Web Camici Et Al 2011 WRR (1)

Design soil moisture estimation by comparing continuousand storm-based rainfall-runoff modeling

S. Camici,1 A. Tarpanelli,1 L. Brocca,1 F. Melone,1 and T. Moramarco1

Received 11 March 2010; revised 4 February 2011; accepted 11 February 2011; published 20 May 2011.

[1] In recent years local, national, and international authorities have showed an increasingawareness of flood and inundation hazard, likely due to the large floods which occurred inthe past years in many regions of the world. In this context, the estimation of the design floodvalues to be adopted for flood risk assessment or floodplain management represents a crucialfactor. In the case of ungauged or scarcely gauged catchments where a sufficiently longdischarge time series is missing, a relevant uncertainty is involved in the flood frequencyanalysis and a possible solution to reduce this uncertainty is the application of continuoussimulation (CS) approaches. Because of the complex structure of this type of approaches andpursuing the parameters parsimony criteria, in the hydrological practice the approachesbased on the design storm (DS) estimation are more widely known and applied, mainly fortheir simplicity. However, one major limit of the DS method is the choice of the ‘‘design soilmoisture’’ conditions, representing a critical parameter for assessing the initial wetness of thebasin. To that end, this study of investigating six subcatchments of the upper Tiber Riverbasin (Central Italy), with drainage area ranging from 13 to 284 km2, proposes a procedurebased on the application of the CS approach as a tool to define the design soil moisture to beafterwards incorporated into the more simple DS method. For each catchment, the procedureconsists of (1) stochastic generation of long synthetic rainfall and temperature series startingfrom observed hourly data; (2) application of a lumped continuous rainfall-runoff model togenerate synthetic discharge series and, hence, to obtain the corresponding flood frequencycurves; (3) estimation of the design soil moisture, for each return period, by varying in theDS approach the initial wetness conditions of the catchment so that the peak dischargeestimated by the DS method matches the one given by the synthetic flood frequency curve.Moreover, in order to apply the more simple DS approach avoiding the use of the CS one,a preliminary analysis to regionalize the design soil moisture as a function of the geo-morphological characteristics and the return period is also shown.

Citation: Camici, S., A. Tarpanelli, L. Brocca, F. Melone, and T. Moramarco (2011), Design soil moisture estimation by comparing

continuous and storm-based rainfall-runoff modeling, Water Resour. Res., 47, W05527, doi:10.1029/2010WR009298.

1. Introduction[2] In recent years, the effects of flood damages have

motivated the development of new methodologies for thesimulation of the hydrologic/hydraulic behavior of river sys-tems to address territorial planning as well as floodplainmanagement and risk analysis. The valuation of the flood-prone areas and the assessment of dam safety rely on theestimation of the design flood for an assigned probability ofexceedence. The magnitude of floods (i.e., the design floodvalue) depends, in general, on flood peak, volume, and dura-tion; therefore, for design flood estimation a multivariateanalysis should be carried out [Klein et al., 2010]. Address-ing the estimation of the design flood in terms of peakdischarge, in the scientific literature four methods have been

proposed: statistical, design storm, derived flood frequency,and continuous simulation approaches.

[3] The statistical method attempts to estimate the designflood by analyzing the observed record of peak flows. Forgauged catchments, where observations of extreme floodevents for a river cross section of interest are available, theapplication of statistical methods consists of fitting the an-nual maximum discharge series, usually inferred by apply-ing a rating curve to a stage series, through an appropriateextreme-value probability distribution. When streamflowdata at a given site are not available or not representative(e.g., for the construction of a dam) or insufficient for a reli-able estimation of flood quantiles, statistical flood frequencydistribution can be achieved by using regionalization techni-ques directly applied to flood quantiles themselves [Mimi-kou and Gordios, 1989; Pandey and Nguyen, 1999; Wang,2000] or on distribution parameters [Fiorentino et al., 1985;Kumar et al., 2003]. The main condition, and in many casesthe greatest limitation, for the implementation of statisticalmethods is the need of a robust number of peak flow obser-vations collected, at least, near to the river cross section of

1Research Institute for Geo-hydrological Protection, National ResearchCouncil, Perugia, Italy.

Copyright 2011 by the American Geophysical Union.0043-1397/11/2010WR009298

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WATER RESOURCES RESEARCH, VOL. 47, W05527, doi:10.1029/2010WR009298, 2011

interest. Another large limitation of statistical methods,mainly in a climate changing context, is the need to assumethat the flood frequency behavior is stationary over the time[Sivapalan and Samuel, 2009].

[4] Generally, long rainfall time series are much moreavailable than discharge ones that, unfortunately, are usu-ally not sufficient for a reliable flood frequency. Therefore,the classical approach based on the use of the design storm(DS), that requires the application of a rainfall-runoff (RR)model, allows us to estimate the entire flood hydrographand not only the peak discharge as derived by the statisticalmethod [Kjeldsen, 2007]. Although reasonably easy toimplement, this approach frequently simplifies the physicalprocess of rainfall-runoff transformation and, additionally,three critical assumptions have to be made: (1) the choiceof the design rainfall hyetograph (shape and duration); (2)the equality between the rainfall and discharge return peri-ods; and (3) the selection of soil moisture conditions beforethe storm event, named henceforth as ‘‘design soil mois-ture.’’ As far as the initial moisture state of the catchmentis concerned, some investigations have argued that it is themost important factor to determine the predictive outcomeof an event [De Michele and Salvadori, 2002; Berthetet al., 2009; Brocca et al., 2009a]. On the contrary, otherinvestigations have inferred that it might be not so critical,particularly in the case of large events [Bronstert andBardossy, 1999; Castillo et al., 2003].

[5] The derived flood frequency approach, at first pro-posed by Eagleson [1972], combines the probability densityfunction of rainfall and the basin response function to obtaina physically based probability distribution of flood discharge[Fiorentino and Iacobellis, 2000; Franchini et al., 2005;Haberlandt et al., 2008; Bocchiola et al., 2009]. Eventhough this method is able to overcome the problem relatedto the choice of the design hyetograph, the problem of theinitial soil moisture definition still remains [De Michele andSalvadori, 2002; Hlavcova et al., 2005; Lastra et al., 2008;Gul et al., 2010, Verhoest et al., 2010]. In this context, DeMichele and Salvadori [2002] analyzed the influence of an-tecedent soil moisture conditions on the derived flood fre-quency distribution for several catchments located innorthern Italy. The importance of the knowledge of the ante-cedent wetness conditions for the estimation of flood quan-tiles was there underlined, showing, for instance, that for the100 year return period, the peak flood might be twice fromdry to wet soil moisture conditions. Moreover, it is worthnoting that the derived flood frequency approach, as well asthe DS approach, leans on the unrealistic hypothesis that a Tyears rainfall depth leads to the formation of a T years flood.

[6] In the last decades, also thanks to the increasing ofcalculation power, there has been an increasing interest indeveloping and using the continuous simulation (CS)approach for flood frequency estimation. This approachrepresents a possible solution to overcome the three abovementioned critical points, namely the choice of the rainfallhyetograph, the assumption on the return periods, and theestimation of the antecedent wetness conditions [Calveret al., 2009]. In fact, this technique has the potential toproperly represent the way in which rainfall characteristics,antecedent conditions in a catchment, and flood runoffgeneration processes change with the time and the severityof an event [Blazkova and Beven, 2009]. Calver and Lamb

[2000] expressed the opinion that the CS approach mayform the basis for the next generation of flood frequencyestimation in the United Kingdom. The method is based onthe computation of long synthetic discharge time seriesthrough the application of rainfall and temperature stochas-tic generation models coupled with a continuous rainfall-runoff (RR) model. From the discharge time series, the an-nual maxima peak flows can be extracted (but also the floodvolume and duration) and, hence, the design flood for dif-ferent return periods can be estimated. Therefore, the appli-cation of the CS approach requires the selection of both astochastic rainfall (and temperature) generation model and acontinuous RR model. As first applications, the CS approachwas run with historical rainfall and temperature data (notstochastically generated) mainly to test and to select the bestcontinuous RR model to be adopted within the procedure[Calver and Lamb, 1996; Lamb, 1999; Lamb and Kay,2004; Calver et al., 2009]. Subsequently, the RR model wascoupled with the stochastic ones thus proving the reliabilityof the CS approach for the purpose of design flood estima-tion [Blazkova and Beven, 1997, 2002, 2009; Cameronet al., 1999, 2000; Hashemi et al., 2000; Brath et al., 2002;Rulli and Rosso, 2002; Faulkner and Wass, 2005]. Forinstance, for the gauged Wye catchment in Wales, Cameronet al. [1999] used the stochastic rainfall generator providedby Eagleson [1972] to drive a RR model (TOPMODEL)obtaining a good agreement with observed data. The studywas extended by Blazkova and Beven [2002, 2009] to theproblem of estimating the flood frequency characteristics foran ungauged basin by taking account of uncertainties on pa-rameters estimation and calibrating the RR model with amore comprehensive data set (including snow water equiva-lent and flow duration curve information). McMillan andBrasington [2008] coupled the CS approach, incorporatinguncertainties, to a hydraulic model to produce robust esti-mates of flood risk. The comparison with the classical deter-ministic methodology for floodplain management was alsocarried out to identify the role and the source of predictiveuncertainty. The CS approach was also applied to the Sec-chia River basin, located in northern Italy, in a study con-ducted by Moretti and Montanari [2008]. The authorsemployed a spatially distributed RR model in order to esti-mate the flood frequency distribution for every site of thecatchment. The model was calibrated with 1 year record ofdischarge data at the outlet of the catchment and then wasvalidated in the estimation of the flood frequency for an in-ternal river cross section, treated as ungauged. The obtainedresults confirmed the reliability of the CS approach, thushighlighting interesting perspectives for the application ofspatially distributed RR models to estimate design flood val-ues over ungauged catchments.

[7] From the above discussion it can be inferred that theclassical DS approach might greatly benefit if right initialwetness conditions are defined for a given basin. It is im-portant to point out here that the DS approach is wellknow, particularly among practicing water resource engi-neers, as a simple and easy method to implement. Thesecharacteristics make it widely applied in the hydrologicalpractice in spite of its drawbacks as highlighted above.

[8] For this reason, this paper addresses how the initialwetness conditions can be set in the DS approach by con-sidering the CS approach as a benchmark for design flood

W05527 CAMICI ET AL.: DESIGN SOIL MOISTURE ESTIMATION W05527

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values estimation. To this end, a procedure to estimate thevalue of the initial wetness conditions for the DS approachis proposed. In particular, for each return period, the initialwetness conditions are computed by matching the floodpeak provided by the DS and the CS approaches; this valuerepresents the design soil moisture. It has to be noted thatin the CS approach there is no link in terms of return periodbetween rainfall, initial soil moisture, and discharge, andimplicitly, this occurs also in the DS approach if the designsoil moisture is adopted. Six subcatchments of the upperTiber basin, with drainage area ranging from 13 to 284 km2,are used as a case study. In particular, the Neyman-Scottrectangular pulse model (NSRP) [Cowpertwait et al., 1996],for stochastic rainfall simulation, and the fractionally differ-enced ARIMA model (FARIMA) [Montanari et al., 1997],for stochastic temperature simulation, are coupled with acontinuous RR model named modelo idrologico semidistri-buito in continuo (MISDc) [Brocca et al., 2010] specificallydeveloped for flood prediction in the study area. Finally, forDS applications the design soil moisture is regionalized as afunction of geo-morphological characteristics and the returnperiod, thus avoiding the use of the more complex CSmethod in the study area.

2. Method[9] The procedure proposed here for inferring the flood

frequency curves is based on the NSRP and FARIMA sto-chastic models coupled with the continuous RR model,MISDc. Specifically, the lumped version of the MISDcmodel is employed due to the limited extension of the ana-lyzed catchments. The steps necessary to generate a peakflow time series are summarized below.

[10] First, a series of hourly rainfall and temperaturerecords are generated using the NSRP and FARIMA model,respectively. For both models the parameters are estimatedfrom observed hourly data. The two series are thenemployed for discharge computation through the MISDcmodel, previously calibrated on a number of significantobserved flood events. In fact, as specified below, MISDc isa continuous model that is addressed to simulate dischargehydrograph in correspondence of flood events. Finally, theannual discharge maxima are taken out from the simulateddischarge series and, hence, the design flood value for agiven recurrence interval can be easily estimated throughthe flood frequency curves.

[11] For the estimation of the design soil moisture, thedesign flood values are also computed through the DSapproach. Starting from the same observed rainfall seriesused in the continuous simulation approach, the depth-duration-frequency (DDF) rainfall curves are computed.Then, for a given return period, the rainfall hyetographduration and shape are set. The duration producing the largestpeak discharge is used and the alternating block hyetograph[Chow et al., 1988] is chosen for the computation of thestorm temporal evolution. Assuming that the return periodof rainfall and runoff is the same, the design hydrograph iscomputed through an event-based RR model (MISD) con-sidering different values of the curve number (CN) of theSCS-CN method for abstraction. The value of CN furnish-ing a peak discharge equal to that provided by the CSapproach is selected as the design soil moisture.

[12] Finally, in order to make the application of the DSapproach independent from the CS approach, a method toregionalize the design soil moisture value for differentreturn periods is presented. At first, a relationship betweenthe design soil moisture value and the main geo-lithologicalcharacteristics of the study catchments is considered. After-ward, a function describing the variability of these valueswith return period is proposed and analyzed.

2.1. Stochastic Rainfall Model[13] The NSRP model is characterized by a flexible

structure in which the model parameters broadly relate tounderlying physical features observed in rainfall fields. Fulldetails of the NSRP may be found by Cowpertwait et al.[1996], therefore only a brief description of the model isgiven here.

[14] The NSRP model supposes that each storm originfollows a Poissonian process with parameter �r. Then, arandom number (C) of cell origins is displaced from thestorm origins by exponentially distributed distances withparameter �r. A rectangular pulse is associated with eachcell origin, with duration and intensity expressed by twoother independent random variables assumed exponentiallydistributed with parameter �r and �r, respectively. The totalintensity at any point in time is then the sum of all theactive cell intensities at that particular point.

[15] The NSRP model has a total of five parameters thatcan be estimated by minimizing an objective function eval-uated as the weighted sum of the normalized residualsbetween the statistical properties of the observed time se-ries and their theoretical expression derived from themodel. As showed by previous studies [Rodriguez-Iturbeet al., 1987; Cowpertwait 1991a, 1991b], the main featureof the model is its ability to preserve statistical propertiesof a rainfall time series over a range of time scales.

2.2. Stochastic Temperature Model[16] Stochastic hourly temperature records are simulated

applying the FARIMA model to observed temperatureseries [Montanari et al., 1997]. Unlike classical ARIMAmodels that are a powerful tool for modeling stationarytime series, the FARIMA models are able to fit autocorrela-tion functions characterized by a slow decay suggesting thepresence of a long-term persistence. This dependence,namely the Hurst effect [Hurst, 1951], has been detectedin many temporal series of hydrological data and veryoften in the air temperature series [Moretti and Montanari,2008].

[17] The procedure for the implementation of the FAR-IMA model is not straightforward, particularly in the iden-tification phase for the preliminary evaluation of modelparameters. The method employed in this study is the onesuggested by Montanari et al. [1997] that consists of thefollowing steps:

[18] 1. Deseasonalization of observed time series toremove the periodic component which is added back at theend of the simulation procedure.

[19] 2. Preliminary estimation of model parameters. Thisis achieved by estimating an initial guess of the Hurstexponent value and then evaluating the coefficients of theFARIMA model applied to the filtered series that takes theHurst exponent into account.


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[20] 3. Estimation of all the FARIMA model parametersby applying an approximation in the spectral domain of theGaussian maximum likelihood function.

[21] 4. Model validation and generation of the synthetictemperature series.

2.3. Rainfall-Runoff Model[22] The lumped version of the MISDc model used in

this study consists of two main components, i.e., a soil waterbalance (SWB) model to simulate the soil moisture tempo-ral pattern and an event-based RR model (MISD) for floodsimulation. The two models are coupled through an experi-mentally derived linear relationship and, hence, the struc-ture of a parsimonious continuous RR model was derived(see Figure 1). It has to be highlighted that the MISDc struc-ture was established by analyzing the hydrologic responseof a small experimental catchment equipped with an auto-matic soil moisture monitoring system operating on a hill-slope of the experimental area [Brocca et al., 2010].2.3.1. Soil Water Balance Model

[23] The structure and the components of the model wereselected after a thoroughly analysis of soil moisture meas-urements carried out at an experimental plot (1 ha) by anautomatic system. The reader is referred to Brocca et al.[2008] for the full description of the analysis ; in the fol-lowing the governing equations are reported.

[24] The surface soil layer is assumed as a lumped sys-tem for which the following soil water balance equationholds:

dW tð Þ=dt ¼ f ðtÞ � eðtÞ � gðtÞW tð Þ ¼ Wmax

�W tð Þ � Wmax

otherwise; ð1Þ

where W(t) is the amount of water in the investigated soillayer, t is the time, f(t) is the fraction of the precipitationinfiltrating into the soil, e(t) is the evapotranspiration rate,

g(t) is the drainage rate due to the interflow and/or the deeppercolation, and Wmax is the maximum water capacity ofthe soil layer (Figure 1).

[25] The infiltration rate is estimated by using the Green-Ampt equation

f tð Þ ¼ Ks 1� Wmax �Wið Þ=FL½ �f tð Þ ¼ r tð Þ

�f tð Þ � r tð Þotherwise

; ð2Þ

where Ks is the saturated hydraulic conductivity, is thewetting front soil suction head, Wi is the amount of water atthe beginning of the rainfall event, L is the thickness of thesoil layer, F is the cumulated infiltration depth from theonset of the rainfall, and r(t) is the rainfall rate.

[26] For the drainage component, the following relationis adopted [Famiglietti and Wood, 1994]:

g tð Þ ¼ Ks W tð Þ=Wmax½ �3þ2=�; ð3Þ

where � is the pore size distribution index linked to thestructure of the soil layer.

[27] Evapotranspiration, which mainly controls the soilmoisture temporal pattern in the periods without rainfall, isrepresented by a linear relation depending on the potentialevapotranspiration ETp(t) and the soil saturation:

e tð Þ ¼ ETp tð ÞW tð Þ=Wmax: ð4Þ

[28] The potential evapotranspiration is computedthrough the empirical relation of Blaney and Criddle asmodified by Doorenbos and Pruitt [1977]:

ETp tð Þ ¼ �2þ b � 0:46Ta tð Þ þ 8:13½ �f g; ð5Þ

where Ta(t) is the mean air temperature in �C, � is the per-centage of total daytime hours for the period used (daily or

Figure 1. Structure of the lumped continuous rainfall-runoff model used in the study (MISDc).


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monthly) out of total daytime hours of the year (365 � 12),and b is a parameter to be calibrated.2.3.2. Event-Based Rainfall-Runoff Model

[29] The lumped MISD model adopted for this studyemploys the soil conservation service-curve numbermethod for abstraction (SCS-CN) for estimation of lossesand the geomorphological instantaneous unit hydrograph(GIUH) for routing of rainfall excess. We have to point outthat the GIUH approach is used here because it is alreadydeeply tested on several catchments located in central Italy.Therefore, the rainfall excess re is given by

re tð Þ ¼ r tð Þ R tð Þ��1S t0ð Þ½ � R tð Þþ 2��1ð ÞS t0ð Þ½ �f gR tð Þþ 1��1ð ÞS t0ð Þ½ �2

re tð Þ ¼ 0

(R tð Þ � �1S t0ð Þ

otherwise; ð6Þ

where r(t) is the rainfall rate, R(t) is the rainfall depth fromthe beginning of the storm, t0, S(t0) is the soil potentialmaximum retention related to the curve number (CN), and�1 is the parameter linked to the initial abstraction. Accord-ing to the most recent studies on the initial abstraction com-ponent of the SCS-CN formula [e.g., Hawkins et al., 2009],the parameter �1 was set equal to 0.05. The quantity S(t0) isderived as a function of the saturation degree simulated bythe SWB model through

S t0ð Þ ¼ aWmax 1�W t0ð ÞWmax

� �; ð7Þ

where a is a parameter to be estimated. A linear relation-ship between S(t0) and the saturation degree W(t0)/Wmaxwas observed analyzing a set of RR events occurred in thestudy area and relating the soil moisture observations (insitu and from satellite sensors) to the ‘‘observed’’ S(t0) pa-rameter, i.e., assuring the observed direct runoff volumeestimation [Brocca et al., 2009a, 2009b].

[30] Finally, the discharge hydrograph at the basin outletis given by the convolution of re(t) and the GIUH proposedby Gupta et al. [1980], where the lag time is given by theempirical relationship estimated by Melone et al. [2002]for the study area:

L ¼ �1:19A0:33; ð8Þ

with L lag time (in hours), A drainage area (in km2), and �a parameter to be calibrated.2.3.3. Input/Output Data and Parameter Estimation

[31] The MISDc model requires as input data the meteor-ological variables routinely measured (rainfall and air tem-perature) and the model output is both the direct runoffhydrograph in correspondence to flood events and the catch-ment average saturation degree W(t)/Wmax. In simulationmode, the total runoff is computed by adding the dischargeobserved at the beginning of each flood event. In predictionmode, only direct runoff is determined. However, for designflood estimation, the contribution of base flow can be con-sidered negligible, mainly for high return periods.

[32] For the proposed continuous RR model, only sevenparameters have to be estimated, i.e., the maximum watercapacity of the soil layer Wmax, the saturated hydraulicconductivity Ks, the ratio between the wetting front soilsuction head and the soil layer thickness =L, the pore size

distribution index �, the correction coefficient for potentialevapotranspiration b, the lag-area relationship parameter �,and the parameter a of the S versus W relationship (equa-tion (7)). It has to be noticed that the parameter =L of theinfiltration component was found to have a very low influ-ence on model results and, hence, it was set constant andequal to �0.22 [Brocca et al., 2010]. A sensitivity analysison the model parameters can be found by Brocca et al.[2008] for the SWB model and by Brocca et al. [2009a]for the lumped version of MISDc. The range of the six cali-bration parameters is reported in Table 1. For model cali-bration, a standard gradient-based automatic optimizationmethod is adopted because, due to the relatively low num-ber of involved parameters, it furnished similar results ofmore efficient but slower methods, as the shuffled complexevolution algorithm by Duan et al. [1992]. The minimiza-tion of the absolute value of the percentage error on peakdischarge j"Qpj is used as an objective function because, asrevealed by a sensitivity analysis of the model performancerelated to different objective functions, it provides the bestresults when high-flood conditions have to be simulated[Faulkner and Wass, 2005; Gupta et al., 2009]. The Nash-Sutcliffe efficiency coefficient NS and the absolute valueof the percentage error on runoff volume j"V j are alsoexploited as indicators of model performance.

2.4. Regionalization of the Design Soil Moisture[33] A preliminary analysis to regionalize the design soil

moisture values was also carried out in this study. At first,for a specific return period, a relationship between thedesign soil moisture, CN, and the morphological and geo-lithological catchment characteristics Xi was investigatedby using a multiple linear regression:

CN^¼ �0 þ

Xn

i¼1

�iXi; ð9Þ

where the � parameters can be estimated by applying theleast-square method. The root mean square error (RMSE)and the coefficient of determination R2 evaluated betweenthe CN values estimated from the DS approach for all thecatchments, and the ones calculated through equation (9),were exploited for defining the Xi, furnishing the highestperformance in terms of RMSE and R2. To validate theregression model in predicting the response variable, across-validation procedure was also applied.

[34] Successively, the variability of the design soil mois-ture with return period was surmised to be represented bythe following relationship:

CNðTr;CN^Þ ¼ ½�1 � CN

^þ �2�½�3 � lnðTrÞ þ �4� þ CN

^; ð10Þ

where �1; �2; �3; �4 are parameters to be estimated.

3. Study Area[35] The study area is situated in an inland region of cen-

tral Italy and it includes the six subcatchments of the upperTiber River basin selected to develop and verify the proce-dure proposed here: Assino at Serrapartucci, Caina at Mon-ticelli, Cerfone at Lupo, Colorso at C. Mandorle, Genna at


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Palazzetta, and Niccone at Migianella (see Figure 2). Themain features of these catchments are reported in Table 2.As it can be seen in Table 2, the drainage area ranges from13 to 284 km2 and the mean catchment slope rangesbetween 9.8% and 27.7%. The main channel length variesfrom 5.4 km for the Colorso catchment to 30.7 km for theCerfone catchment.

[36] The climate is Mediterranean with mean annual pre-cipitation of about 950 mm, ranging from 700 mm at lowerelevations to 1600 mm along the ridges. Higher monthlyprecipitation values are generally observed during theautumn-winter period when floods caused by widespreadrainfall normally occur. Mean annual temperature rangesfrom 5.5�C at higher elevations to 16�C at lowlands. Snow-fall represents a low percentage of precipitation and is un-usual and ephemeral at altitudes below 500 m above sealevel (asl).

[37] The availability of a geo-lithological map (scale1:100,000) and a land use map defined in the Corine–LandCover European project allowed us to calculate the dimen-sionless curve number for normal antecedent moisture con-ditions (CN(II)) through the tables furnished by the SoilConservation Service [Chow et al., 1988]. In particular,from the geo-lithological map the four hydrologic soilgroups (A, B, C, D for high, medium-high, medium-low,low permeability group, respectively) were identified foreach catchment and their percentage is reported in Table 2.As it can be seen, most of the basins’ surface is featured bymedium-low permeability (from 57.4% for the Caina catch-ment to 95.3% for the Colorso catchment), whereas minorpercentages of territory belong to A and B groups. More-over, the low-permeability soil group is present only on asmall portion of the Assino catchment. Concerning the landuse, the main types are woods and crops with a differentpercentage from one catchment to another, whereas pastureand urban areas cover only a small portion of the territory.By closely inspecting Table 2, it can be seen that the studycatchments are characterized by different runoff producingcapability as inferred from the CN values ranging from69.0 (Colorso catchment) to 77.6 (Genna catchment) fornormal antecedent wetness conditions.

[38] In the study area, a dense hydrometeorological moni-toring network (1 station every 150 km2) has been operatingfor more than 20 years and the data are recorded with a timeinterval of 30 min. The existing network consists of 84 raingauges, 36 thermometers, and 43 hydrometric gauges. Forthis study 19 years of rainfall and temperature data recordedfrom January 1989 to December 2007 were considered.Regarding streamflow data, the record length ranges from 9years for the Colorso catchment to 24 years for the Gennacatchment. As neighborhood catchments exhibited a strong

correlation between the annual maximum peak flow, thestreamflow data for Caina and Colorso catchments wereextended using data of Genna and Niccone catchments,respectively. Thus, more than 20 years of annual maximumdischarge data were available for all catchments. Beingaware of the good quality of the hydrometereological obser-vations in the region, it is expected that the analysis pro-posed here might give reliable outcomes.

4. Results and Discussion[39] In the following, the analyses performed for the six

selected catchments are reported. For each catchment, theestimation of the parameters of the rainfall and tempera-ture stochastic models and the analysis of their perform-ance is first described. The MISDc model behavior, whensimulating the most significant flood events, is also ana-lyzed. Then, for 100 and 5000 year simulation periods, theflood frequency curves are derived through the applicationof the CS approach. By comparing the results of the CSand DS approaches, the design soil moisture values for dif-ferent return periods are shown and, for them, a discussionon the applicability and reliability of their regionalizationis done.

4.1. Neyman-Scott Rectangular Pulse Model[40] For each catchment the mean areal rainfall series,

computed through the Thiessen polygon method, wereassumed as the observed rainfall series. In accordance withprevious studies [Cowpertwait et al., 1996; Cowpertwait,1998; Calenda and Napolitano, 1999; Burton et al., 2008],the NSRP model calibration was carried out for each monthof the year on the basis of four sampling statistics at differ-ent temporal aggregation levels: the hourly mean, thehourly and daily variance, and the lag-one autocorrelationof daily data. Therefore, for each month, five parameterswere estimated by minimizing a weighted sum of normal-ized residuals between sample and theoretical moments. Inparticular, the greatest weight was assigned to the hourlymean and to the lag-one autocorrelation of daily data.Moreover, in order to ensure that the parameters do notassume unrealistic values, they were constrained to liewithin physically meaningful ranges [Cowpertwait, 1998].With the optimal parameter set, the NSRP model was thenused to simulate 10 series of 100 and 5000 years of hourlyvalues. Many simulation runs were considered to takeaccount of the uncertainty in the realization of rainfall se-ries linked to the stochastic nature of the model. It has to bepointed out that the uncertainty analysis of NSRP modelparameters was not carried out here because it is not funda-mental in this first part of the work and will be addressed infuture investigations.

Table 1. Description, Unit of Measure and Range of Parameters for the Lumped MISDc Model

Parameter Description Unit Range

Wmax maximum water capacity of the soil layer mmol 50:700Ks saturated hydraulic conductivity mmol/h 0.3:20.0 =L wetting front soil suction head divided by soil layer thickness – �0.22 (const.)� pore size distribution index – 0.05:0.5b correction factor for evapotranspiration – 0.7:2.0� lag-area parameter – 0.5:2.0a parameter of the relationship linking the SWB model and MISD – 1.0:5.0


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Figure 2. Morphology of the upper Tiber River basin and location of the hydrometeorological moni-toring network. The shaded regions refer to the six catchments selected for this study.


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[41] The performance of the NSRP model was validatedin terms of its ability to reproduce the observed extremestorms because they play the major role in extreme floodproduction. Accordingly, for each study catchment, thedepth-duration-frequency (DDF) curves were estimatedfrom the synthetic rainfall record, and compared with thosecomputed from the lognormal distribution fitted on theobserved data for return periods of 50, 100, 200, and 500years. In particular, a classical bootstrap procedure wasapplied to characterize the uncertainty in fitting the lognor-mal distribution on 20 years of observed rainfall data[Overeem et al., 2008]. Unlike previous studies [Rulli andRosso, 2002; Moretti and Montanari, 2008] in which thestochastic rainfall model overestimated the historicalextreme values of rainfall, in this analysis the observed andthe simulated DDF curves showed a good agreement for allreturn periods. This outcome mainly occurred for the 10DDF curves derived from 5000 years of simulated datawhich also showed a negligible variability among them. Byway of example, for the return period of 500 years, Figure3 illustrates the DDF curves for the six investigated catch-ments along with the confidence intervals corresponding tothe 10th and 90th percentile estimated through the boot-strap procedure applied to the observed data. As it can beseen, the uncertainty due to the size of the observed data islarger than the other sources of uncertainty here analyzed,i.e., those connected to the stochastic nature of the NSRPmodel. Moreover, Figure 3 shows that for three of the sixcatchments the synthetic derived DDF curves well fit theobserved ones, whereas for the other catchments a slightoverestimation was detected for long durations. For shortdurations an underestimation was observed only for theColorso catchment.

[42] In accordance with Cowpertwait et al. [1996], thegoodness of the NSRP model was evaluated by analyzingthe dry spells, that is the sequences of consecutive days withrainfall less than 0.2 mm, in the autumn-winter period whenfloods can occur. In particular, the distribution of dry spells

duration derived by the observed and 100 year and 5000year simulated time series is compared. The 100 year simu-lated time series showed dry spell sequences underestimatedwith respect to the observed ones (see Figure 4 for the Nic-cone catchment), particularly for short durations, as alsofound by Cowpertwait et al. [1996]. However, these resultshave a minor effect on the overall procedure for flood fre-quency estimation.

[43] Finally, the ability of the NSRP model to reproducethe main statistical properties of observed data was alsoinvestigated. For instance, in Figure 5 the hourly mean andthe hourly variance, for each month of the year, are shownfor Assino, Cerfone, and Genna catchments. As it can beseen, the ability of the model to preserve the statisticalproperties of observed rainfall series is confirmed [Cow-pertwait et al., 1996].

4.2. FARIMA Model[44] The procedure for the generation of temperature

time series requires a preliminary analysis of the observeddata in order to detect and eliminate the seasonal compo-nent. Specifically, the seasonal nonstationarity in mean andvariance was handled by externally estimating the first twomoments and then normalizing the series to a zero mean,unit variance process [Bras and Rodriguez-Iturbe, 1985].This methodology was applied to the observed mean dailytemperature series, extracted from the hourly data recordedat the gauging stations of interest for each study catchment.

[45] Successively, a rough estimate of the Hurst expo-nent value H was carried out by using three heuristic meth-ods: the rescaled range statistic, the aggregation variancemethod, and the differenced variance method [Montanariet al., 1997]. Values of H greater than 0.7 were found forall the deseasonalized series of mean daily temperature,confirming the presence of long-memory components.Through the estimation procedure previously described, theFARIMA model for daily temperature was identified foreach catchment and 10 series of 100 and 5000 years length

Table 2. Main Characteristics of the Investigated Catchments

Catchment

Assino Caina Cerfone Colorso Genna Niccone

Drainage area (km2) 165 206 284 13 90 137Mean catchment slope (%) 27.6 16.26 25.9 27.7 9.8 25.0Mean channel length (km) 25.16 30.63 30.66 5.4 22.38 16.37

Hydrologic Soil Group—Soil Conservation Service (%)A: High permeability 9.2 14.7 2.2 1.1 7.6 3.5B: Medium-high permeability 7.9 27.9 19.4 3.6 13.0 12.7C: Medium-low permeability 81.5 57.4 78.4 95.3 79.4 83.9D: Low permeability 1.4 0.0 0.0 0.0 0.0 0.0

Land Use (%)Woods 41.8 27.4 65.9 71.1 4.5 65.0Crops 48.2 62.3 32.4 17.9 80.0 32.0Pasture 8.9 1.8 0.8 10.9 0.0 2.7Urban 1.1 8.5 0.9 0.1 15.4 0.3

Curve Number—Soil Conservation ServiceCN(I) 53.3 50.7 52.8 48.3 59.3 51.9CN(II) 73.1 71.0 72.7 69.0 77.6 72.0CN(III) 86.2 84.9 86.0 83.7 88.9 85.5


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Figure 4. Niccone catchment: comparison of dry spell sequences computed from the observed and100 year simulated time series over a period of 19 years and for months from October to March.

Figure 3. Comparison of the 500 year return period depth-duration-frequency (DDF) curves derivedfrom the observed rainfall series and through 10 sets of 100 and 5000 years of simulated rainfall. Theconfidence interval for the observed data corresponding to the 10th and 90th percentiles is also shown.


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were generated. Finally, the synthetic series were disaggre-gated at hourly temporal resolution using a sine-cosinewave function [Hashemi et al., 2000].

[46] The accuracy of the model in terms of hourly tem-perature reproduction was tested through a comparativeanalysis of the frequency distribution on a monthly basis.The analysis highlighted a good accordance between theobserved and the simulated hourly temperature, both for100 and 5000 year datasets, keeping on the first and thesecond statistical moments. Figure 6 illustrates the resultsobtained for the Niccone catchment and for a winter andspring month. The sample autocorrelation function of thedeseasonalized daily temperature series was also exploitedfor model validation. By way of example, for the Nicconecatchment Figure 7 shows the autocorrelation computedover a period of 19 years of the observed and simulatedtime series. As it can be seen, the autocorrelation functionof the simulated data lies close to that obtained by theobserved data, allowing us to conclude that the FARIMAmodel provides a good fit.

4.3. MISDc Model Calibration[47] The MISDc was calibrated and tested through its

capability to simulate flood events. To this end, the mostsignificant flood events were extracted from the observedhourly time series of rainfall and discharge. In particular,

an event starts at the time when rainfall becomes greaterthan zero. The ending of an event was determined as thetime when the streamflow decreases below a fixed percent-age of the peak discharge (30%), or when a period equal totwice the catchment lag time with negligible cumulatedrainfall occurs (<1 mm). Then the significant floods, i.e.,the ones exceeding a threshold on rainfall (20 mm) and ondischarge (1 mm/h), were selected. Its purpose, an auto-matic procedure was developed allowing us to extract atotal of 230 significant flood events (39 events for eachcatchment on average) in a few minutes. In particular, theflood events that occurred during the first three years ofobservations were used for model calibration, whereas thereliability of the model was validated during the remainingperiod. The results reported in Table 3 highlight that themodel can be considered fairly accurate in flood simulation.In fact, the median of the absolute value of the percentageerror on peak discharge, j"Qpj, ranges from 13% to 21%and from 14% to 34% in the calibration and validation pe-riod, respectively. Moreover, in the validation period, themedian NS efficiency score is higher than 75% for allcatchments, while the median of the absolute value of thepercentage error on runoff volume j"V j ranges from 19% to27%. In particular, the model was found reliable in repro-ducing both the peak and the shape of the observed hydro-graphs except, as expected, for the RR events producing

Figure 5. Comparison between statistical properties of observed and synthetic rainfall data for Assino,Cerfone, and Genna catchments.


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flooding. By way of example, Figure 8 shows the compari-son between the observed and simulated discharge for threerepresentative catchments (Niccone, Assino, and Colorso).

4.4. Continuous Simulation Approach[48] The 100 and 5000 year generated rainfall and tem-

perature time series were employed as input of the MISDcmodel to obtain the corresponding 10 streamflow sequences.For each sequence the frequency distribution of annual max-imum peak flow was derived and compared with thatobtained from the available observed data set. Figure 9shows the outcomes obtained for the Genna catchment;similar results were found for the other catchments. As it

can be seen, the variability among 5000 year annual peakflow time series is lower than that referring to 100 yearsequences as a consequence of the effects of the stochasticgeneration of rainfall. This suggests for us to consider 5000year time series for flood frequency analysis. Moreover, theaverage frequency distributions obtained from the twogroups (100 and 5000 year) of 10 time series of differentlength showed a very similar pattern.

[49] The suitability of the continuous approach in repro-ducing the observed flood frequency curve can be inferredfrom Figure 10 where, for all the investigated catchments,both the 5000 year simulated and observed maximum an-nual peak flow are plotted according to Cunnane’s plotting

Figure 6. Comparison between the frequency distribution of observed and simulated hourly tempera-ture data for the Niccone catchment: (a) February and (b) May.

Figure 7. Niccone catchment: autocorrelation function of the deseasonalized daily temperature seriesof 19 year length.


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position formula. It is worth noting that the observationsaffected by flooding have to be modified because of thedamping effects on flood peak due to the inundation. There-fore, when flooding occurs the observed peak discharge wasassumed equal to that estimated by the rainfall-runoff modelfor the corresponding flood event. In detail, Figure 10 showsthat for recurrence intervals comparable with the length of theobserved data records, predicted and observed flood fre-quency curves are in good agreement; only for the Assinocatchment a slight underestimation of peak flow can be noted.

[50] In order to analyze the performance of the approachfor greater return periods, the generalized extreme value(GEV) and the three parameter lognormal (LN3) probability

distributions were fitted to the observed data through themaximum likelihood estimator. Obviously, we have to con-sider the low reliability of the statistical analysis owing tothe limited number of observations. However, the differencesbetween the simulated peak flow and those extracted fromboth the probability distributions was found within 30%.Specifically, for return periods greater than 50 years, Figure10 shows that the CS approach provides an overestimation ofpeak flow with respect to both the probability distributionsfor the Cerfone and Niccone catchments and an underestima-tion for the Assino catchment. Furthermore, the CS approachunderestimates the peak flow with respect to the LN3 proba-bility distribution for the Colorso catchment and to the GEV

Table 3. Results, in Terms of Median Values, of the MISDc Model for the Six Study Catchmentsa

Catchments

Colorso Niccone Assino Cerfone Genna Caina

Observation period 2002–2005 1995–2005 1995–2005 1992–2007 1991–2006 1996–2006Calibration

Number of floods 6 17 9 12 12 16j"Qpj (%) 21 13 13 19 20 17NS (%) 87 88 82 80 80 79j"V j (%) 13 11 16 21 22 19

ValidationNumber of floods 12 41 29 34 23 19j"Qpj (%) 25 14 33 34 24 31NS (%) 82 82 78 75 79 76j"V j (%) 27 19 26 19 24 22

aj"Qpj, absolute value of the percentage error on peak discharge; NS, Nash-Sutcliffe efficiency coefficient; j"V j, absolute value of the percentage erroron runoff volume.

Figure 8. Observed versus estimated discharge by the MISDc model for the sequence of the most sig-nificant flood events for (a) Niccone, (b) Assino, and (c) Colorso catchments.


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probability distribution for the Caina catchment. As it can beseen in Table 4, the GEV and the LN3 probability distribu-tions often furnish very different peak flow values. By wayof example, for the Caina catchment and for the 500 yearreturn period, the peak flow estimated through the LN3 dis-tribution corresponds to 68% of the one determined by theGEV distribution. The dispersion diagrams reported in Fig-ure 11 confirm these outcomes for some of the investigatedcatchments. In accordance with Cameron et al. [2000], thisfinding highlights the difficulty of an accurate estimation oflong-return period events from limited data using traditionalstatistical techniques. Conversely, the results of the CSapproach show that it is possible to apply the procedure withonly three years of observed hourly flow data, as used herefor rainfall-runoff model calibration and to obtain valuableresults also for high-return periods.

4.5. Design Storm Approach[51] By using the same data set considered for the CS

approach, the DS approach was also implemented. For afixed return period, the design hyetograph was determinedfrom the DDF curve, defined on the basis of the observedrainfall data, by assessing the duration and the temporalevolution of the storm.

[52] As previously discussed, another important assump-tion has to be made on the antecedent wetness conditions.By considering the period of the year when floods occur,two different antecedent wetness conditions were consid-ered in this study: normal, CN(II), and wet, CN(III). Look-ing at Figure 10, it appears that the flood frequency curvesestimated through the DS approach envelop those predictedthrough the CS approach for all the investigated catchments,except for the Cerfone and Genna ones, for a return periodgreater and less than 100 years, respectively. It has to bepointed out that a strong uncertainty is linked to curve num-ber estimation. First of all, for the study area but also forother regions, the assessment of the hydrological soil groupis based only on the geo-lithological map, whereas detailedinformation on soil texture and type should be used. More-over, appropriate antecedent wetness conditions should be

selected and this can be achieved by applying the CSapproach for different catchments of the region of interest.4.5.1. Design Soil Moisture

[53] As the CS approach has proved to be reliable in esti-mating the flood frequency curves for the investigatedcatchments, then it can be used to assess the antecedentwetness conditions to be applied within the DS approach inthe study area. Specifically, for each return period thedesign soil moisture was identified by the CN value,denoted as optimal CN, furnishing a peak discharge equalto that estimated through the CS approach. In this waythe independence between the recurrent intervals of rainfalland streamflow was implicitly kept also in the DSapproach. The CN values obtained are summarized inTable 5 for different return periods, along with the CN val-ues derived by the SCS method for normal, CN(II), andwet, CN(III), antecedent wetness conditions. By looking atFigure 10, it can be inferred that the optimal CN valueshould increase with return period. In particular, for Col-orso, Niccone, Caina, and Genna catchments, the CN val-ues exhibited a variability with return period higher thanthe Assino and Cerfone ones; for instance, the derived CNvalues ranged from 77 to 88 for the Genna catchment,whereas they ranged from 73 to 76 for the Assino catch-ment. It was found that the differences in the range of theCN values for the investigated catchments seem to berelated to the spatial variability of CN within the catch-ment. The increase of optimal CN with return period canbe explained by the fact that extreme floods are often pro-duced by storms whose magnitude is not so extreme and,hence, with a high wet initial soil moisture state [Gutknechtet al., 2002; Vivoni et al., 2007]. The variability of the CNvalue with return period is also supported by the resultsprovided by Viglione et al. [2009]. Through a syntheticstudy, they analyzed the role of the antecedent conditionsof the basin, expressed by the variability of the runoff coef-ficients, on the relationship between rainfall and floodreturn periods, considered the key point of the DS proce-dure. In particular they showed that the runoff coefficientthat produces a flood peak with the same return period of

Figure 9. Genna catchment: frequency distribution of annual maximum peak flow obtained by 10 runsof the continuous simulation approach applied for a length of 100 and 5000 years.


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the input storm increases with the event magnitude. How-ever, it has to be highlighted that the variability of CNobtained for the investigated catchments is due, besides theantecedent wetness conditions, to the assumptions on theDS approach, i.e., the rainfall hyetograph type (shape andduration) and the concurrent return periods between rainfalland discharge.

[54] The above results suggest that the classical proce-dure for CN estimation based on soil/land use characteris-tics and normal antecedent wetness conditions cannot beconsidered reliable for some of the investigated catchments(see the Cerfone catchment), mainly for high return periods

that are, unfortunately, the most interesting for the design ofhydraulic structures. The poor reliability to predict floodfrequency curves through the traditional table-based SCS-CN method was also shown by Shaw and Walter [2009], fortwo medium sized watersheds in the eastern United States.In fact, the method was found strongly overestimating theobserved flood frequency curves for one catchment and theopposite occurred for the other catchment.4.5.2. Regionalization of the Design Soil Moisture

[55] A drawback that can be highlighted in the proposedprocedure is that it requires a run of the CS approach tofind out the adjusted design soil moisture value to be used

Figure 10. Frequency distribution of annual maximum peak flow for the six investigated catchments.Dots are simulated values and refers to 10 simulations of 5000 years obtained through the continuoussimulation approach; diamonds and circles represent the values estimated by the design storm approachusing CN(II) and CN(III), respectively, as initial moisture conditions; GEV and LN3 refer to the general-ized extreme value and the three lognormal probability distribution fitted to the observed data.


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Table 4. Peak Flood (m3s�1) for Different Return Periods Estimated Through the CS Approach (Average of 10 Simulations for 5000Year Data), the Statistical Analysis (GEV and LN3 Extreme Value Distributions), and the Design Storm Approach for Normal, QCN(II), and Wet, Q CN(III), Antecedent Moisture Conditions

Method

Return Period (years)

20 50 100 200 500

AssinoCS approach 127 161 186 216 254Q GEV 154 190 220 250 293Q LN3 171 221 263 307 372Q CN(II) 134 161 182 204 232Q CN(III) 227 266 294 323 360

CerfoneCS approach 258 309 353 398 451Q GEV 235 280 315 350 399Q LN3 240 288 325 363 415Q CN(II) 177 210 234 258 291Q CN(III) 275 317 347 377 417

GennaCS approach 122 160 195 239 302Q GEV 125 174 221 277 371Q LN3 125 160 192 228 279Q CN(II) 141 170 193 215 246Q CN(III) 201 236 262 288 322

CainaCS approach 120 153 179 206 244Q GEV 118 163 206 258 344Q LN3 118 142 168 196 235Q CN(II) 122 145 163 181 204Q CN(III) 205 237 261 284 315

ColorsoCS approach 14 18 22 26 35Q GEV 13 16 19 22 27Q LN3 16 21 26 31 39Q CN(II) 14 18 21 25 29Q CN(III) 26 32 36 41 47

NicconeCS approach 102 130 151 174 205Q GEV 92 115 134 154 183Q LN3 93 114 131 148 173Q CN(II) 113 137 155 173 199Q CN(III) 189 222 246 271 303

Figure 11. Peak flow value with different recurrence intervals estimated through the continuous simu-lation approach versus that predicted from (a) generalized extreme value (GEV) and (b) three parameterlognormal (LN3) probability distributions derived for the observed data.


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in the DS approach. This matter can be overcome estimat-ing a function to determine the regionalized design soilmoisture in terms of return period. For this purpose, thecoefficients of equations (9) and (10) were calibrated.

[56] Without loss of generality, in equation (9) the CNwas identified as CN50, i.e., the optimal CN value for areturn period of 50 years. (Results based on different returnperiod values were found very similar.) Regarding theX matrix, the main morphological (catchment area, catch-ment slope, channel length), lithological, and land use char-acteristics of the six investigated catchments were takeninto account (see Table 2). All the combinations with two,three, and four predictor variables were considered in theanalysis. To ensure a fair compromise between the numberof the predictors and the performance of the model, theregression model with two independent variables wasselected. Obviously, if more predictors are used betterresults (in terms of RMSE and R2) can be achieved, but inthis case the relation becomes less robust considering thatthe number of catchments employed in the regression islimited to six. In particular, the channel length and the per-centage of high-permeability soil group A were selected asdescriptor variables. The ability of the regression model toreproduce the response variable is shown in Figure 12awhere the CN50 values calculated through equation (9) andthe optimal ones given by the CS approach are plotted. Inparticular, good RMSE and R2 values equal to 1.52 and0.92, respectively, were obtained. Moreover, the perform-

ance kept on fair accurately also in cross validation withRMSE and R2 values equal to 3.80 and 0.56, respectively.These results can be considered quite accurate because, asmentioned above, only two descriptors were used. In addi-tion, a consistent variation of the � coefficients was found;in fact the CN50 increases with the channel length (� posi-tive) while the opposite occurs with the high permeabilitysoil group (negative coefficient). By analyzing the p valuesof the � coefficients, the channel length was found moreimportant than the high-permeability soil group to deter-mine the CN50 spatial variability.

[57] A further analysis was carried out to link the region-alized CN50 values with return period. The � coefficients inequation (10) were estimated by applying the least-squaremethod. In Figure 12b the comparison between the optimalCN values for different return periods and the ones derivedby applying equations (9) and (10) is shown. As it can beseen, the whole procedure of regionalization is suitable inrepresenting the variability of the design soil moisture forwhich the final RMSE value was equal to 1.84. Specifi-cally, Table 6 reports the percentage error on CN estima-tion by the regionalization procedure for each returnperiod, using the optimal CN values provided by the proce-dure based on CS approach as a benchmark. As it can beseen, the errors keep to less than 7% for all catchments andreturn period and their absolute values are equal, on aver-age, to 1.3%. Only for Genna catchment and for higherreturn periods (200 and 500 years) do errors exceed 3%,

Figure 12. Comparison between the optimal CN values and the corresponding ones obtained throughthe regionalization procedure for (a) the six investigated catchments and a return period of 50 years(equation (9)) and (b) all the catchments and all the return periods (equation (10)).

Table 5. Curve Number Values for Different Return Periods Extracted by Comparing the Simulated Annual Peak Flows Through theContinuous Simulation Approach and the Ones Computed Through the Design Storm Methoda

Catchment

Recurrence Interval of Flood Peak (years)

CN(II) CN(III)20 50 100 200 500

Assino 71 71 71 71 71 73 86Caina 73 74 76 77 79 71 85

Cerfone 85 86 87 89 90 73 86Colorso 71 73 76 78 80 69 84Genna 77 78 80 82 87 78 89

Niccone 75 77 79 81 83 72 86

aThe curve number for normal, CN(II), and wet, CN(III), antecedent moisture conditions are also reported.


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likely due to the high variability of the CN values with thereturn period itself (see Figure 10 and Table 5).

5. Conclusions[58] In this study, a procedure for the assessment of the

design soil moisture to be adopted within the classical DSapproach was proposed, so that the use of the CS approachcan be avoided. Based on the analyses and the resultsabove reported, the following conclusions can be drawn:

[59] 1. The rainfall (NSRP) and temperature (FARIMA)stochastic generation models reproduced the observed datawell.

[60] 2. The CS approach, not influenced by arbitrarychoices for the determination of the design rainfall hyeto-graph and the initial soil moisture conditions, was found tobe a useful tool to address the problem of design flood esti-mation in scarcely gauged catchments, mainly for highreturn periods.

[61] 3. Using the CS approach results as a benchmark,the design soil moisture to be adopted in the DS approach,i.e., the CN value determining the antecedent wetness con-ditions, was inferred.

[62] 4. The design soil moisture was found increasingwith return period for all the investigated catchments.

[63] 5. The variability of the design soil moisture inspace and with return period can be described by a simpleregionalization model whose accuracy should be investi-gated by using a larger number of catchments.

[64] The procedure allows us to apply the DS approachover large areas (and also in ungauged basins), overcomingits critical points and avoiding the use of the more complexCS approach. Moreover, it has to be highlighted that theCS approach used here can be easily applied in differentorographic contexts, although same adjustments might benecessary in areas where snowmelt is significant.

[65] Due to the limited number of study catchments, resultson regionalization are preliminary and mainly addressed todemonstrate the possibility to estimate the design soil mois-ture values for catchments where the CS approach cannot beapplied. More robust regionalized functions will be inferredin further investigations where the CS approach will beextended to other catchments of the upper Tiber basin.

[66] Finally, further researches will be addressed to theapplication of the CS approach for larger catchments by cou-pling a spatial-temporal stochastic rainfall (and temperature)model with a spatially distributed rainfall-runoff model.

[67] Acknowledgments. The authors wish to thank R. Rosi for histechnical assistance. They are also grateful to Umbria Region for providingmost of the analyzed data. The authors would like to express special ac-knowledgment to three anonymous reviewers and to the Associate Editor

for their valuable comments and remarks which helped to significantlyimprove the manuscript.

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Table 6. Percentage Error on Design Soil Moisture Value Estimated Through the Regionalization Procedure

Return Period (years)

Catchment

Assino Caina Cerfone Colorso Genna Niccone

20 1.60 0.71 2.18 2.24 0.12 1.4850 0.41 0.41 0.45 0.40 0.42 0.40100 �0.69 0.11 �0.07 �0.67 1.60 �0.60200 �1.20 �0.20 �0.55 �1.21 4.02 �1.41500 �2.55 �0.54 �2.13 0.79 6.71 �2.77


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