this line,

A.G. Koutroulis, I.K. Tsanis / Journal of Hydrology 385 (2010) 150–164 155

topography changes significantly from sea level to 570 m. Ag. Varv-ara hourly precipitation station is located near the mountain head-waters at 570 m above sea level (a.s.l.) (see Fig. 1) and recorded182.8 mm of total precipitation during the 14th of January 1994,while Profitis Ilias (380 m a.s.l.) and Finikia (40 m a.s.l.) precipita-tion stations recorded 43.9 mm and 37.7 mm, respectively. Usingthe previously described methodology for generating distributedhourly precipitation data-sets, total average areal precipitationfor the 1994 flood event was Ptotal = 75.7 mm. A water flow levelgauge is located in the north part of the basin, but about 6 km up-stream from the outlet on the Mediterranean Sea (Fig. 1). At thesame location, the geometric characteristics of the certain cross-

Mean sea level analysis at 1200 UTC 13/1/1994 (isobars in hPa)

4991/1/31)mmerastinu(CTU0021tanoitatipicerpevitcevnoC

Mean sea level analysis at 1800 UTC 13/1/1994 (isobars in hPa)

4991/1/31)mmerastinu(CTU0081tanoitatipicerpevitcevnoC

a

Fig. 2. (a–b) Mean sea level pressure analysis and convective precipitation based on theJanuary 1994 flash flood event.

section site of Giofiros stream were available, as well as the floodextent of the 1994 flood event. The only water flow level gaugewith hourly records was destroyed during the flood of 1994.

Results and discussion

Synoptic meteorological analysis

The meteorological analysis is focused on the synoptic prevail-ing background conditions for heavy, localized rainfall over Crete.ERA-40 re-analysis data (ERA-40 is a re-analysis of meteorologicalobservations from September 1957 to August 2002 produced by

Hih resolution Visible METEOSAT 4 - 12:00 UTC 13/1/94

Infrared METEOSAT 4 - 18:00 UTC 13/1/94

Crete Island

Egypt Libya

ECWMF 40 years re-analysis daily dataset and Meteosat satellite images for the 13

Infrared METEOSAT 4 - 00:00 UTC 14/1/94

Mean sea level analysis at 0000 UTC 14/1/1994 (isobars in hPa)

4991/1/41)mmerastinu(CTU0000tanoitatipicerpevitcevnoC

Hih resolution Visible METEOSAT 4 - 12:00 UTC 14/1/94

Mean sea level analysis at 1200 UTC 14/1/1994 (isobars in hPa)

4991/1/41)mmerastinu(CTU0021tanoitatipicerpevitcevnoC

b

Fig. 2 (continued)

156 A.G. Koutroulis, I.K. Tsanis / Journal of Hydrology 385 (2010) 150–164

the European Center for Medium-Range Weather Forecasts(ECMWF) in collaboration with many institutions – Uppala et al.,2005) supported the synoptic analysis of the conditions prevailingto heavy local rainfall, leading to flash flooding. Moreover, high res-olution visible channel METEOSAT 4 snapshots used during day-light and infrared channel images used during night for cloudyfeatures (storm) generation and tracking (Ottenbacher et al.,1997). The satellite images of 30 min temporal resolution wereprovided from the European Organisation for the Exploitation ofMeteorological Satellites (EUMETSAT).

On January, 1994, a frontal depression in south-east Mediterra-nean moved eastward and north crossing the island of Crete. Onthe surface analysis, a low pressure area was already present at

12:00 UTC 13 January (Fig. 2a) all over the Eastern Mediterraneanarea. The lower pressure area of 1010 hPa appeared at 12:00 UTC13 January over Egypt moving in a northerly direction. This lowpressure area deepens to 1007 hPa centered just south of Crete at00:00 UTC 14 January, producing high precipitation over centralCrete and the flash flood of Giofiros basin. High convective precip-itation rates up to 45 mm per 6 h (00:00 UTC 14/1/1994) were ob-served during 13 and 14 January 1994 (Fig. 2b).

The average areal daily precipitation over the island of Cretewas calculated in order to examine the correspondence with theERA40 convective precipitation dataset. The average areal dailyprecipitation estimated based on 53 daily temporal resolutionrain-gauges through IDW interpolation method (Fig. 3) and then

A.G. Koutroulis, I.K. Tsanis / Journal of Hydrology 385 (2010) 150–164 157

compared with the spatial aggregated convective precipitationover Crete. The average areal daily precipitation of the 14th of Jan-uary 1994 based on gauged data was 61.5 mm while ERA40 esti-mated 12.3 mm resulting in an underestimation of totalprecipitation. For the 13th of January measured precipitation was20 mm while ERA40 results to 1.5 mm and for the 15th of Januarymeasured and ERA40 precipitation was 9 mm and 3.3 mm, respec-tively. The comparison of ERA-40 re-analysis daily convective pre-cipitation (Uppala et al., 2005), results in underestimation ofmeasured precipitation due to lack of incorporating orographic ef-fects on the storm.

The studied flood produced by a heavy, orographic effected,thunderstorm based on the fact that the precipitation in Ag. Varv-ara station deep in the mountain at the furthest south point of thebasin was almost five times larger (182.8 mm in total with peakintensity of 37 mm/h) than the ones recorded in the other two sta-

Fig. 3. Average areal daily precipitation based on 53 rain-gauges through inverse dist

Fig. 4. Giofiros basin, Psiloritis mountain range location and t

tions (Fig. 4). In fact, a station close to the sea east of the Mediter-ranean Sea and east of the outlet of Giofiros basin (Heraklio EMYstation) recorded less than 28.4 mm of rain with the peak rainfallintensity of 7.8 mm/h (Fig. 5). The warm air masses with highdew points with a southwest–northeast flow (analysis at500 hPa) and high positive relative vorticity were primary blockedby the Psiloritis Mountains’ steep topography (Fig. 4). The air masswas forced to higher elevations, thus temperatures cooled and pro-duced high rates of precipitation of up to 37 mm/h at Ag. Varvarastation.

Hydrological analysis

A digital terrain model DTM of the island of Crete in 1:10 000scale (Fig. 1) was used with the HEC-GeoHMS extension ofArc-View GIS in order to delineate the Giofiros watershed. The

ance weighting spatial interpolation method for the 13 January 1994 flash flood.

otal daily precipitation during 13–14 January 1994 flood.

0

5

10

15

20

25

30

35

4013

/1/9

4 9:

0013

/1/9

4 10

:00

13/1

/94

11:0

013

/1/9

4 12

:00

13/1

/94

13:0

013

/1/9

4 14

:00

13/1

/94

15:0

013

/1/9

4 16

:00

13/1

/94

17:0

013

/1/9

4 18

:00

13/1

/94

19:0

013

/1/9

4 20

:00

13/1

/94

21:0

013

/1/9

4 22

:00

13/1

/94

23:0

014

/1/9

4 0:

0014

/1/9

4 1:

0014

/1/9

4 2:

0014

/1/9

4 3:

0014

/1/9

4 4:

0014

/1/9

4 5:

0014

/1/9

4 6:

0014

/1/9

4 7:

0014

/1/9

4 8:

00

Prec

ipita

tion

(mm

)

Heraklio EMY raingauge Ag. Varvara raingauge

Fig. 5. Hourly Precipitation intensity of Ag. Varvara rain-gauge (total precipitationof 182.8 mm at 570 m a.s.l.) and Heraklio rain-gauge (total precipitation of 28.4 mmat 40 m a.s.l.).

158 A.G. Koutroulis, I.K. Tsanis / Journal of Hydrology 385 (2010) 150–164

same DTM was also used for the delineation of the stream networkand the sub-basins. Subsequently, HEC-GeoHMS output was im-ported in HEC-HMS. Regarding the rest of the input for HEC-HMS, basin parameters were estimated through the calibration ofgauged rainfall–runoff events and based on hydrologic and physio-graphic characteristics of the basin from land use, soil type, basin

Table 1Sensitivity analysis results on the 11–12 January 1995 rainfall–runoff event with total are

(a)Variable = initial deficit, steady values: constant rate 5.7 mm/h, impervious 5%, Clark

constant = 0.99, baseflow threshold ratio = 0.14Initial deficit (mm) 5 6 7 8Volume error (%) 40.1 36.7 32.9 28.3Peak flow error (%) 28.5 24.5 19.4 13.6Phase error (h) 0 0 0 0Variable = constant rate, steady values: initial deficit = 10.3 mm, impervious 5%, Clark

constant = 0.99, baseflow threshold ratio = 0.14Constant rate (mm/h) 1.5 2 2.5 3Volume error (%) 74.5 71.0 66.9 62.0Peak flow error (%) 68.2 63.8 58.3 52.6Phase error (h) 1 1 1 0

Variable = impervious, steady values: initial deficit = 10.3 mm, constant rate 5.7 mm/constant = 0.99, baseflow threshold ratio = 0.14

Impervious (%) 1 2 3 4Volume error (%) �36.9 �16.6 �1.5 10.0Peak flow error (%) �54.3 �35.0 �20.0 �8.0Phase error (h) 0 0 0 0

(b)Variable = Clark time of concentration, steady values: initial deficit = 10.3 mm, consta

constant = 0.99, baseflow threshold ratio = 0.14Clark time of concentration (h) 0.5 1 1.5 2Volume error (%) 6.6 12.2 15.9 17.9Peak flow error (%) 1.8 6.1 0.9 2.7Phase error (h) �2 �2 �2 �1

Variable = Clark storage coefficient, steady values: initial deficit = 10.3 mm, constantconstant = 0.99, baseflow threshold ratio = 0.14

Clark storage coefficient (h) 2.5 3 3.5 4Volume error (%) 24.6 22.7 20.3 17.5Peak flow error (%) 20.6 12.9 5.3 �2.9Phase error (h) 0 0 0 0

Variable = recession constant, steady values: initial deficit = 10.3 mm, constant rate 5coefficient 3.7 h, baseflow threshold ratio = 0.14

Recession constant 0.01 0.1 0.2 0.3Volume error (%) 7.0 9.6 11.7 12.9Peak flow error (%) �6.9 �4.9 �3.8 �2.9Phase error (h) 0 0 0 0

Variable = baseflow threshold ratio, steady values: initial deficit = 10.3 mm, constantcoefficient 3.7 h, recession constant = 0.99

Baseflow threshold ratio 0.01 0.1 0.2 0.3Volume error (%) 19.0 19.0 19.0 19.0Peak flow error (%) 1.8 1.8 1.8 1.8Phase error (h) 0 0 0 0

slope, and geological maps of the study area, provided by theWater Resources Department of the Prefecture of Crete. Hourlygridded precipitation of 1 km2 spatial resolution was generatedaccording to the previously described methodology. Rainfall–run-off simulation of several events were conducted for the area(158 km2) upstream from the Finikia flow stage gauge (Fig. 1).The extent of the hydraulic simulation of the 1994 flood eventwere downstream of the flow stage gauge to the outlet of the basin(a distance of about 6 km), where the most significant impacts ofthe flood were observed.

Sensitivity analysis

For a successful simulation of the 1994 flood, model calibrationwas based on the simulation of eight rainfall–runoff events of var-ious intensities, prior and posterior to the 1994 flood. These eventswere derived from two time periods (from 1981 to 1995) with totalareal rainfall up to 74.4 mm and were the only clearly gauged andconsistent for simulation events. Before the calibration of the rain-fall-produced floods and the simulation of the flood, one of thesefloods (11–12 January 1995) was used to assess the sensitivityanalysis of the model, which was based on all the parameters ofthe model. The results of sensitivity analysis are presented in Table1a and b, based on the total runoff volume, the peak flow, the

al rainfall of 16.0 mm.

time of concentration 3.45 h, Clark storage coefficient 3.7 h, recession

9 10 11 12 13 1423.8 19.0 14.4 10.3 6.5 3.07.7 1.8 �4.9 �11.3 �17.4 �24.10 0 0 0 0 0

time of concentration 3.45 h, Clark storage coefficient 3.7 h, recession

3.5 4 4.5 5 5.5 655.8 48.3 39.4 30.6 22.6 14.146.3 38.3 28.5 18.2 6.9 �6.90 0 0 0 0 0

h, Clark time of concentration 3.45 h, Clark storage coefficient 3.7 h, recession

5 6 7 8 9 1019.0 26.8 32.8 38.1 42.5 46.41.8 10.0 16.9 22.3 27.5 32.10 0 0 0 0 0

nt rate 5.7 mm/h, impervious 5%, Clark storage coefficient 3.7 h, recession

2.5 3 3.5 4 4.5 519.2 19.4 19.1 18.4 17.4 16.32.7 �0.9 1.8 �4.9 �0.9 �4.9�1 0 0 1 1 1

rate 5.7 mm/h, impervious 5%, Clark time of concentration 3.45 h, recession

4.5 5 5.5 6 6.5 714.6 11.7 8.8 5.6 2.1 �0.7�11.3 �18.7 �25.6 �33.3 �42.1 �47.90 0 0 0 0 0

.7 mm/h, impervious 5%, Clark time of concentration 3.45 h, Clark storage

0.4 0.5 0.6 0.7 0.8 0.9914.3 15.0 16.1 17.0 17.9 19.0�1.9 �0.9 0.0 0.0 0.9 1.80 0 0 0 0 0

rate 5.7 mm/h, impervious 5%, Clark time of concentration 3.45 h, Clark storage

0.4 0.5 0.6 0.7 0.8 0.920.0 22.8 26.6 30.8 35.2 39.61.8 1.8 1.8 1.8 1.8 1.80 0 0 0 0 0

0

4

8

12

16

200

2

4

6

8

10

12

14

1618

:00

20:0

0

22:0

0

0:00

2:00

4:00

6:00

8:00

10:0

0

12:0

0

14:0

0

16:0

0

18:0

0

20:0

0

22:0

0

59-naJ-2159-naJ-11

Prec

ipita

tion

(mm

)

Out

flow

(m

3 /s)

0

5

10

15

20

250

10

20

30

40

50

60

12:0

014

:00

16:0

018

:00

20:0

022

:00

0:00

2:00

4:00

6:00

8:00

10:0

012

:00

14:0

016

:00

18:0

020

:00

22:0

00:

002:

004:

006:

008:

0010

:00

15-Feb-1981 16-Feb-1981 17-Feb-1981

Prec

ipita

tion

(mm

)

Out

flow

(m

3 /s)

0

5

10

15

20

25

300

10

20

30

40

50

60

70

80

1:00

3:00

5:00

7:00

9:00

11:0

013

:00

15:0

017

:00

19:0

021

:00

23:0

01:

003:

005:

007:

009:

0011

:00

13:0

015

:00

17:0

019

:00

21:0

023

:00

1:00

22-Feb-1981 23-Feb-1981 24

Prec

ipit

atio

n (m

m)

Out

flow

(m

3 /s)

Precipitation Q simulated Q observed

Fig. 6. Flow hydrographs for three of the rainstorms, used for the hydrologicalanalysis.

Table 2Model calibration results for the simulation of the eight raistorms.

Event Date Volume(m3)

Average rainfallintensity (mm/h)

P** (mm) Id (mm) Pe(m

1 30–31 January 1993 33,812 0.83 2.5 3.9 22* 11–12 January 1995 180,579 2.67 16.0 10.3 103 13–14 January 1995 151,577 0.32 10.4 11.0 104 29–31 January 1994 482,020 1.26 26.4 9.1 95 14–15 January 1995 408,760 2.91 32.0 8.0 206 7–8 February 1994 834,502 1.06 21.8 5.1 207* 15–17 February 1981 1,394,986 2.21 53.1 5.0 408* 22–24 February 1981 3,333,347 1.58 74.4 37.0 61

Average values

* Storms corresponding to flow hydrographs of Fig. 6.** P is average rainfall over the basin.

A.G. Koutroulis, I.K. Tsanis / Journal of Hydrology 385 (2010) 150–164 159

hydrograph, and the time phase of the peak discharge. Constantrate (CR) parameter, Clark storage coefficient (R), impervious per-cent of the basin, and initial deficit were found to be the parame-ters that could mostly affect the simulation results. The initialdeficit varies depending to the antecedent soil condition of eachevent. A range from 5 mm to 14 mm has been tested for this rain-fall event of 16 mm of total average precipitation. Sensitivity anal-ysis of this parameter resulted to a peak flow error from 28.5% to�24.1% and a volume error from 40.1% to 3.0%. Timing of the peakflow is not affected by initial deficit (Table 1a, first rows). The CRparameter depends on the physical properties of the watershedsoils, the land use and the storm precipitation characteristics(e.g., intensity) and represents the infiltration rate. Different valuesof CR were tested during sensitivity analysis varying from 1.5 to6 mm/h, taking into account Giofiros basin soil properties and landuse. Results show a peak flow error from 68.2% to �6.9%, a volumeerror from 74.5% to 14.1% and a phase error of 1 h for CR values be-tween 1.0 and 2.5 mm/h (Table 1a, middle rows). Imperviousparameter represents the percent impervious area of the basinand is defined based on the land use and soil properties of the ba-sin. Giofiros basin can be characterized by 5% impervious based onwatershed properties. Moreover, values ranging from 1% to 10%tested in order to examine the effect of the parameter, resultingto a peak flow error from �54.3% to 32.1% and a volume error from�36.9% to 46.4%, with no effect on phase error (Table 1a, lowerrows). The R parameter accounts for both translation and attenua-tion of excess precipitation as it moves over the basin toward theoutlet and depends on basin attributes and precipitation character-istics. Values ranging from 2.5 to 7 h tested resulting to a peak flowerror from 20.6% to �47.9% and a volume error from 24.6% to�0.7% (Table 1b, middle rows).

Calibration procedure and parameter estimation

Following the sensitivity analysis, rainfall–runoff simulationwas carried out for the eight precipitation events calculating theoptimum hydrological model parameters using the indices givenin Eqs. (9) to (16). The estimated and observed hydrographs withthe corresponding hourly precipitation data of three most repre-sentative rainstorms (in terms of peak discharge amplitude) arepresented in Fig. 6. Model calibration was based on the minimiza-tion of the error of the water volume (VE) from Eq. (11), the peakflow error (PFE) from Eq. (9), the phase error (PE) from Eq. (10)and the best performance of the time step based evaluation criteriafrom Eqs. (12) to (16). The calibration procedure resulted to theestimation of the characteristic parameters for the Giofiros basinrepresenting the physical properties of the watershed soils andland use and the antecedent-moisture condition. The initial deficitof the storms varied from 3.9 to 37 mm (Table 2) and is used as a

ak flow3/s)

Peak flowerror (%)

Phaseerror (h)

Nash–Sutcliff

Volumeerror (%)

RMSE AAPE(%)

r EV (%)

.3 0 0 0.90 �1.9 0.19 22.0 0.99 90.5

.8 1.8 0 0.90 13.4 0.96 16.5 0.99 91.7

.0 �4.2 0 0.69 18.5 1.10 17.4 0.99 82.2

.5 0.0 0 0.88 13.1 0.90 28.4 1.00 90.5

.1 �2.0 0 0.88 13.0 1.60 16.6 1.00 93.0

.3 0.0 0 0.53 3.2 3.07 26.9 0.98 53.2

.5 1.7 0 0.74 �5.4 3.51 27.0 1.00 88.5

.0 4.1 0 0.70 9.2 3.93 15.3 0.98 92.9

0.2 0 0.78 7.9 1.91 21.3 0.99 85.3

160 A.G. Koutroulis, I.K. Tsanis / Journal of Hydrology 385 (2010) 150–164

fitting parameter (during the present study Id was poorly linked toits physical meaning). The maximum deficit estimated at 91 mmand the impervious area to 5% of the basin based on land-use, geol-ogy, and soil maps. The parameter CR varied from 2.5 to 5.5 mm/haccording to the average precipitation intensity (API) (high API re-sults to high CR for all the storms). Fig. 7a contains the values of CRfor the calibration events plotted against the API. The time ofconcentration for Giofiros basin was estimated from the Kirpichformula (Kirpich, 1940) tc ¼ 0:0078ðL0:77=S0:385Þ ¼ 3:45 h, whereL is the basin’s travel length and S is the slope along main channel.R varied from 2.5 to 5.5 h according to API (high precipitation ratesresults to faster basin response and eventually to lower R values).

CR= 1.73API + 0.99R² = 0.8801

1

2

3

4

5

6

7

8

9

0 1 2 3 4 5

Con

stan

t Rat

e-C

R (

mm

/h)

API (mm/h)

StormEvents Flood

R= -1.31API + 6.71R² = 0.8696

1

2

3

4

5

6

7

0 1 2 3 4 5

Cla

rk S

tora

ge C

oeff

icie

nt-R

(h)

API (mm/h)

StormEvents Flood

(a)

(b)

Fig. 7. Correlation of ‘‘event scale” API (average precipitation intensity – mm/h)with CR (a) and R (b) values for the calibration events and estimation of parametersvalues for the flash flood event.

0

5

10

15

20

25

30

35

40

45

500

50

100

150

200

250

300

350

400

450

500

0:00

2:00

4:00

6:00

8:00

10:0

012

:00

14:0

016

:00

18:0

020

:00

22:0

00:

002:

004:

006:

008:

0010

:00

12:0

014

:00

16:0

018

:00

20:0

022

:00

13-Jan-94 14-Jan-94

Prec

ipita

tion

(mm

)

Out

flow

(m

3 /s)

Uncertainty boundariesPrecipitationQ observedQ simulatedStage gauge failure

Fig. 8. Simulation of 1994 Giofiros flood hydrograph at Finikia location by HEC-HMS model and uncertainty bars. The river gauge washed out at a very lowdischarge, probably from the suspending large particles of the bouldery front(Pierson, 1986).

Fig. 7b contains the values of R plotted against API, for the calibra-tion events. Base flow for each event was estimated and recessionration and threshold flow calibrated at 0.99 and 0.14, respectively.The calibration for the eight events resulted in (Table 2) an averageR2 of 0.99 and a zero phase error (PE) for all the events. The averagevolume error was 7.9% and the average value of the peak flow errorwas approximately 0.18%, while the average Nash and Sutcliffe(1970) criterion was 0.78. Overall, the calibration of the modelon the eight events was successful, showing good efficiency.

Flash flood peak flow estimation through hydrologic and hydraulicsimulation

Time series of 1 km2 spatial resolution hourly precipitationfields were generated from the three rainfall stations of Giofirosbasin according to the method that was previously described.The effect of initial deficit on the flood peak discharge estimatewas tested and proved to slightly affect the result. The Id was setat 8 mm, used as a fitting parameter to the measured hydrographuntil the stage gauge failure (Fig. 8).The CR based on Fig. 7a wasestimated at 7.1 mm/h and R at 1.5 h based on Fig. 7b. The simu-lated flow hydrograph with the data from the damaged river gaugeis presented in Fig. 8. The estimated total water volume was5.20 Mm3. The peak flow value was 296 m3/s. The maximum pre-cipitation intensity as well as the center of mass of precipitationtime series was observed at 20:00 of 13 January 1994, while thepeak discharge based on the simulation was observed at 24:00(Fig. 8). According to the rain-gauge measurements and the mete-orological analysis, high precipitation rates were observed over the

Fig. 9. A three dimension representation of the 1994 flood wave simulation – 3 htime step facing upstream. The upper cross-section is the Finikia control cross-section presented in Fig. 10. The lower cross-section is near the outlet of Giofirosbasin on the Mediterranean Sea.

Fig. 10. Channel-geometry characteristics of the Finikia River gauge control cross-section of the 1994 flood and measured flood extend.

H = 0.71Q0.43

D=R2 = 0.99

H = 1.16Q0.26

D=R2 = 0.99

0

1

2

3

4

5

6

0 100 200 300 400

H (

m)

Q (m3/s)

field measurements

Estimated values for n1=0.03 and n2=0.06

Estimated values for n1=0.03 and n2=0.08

Estimated values for n1=0.03 and n2=0.04

Estimated values for n1=0.04 and n2=0.06

Estimated values for n1=0.04 and n2=0.08

Estimated values for n1=0.04 and n2=0.04

Fig. 11. Water level stage-flow curve at the cross-section of Finikia (grey trianglescorresponds to the direct field measurements).

A.G. Koutroulis, I.K. Tsanis / Journal of Hydrology 385 (2010) 150–164 161

south part of the basin far from the outlet. Moderate precipitationwas recorded at the center and north part of the watershed. Postevent field campaigns confirm the timing of the flood peak throughwitness interviewing. An attempt to examine the propagation ofuncertainty of the CR and R parameters on the simulated peak flowmade by adding a percent of variation to these parameters, from�10% up to 10%. In addition, different precipitation realizationsin terms of temporal (±1 h offset) and intensity distribution(±40% peak precipitation intensity) between the stations with dailyand the one with hourly precipitation as described in Section‘‘Reconstruction of precipitation realizations of variable spatiotem-poral distribution”, constructed to examine the uncertainty of pre-cipitation records. A set of 343 different parameter combinationsand precipitation realizations, used in the hydrological model,resulting to an ensemble of output hydrographs. The effect of theCR and R parameters and precipitation component variation onthe hydrograph and peak flow is presented in Fig. 8 within theuncertainty area (boundaries). The uncertainty boundaries are de-fined by the ensemble area formulated by the 343 output hydro-graphs. Peak flow shows a linear rate of decrease as Clark storagecoefficient (R) increases (shorter response time of the basin). Therate of decrease is expressed by the equation peak flow ¼�43:79Rþ 361:91 taking into account a CR = 7.1 mm/h and valuesof R varying from 1.35 to 1.65. Moreover, peak flow shows a linearrate of decrease as CR increases (higher infiltration rates). The rateof decrease given by the equation peak flow ¼ �26:28CRþ 504:03for R = 1.5 and values of CR varying from 7.1 to 8.9 mm/h.

HEC-RAS was used for hydraulic modeling in order to validatethe flood extent at a control cross-section (cross-section with mea-sured flood high-water marks) and to simulate the flood wave. Thearea of simulation is presented in Fig. 1 as the outflow sub-basin.The flood hydrograph resulted from rainfall–runoff modeling usedas input for the hydraulic model and the geometric setup of themodel was based on information retrieved by cross-sections andthe DTM of the study area. A three dimensional flood wave simu-lation is presented in Fig. 9 at a 3-h time step. The simulated floodextent corresponds to the measured flood extent in the controlcross-section as presented in Fig. 10. The observed value of thepeak flood flow level was 5.1 m and the simulated value was5.08 m at 24:00 January 13. The maximum value of average flowvelocity at the control cross-section and the corresponding Froudenumber were estimated at 3.62 m/s and 0.62, respectively for Jan-uary 13th at 24:00. Moreover, the propagation of uncertaintythrough the hydraulic model was examined. The previously pre-sented ensemble of 343 hydrographs imported to the hydraulicmodel providing 343 realizations of the maximum flood extendfor the control cross-section. The maximum flow level varied be-tween 4.96 m and 5.19 m, the maximum average flow velocity var-ied from 3.47 m/s to 3.77 m/s and the corresponding Froudenumber varied from 0.61 to 0.64.

Flash flood peak flow estimation from post flood measurements

Because there were no observed field flow data, the evaluationof the results was based on an indirect method for the estimationof the real peak flow, from a specific cross-section called Finikia(Fig. 10). This cross-section was at the location where the waterflow level gauge was located, during the flood. Eq. (5) was appliedusing S (energy slope) equal to 0.003 m/m as calculated from thestream’s topography. Giofiros is a natural stream channel withfairly regular sections with some grass weeds and little brush init. Flood plains, during winter time, are covered by short grassand medium to dense bushes. The literature (Arcement andSchneider, 1989; Chow et al., 1988) suggests n1 value of 0.03 forthe main channel (the main channel is a weedy – stony earth chan-nel) and n2 values for floodplains from 0.04 (short grass with minorobstructions and moderate rises and dips) to 0.08 (medium todense brush with appreciable obstructions and very irregularshape of floodplain). Flow rates were available from the existingrating curves for up to 2.8 m water level. Furthermore the totalflow was estimated for selected values of water level, starting from3.0 m up to 5.1 m (Fig. 11). Roughness coefficient is the mostimportant parameter of Eq. (5). A sensitivity analysis of flow out-put for different values of n1, ranging from 0.03 to 0.04 and forn2, ranging from 0.04 to 0.08 was performed. Table 3 containsthe parameters of Eq. (5) for various flow levels up to 5.1 m thatwas the maximum flood level of the control cross-section. Theresults of this analysis showed that Q varied from 220 m3/s forn1 = 0.04 and n2 = 0.08 to 350 m3/s for n1 = 0.03 and n2 = 0.04(Table 3). Peak flow for 1994 flood was estimated using Eq. (5) at

Tabl

e3

Var

iati

onof

flow

for

diff

eren

tflo

wle

vel

and

n 1an

dn 2

valu

es.

n 10.

030.

040.

030.

040.

030.

04n 2

0.04

0.04

0.06

0.06

0.08

0.08

h(m

)A

1(m

2)

A2

(m2)

P 1(m

)P 2

(m)

R 1(m

2/m

)R

2(m

2/m

)S

(m/m

)Q

tota

l(m

3/s

)Q

tota

l(m

3/s

)Q

tota

l(m

3/s

)Q

tota

l(m

3/s

)Q

tota

l(m

3/s

)Q

tota

l(m

3/s

)

319

.63

015

.90

1.23

00.

003

41.2

30.9

41.2

30.9

41.2

30.9

3.2

22.2

80

17.0

30

1.31

00.

003

48.6

36.4

48.6

36.4

48.6

36.4

3.4

25.1

40

18.1

70

1.38

00.

003

56.9

42.7

56.9

42.7

56.9

42.7

3.6

28.1

820

.61

18.8

438

.57

1.5

0.53

0.00

385

.869

.079

.662

.876

.559

.73.

831

.328

.519

.23

40.2

31.

630.

710.

003

110.

090

.399

.779

.994

.574

.84

34.4

836

.59

19.6

340

.85

1.76

0.9

0.00

313

8.2

115.

212

2.6

99.7

114.

992

.04.

237

.74

44.8

20.0

341

.49

1.88

1.08

0.00

316

9.6

143.

414

8.1

121.

813

7.4

111.

14.

441

.07

53.1

320

.43

42.1

2.01

1.26

0.00

320

4.4

174.

517

6.0

146.

216

1.9

132.

04.

644

.46

61.5

720

.82

42.7

32.

141.

440.

003

242.

120

8.5

206.

317

2.6

188.

315

4.7

4.8

47.9

270

.13

21.2

343

.36

2.26

1.62

0.00

328

2.8

245.

223

8.7

201.

121

6.7

179.

05

51.4

678

.81

21.9

744

.58

2.34

1.77

0.00

332

3.4

282.

027

0.8

229.

424

4.5

203.

15.

153

.25

83.2

21.8

244

.32.

441.

880.

003

349.

630

5.6

291.

824

7.8

262.

921

8.9

162 A.G. Koutroulis, I.K. Tsanis / Journal of Hydrology 385 (2010) 150–164

292 m3/s for n1 = 0.03 and n2 = 0.06, compares well with the simu-lation result based on hydrological model.

Flash flood peak flow estimation based on an empirical method

A number of non-flood causing rainfall events when the water-stage gauge was operating were used for the estimation of theparameter d of Eq. (4). The hydrologic characteristics of the rain-fall–runoff events are included in Table 4. When the total runoffvolume VT (m3) for a sufficient number of gauged events are plot-ted against the product of the square of total precipitation P andthe standard deviation of precipitation rP (Fig. 12), a linear relationis evident described by Eq. (2) with a = 215 as a coefficient for Gio-firos basin. The extrapolation of the regression line meets the val-ues of the 1994 flash flood event. Moreover, when the total runoffvolume VT (m3) for the same events, are plotted against the productof the peak discharge Qpeak and duration of precipitation time ser-ies D of each event (Fig. 13) provides the power regression Eq. (3)with b = 0.0118 and c = 1.3702 as coefficients for Giofiros basin.The elimination of VT from Eqs. (2) and (3) results in d = 18.5 andconsequently to Eq. (17), so given the coefficients and the precipi-tation time series allows estimating the peak discharge of an eventfor Giofiros watershed.

Qpeak ¼18:5

DðP2

TrPÞ1:3702 ð17Þ

Based on Eq. (17) the peak flow of the gauged and the flash floodevents was estimated. Table 4 contains the estimated peak flow.Peak flow for the 1994 flash flood event based on the empirical

V= 215P2σP R² = 0.9093

0.0E+00

1.0E+06

2.0E+06

3.0E+06

4.0E+06

5.0E+06

6.0E+06

7.0E+06

0 5000 10000 15000 20000 25000 30000

Tota

l Eve

nt V

olum

e (m

3 )

P2σP (mm3)

Events 1994 FF Event

Fig. 12. Total runoff volume VT (m3) as a function of precipitation squared times itsstandard deviation.

QpeakD= 0.0118V1.3702

R² = 0.9709

0.0E+00

5.0E+06

1.0E+07

1.5E+07

2.0E+07

2.5E+07

Qpe

akD

(m

3 )

Total Event Volume (m3)

Events 1994 FF Event

Fig. 13. Total runoff volume VT (m3) as a function of the product of the peakdischarge and the duration of precipitation for each event.

Table 4Hydrologic characteristics of rainfall–runoff events for peak discharge estimation based on the empirical equation. Peak flow for flash flood event (case 9) is estimated throughhydrological modeling.

Case Date Total event runoffvolume (m3)

Totalprecipitation (mm)

rp DEV ofprecipitation mm)

Duration ofprecipitation (h)

Runoffcoefficient

Peak flow(m3/s)

Estimated peakflow (m3/s)

1 30–31 January 1993 33,812 2.5 0.59 3 0.09 2.3 0.02 11–12 January 1995 180,579 16.0 2.24 6 0.07 10.8 5.23 13–14 January 1995 151,577 10.4 4.67 2 0.09 10.0 13.04 29–31 January 1994 482,020 26.4 0.87 17 0.12 9.5 2.05 14–15 January 1995 408,760 32.0 2.74 11 0.08 20.1 24.86 7–8 February 1994 834,502 21.8 0.76 21 0.24 20.1 0.87 15–17 February 1981 1,394,986 53.1 2.51 24 0.17 40.5 40.48 22–24 February 1981 3,333,347 74.4 2.74 47 0.28 61.0 58.69 (FF) 13–14 January 1994 5,195,000 75.7 4.36 19 0.43 296 287.4

A.G. Koutroulis, I.K. Tsanis / Journal of Hydrology 385 (2010) 150–164 163

method estimated to 287 m3/s that compares very well with therainfall–runoff simulation output. The empirical equation hassmaller error in higher peak flows which is the operational rangeof interest. Storm events with low standard deviation of precipita-tion are not well represented by the empirical approach as shownin Table 4 and in Fig. 12.

Empirical equation rationale

Based on hydrological characteristics of the 1994 flash floodevent (PT, rP, D, VT) we examine the rationale of the empiricalEq. (4). The duration of the event was D = 19 h, the total arealprecipitation over the basin was PT = 75.5 mm, the standard devia-tion of the precipitation time series was rP = 4.36 mm and the total

Qpeak = 38.213σP1.3702

0

50

100

150

200

250

300

350

400

450

500

0 2 4 6 8

Peak

Flo

w (

m3 /

sec)

σP (standard deviation of precipitation in mm for a 19h rs duration event of 75.7 mm total P

Generated events FF Event

Qpeak = 5459.9D-1

0

50

100

150

200

250

300

350

400

450

0 10 20 30 40 50

Peak

Flo

w (

m3 /

sec)

D (duration in hrs for an event of 75.7mm total P and σP of 4.36 mm

Generated events FF Event

(a)

(b)

Fig. 14. Flash flood peak flow variation with storm duration and standard deviationof the total precipitation (75.7 mm) (a) storm duration = 19 h and (b) standarddeviation = 4.5 mm.

volume based on rainfall–runoff simulation was estimated VT =5.20 Mm3. Assuming a set of the same total precipitation and dura-tion but of different standard deviation varying from 1 mm up to6 mm increasing by 0.5 mm, the expected peak flow was estimatedto be 287 m3/s. Fig. 14a illustrates the expected peak flow versus aprecipitation event with the same total precipitation and durationof the 1994 flash flood event but different temporal distribution ofrainfall expressed by the standard deviation of the precipitationtime series. Precipitation distributions with higher standard devia-tions results in higher peak discharges. By keeping the total precip-itation the same and increasing the standard deviation by 20%,which corresponds four times higher precipitation intensity atthe 2-h peak of the storm, the peak flow was estimated viaFig. 14a at 365 m3/s which agrees with the value obtained withthe other two methods. With the duration varying from 13 h upto 46 h in increments of 3 h, but keeping the total precipitationand standard deviation the same, the peak flow was estimated.Fig. 14b shows that shorter duration events correspond to higherpeak discharges.

Conclusions

During many flash flood events there may be a water-stagegauge failure or the flood stage far exceeds the maximum valueof the gauge’s rating curve that makes the estimation of the peakdischarge difficult. A method for estimating flash flood peak dis-charge, hydrograph, and volume is presented that uses the mea-sured rainfall data and river hydrographs in a number of non-flood causing rainstorms with an operating water-stage gauge forcalibration and verification of the simulated stage-dischargehydrographs. An empirical equation also was developed in orderto provide the peak discharge as a function of the total precipita-tion, its standard deviation and storm duration while the value ofthe coefficients depend on the characteristics of the basin. Thepeak discharge for a flash flood case based on the empirical equa-tion, is in agreement with the one calculated via the verified hydro-logical model and the one derived based on Manning’s equationand post flood measurements of the control cross-section (e.g.,all values were close to 290 m3/s for the 1994 flood on the GiofirosRiver). These methods can be applied to other poorly gauged basinsfacing common stage gauge failures or poorly defined rating curvesduring flash floods caused by severe convective rainstorms. Thecoefficients that represent the characteristic of the basin have tobe developed for the individual basin.

A severe storm that produces a flash flood can be approachedwith a variety of methods. Among others, meteorological analysis,hydrological modeling, hydraulic modeling and analysis, postevent campaigns for data retrieving (flood marks, peak flow timingthrough interviews) can be used to provide additional informationfor reliable peak discharge estimations. This multilateral approach,

164 A.G. Koutroulis, I.K. Tsanis / Journal of Hydrology 385 (2010) 150–164

as described in the present study, reduces uncertainty in the eventinterpretations.

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