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HYDROLOGICAL PROCESSESHydrol. Process. (2011)Published online in Wiley Online Library(wileyonlinelibrary.com) DOI: 10.1002/hyp.8384

Design hydrograph estimation in small and ungaugedwatersheds: continuous simulation method versus

event-based approach

S. Grimaldi,1,2,3* A. Petroselli4 and F. Serinaldi5,61 Dipartimento per l’innovazione nei sistemi biologici, agroalimentari e forestali (DIBAF Department), University of Tuscia, Via San Camillo De Lellis snc,

01100 Viterbo, Italy2 Honors Center of Italian Universities (H2CU), Sapienza University of Rome, Via Eudossiana 18, I-00184 Roma, Italy

3 Department of Mechanical and Aerospace Engineering, Polytechnic Institute of New York University, Six MetroTech Center, Brooklyn, NY 112014 Dipartimento di Scienze e Tecnologie per l’Agricoltura, le Foreste, la Natura e l’Energia (DAFNE Department), University of Tuscia, Via San Camillo

De Lellis snc, 01100 Viterbo, Italy5 School of Civil Engineering and Geosciences, Newcastle University, Newcastle Upon Tyne, NE1 7RU, UK

6 Willis Research Network, 51 Lime St., London, EC3M 7DQ, UK

*Csistof TE-m

Co

Abstract:

The proper assessment of design hydrographs and their main properties (peak, volume and duration) in small and ungauged basins is akey point of many hydrological applications. In general, two types of methods can be used to evaluate the design hydrograph: oneapproach is based on the statistics of storm events, while the other relies on continuously simulating rainfall-runoff time series. In thefirst class ofmethods, the design hydrograph is obtained by applying a rainfall-runoffmodel to a design hyetograph that synthesises thestorm event. In the second approach, the design hydrograph is quantified by analysing long synthetic runoff time series that areobtained by transforming synthetic rainfall sequences through a rainfall-runoff model. These simulation-based procedures overcomesome of the unrealistic hypotheses which characterize the event-based approaches. In this paper, a simulation experiment is carried outto examine the differences between the two types of methods in terms of the design hydrograph’s peak, volume and duration. Theresults conclude that the continuous simulation methods are preferable because the event-based approaches tend to underestimate thehydrograph’s volume and duration. Copyright © 2011 John Wiley & Sons, Ltd.

KEY WORDS synthetic design hydrograph; intensity–duration–frequency curves; WFIUH model; continuous models;ungauged basins

Received 26 June 2011; Accepted 12 October 2011

INTRODUCTION

Evaluation of the Synthetic Design Hydrograph (SDH)for small and ungauged watersheds is a fundamental topicin hydrology because the SDH is the input of severalwater construction designs and flood risk mappingprocedures (PAI, 2006; Directive 2007/60/EC, 2007;FEMA, 2009). The literature and textbooks suggest twodistinct approaches to evaluate the SDH, which are called‘event-based’ and ‘continuous simulation’ methods.The well-known ‘event-based’ schemes define the SDH

through the rainfall-runoff transformation of a designhyetograph with an assigned return period (T), which isdeduced by the intensity–duration–frequency (IDF) curves(Soczyñska et al., 1997; Hsieh et al., 2006; Alfieri et al.,2008). The more recent ‘continuous simulation’ schemesconsist of generating a long synthetic rainfall time series andtransforming it through a continuous rainfall-runoff model(Boughton and Droop, 2003; Faulkner and Wass, 2005;Haberlandt et al., 2008; McMillan and Brasington, 2008;

orrespondence to: S. Grimaldi, Dipartimento per l’innovazione neiemi biologici, agroalimentari e forestali (DIBAF Department), Universityuscia, Via San Camillo De Lellis snc, 01100 Viterbo, Italy.ail: [email protected]

pyright © 2011 John Wiley & Sons, Ltd.

Moretti and Montanari, 2008; Blazkova and Beven, 2009;Calver et al., 2009, Viviroli et al., 2009, Grimaldi et al.,under review). The SDH with an assigned return periodis obtained by a subsequent analysis that synthesisesthe main statistical and physical properties of thesimulated hydrographs (Pramanik et al., 2010; Serinaldiand Grimaldi, 2011).The event-based procedure is widely adopted due to the

availability of extreme value observations provided by theannual reports of hydrologic offices, which allows easyestimation of the IDF curves. However, this approach isbased on some concepts and assumptions whose effectsare difficult to quantify. Indeed, the simplified hyetographshape, the concept of critical rainfall duration, the lack ofinformation about the antecedent soil wetness conditionsand the hypothesis that the design storm and the SDHhave the same return period can influence the results(Rahman et al., 2002; Hoes and Nelen, 2005; Alfieriet al., 2008; Verhoest et al., 2010).Many authors have evaluated, directly or indirectly, the

event-based and continuous simulation methods duringthe past years. For instance, Nnadi et al. (1999) comparedthe two approaches and found that the differences betweenthe resulting peak discharge (Qp) were significant andvaried with the return period. Grimaldi et al. (2005) and

S. GRIMALDI, A. PETROSELLI AND F. SERINALDI

Verhoest et al. (2010) showed that the available event-basedmethods are not well suited for reproducing the SDHvolume (V) and duration (D), given the SDH’s Qp. There-fore, the influence of the assumptions underlying the event-based method is pivotal when the SDH is used in hydraulicriskmapping procedures, whereby the SDH’sV andD are asimportant as the Qp. As recalled by Viglione and Bloschl(2009), the hypothesis that the hyetograph peak and theSDH’s Qp have the same return period is considered to berather ‘obscure’ in the seminal study by Pilgrim andCordery(1975), where the design storm concept was introduced. Inthis context, Viglione and Bloschl (2009), Viglione et al.(2009) and Rahman et al. (2002) performed some simplifiednumerical and theoretical experiments to clarify therelationship between the Qp return periods obtained by thetwomethods, while Nishat et al. (2010) investigated the roleof the antecedent soil moisture condition in the event-basedapproach. To evaluate the performance of five designhyetographs, Alfieri et al. (2008) developed an idealexperiment whereby a synthetic rainfall time series wasgenerated and transformed by a simple rainfall-runoffmodel. The resulting runoff series were analysed to definetheQpwith an assigned return period. The synthetic rainfallwas also used to extract the IDF curves and to define fivedesign hyetographs, which were transformed by the samerainfall-runoff model. Finally, the five event-based Qp

values were compared with the corresponding continuoussimulation Qp (with the same nominal return period).In this study, the event-based and continuous simulation

methods are compared through a simulation experimentsimilar to that described by Alfieri et al. (2008); however,the simple IUH model is replaced by a complete simulationframework devised for small and ungauged basins(Grimaldi et al., under review) and calibrated with a real-world scenario. Moreover, the analysis is extended to theSDH’sV and D, which are key attributes in hydraulic riskmapping analyses and water resource management prob-lems. Finally, the sensitivity of the results is also examinedto provide insight into the nature of the differences betweenthe event-based and continuous simulation methods.The paper is organised as follows. Next Section provides

an overview of the simulation experiment and brieflydescribes the modelling framework. Further Sectionpresents the observed data used to calibrate the rainfall-runoff model. In the last two Sections, we discuss the resultsrelated to the set of parameters calibratedwith the real-worldscenario, presenting also a comparison of 100 combinationsof rainfall-runoff model parameters. Conclusions and finalrecommendations close the study.

DESCRIPTION OF THE SIMULATIONEXPERIMENT

a. Overview

The quantitative comparison of the event-based andcontinuous simulation methods relied on 500 years ofsynthetic rainfall data at a time resolution of 5min that

Copyright © 2011 John Wiley & Sons, Ltd.

was generated by a two-stage rainfall model (Serinaldi,2009, 2010), which had been transformed into arunoff time series by a continuous rainfall-runoff model(Grimaldi et al., under review). As previouslymentioned,the framework was devised for small and ungaugedbasins for which only rainfall and geomorphologicalinformation are available. Therefore, when the modelparameters were calibrated to the real basin’s data, themodel yielded realistic pseudo-observed runoff timeseries. Thus, the resulting values of the hydrograph’sQp, V and D with a fixed return period T, whichwere extracted from the synthetic runoff time series, areconsidered to be pseudo-observed and represent thecontinuous simulation reference data set. For the event-based procedure, the IDF curves were estimated based on500 years of synthetic rainfall. The rainfall intensitieswith assigned T values were used to construct fivedifferent synthetic hyetographs, which were in turntransformed using the same rainfall-runoff parametersand theoretical schemes applied in the continuoussimulation method. The procedure yielded event-basedSDHs whose Qp had the same nominal T as the synthetichyetograph. Thus, the differences between the results ofthe two methods should be exclusively due to theassumptions underlying the event-based synthetic hyeto-graphs. In the following subsections, we provide a briefdescription of the continuous simulation model and theevent-based method, which were applied in the subse-quent analyses; the cited references should be referred tofor further details.

b. Continuous model

The applied continuous simulation framework (COn-tinuous Simulation MOdel for Small Ungauged Basins -COSMO4SUB) is a multi-step procedure recentlyproposed by the authors (Grimaldi et al., under review).In the first step, a two-stage rainfall generator was usedto simulate 500 years of 5-min synthetic rainfall. Therainfall model consisted of a single-site copula-baseddaily rainfall generator (Serinaldi, 2009) and thecontinuous-in-scale universal multifractal model(Schertzer and Lovejoy, 1987) to disaggregate the dailyrainfall to a 5-min time scale. The parameters related tothis step (six for each month for the daily rainfallsimulator and three for the disaggregation model) werecalibrated by using the available rainfall observations. Inthe second step, the Soil Conservation Service-CurveNumber (SCS-CN) method (USDA, 1986; Chow et al.,1988; Tramblay et al., 2010) was applied to the simulatedrainfall scenario to determine the excess rainfall. For theproposed analyses, the SCS-CN method was applied byselecting l= 0.2 (as suggested by USDA-NRCS, 2010).As explained in detail by Grimaldi et al. (under review),continuous implementation of the SCS-CN methodrequired an additional parameter called the eventseparation time (Ts). This is the no-rain time interval forwhich the SCS-CN initial abstraction is independent tothe previous storm. From a practical point of view, Ts

Hydrol. Process. (2011)DOI: 10.1002/hyp

DESIGN HYDROGRAPH ESTIMATION: CONTINUOUS VERSUS EVENT-BASED APPROACH

helps to select the instant at which the cumulative grossand excess precipitation must be reset to zero in the SCS-CN implementation. In the third step, a geomorphologi-cal rainfall-runoff filter was applied to the excess rainfalltime series to obtain the corresponding runoff scenario.We used an advanced version of the well-known WidthFunction Instantaneous Unit Hydrograph (WFIUH)(Grimaldi, et al. 2010; Grimaldi et al., in press) thatallowed the watershed IUH to be defined by assumingonly one parameter (WFIUH-1par), which was calibratedwith the value of the concentration time (Tc). Therefore,the excess rainfall is convolved through the IUH to obtainthe runoff scenario. Finally, the event hydrographs areidentified as continuous sequences of positive runoffvalues separated by at least one zero value.

c. Event-based model: IDF and design hyetographs

The rainfall frequency analysis and estimation of the IDFcurves were carried out as by Alfieri et al. (2008) to havecomparable results. The IDF curves were modelled by athree-parameter formula (Chow et al., 1988):

i d; Tð Þ ¼ a Tð Þb Tð Þ þ dc Tð Þ (1)

where i(d,T) is the rainfall intensity related to the dduration [h] and to the T return period (in years). Anonlinear least-squares method was applied to estimatethe parameters a(T), b(T) and c(T). In more detail, thereturn period was computed from the series of n annualmaxima for each duration from 5min to 24 h by using therelationship between T and the empirical cumulativedistribution function, which is expressed by the Weibullformula:

j

nþ 1¼ 1� 1

T(2)

where j=1,. . ., n denotes the jth observation of thesamples arranged in ascending order.The rainfall inten-sity was rearranged over the time span d by fivehyetographs: the rectangular hyetograph (related to therational method), the Chicago hyetograph and the BLUE

Divide

River network

Elevations

85 - 100

100 - 200

200 - 300

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400 - 500

500 - 600

600 - 625

Figure 1. DEM for the watershed case study. The


hyetograph applied by Alfieri et al. (2008) as well as thetriangular and Sifalda hyetographs. Referring to Alfieriet al. (2008) for a description of the first three methods,we recall that each design hyetograph is characterised bythe same cumulative rainfall depth P [mm]. In thetriangular hyetograph, the rainfall intensity is equal tozero at the beginning of the event (t=0), increaseslinearly until the middle of the event (t=D/2) when itassumes a value of 2P/D, and then decreases linearly untilthe end of the event (t=D) when it is again equal to zero.In the Sifalda hyetograph, the rainfall intensity starts at avalue of 0.15P/D, increases linearly until t=D/4 where ithas value of P/D, then increases abruptly at t=D/4assuming the value of 2.3P/D, maintains this value untilt=D/2, and decreases linearly until the end of the eventwhere it assumes the value of 0.2P/D. The Chicagohyetograph was set up by assuming a symmetric patternwith rC= 0.5, where rC is the ratio between the peakposition and the concentration time. Therefore, the SCS-CN procedure was applied to the five hyetographs todefine the excess hyetographs by using the same CNvalue that was applied in the continuous simulationscheme. Moreover, as prior rainfall information was notavailable, we assumed the Antecedent Moisture Condi-tion AMC=2. Finally, the hydrograph was determinedby applying the same WFIUH-1par and Tc value used inthe continuous simulation.

DATA AND MODEL SETUP

To provide grounded conclusions, the models werecalibrated using rainfall and geomorphological data fromthe Torbido River (basin drainage area 61.67 km2), whichis a small tributary of the Tiber River located in centralItaly. The Italian Geographic Military Institute (IGMI)(IGMI, 2003) provides integer precision DEM at a 20-mspatial resolution, while land cover is available from thewebsite CORINE (CORINE, 2000). The watershed DEM,drainage network and land cover map are shown inFigure 1, while Table I summarises the watershed’s maincharacteristics.Observed rainfall data are available from the Castel

Cellesi rain gauge station for a period of 49 years (1951 to

Divide

Discontinuous urban fabric Mineral extraction sites

Non-irrigated arable land Vineyards

Olive groves

Complex cultivation

Land principally occupied by agriculture

Broad-leaved forest Moors and heathland

Transitional woodland shrub

Sparsely vegetated areas

drainage network and soil use map are shown


Table I. The main characteristics of the watershed case study

Torbido watershed properties

DEM source IGMIcellsize (m) 20Precision integeroutlet coordinate north - UTM 33N 4721505outlet coordinate east - UTM 33N 272623area (km2) 61.67min elevation (m) 85.0max elevation (m) 625.0mean elevation (m) 373.8max slope (%) 375.0mean slope (%) 21.9main channel length (km) 24.50maximum divide-outlet distance (km) 25.81


1971, 1976 to 1982, 1989 to 2002) at a daily time scale(Serinaldi, 2009) and for a period of 10 years (1995 to 2000,2002, 2003, 2005, 2006) at a 5-min resolution (Serinaldi,2010). These data were used to calibrate the two-stagerainfall model by exploiting the longer daily series to obtainreliable synthetic daily rainfall simulations in the first stageand by using the shorter 5-min series to calibrate the

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disaggregation model in the second stage. The mainphysical attributes that were computed for the observedand simulated 500 years of rainfall are shown in Figure 2.The 5-min rainfall intensity is reproduced quite well(Figure 2a). The upper tail is strongly skewed, as thecalibrated universal multifractal model applied in thedisaggregation stage allows for unbounded singularities.Even though the physical meaning of these extreme valuescould be questioned, these rare and large rainfall valuescannot be excluded a priori, because of the limited size of theobserved time series. Defining rainfall event as sequences ofrainfall values that are separated by at least seven hours of norain, it can be seen that the event rainfall amount is simulatedrather well (Figure 2b). It is worth noting that theaccumulation process smoothes out the extreme valueswhich therefore do not influence the storm rainfall amount.The wet and dry spell lengths exhibit a positive and negativebias, respectively. This behaviour is related to the simulationof small, isolated, positive rainfall values. In fact, looking atthe left side of Figure 2c,we can see that themodel simulatesa percentage of 5-min isolated values larger than theobserved percentage, and, then, this initial bias propagatesalong the whole distribution. On the other hand, these

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12- and 24-h data


isolated values break the dry periods, thus reducing theirlength. Even though these spurious values can be corrected,they were preserved, as the overall pattern of the simulatedseries is not really influenced, and reproduces the observedrainfall sequences and the scaling properties rather well. Asmentioned previously, since the calibrated universal multi-fractal model produces unbounded singularities, the meanand standard deviation of the annual maxima at the finesttime scales tend to be overestimated. On the other hand, theaggregation process smoothes out the isolated, raremaxima,thus giving coarse-scale annual maxima close to theobserved values. Therefore, the simulated rainfall seriesallows for testing the rainfall-runoff model against a suitableset of storms similar to the observed events and againstunobserved and severe storms as well.As previously mentioned, the excess rainfall time series

was obtained by applying the SCS-CN method, settingl = 0.2 and CN= 74.6. The CN value was estimated fromthe land cover map and from the table shown in USDA-NRCS (2010 - Chapter 9, pp. 2–3). The event separationtime Ts was assumed equal to 24 h making the physicalhypothesis that, in this region, the initial abstractionphenomena return to the pre-event condition in one day.This parameter was the only one that was not applied inthe event-based scheme. As shown in Grimaldi et al.(under review) and in the next section, Ts does not stronglyinfluence the results. The WFIUH-1par and the convolutionof the excess rainfall series were computed as describedby Grimaldi et al. (2010) and Grimaldi et al. (in press).The only calibration parameter (the channel velocity)required to determine the flow time was estimated byusing the concentration time Tc = 4.5 h, which wasquantified through an empirical formula (Giandotti,1934) widely used in Italy.

EXPERIMENTAL RESULTS AND DISCUSSION

Comparison of the event-based and continuous simulations

The 500 years of synthetic rainfall and runoff that weresimulated with the continuous model (calibrated on theTorbido River data) have been used to compare thehydrographs resulting from the event-based and continuoussimulation approaches.First, the event-based T-year hydrograph was con-

structed starting from the definition of the three-parameterIDF curves (Equations 1 and 2). For T equal to 5, 10, 20,50 and 100 years, Figure 3 shows the amount–duration–frequency (ADF) curves corresponding to the IDF curves.The empirical ADF values (dots) were estimated for all ofthe durations from a multiple of 5min up to 24 h, whilethe three-parameter IDFs (and the corresponding ADFs)were estimated from the 1-, 3-, 6-, 12- and 24-h data to bemore consistent with common practical applications. Forhigh T values, there are some differences between theempirical and theoretical ADF curves. However, eventhough they may under- or overestimate the hyetographproperties, this specific discrepancy is not considered andnot further analysed in this study.


For a duration D equal to the concentration time of theTorbido River basin (Tc = 4.5 h), the IDF (ADF) curvesprovide the event rainfall intensity (amount) for theassigned T values. The corresponding five synthetichyetographs that were previously described are shown inFigure 4a for T= 10 years.As expected, there is an evident difference among the

five approaches. In particular, the Chicago methodexhibits the most prominent peak (about three times thepeak of the other hyetographs); this behaviour is similarfor every T (figure not shown). These differences are lessevident for the net rainfall hyetographs obtained by theSCS-CN method (see Figure 4b and 5).The five hydrographs corresponding to the five

hyetographs were obtained by applying the sameWFIUH-1par. Figure 6 shows the relationships betweenthe resulting event-based Qp, V and D, and the returnperiod T.The following observations can be drawn from

Figure 6:

• for T values lower than 20 years, the Qp valuescorresponding to the five parent hyetographs aresimilar to each other;

• the BLUE hyetograph overestimates the peak dis-charge as given by the rectangular hydrograph by16.1% and 17.6% for T= 50 and 100 years, respect-ively;

• the BLUE and Chicago methods yield similar Qp

values as T increases; and• for V and D, no particular behaviour is evident. Thevalues are stable with small variation (the maximumrelative difference between the rectangular andChicago volumes is about �3.5% for T= 100 yearsand about 12.1% between the rectangular and BLUEdurations for T= 100 years).


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To compare the event-based method and the continu-ous simulation approach, the hydrographs with an annualmaximum Qp were selected from the synthetic runoff timeseries. Then, the continuous simulation T-year Qp wascomputed from the empirical distribution function viaEquation 2. The V and D values associated with theannual maximum Qp were computed for the selectedhydrographs; their relationship with Qp was synthesisedby linear regressions of both Qp and V, and Qp and D assuggested by Serinaldi and Grimaldi (2011). Therefore,the T-year Qp and the corresponding V and D areavailable for comparison with the event-based T-year Qp,V and D. Figure 7 shows the event-based results (alreadydisplayed in Figure 6) and the continuous simulationresults. The differences between the two methods arerelevant for all three hydrograph attributes and arehomogeneous for T greater than 20 years. For instance,for T= 100 years, the relative difference between theChicago and continuous simulation approach is about11.6% for Qp, -47.5% for V and �82.7% for D).Because the continuous approach included the Ts

parameter, which was not present in the event-basedscheme, we verified whether its variability can modify theresults. To accomplish this task, the continuous simulation


model was applied by varying Ts between the tworeasonable limit values of 6 and 36 h. The grey areas inFigure 7 denote the range of Qp, V and D valuescorresponding to the range of Ts and confirm that Ts doesnot influence the results very much.

Analysis of the influence of the infiltration scheme and theshape of the rainfall pattern

The relevant differences between the event-based andcontinuous simulation approaches shown in Figure 7 wereprobably due to several reasons. However, in the following,two aspects are studied in more depth:

• the effect of the infiltration method’s implementation,which was rather different in the two schemes;

• the effect of the rainfall event’s time pattern, whichmight have been too simple in the event-based synthetichyetographs.

To evaluate the role of the infiltration method’simplementation, the event-based approach was applieddirectly to the 500 years of excess synthetic rainfall. In otherwords, by keeping the event-based procedure (and setup)


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unchanged, the infiltration step was moved to the beginningof the analysis as in the continuous simulation method.Figure 8 compares the five new event-based relationshipsbetween the hydrograph’s attributes and T corresponding tothe analysis developed directly from the excess rainfall timeseries. The relevant role of the infiltration step is clear. Allfive hyetographs provide higher values ofQp,V andD for allof the T values. The Qp values are now close to thoseresulting from the continuous simulation method, while Vstill exhibits a significant difference (e.g. �24.2% betweenChicago hyetograph and continuous simulation method forT=100 years) but is smaller than that in Figure 7. The Dvalues seemed to be rather insensitive to the infiltrationscheme’s application.Once the importance of the infiltration scheme was

established based on the differences between the event-based and continuous approaches, a further analysis wasconducted to understand the reasons for this relevantdifference. Apparently, this discrepancy could be due tothe AMC parameter used in the SCS-CN approach.Indeed, the CN value can be adapted to the initial soilmoisture condition only if the antecedent five-day rainfallamount is known. However, this quantity was notavailable in the event-based approach, which led to thechoice of AMC=2. To clarify the role of this parameter,


the continuous simulation approach was applied bysetting AMC=2 without considering the antecedent soilwetness. The attribute values obtained are higher thanthose obtained by varying the AMC parameter for all Tvalues. Thus, the AMC could not explain the above-mentioned difference.The reason for the relevant effect of infiltration is

probably related to rainfall patterns (the second possiblecause mentioned at the beginning of this section). In theevent-based method, V and D resulted from the analyticalformula of the five hyetographs (once Tc and i(Tc,T) wereselected), whereas the real simulated rainfall eventsusually exhibited a highly variable time pattern with alonger duration and greater volume than the syntheticpatterns. Figure 9 shows some examples of rainfall-runoffevents that were obtained from the continuous model. Thesmall spikes at the beginning of the rainfall event areapparently not influential, but they contribute to the initialrainfall losses by reducing the effect of the SCS-CN


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200

120

100

80

60

40

20

0

Figure 9. Rainfall-runoff events that were obtained by the continuoussimulation approach corresponding to 20-, 50- and 100-year Qp. The grey

area is defined as the ‘critical’ part of the flood event


procedure on the final and critical part of the event. Acomparison of the excess rainfall pattern shown inFigure 9 and Figure 4b clarifies this point. In the fivesynthetic hyetographs, the infiltration step significantly

0 20 40 60 80 100

-50

0

50

100

150

200(a)

Per

cent

age

diffe

renc

eof

hye

togr

aph

peak

s [%

]

T [years]

Continuous hyetographpeak reference

Figure 10. Percentage differences between the peaks of synthetic hyetograhyetographs were assumed as a reference. Panels (a) and


reduces the intensity and modifies the rainfall pattern,whereas the simulated rainfall events are rather unaffectedby the infiltration procedure. To support this observation,Figure 10 shows the differences in terms of the gross andnet rainfall peak intensities between the synthetic

0 20 40 60 80 100

-50

0

50

100

150

200(b) BLUE

Chicago Rectangular Sifalda Triangular

T [years]

Continuous hyetographpeak reference

phs and continuous rainfall events for different values of T. Continuou(b) refer to the gross and net hyetographs, respectively

Hydrol. Process. (2011DOI: 10.1002/hyp

s

)


hyetographs and the continuous rainfall events; the resultsshow that the reduction of the hyetograph peaks wasrelevant for the Chicago hyetograph, especially for highreturn periods.For V and D, the significant differences shown in

Figure 7 need further explanation. These values weresurely affected by the realistic pattern of the continuousrunoff time series (see Figure 9). The flood eventselection (as a sequence of consecutive positive runoffvalues separated by at least one zero value) influenced thecomputation of V and D. Therefore, while the hydro-graphs obtained by the synthetic hyetographs in theevent-based scheme are unimodal and rather symmetric,the continuous simulated runoff signals exhibit severalpeaks and variable tails. To analyse the effect of the floodevent selection method, we considered the first 25 mostintensive (in terms of peak annual maxima) simulatedrunoff events. The ‘critical’ area of the flood wave wasselected by visual inspection (as the grey areas inFigure 9), and V and D were estimated. On average, the‘critical’ volume is about 19% smaller than the totalvolume, and the ‘critical duration’ is about 47.3% shorterthan the total duration. Although these differences arerelevant, they cannot explain the differences obtained in

4 5 6 7 8

40

50

60

70

80Qp

Tc [h]

CN

4 5 6

40

50

60

70

80

V

Tc [h]

Figure 12. Percentage error of Qp (left), V (middle) and D (right) obtainedT= 100 years in the 100 combinations

0 2 4 6 80.00

0.02

0.04

0.06

0.08

0.10

7.0

8.07.5

6.55.5

6.0

5.04.5

4.0

3.5

WF

IUH

t [h]

Figure 11. WFIUH obtained with ten Tc values (from 3.5 to 8 h, left to right)


the simulation experiment and shown in Figure 7(�47.5% and �82.7% on average for T= 100 years),which confirm the strong impact of the realistic timepatterns provided by the continuous simulation method.

THE ROLE OF THE RAINFALL-RUNOFFPARAMETERS’ VARIABILITY

The results discussed in the previous sections referred to theparameters CN=74.6 and Tc=4.5 h, which were estimatedfor the Torbido River basin. To generalise the previousresults, we performed a sensitivity analysis that considered100 combinations of CN and Tc values; CN ranged between35 and 80 with increments of 5, while Tc ranged between3.5 and 8 h with steps equal to 0.5 h. These combina-tions allowed a wide range of possible physical condi-tions to be simulated from a watershed that was entirelycovered by a brush surface to an almost waterproofedterrain. Figure 11 shows the large variability induced in theadopted WFIUH by the range of Tc values.For each combination of CN and Tc, two new 500-year

series of synthetic rainfall and runoff were simulated. Theevent-based procedure was applied, as described at thebeginning of the previous section, for comparison withthe continuous simulation approach. To obtain readableresults, the analysis was limited to the Chicago hyetograph,T = 100 years (which is a value of interest for thehydrological analyses) and Ts=24h (its influence on theresults is rather negligible). The differences betweenthe event-based (Chicago) approach and the continuoussimulation were quantified through the percentage error:

Ea ¼ aEB � aCaC

� 100 (3)

where a is a hydrograph attribute (Qp, V or D), and thesubscripts ‘EB’ and ‘C’ denote the results given by the event-based approach and the continuous method, respectively.Figure 12 shows that the results confirm the behaviour

described in the previous section. Only a few combina-tions of parameters yielded event-based peaks higher thanthe continuous model peaks. These combinations corre-spond to configurations with a very short concentration

7 8 4 5 6 7 8

40

50

60

70

80

D

Tc [h]

-100 %-90 %-80 %-70 %-60 %-50 %-40 %-30 %-20 %-10 %0.0 %10 %20 %

by comparing the event-based and continuous simulation approach forof parameters described in the text



time and high CN values for which the infiltration effectis rather negligible. The V and D values are alwaysunderestimated in the event-based approach. For V, thedifferences tend to decrease for high values of Tc and CN,with the dependence on CN being stronger. For D,the differences are stable and rather independent of Tcand CN.

CONCLUSION

This study presented a comparison between the event-basedand continuous simulation methods to estimate the designhydrograph in small and ungauged basins. A continuousrainfall-runoff generation framework, which was calibratedwith a real case study watershed, was used to perform anextensive Monte Carlo experiment to assess the differencesbetween the event-based and continuous simulation meth-ods in terms of the design hydrograph’s attributes. Ourresults point out that these differences are relevant for thehydrograph’s volume (�47.5% for the return periodT= 100years) and duration (�82.7% for T=100 years) aswell as for the peak (�11.6% for T=100 years). Theanalyses support the hypothesis that the main cause of thediscrepancies between the twomethods is related to the jointeffect of the infiltration scheme and the simulated rainfallpatterns. In more detail, the realistic rainfall time patterngiven by the continuous simulation method influences theinitial losses and allows preservation of the rainfall peaks.On the other hand, the shape of the synthetic hyetographscauses infiltration patterns that lead to an underestimation inthe event-based approaches.In some hydrological applications, the hydrograph

volume and duration are a fundamental piece of informa-tion, whichmay be, for instance, the input of bi-dimensionalhydraulic models for flood risk mapping. Therefore, theresults discussed in this study highlight the importance ofan appropriate assessment of the design hydrograph.Because of the increasing availability of rainfall data athigher resolutions in both space and time, and the increasingreliability and refinement of simulation models, the resultsof this study suggest that we should begin to tackle theproblem of modelling small and ungauged basins from adifferent point of view by moving progressively from theevent-based approach to continuous simulation computer-based methods.

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