A Distributed Hydrological Model for Urbanized

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A distributed hydrological model for urbanized

areas Model development and application to

case studies

Fabrice Rodriguez *, HerveAndrieu, Floriane Morena

Laboratoire Central des Ponts et Chaussees, Nantes, Division Eau and Environment, LCPC, BP 4129,

F 44341 Bouguenais Cedex, France

Received 22 December 2006; received in revised form 3 December 2007; accepted 4 December 2007

KEYWORDS

Hydrology;Urban;

Modelling;Water budget;Urban databanks;Distributed

Summary The circulation of rainwater within urban areas has not yet been described in adetailed manner, as studies on this topic often remain limited to the runoff on impervioussurfaces. The need for innovative and sustainable methods of water management has

incited increased research efforts on the hydrological processes at work in urban areas.A distributed hydrological model based on information supplied by current urban data-banks has been developed in this aim. The components of rainwater flux (i.e. surface run-off, soil runoff, drainage flow via the sewer, and evapotranspiration) as well asinformation on the hydric state of the urban soil (saturation level, storage capacity) aremodeled at the parcel scale, and then coupled with a detailed description of the hydro-graphic network. This model runs continuously and has been intended to reproduce hydro-logical variables over very long time series. In order to evaluate this model, it has beenapplied at two different scales, on two urban catchments of various land use, wherehydrological data were available. This evaluation is based on the comparison of observedand simulated flowrates and saturation levels, and details the various compartments (soil,impervious or natural areas) to the outflow. This study shows the importance of waterfluxes often neglected in urban hydrology, such as the evapotranspiration or the soil infil-

tration into sewers. This first evaluation has highlighted the capability of mapping most ofthe hydrological fluxes on urban catchments, such as the capacity of soil to store water. 2007 Elsevier B.V. All rights reserved.

Introduction

Evolution in the field of urban rainwater management hasfavored sustainable practices and innovative technologies

0022-1694/$ - see front matter 2007 Elsevier B.V. All rights reserved.doi:10.1016/j.jhydrol.2007.12.007

* Corresponding author. Tel.: +33 2 40 84 58 78; fax: +33 2 40 8459 98.

E-mail address:[email protected](F. Rodriguez).

Journal of Hydrology (2008) 351, 268287

a v a i l a b l e a t w w w . s c i e n c ed i r e c t . c o m

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / j h y d r o l
mailto:[email protected]:[email protected]


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and, in turn, created various research needs. The hydrolog-ical behavior of urban areas can no longer be restricted tothe runoff of rainwater on impervious surfaces, which con-stitutes the dominant flow component for design purposes.Experimental data indicate that the flow coefficient for ur-ban catchments varies from one rainfall event to the next(Berthier et al., 1999). Urban surfaces, such as road pave-ments and parking lots, are not impervious, as shown byRa-

gab et al. (2003), who observed that 69% of total annualrainfall on a paved street infiltrates and that 2124% evap-orates. This result is consistent with the findings of Grim-mond and Oke (1991, 2002), confirmed by Berthier et al.(2006) and Dupond et al. (2006), who considered evapo-transpiration to be a major component of the water budgetwithin urban areas. Facilitating the infiltration of rainwaterresults in a higher groundwater level (Gobel et al., 2004).Draining the saturated zone through the sewer system maybe considered as a base flow that produces significant runoffvolumes (Belhadj et al., 1995). Urban soil can contribute tothe flow rate in the form of a subsurface flow component(Berthier et al., 2004). Such studies confirm that the hydrol-ogy of urbanized zones is far from being simple: the urban

environment is highly heterogenous in terms of land use,subsoil characteristics and other factors, which serve toinfluence all hydrological processes. This body of literatureemphasizes the benefit of an integrated modeling approachto address the entire array of hydrological processes withinurban areas. This issue has recently been examined byJiaet al. (2001), who developed a distributed hydrologicalmodel that spatially simulates variable water and energyprocesses in watersheds with complex land use/cover.

Urban areas have been well documented, thanks to thedevelopment of urban databanks (UDB). From a hydrologicalstandpoint, UDBs are attractive tools and this for at leasttwo reasons: they readily provide information on the mor-

phology of catchments at a level of detail seldom accessiblein hydrological studies; and they retain a record of the evo-lution in basin morphology thanks to regular updates. Inaddition, they facilitate the description of local-scale waterbehavior within the urban area and of its evolution overtime. Despite this advantage, use of such information forthe hydrological modeling of urban catchments is still notvery widespread. The areas drained by sewer system weredefined and estimated for each property block connectedto the sewer inlets (Djokic and Maidment, 1991; Greeneand Cruise, 1995). Water flow paths at the surface wereidentified from high-resolution digital elevation models,and the drainage pipes were modeled as open thalwegs(Zech and Escarmelle, 1999; Rodriguez et al., 2000). Sui

and Maggio (1999) observed that the conceptualization ofspace and time embedded in current Geographical Informa-tion Systems (GIS) are not always compatible with that inhydrological models. The modeling power of HSPF (Hydro-logical Simulation ProgramFortran) has been integratedthrough multipurpose environmental analysis system, likeBASINS (Brun and Band, 2000). Moreover, Rodriguez et al.(2003) have demonstrated that representative unit hydro-graphs can be derived from UDBs.

The objective of this study is to develop a distributedhydrological model (called URBS-MO, for Urban RunoffBranching Structure MOdel) based on the morphologicaldescription of the urban environment. This model is in-

tended to: (i) estimate, at different scales (parcel, catch-ment) and for different land uses, the components ofrainwater fluxes (surface runoff, soil runoff, drainage flowthrough the sewer, evapotranspiration, outflow); and (ii)supply information on the hydric state of the urban soil (sat-uration level, storage capacity). The model runs continu-ously and has been designed to reproduce hydrologicalvariables over long time series. This model could potentially

make a significant contribution to a new generation of urbanhydrological models that address the integrated manage-ment of urban rainwater, in promoting best managementpractices on the basis of rainwater infiltration and storage(Rivard et al., 2005).

This paper is devoted to formulating the URBS-MOmodel and to assessing the model with respect to its sim-ulation outputs. The validation of a hydrological model isusually based on comparing simulated flow rates at thecatchment outlet with observed values at the same loca-tion; the data available for calibrating the model is in factoften limited to outlet discharges (Anderton et al., 2002).This type of validation may be applied to URBS-MO butwould not be entirely satisfactory given the array of

simulated hydrological variables. Moreover, the spatial dis-tribution of hydrological fluxes or outputs could lead to abetter understanding of the hydrological behavior of urbancatchments. Thanks to the available hydrological data, thispaper will focus on validating URBS-MO on the basis ofboth flow rates and saturation levels. Two case studies willbe introduced for this purpose.

This paper has been organized as follows. Urban mor-phology and hydrological modeling section presents themodeling principles, which are based on the urban morphol-ogy as recorded in urban databanks. Modeling of hydrologi-cal processes at the UHE scale section lays out theprocedure for modeling the urban hydrological element

(UHE) and constitutes the papers main contribution. Model-ing of hydrological processes at the catchment scale sectionsummarizes the mechanism of water transfer from the UHEto the catchment outlet. Presentation of the case studiessection presents the main characteristics and experimentaldevices used in the case studies for evaluating model accu-racy. Initial URBS-MO validation on the Reze catchment: Fo-cus on water budget restitution section is devoted tovalidating the water budget model on the Reze catchment(5 ha), as regards both flow rates at the outlet and the hyd-ric state of the soil. URBS-MO validation on the Gohardscatchment section addresses validation of the completemodel on the Gohards catchment (180 ha) and illustratesthe model capability of simulating the spatial distribution

of different hydrological variables. Finally, the last sectionconcludes the paper and draws perspectives.

Urban morphology and hydrological modeling

The role of a catchments geometrical features and drainagenetwork on hydrological behavior has been highlighted anddiscussed by many authors. Thanks to the development ofhigh-resolution digital field models, land use data obtainedfrom remote sensing and GIS applications, river catch-ments are easier to describe and hydrological modeling hasundergone improvements, including the development of

A distributed hydrological model for urbanized areas Model development and application to case studies 269


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distributed hydrological models (Vieux, 2001) and geomor-phological approaches (Rodriguez-Iturbe and Rinaldo,1997). The geometric properties of catchments appear tobe highly important to this process, with the conclusionsdrawn remaining valid for urban catchments. UDBs enablerepresenting an urban catchment as a set of elementary sur-faces connected to a hydrographic network, based on the ci-tys main structural components, which serve to imprint the

morphology of the urban surface: the parcels and the streetnetwork. The urban cadastral map covers the main geo-graphical elements needed to describe urban catchments(Rodriguez et al., 2003): (i) parcels, houses, street sections,and possibly vegetation to provide a 2D description of the ur-ban surface; and (ii) topography, street segments, stormsewers and rivers for the hydrographic network description(seeFig. 1). This morphological description of a city appearsto be consistent with the hydrological modeling needs andallows considering an urban catchment as being composedof a set of urban hydrological elements (UHE) connected tothe catchment outlet by means of a runoff branching struc-ture (RBS).

(i) A UHE encompasses a cadastral parcel and its corre-sponding adjacent street segments. The geometricalcharacteristics of UHEs have been defined in urbandatabanks and comprise: surface area, the imperviousfraction including buildings and street surface area,the vegetation fraction, slope and length, connectionpoint to the RBS, and depth of the drainage networkat this point. These characteristics allow for a surface

representation of both the UHE and its cross-section(seeFig. 2).Berthier et al. (2004)modeled hydrologi-cal processes at the UHE scale and provided a detailedassessment of the role of subsurface processes.

(ii) The RBS describes the flow paths from each UHE tothe catchment outlet; each UHE is connected to thestreet and thus to the sewer and/or hydrographic net-work (Fig. 3). An RBS is represented by a vector map

of water flow paths, composed of a series of street

Figure 1 Map representing the different layers of an urban databank (UDB) used in the present study. The represented catchment

is located in the Nantes metropolitan area in France. An example of a UHE is plotted in bold dotted line, with its connection point Pc.

Figure 2 2D Representation of the urban hydrological ele-

ment, including the three vertical profiles.

270 F. Rodriguez et al.


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and sewer segments characterized by their length,slope and diameter (Rodriguez et al., 2003).

Modeling of hydrological processes at the UHEscale

Modeling set-up

Urban hydrology models normally take into account theinfiltration on pervious surfaces; they do however neglectthe circulation of water in the soil layer close to the groundsurface, which includes water exchanges between the soiland the sewer network. The hydrological influence of thissoil layer can no longer be neglected inasmuch as certainprocesses, such as evapotranspiration (Grimmond and Oke,2002) and drainage of soil water through the sewer network(Belhadj et al., 1995), prove to be significant components ofthe urban water budget. In addition, the hydrological influ-ence of soil increases with the implementation of best man-

agement practices promoting rainwater infiltration. Thefirst UHE model, as defined in the previous section, was de-rived byBerthier et al. (2004); their study focused on therole of soil in the generation of urban flows and adoptedan explicit model of water fluxes within the upper soil layerthat included exchanges with the sewer. This detailed rep-resentation is well adapted to hydrological simulation atthe parcel scale, yet cannot be applied according to a dis-tributed format at the catchment scale to simulate exten-sive time series of atmospheric forcing. That studyhowever did inspire the modeling principle behind the workpresented herein, which has been based on the following sixkey points:

A UHE is modeled by its cross-section, composed of threeland use types including roofs, streets and natural soils,with the two latter types potentially being covered bytrees;

The UHE is represented by three vertical profiles corre-sponding to the three land use types, as illustrated inFig. 2;

Each vertical profile can be diagrammed by four reser-voirs representing: interception over the surface, thesurface area, the vadose zone, and the saturated zone,respectively;

It is assumed that the horizontal water exchangesbetween the vertical profiles of a UHE occur only in thesaturated zone;

The sewer network drains the saturated zone; it isassumed that drainage density is high enough to fullycontrol the horizontal circulation of water within the sat-urated zone via the drainage performed by trenches andsewer pipes; and

The contribution of soil water due to water supply system

leakage has been neglected in this work.

The processes modeled at the UHE scale entail: interceptionby trees over the surface area, surfaces processes includingwater infiltration into the soil, surface runoff, the evapora-tion of water intercepted at the ground surface, subsoil pro-cesses consisting of plant transpiration, drainage of soilwater through trenches and sewer pipes. The modelingset-up is illustrated in Fig. 4. The following sections setforth a description of processes applicable to the threetypes of surfaces. In these sections, land use designationswill be denoted: nat for natural soil, hou for houseand str for streets. For the sake of convenience, the

=Outlet

LEGEND

Street segments

Sewer system segments

HE-street connections

Figure 3 Map representing the runoff branching structure of an urban catchment located in the Nantes metropolitan area in

France. A flowpath borned in a hatched UHE is represented in bold line.



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current land use type will not be recalled in the modelvariables.

On the surface: Interception by trees

Trees are not only numerous in cities, gardens and naturalareas, but also along streets and urban roads. Trees inter-cept a portion of the rainfall and indirectly contribute, ina limited yet active way, to improving the management ofurban rainwater. In this paper, the interception by treesconcerns both streets and natural surfaces. Various dia-grams can represent rainfall interception (Rutter et al.,1971; Calder, 1977; Vrugt et al., 2003); due to both its sim-plicity and its current use, we have adopted herein the for-mulation proposed by Calder (1977). The tree leaves arerepresented by a simple model reservoir supplied withwater by rainfall and then drained by both evaporation

and a drainage function that occurs whenever water storageexceeds a minimum value Stree,min. The potential inter-cepted rainfall is then subtracted from the rainfall value in-put for each land use type. The continuity equation for thewater intercepted by trees is:

Street Street Dt Pt Etreet OtreetDt 1

where t denotes time, Dt is the time increment, Stree therainwater stored by the trees, Pthe precipitation rate overthe time interval [t-Dt, t], Etree the evaporation flux fromtrees, and Otree(t) the throughfall drainage rate from treesto ground. These two latter variables are expressed asfollows:

if Street Dt 6 Stree;min then Etreet Street Dt

Stree; minPETt

and Otreet 0:0 2

if Street Dt> Stree; min then Etreet PETt

and Otreet abStreet Dt Stree; minc 3

with PET being the PenmanMonteith potential evapotrans-piration,Stree,minthe threshold allowing for ground drainage

of the stored water, and a a drainage law parameter. Itshould be noted thatStree,minanda both depend on the typeof trees and season.

Surface processes

The surface is represented by an interception reservoir(Rutter et al., 1971), whose capacity depends on the landuse type: natural soil, streets or roofs. The non-interceptedrainwater is separated into three components: evapotrans-piration, infiltration into the vadose zone, and surface run-off. The continuity equation for water stored in the surfaceinterception reservoir is expressed as:

Ssurft Ssurft Dt b1ftreePt ftreeOtreet

Esurft It RtcDt 4

where Ssurf is the water storage height in the interceptionreservoir,ftreethe fraction of surface area covered by trees,Esurf the evaporation flux from the interception reservoir, Ithe infiltration flux within the vadose zone, and R the sur-face runoff flux over the same time interval.

The evaporation flux is assumed to be proportional to thepotential evapotranspiration and water storage. This usedformulation (Rutter et al., 1971) allows incorporating, in asimple manner, the dual atmosphere and soil controls:

Esurf

t

Ssurft Dt

Ssurf; maxPET

t

5

where Ssurf,max is the storage capacity of the interceptionreservoir and PET the potential evapotranspiration flux.

The infiltration flux in the vadose zone is limited eitherby the soils infiltration capacity or by the water stored inthe surface interception reservoir, i.e.:

It minbKS; Ssurft Dt=Dtc 6

whereKS is the hydraulic conductivity at ground level satu-ration (see Eq.(8)).

Surface runoff,R (expressed in mm/h), occurs only whenthe storage Ssurfexceeds its capacity Ssurf,max:

Rt

max

h0;

Ssurf

t

Dt

Ssurf; max=

Dti

7

Principles for modeling soil processes

The objective here is to simulate, in a distributed fashionover a long time series, the following variables: saturationlevel, which controls soil water drainage through the sewernetwork; and the saturation deficit, defined as the waterdepth needed to saturate the vadose zone (Beven and Kirk-by, 1979). The saturation deficit serves as an important var-iable once it becomes preferable to manage rainwater bymeans of infiltration. Modeling the evapotranspiration andinfiltration is necessary to achieve this objective. A typical

Vadose zone

P

P

Etree

Stree

Saturated zone

Surface

Tree

Ssurf

Svad

z

zs

0

Otree

Esurf T

I

R

FIdrain

zroot

Figure 4 Vertical profile adopted for each land use type,

regrouping the 4 up-to-down reservoirs. The main processes

calculated in the model are represented.



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simplification consists of modeling the soil water by two res-ervoirs representing the vadose zone and saturated zone,respectively (Noilhan and Planton, 1989). These authorsdeveloped a specific two-reservoir approach to allow deter-mining two important variables: the saturation level, andthe mean moisture content of the vadose zone, which inturn yields the storage capacity at any time for any catch-ment parcel.

The influence of soil structure, which tends to be morecompact as depth increases, has been taken into accountby introducing an exponential decrease in hydraulic conduc-tivity at saturation (Ksat) with depth z, as inspired by workon Top Model (Beven and Kirkby, 1979):

Ksatz KSexpz=M 8

where KS is the hydraulic conductivity at ground level satu-ration and M a model parameter.

Parameterization of the vadose zone

The water stored in the vadose zone can be written as

follows:Svadt htzSt 9

wherezSis the depth of the saturation level at time t, andhrepresents the mean moisture content in the vadose zone.The water stored in the vadose zone is expressed as a func-tion of the two variables thickness and mean moisture con-tent, whose temporal evolution is also required herein. Thevadose zone is considered as a reservoir that receives infil-trated water from the surface, exchanges water with thesaturated zone just below, and provides the water tran-spired by trees (for both natural and root surfaces). Thecontinuity equation for the vadose zone takes on the follow-ing form:

Svadt Svadt Dt It Ft TtDt 10

where Svad is the water stored in the vadose zone, I theinfiltration flux originating from the surface (see Eq.(6)), F the water flux between vadose and saturatedzones, and T the transpiration flux of soil water throughthe roots of trees.

For the sake of simplicity, it is assumed that the vadosezone can be parameterized as illustrated in Fig. 5 by itsmean moisture contenth, presumed to be vertically uniformabove the capillary fringe, and by a capillary fringe of thick-ness Dzcf located immediately above the saturated zone.The moisture content in the capillary fringe is close to thesaturation moisture content, even though the capillary

fringe behaves like an unsaturated medium. The value ofDzcf is set equal to the air entry suction, We, introducedin Eq.(15)below.

Exchanges between the vadose and saturated zones,whether positive or negative, have been estimated usingDarcys law. It is assumed that Darcys law can be appliedbetween the saturation level and a point Vrepresentativeof the global behavior in the vadose zone. The depth of V,denotedzV, is expressed as:

zVt aVbzSt Dzcfc 11

where aV is a model parameter whose calibration will bepresented inAppendix.

The application of Darcys law between Vand the satu-rated zone then leads to the following expression:

Ft KVt HSt HVt

zt zVt

12

with KV being the hydraulic conductivity, HS the hydraulichead at the saturation level, and HV the hydraulic head atpointVrepresentative of the vadose zone. These quantitiesare written out as follows:

HSt zSt and HVt zSt Wht 13

KVt MinKsatzS; Khht; zVti 14

where W and Kare the suction and hydraulic conductivityrespectively for moisture content h at the representativedepthV, andKsat(zS) is the hydraulic conductivity at satura-tion at depth zS. W and Kadhere to the BrooksCorey Law,i.e.:

Wh Weh=hSb and Kh; z Ksatzh=hS

32b 15

where hS is the water content at natural saturation, Wethe suction head at air entry, and b a dimensionlessparameter that defines the shape of the water retention

and conductivity curve. These parameters may be esti-mated from soil texture (Clapp and Hornberger, 1978).The BrooksCorey Law has been adapted to take into ac-count the variation in hydraulic conductivity at saturationwith depth:

Ft KV 1 Whhti

zSt zVt

16

The transpiration flux from vegetation, including trees,serves to empty the vadose zone proceeding upwards. Thisflux has been determined by introducing both the depth ofthe root zone and the wilting point water content (Feddeset al., 2001):

zs

Vadose zone

Capillarity fringe

zs -zcf

zv

0

z

Saturated zone

Figure 5 Detail of the representation of the vadose zone.

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Tt hroott Dt hwp

hShwpPETt

for the natural soil type of land use

Tt hroott Dt hwp

hShwpPETtfstrtree for the street type

Tt 0 for the house type

17

where hrootis the mean water content within the root zone(depending on the model parameter zroot), hwp the wiltingpoint water content (i.e. the point where the suction headW(h) = 150 m in Eq.(15)), andfstrtreethe fraction of street sur-face area covered by trees.

hroott Dt ht Dt if z root 6 zSt Dt Dzcf;

hroott Dt zSt Dt Dzcf

zroot

ht Dt

1zSt Dt Dzcf

zroot

hS otherwise

18

A critical analysis of vadose parameterization is addressedinAppendixby means of a comparison between this simpli-fied layout and a more rigorous approach based on Richardsequation.

The saturated zone

The saturated zone is characterized by the saturation level;it exchanges water with the vadose zone and is drained bythe sewer pipe contiguous with the UHE. Moreover, the sat-urated zone is used to represent horizontal water exchangesbetween the three types of surfaces.

The saturation level is assumed to be uniform for a givenUHE. This mean saturation levelzS is expressed as the aver-

age saturation level of each surface type weighted by theland use surface proportion.If this saturation level is higher than the depth of the

drainage network znet, soil water may infiltrate into thedrainage network via groundwater drainage due to defectsin the tightness, which leads to network infiltration andempties the saturated zone. This infiltration flux has beenestimated by considering that the pipe behaves like an idealdrain (Cassan, 1986; Gustafsson et al., 1996):

Idraint KnatS e

zSt=Mk

L zsoilznetzSt l

19

where Idrain denotes the flux of water from the saturatedzone into the drainage network, L,zsoilandznetare geomet-

rical features of the UHE, k and l parameters that dependon the type and state of both the drain and trench contain-ing the drain. This groundwater drainage modifies the meandeficit and saturation levels according to:

zSt zSt Dt Idraint

hSDt 20

UHE water budget

Runoff at the outlet of a UHE equals the sum of the variousflow contributions, which encompass the runoff flows fromeach land use type and the groundwater drainage, i.e.:

Rtott fhouAhouRhout fstrAstrRstrt fnatAnatRnatt

fdrainrwAtotIdraint 21

wherefhou,fstr andfnat represent the fractions of each landuse type surface connected to the drainage system, andfdrainrw represents the fraction of soil infiltration waterdraining into the rainwater drainage system.

The surface runoff that does not contribute to direct run-

off because of the absence of direct connection to thedrainage network is allocated to the surface reservoir ofthe uncovered land use type, hence modifying the waterbudget of Snatsurf (see Eq.(4)) as follows:

Snatsurft Snatsurft 1f

houRhout 1fstrRstrt

1fnatRnatt 22

The 1D modeling representation does not include lateralexchanges between the three types of land use. These lat-eral fluxes within the vadose zone are indirectly introducedby averaging the water stored in the land use, weighted bythe land use surface area proportion.

Summary of the model running at the UHE scale

Model inputs at the scale of an urban hydrological elementconsist of: the meteorological forcing, which includesprecipitation and potential evapotranspiration; and theinitial saturation depth. The model has been designed tosimulate the evolution in hydrological variables over along time series with short time steps of just a few min-utes to remain consistent with the dynamics of urbancatchments. Model outputs contain the various waterfluxes computed for each time step, which can then beseparated into: (i) transfer of water from soil to atmo-sphere; (ii) rainwater infiltration into the vadose zone I

(iii) flow rate in the rainfall drainage system includingthe surface runoff on each land use type, and infiltrationflux into the sewer network Idrain; (iv) water storage withinthe various compartments, including mean moisture con-tent of the vadose zone and mean saturation level ofthe UHE.

The model requires both morphological features andphysical parameters. The morphological features are listedinTable 1and encompass, for each UHE, the surface areasof each land use type, the fraction of surface covered bytrees ftree, and the sewer depth znet. These features havebeen deduced from urban databanks, but could still benefitfrom an analysis of satellite imagery and aerial photogra-phy. The factors fhou, fstr and fnat, which represent the di-

rect connection of each land use type to the drainagenetwork, may be deduced from either local surveys or sta-tistical studies, and the factor fdrainrw, depicting the sepa-ration between direct infiltration of soil water into therainwater network and into the wastewater network, hasbeen estimated from the relative drainage densities of eachnetwork.

The model parameters are listed inTable 2; most entriesshould have been deduced from physical considerations,either literature reviews or field measurements. Thisparameterization has also resulted from a more detailedmodeling layout that served to solve the reference Rich-ards equation (Berthier et al., 2004).

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Modeling of hydrological processes at thecatchment scale

Flow routing

Rodriguez et al. (2003) have shown that the geometricinformation available from UDBs allows constructing thedetailed vector map of water flow paths along UHEs, streetgutters and inside the sewer network (hereafter referredto as the runoff branching structure and denoted RBS)and to derive the transfer function of urban catchments.The present study extends the paper of Rodriguez et al.(2003). The vector map of flow paths provides a basis for

routing water from each UHE to the catchment outletand, more generally, for calculating the flow at any pointof the catchment drainage system. The hydraulic routingconfiguration has been modified to contain two modelingstages: (i) routing of surface runoff on streets from UHEsup to the sewer inlets, as represented by the travel timerouting procedure used in URBS-UH (Rodriguez et al.,2003); and (ii) hydraulic routing inside sewer networks,

as represented by using the classical MuskingumCungescheme, which offers an approximate solution to the diffu-sive wave equation (Cunge, 1969).

The routing configuration is given for each segment ofthe RBS, i.e.:

Qj1t Dt C0Qjt Dt C1Q

jt C2Qj1t 23

withQdenoting the discharge at any node, j andj + 1 the upand down nodes of the RBS segments, and C0,C1and C2therouting coefficients whose sum equals 1:

C0 kx0:5Dt

k1x0:5Dt;

C1 kx0:5Dt

k1x0:5Dt and C2

k1x0:5Dt

k1x0:5Dt 24

with k and xdenoting the routing parameters. Parameter kis interpreted as the time taken by the wave to propagatealong the network segment, and parameterxis a dimension-less coefficient weighting the effect of inflow and outflowon the water stored in the network segment. These param-eters may be estimated from the following equations (Mont-aldo et al., 2004):

k Lj=x and x1

2 1

Qj

BjxSjLj

! 25

wherex is the kinematic wave celerity,Ljand Sjthe lengthand slope of the consideredjth segment respectively, B

jthe

segment width, and Qj the current discharge.

Model flowchart

The initial conditions are first determined to be homogenousover the entire catchment: the storage reservoirs are zer-oed and the saturation level initialized to an acceptable va-lue, corresponding to the actual saturation level on thecatchment at this initial date (possibly measured in numberof wells or piezometers). If such saturation level is not avail-able, a warm-up period will be needed. A sensitivity analysisshowed that an error of 43% on the initial saturation levelleads to a necessary 3 months warm up period. The tree

interception module is to be implemented first; the rainwa-ter falling on surfaces covered by trees gets subtracted fromthe intercepted water quantity. The modeling approach isthen applied to each UHE independently one from the other.The entire water budget is allocated with the surface pro-cesses and soil processes modules and generates the flowrate contribution of any UHE. The routing configuration isnext applied to each stream of the RBS for calculating theflow rate in any stream, especially that at the catchmentoutlet. All other hydrological variables introduced in Model-ing of hydrological processes at the UHE scale section re-main available for each time step on any UHE of thecatchment (seeTable 3).

Table 2 Model parameters of one UHE

Parameter Unit Description

Stree,min mm Minimum value of the tree interception

reservoir

a min1 Drainage law coefficient for tree

interception

Ssurf,max mm Maximum capacity of the surface

reservoir (for each land use)

KS m/s Hydraulic conductivity at natural

saturation(for each land use)

hS Water content at natural saturation

We Suction head at air entryb Retention curve exponent

M Scaling parameter of the hydraulic

conductivity

aV Representative position of the vadose

zone

Dzcf m Thickness of the capillary fringe

zroot m Root depth

k Groundwater drainage coefficient

l Groundwater drainage exponent

Table 1 Morphological features of one UHE

Feature Unit Description

A* m2 Surface area of each land use type: house

(hou), street (str), non-covered surface

(nat)

Atot m2 Total surface area of UHE:

Atot =Ahou +Astr +Anat

fstrtree Street surface area covered by treesfnattree Natural soil surface area covered by trees

L m Length of the UHE

znet m Depth of the rainwater drainage network

zsoil m Altitude of the UHE

fdrainrw Proportion of rainwater drainage network

fhou Fraction of house surface connected to

the rainwater drainage network

fstr Fraction of house street connected to the

rainwater drainage network

fnat Fraction of natural soil connected to the

rainwater drainage network



9/20

The minimum data required to run the model are hydro-logical data of precipitation and PET (Potential evapotrans-piration) taken from the closest meteorological station. Aninitial value of saturation level is welcome, as discussedabove. In the end, some field experiments could help toestimate soil hydrodynamic properties, as discussed in Ini-tial URBS-MO validation on the Reze catchment: Focus onwater budget restitution section.

Presentation of the case studies

Two urban catchments within the Nantes metropolitan area(Western France) have been considered for our evaluationof URBS-MO. The first one is located in Reze; the drainagenetwork associated with this catchment is composed of sep-arate sewers and its land use is homogenous residential.Impervious surfaces account for 37% of drainage networkconnections and the soil has been assessed as a silty clay.

This catchment was monitored over a 10-year period (Ber-thier et al., 1999) and is currently being used to conducthydrological modeling tests (Rodriguez et al., 2000; Rodri-guez et al., 2003; Berthier et al., 2004). The data measuredcomprise: (i) rainfall intensity and discharge at the outletfrom 1991 until 2002; (ii) the water table level throughtwo piezometers installed at two locations of the catch-ment, from September 1995 until December 1998; (iii) thegroundwater drainage runoff measured during three winterperiods in the wastewater drainage network (Belhadjet al., 1995), which provides an estimation of both the rain-water and wastewater components in groundwater drainage(Berthier et al., 2004); and (iv) meteorological data, such as

Penman evapotranspiration, collected from the meteoro-logical station located 5 km from this catchment.Fig. 6dis-plays the experimental set-up and catchment morphology.

The second catchment is located within the Nantes citylimits and is called Gohards (180 ha) and has already beenused to identify hydrological response of urban catchments(Rodriguez et al., 2005). The drainage network of this catch-ment is composed of separate sewers, and the basin contains

single- and multi-family housing, commercial areas and indus-trial zones. The data derived comprise: (i) rainfall intensityand discharge at the outlet measured from 1998 until 2002;(ii) meteorological data, such as Penman evapotranspiration,collected from the meteorological station located 13 km fromthe catchment outlet. The Gohards catchment is shown inFig. 7, along with the various measurements points.

The rainfall event sample forReze is constituted of 850events (exceeding 2 mm) over 10 years, while the rainfallevent sample forGohardscontains 330 events over 4 years.:the mean cumulative rainfall depth is around 9 mm for bothrainfall event samples. The primary morphological charac-teristics of both catchments have been listed in Table 4,which shows how the two catchments differ. In terms of

land use, theRezecatchment is more homogenous than Go-hards(mainly due to its much smaller size); the mean size oftheRezeparcels is three times smaller than that of the Go-hardsparcels, with the standard deviation of all character-istics being higher in the Gohards data.

Initial URBS-MO validation on the Rezecatchment: Focus on water budget restitution

The Reze catchment has been chosen for the validation ofwater budget processes, according to URBS-MO depiction.Three reasons explain this choice. First, the catchment issmall and may be represented in its entirety by a set of sim-

ilar hydrological elements. Second, The hydrological dataavailable (flow rates at the outlet, piezometric measure-ments, groundwater drainage runoff data), make it possibleto evaluate both the soils contribution to total flow rateand the simulation of saturation level variation. Third, sev-eralin situinvestigations have been performed to estimatethe hydrodynamic characteristic conditions within the soil.

Three comparison criteria were adopted for the modelevaluation: the Nash criterion (denoted CNash), a bias crite-rion (denoted Cb), and the determination coefficient R

2:

CNash 1

Ptntt1

V2t V1t2

Ptntt1

V1t V12

CbPtn

tt1 V2t V1tPtntt1

V1t

R2

Ptntt1

V2t V2V2t V1 2

Ptntt1

V1t V22Ptn

tt1V1t V1

2 26

whereV1is the reference variable, V1the temporal averageof this variable, and V2 the simulation variable.

This work has focused on two variables representative ofthe general model behavior: flow rate at the catchment out-letQoutlet, to be denotedQfor the sake of convenience; andthe saturated zone level zS, considered to be uniform overthis small catchment.

Table 3 Hydrological variables (storages and flux) of the

model Dt is the model time increment

Variable Unit Description

Stree mm Tree reservoir storage

Ssurf mm Surface reservoir storage of each land

use type

Svad mm Vadose zone storage of each land use

typeh % Mean moisture content in the vadose

zone of each land use type

zS mm Depth of the saturated zone of each

land use type

zV mm Representative depth of the vadose

zone

Etree mm Evaporation flux from trees

P mm/Dt Precipitation

Otree mm/Dt Non-intercepted precipitation

ETP mm/Dt Potential evapotranspiration

I mm/Dt Infiltration flux from surface to vadose

zone

Esurf

mm/Dt Evaporation flux from surface

R mm/Dt Surface runoff flux

T mm/Dt Transpiration flux

F mm/Dt Flux between vadose zone and

saturated zone

Idrain mm/Dt Groundwater drainage

Q m3/Dt Runoff flow at the UHEs outlet



10/20

Figure 7 Gohards catchment: triangles show the pluviometers, the star shows both the outlet and the discharge measurement in

the stormwater drainage system.

Figure 6 Rezecatchment: circles show the piezometers location, triangles the pluviometers, the star shows both the outlet and

the discharge measurement in the stormwater drainage system, and the diamond the discharge in the wastewater drainage system.



11/20

Model implementation principle

Given the homogenous type of housing stock (Rodriguezet al., 2003), the 70 component parcels have been repre-sented by a single UHE, whose morphological features (asdeduced from UDBs) are listed inTable 4. Continuous simu-lation runs have been carried out over a 10-year period usinga 5-min time step. The base run could be initialized thanksto a realistic set of parameters (listed inTable 5) whose val-ues are explained below.

A sensitivity analysis has been conducted and led to the

following conclusions: two parameters may cause majormodifications to hydrological behavior within URBS-MO:the hydraulic conductivity at natural saturation of thenatural soil type KnatS , and the groundwater drainage coeffi-cient k. Regarding the hydraulic conductivity of the natural

soil type, its estimation should be deduced from field mea-surements as well as from a hydrodynamic study of the tar-get soil. This concern remains fairly infrequent within theurban environment, where soil processes tend to get ne-glected, yet becomes prominent once it has been acceptedthat the urban soil plays a role in the hydrological processesfor urban areas. The saturated hydraulic conductivity of ur-ban soils however is difficult to estimate, due both to the

heterogeneity of this soil, which encompasses differentcomposite materials, and to the presence of various under-ground sewers (De Kimpe and Morel, 2000). An average rep-resentative value is not easy to estimate. To apply themodel to theRezecatchment, the value of KnatS has been ex-tracted from previous field measurements on this catch-ment (see below).

Estimating the groundwater drainage coefficient k is amore ambiguous undertaking. This parameter could a prioribe deduced from physical considerations, given its impacton sewer pipe infiltration capacity and its dependence onsewer network conditions: age, pipe materials, etc. Thistype of information should be available within urban data-banks in the future and could be examined for specific stud-

ies. Moreover, since groundwater drainage fluxes depend onthis parameter to a great extent, the parameter value couldbe deduced from sewer base flow measurements. The meth-ods developed to quantify clear parasitic water (or infiltra-tion/inflow) within wastewater systems (Joannis, 1994)could prove useful in quantifying the base flow of rainwatersystems. To proceed with estimation of this factor and pro-vided observed flow rates at the catchment outlet are avail-able, we would suggest: (i) estimation adjustment in orderto minimize the discrepancy between observed and simu-lated volumes, and (ii) the use of groundwater flow rateobservations if available. Further discussion will be providedon this topic, which will necessitate further research inves-

tigations to be able to effectively model and measure soilwater infiltration into pipes.The values of tree interception parameters were ex-

tracted fromCalder (1977) and Grimmond and Oke (1991);they are representative of deciduous trees. The minimumvalue of tree interception reservoir Smin is 1 mm, exceptduring the winter season when it equals 0.3 mm due tothe lack of leaf cover. The maximum reservoir capacitieshave been extracted from Hollis and Ovenden (1988) forimpervious land uses and from Grimmond and Oke (1991)for the green areas; these reveal a large storage capacityof green areas, in comparison with the small storage capac-ities of roofs and streets (Zech et al., 1994). The hydraulicconductivity of the street has been extracted from Hassan

and White (1997). The hydraulic characteristics of the soilwere mainly derived from field measurements taken on soilsamples from two different depths (0.2 m and 1.5 m belowthe surface) in Reze(Berthier et al., 2004). This sample wascharacterized by ahSof 0.43, aweof 0.2 m andbequal to 5.These values are characteristic of a loamy or sandy loam soiltype, according to the classification of Cosby et al. (1984);the natural hydraulic conductivity KnatS equals1.3 105 m s1. M was deduced from fitting of Eq.(8) fora 1.5-m soil depth. The point assumed to be representativeof the vadose zone definitely constitutes one of the compu-tational parameters; a value ofav= 0.5 m has been adopteda priori, in accordance with the sensitivity analysis

Table 4 Morphological features for Reze and Gohards

catchment

Catchment Reze Gohards

Mean Surface area (m2) 709 1948

Standard deviation 139 5405

Mean fraction of house land use type fhou 0.16 0.19

Standard deviation 0.05 0.14Mean fraction of street land use type fstr 0.19 0.27

Standard deviation 0.08 0.12

Mean fraction of natural land use type fnat 0.65 0.54


Mean fraction of tree surface ftree 0.14 0.16

Standard deviation 0.06

Mean UHE length L (m) 43.3 62.5


Mean sewer network depth znet(m) 1.2 3.55


Table 5 Physical parameters for Reze catchment

Parameter Unit Value Variation range

(sensitivity analysis)

Smin mm 1/(0.3 in winter) 0.0015

a min1 0.04 00.2

SnatS max mm 5 0.00140

ShouS max mm 0.5 0.0012.5SstrS max mm 3.5 0.00117.5

KnatS m/s 1.3e5 1.e81e4

KstrS m/s 7.5e8 1.e91e6

hS / 0.43 0.300.50

We / 0.20 0.050.70

b / 5 212

M / 0.2 0.0510

aV / 0.5

zroot m 1.3 0.14

k / 4 0100

l / 2 0.15



12/20

presented in Appendix. The depth of root zone has beenused as a mean representative value of 1.3 m was chosen,with respect to a depth of 0.1 m for grass and 3 m for smalldeciduous trees (Feddes et al., 2001) and to the respectivesurface areas of these vegetation land use. The groundwa-ter drainage law parameters may be correlated with thestate of the sewer system: a small value of k characterizesa sewer network with few defects, while a high k value is

more typical of a sewer network in poor condition, withthe potential for considerable water infiltration. The valuesselected for this base run are those proposed by Cassan(1986) for an agricultural drain, although this parameterwould still need to be calibrated.

As mentioned above, the high sensitivity of the model tothe value of groundwater drainage coefficient k and its lackof physical meaning impose adjusting this value with re-spect to the discrepancy between simulated and observedrunoff volumes.Fig. 8a shows the comparison between run-off depths simulated for each rainfall event, using the refer-ence value, and the observed runoff depths. The flow ratehas been overestimated and the bias criterion on runoffdepths equals 46%. This scatter plot indicates a discrepancy

due to winter rainfall events: for these events, groundwaterdrainage is very low, since a small value has been assignedto drainage coefficient k, which consequently results in avery high saturation level. This situation induces a largecontribution from natural soil to runoff, which amounts toapproximately 10% of total rainfall (seeTable 6), i.e. equiv-alent to the house or street runoff (not a realistic resultwithin this urban catchment). Moreover, in this case, thesimulated groundwater drainage flux has been underesti-mated, in comparison with observed infiltration flow rates.A trial-and-error calibration of this k coefficient has beencarried out with respect to the bias criterion estimated onthe total flow rate and has led to a value of k= 40. With this

value, both the agreement between observed and simulatedgroundwater drainage fluxes and the bias criterion on rain-fall events are improved (Fig. 8b). Increasing groundwaterdrainage then contributes to decreasing the saturation leveland facilitates infiltration of surface water into the vadosezone. Runoff produced by streets and natural soils thereforegets reduced (Table 6) and the contribution of natural soil issignificantly reduced, reading close to zero.

Water budget evaluation

The availability of a very long and continuous data series offlow rates and saturation levels enables focusing the modelevaluation step on the simulation of runoff production andon the evolution in the soils hydric state. Model perfor-mance is to be illustrated through its capacity to simulatethe various contributions to runoff.

How rainfall contributes to runoff?

The model provides a comparison of the various hydrologicalfluxes occurring over the entire simulation period.Fig. 9as-

sesses simulated fluxes on the representative UHE. Valuesare expressed as a percentage of rainfall and depend onthe chosen reference parameter configuration. A value of100% rainfall transforms into 97% non-intercepted rainfall,which gets split into 60% on natural soils, 17% on roofs and20% on streets, due to the relative proportions of these landuse types on the Reze catchment. Evaporation and transpi-ration fluxes amount to more than 40% of the total rainfall.The tree interception rate remains small: this result is cor-related with the low level of tree coverage on this catch-ment (0.17% of street surfaces and 24% of natural soilsurfaces). The main contribution to flow rate stems fromcovered surfaces, with 15% from houses and 7.5% fromstreets; the natural soil contribution lies close to zero.The soil contribution is due solely to groundwater drainage,which represents about 30% of the total rainfall, as dividedbetween the wastewater (18.4) and stormwater sewer(10.7) networks. This result, unfortunately, cannot be vali-dated at the present time, yet it is consistent with otherexperimental results observed on urban catchments (Hollisand Ovenden, 1988).

0 5 10 15 20 25 30 350

5

10

15

20

25

30

35

Observed runoff depth (mm)

Simulatedrunoffdepth(mm)

0 5 10 15 20 25 30 350

5

10

15

20

25

30

35

Observed runoff depth (mm)

Simulatedrunoffdepth

(mm)

(a)=4 CNash= -0.30 and Cb= 0.46 (b) =40 CNash= 0.95 and Cb= 0.1

Figure 8 Comparison of the runoff volume produced by each rain event, observed inx-coordinate and simulated by URBS-MO iny-

coordinate Simulation realized with two different values of k.

Table 6 Various runoff contributions to the total flow rate,

expressed in percentage of the gross rainfall for Reze

catchment

k Qhou Qstr Qnat Qdrain Qtot P

4 15.1 8.8 10.4 5 45.26 100

40 15.1 7.5 0 10.7 33.3 100

http://-/?-http://-/?-


13/20

Flow rate simulation

Three types of results have been compared (see Table 7).First, the instantaneous flow rates Q during rainfall eventswere compared with the observed rates. For each rainfallevent, the flow rate volumes Vand flow coefficient CFwerethen compared with observations: a very strong agreementwas found between the simulated flow rate volumes V,which proves the ability of the model to simulate the waterbudget for the given catchment. The URBS-MO model repro-duces more than half of the observed variability in the flowcoefficient (R2 = 54%) of the series of rain events; this per-formance is similar to that of a highly detailed 2D model

(UHE model) applied to the same catchment over the sameperiod (Berthier et al., 2004).

Saturation level simulation

The simulated saturation level is assumed to be uniform;this assumption admittedly is not fully realistic, as illus-trated in Fig. 10, which shows the temporal evolution inthe piezometric measurements at two points on the catch-ment. The comparison will focus on the dynamic evolution

Treeinterception

evaporation

97.3

100

2.7Rainfall

Non

intercepted

Rainfall

0

storage = -0.9

0.02

0.04

2.015.1

7.5

0.9

60.1 43.511.6

10.7

60.2

17.1

20.0

Rainfall

Surfaceevaporation

Surface runoff

Transpiration

Infiltration

Groundwater drainage into

rainwater sewer system

wastewater sewer system

18.4

Treeinterception

evaporation

Rainfall

Non

intercepted

Rainfall

Treeinterception

evaporation

Rainfall

Non

intercepted

Rainfall

Rainfall

Non

intercepted

Rainfall

storage =

Rainfall

Surfaceevaporation

Surface runoff

Transpiration

Infiltration



wastewater sewer system storage =

Rainfall

Surfaceevaporation

Surface runoff

Transpiration

Infiltration



wastewater sewer system

trees

Figure 9 Hydrological variables on the UHE for the whole simulation period (01/01/199131/12/2000), expressed in percentage

of the gross rainfall. Water fluxes are detailed for natural soils, and are omitted fro street and roof land uses, for a sake of

conveniency. Values indicated in italic are valid for the whole UHE, other values are only valid for each land use type.

Table 7 Comparison criteria for simulations of runoff

volumes V, flow coefficient CF and instantaneous flow rates

Qfor the whole period (Reze)

Cb R2 CNash

V +1.4 % 0.95 0.95

CF 0.5% 0.54 0.50

Q 0.58% 0.59 0.51

0 200 400 600 800 10003

2.5

2

1.5

1

0.5

0

Time (days)

saturationlevel

(m)

PZ1

PZ2

simulation

Figure 10 Saturation level evolution on catchment Reze

between 1996 and 1998, observed in 2 piezometers and

simulated by URBS-MO.



14/20

of saturation levels over a three-year period of availabledata. The variation in simulated saturation level agrees withobservations over the entire simulation period, except forsummer 1998, for which the model is unable to reproducethe particularly sharp and rapid decrease in the saturationlevel. Two arguments can be forwarded to explain this dif-ference: either the model cannot successfully simulate in-tensely dry meteorological periods, or this decrease is

caused by human activity (e.g. pumping in the vicinity ofthe catchment). In the latter case, this kind of hydrologicalbehavior cannot be reproduced by URBS-MO due to the setof assumptions concerning the saturated zone of the catch-ment. Potential exchanges between the saturated zone ofthe catchment and the surrounding saturated zone werenot taken into account herein. This assumption would bereasonable in an urban catchment, but might be debatableshould the soil contribution appear to be sizable.

URBS-MO validation on the Gohards catchment

TheGohardscatchment has been selected for the validationof the complete model, including the water budget andtransfer processes. Due to its size and land use heterogene-ity, this catchment serves to illustrate the value of thespatially distributed modeling approach inherent inURBS-MO.

Principle of model implementation

This catchment encompasses 911 cadastral parcels, whichcombined represent as many individual UHEs. The morpho-logical features of each UHE have been estimated thanksto the urban databanks available for the Nantes metropoli-tan area (France) and reveal a broad range of surface areas,

and natural and impervious fractions (see Table 4). Themodel has been implemented according to the flowchart de-scribed in modeling of hydrological processes at the catch-ment scale section, with special emphasis on applying thewater budget allocation to every UHE, and has generatedthe simulation of spatially-distributed flow rates and satura-tion levels. Rainfall intensities have been consideredhomogenous over the entire catchment, as deduced fromthe average rainfall intensity observed on the two pluviom-eters. With rainfall intensities and flow rates available at 5-

min time steps, a continuous simulation could be run for 4full years using these 5-min interval data records.

As for the estimation of water budget parameters, thefollowing assumptions have been adopted. Due to proximityof the Reze and Gohards catchments and the similarity oftheir surface and soil properties, the parameter set ac-cepted for Reze has been transposed to Gohards, exceptfor the groundwater drainage parameter k, which is specific

to the sewer network. These parameters were assumed tobe identical for all UHEs in the Gohards catchment. Theparameter k was calibratedby making an adjustment withrespect to the discrepancy between simulated and observedrunoff volumes (Fig. 11a). The bias criterion has its mini-mum value for k = 17, which might indicate that the Go-hards sewer pipes and trenches system displays differentcharacteristics than those of Reze; this statement howevercannot be verified, the only available data for that is the ageof the sewer pipe implementation, and it was similar onboth catchments.

Transfer parameters associated with the Muskingumrouting configuration have been estimated in applying thefollowing assumptions. The routing parameter xis assumed

equal to 0.2, which is a mean current value adopted for ur-ban hydraulic routing (Chocat, 1997, p. 658). The meantime k has been estimated by considering that wave veloc-ity x is spatially variable. We have chosen the followingformulation, as deduced from Mannings Equation and sug-gested bySemsar (1995): xj= 0.8Vj, where Vj is computedfrom Mannings Equation applied to the jth segment of thedrainage network (Rodriguez et al., 2003). The calculationof Vj involves the pipe filling rate h. Semsar (1995) sug-gested a filling rate corresponding to 80% of the maximumflow rate through the pipe. We tested model sensitivity tothis parameter. Year 2000 data served as inputs for thistest, and the Nash criterion on instantaneous flow rates

was considered (Fig. 11b). This routing parameter provesinfluential for very small values of the filling rate. Themodel performs better when the filling rate ranges be-tween 50% and 100%. We ultimately decided on a valueof 50% for this parameter.

Flow rate evaluation

A strong level of agreement has been found between simu-lated flow rate volumes V and observations (see Table 8),

-20

-10

0

10

20

30

40

0 10 20 30 40

Cb(H)

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.2 0.4 0.6 0.8 1

Filling rate

CNash(Q)

a b

Figure 11 Application of the model to catchment Les Gohards Sensitivity (a) to the parameter k (groundwater drainage

coefficient) with regards to the bias criterion and (b) to the parameter h (filling rate of sewer pipes) with regards to the Nash

criterion.



15/20

although the comparison criteria are not as effective as forthe Reze catchment simulation. On the one hand, resultsshow a marginal overestimation of runoff volumes withURBS-MO, while on the other, the mean simulated flowcoefficient (0.33) is slightly smaller than the mean observedflow coefficient (0.35) and the bias criterion on flow coeffi-cients is negative. The simulation of instantaneous flowrates displays a good correlation coefficient (R2 = 0.74)

and a correct Nash coefficient (CNash= 0.54). At this point,it must be emphasized that theGohardscatchment simula-tion extends over a continuous four-year time period andcomprises 330 rainfall events, spanning the entire range ofhydrological behavior of the catchment. The results ob-tained must be assessed in light of this array of evaluationconditions, which makes for a rather different test thanmost hydrological models.

The models ability to simulate peak flow rates has beenanalyzed by displaying the scatter diagram of simulated vs.observed peak rates for all 330 rainfall events occurring dur-ing the 4-year simulation period. This plot is characterizedby a high proportion of small peak flow values (Fig. 12). Agood agreement has been found between the two peak val-ues, as assessed by a correlation coefficient R2 of 77%.

The contributions to outflow from the various land usesare summarized inTable 9. It appears that the runoff pro-duced by pervious surfaces is significant on this catchment(about 6% of the rainfall, i.e. 16% of the total flow rate dur-ing rainfall events). Such a contribution varies considerablyfrom one rainfall event to the next and depends on the par-ticular season. The runoff produced by pervious surfacesduring rainfall events is very small during the summer (1%)and increases up to 20% of the total flow rate during winter-time (Table 10). This contribution seems to be overesti-mated, compared to the results obtained both by Boydet al. (1993) on several urban catchments and by Berthier

et al. (2004) on the Reze catchment. This result howevermay be explained by the way the model functions. It is pres-ently assumed that the rainwater in excess of the infiltra-tion capacity of UHE natural surfaces actually adds torunoff. In many cases, surrounding walls or hedges preventrunoff from occurring, with the excess water being storedin the parcel and then infiltrating after the rainfall event.This process has not been built into in the model due to alack of sufficient information concerning those UHEs onwhich the natural component cannot contribute to runoff.

Distributed nature of the results

First of all, the simulations conducted with the 911 UHEs of

the catchment have been compared to those performedwith just a single representative UHE, in assuming a homog-enous catchment. The morphological characteristics of thisUHE have been deduced by averaging characteristics overthe entire catchment; the process parameters turn out tobe the same. As indicated inTable 10, the distributed re-sults are consistently better than the homogenous ones,which confirm the benefit of a spatially distributed descrip-tion of hydrological processes for urban catchments. Thesimulation performed with the homogenous configurationshows that the model underestimates flow rate volumes,as a consequence of the small contribution of natural soilto runoff. The saturation level, in this case, is much lower

Table 8 Comparison criteria for simulations of runoff

volumes V, flow coefficient CF and instantaneous flow rates

Q for the whole period (Gohards) values in brackets

represents the results with one sole UHE for the whole

catchment

Cb R2 CNash

V +7.1% (1.3%) 0.89 (0.86) 0.79 (0.69)CF 5.8% (15.6) 0.43 (0.35) 0.20 (0.22)

Q +2.2% (7.5) 0.74 (0.65) 0.54 (0.37)

0 2000 4000 6000 80000

1000

2000

3000

4000

5000

6000

7000

8000

Observed peak flowrate (l/s)

Simulatedp

eakflowrate(l/s)

Figure 12 Comparison of observed and simulated peak flows

of Les Gohards catchment for the whole simulation period.

Table 9 Various runoff contributions to the total flow rate,

expressed in percentage of the gross rainfall for Gohards

catchment

k Qhou Qstr Qnat Qdrain Qtot P

17 13.3 13.5 6.7 10.1 43.7 100

Table 10 Seasonal variation of the pervious runoff contri-

bution on Gohards catchment during the simulation period

(19982001)

Season Percentage

of the

gross rainfall

Percentage

of the total

flow rate

Considered

flow rate in

the year (%)

Winter 11.4 21 33.7

Spring 2.8 7 14.9

Summer 0.3 1 14.5

Autumn 9.1 19 36.9



16/20

than in the distributed configuration, and both the naturalsoil and groundwater drainage components are inexistent.It may be observed that in the distributed configuration,the hydrological behavior may be quite different from oneUHE to the next, and the portion of runoff generated by nat-ural surfaces and the soil vary considerably. The UHEs with ahigh natural soil contribution generally display special mor-phological features; their mean surface area amounts to

29,000 m2

since the mean value equals 1948 m2

for the en-tire catchment. This large number stems from two factors:(i) a high pervious surface area leads to a sizable amount ofinfiltrated water; and (ii) an elongated shape, relative to ahigh value of the UHE length L, leads to a small value ofgroundwater drainage Qdrain. For these UHEs, both factorsinduce an increase in water content within the vadose zoneand an increase in saturation level during the winter season,in addition to producing runoff on pervious surfaces. Thishigh variability in pervious surface runoff however is unreal-istic and constitutes a limitation to our modeling method.The simulation result is due mainly to model assumptions,which consider every elementary unit as a parcel drainedby the adjacent sewer system. Such assumptions might no

longer be valid for parcels whose characteristics vary more

widely, and especially the large natural parcels. Underthese conditions, the natural circulation of groundwateralong the hill slope can no longer be neglected and mustcertainly become a significant contribution to the water fluxduring wintertime. This function seems to be well suited tosmall parcels but fails for parcels with a greater length L: inthis case, drainage is too slow, which induces an artificial in-crease in saturation level and generates excessive pervious

runoff on specific UHEs. This finding was not observed onthe Reze catchment, where parcels were very homogenousand not as long, in comparison with the Gohardscatchment(seeTable 4).

Moreover, this distributed model allows for the estima-tion of many hydrological variables for each UHE, such asthe various contribution components to runoff, saturationlevel, water content and the actual evapotranspiration.Fig. 13illustrates the spatial variability in total evapotrans-piration for the entire simulation period. The mean evapo-transpiration value for all UHEs amounts to 33.8% ofrainfall, with this variable ranging from 4% to 61%; it tendsto be higher on those UHEs characterized by a high percent-age of natural land use. The scatter diagram of this evapo-

transpiration vs. the natural fraction of each UHE (Fig. 14)

250 m

50 - 61

40- 50

30- 40

20- 30

3,7 - 20

Figure 13 Spatial distribution of the cumulated evapotranspiration (in percentage of the total rainfall depth) simulated by

URBS-MO between January, 1999 and December, 2002 on catchment Les Gohards. Dark parcels are characterized by high

evapotranspiration values.



17/20

confirms the obvious proportionality between evapotranspi-ration and natural soil fraction, but shows the existence of asignificant dispersion in evapotranspiration for a given frac-tion of natural soil, a significant dispersion in evapotranspi-ration appears on the order of 10% or 15%. Factors otherthan the morphological parameters, such as soil water con-tent and a representation of soil storage capacity in themodel, may serve to explain this variability. It can be re-

marked that these factors are likely to be influenced bysewer pipe depth.Fig. 15shows the distribution in storagecapacity, as can be deduced from the saturation level; theestimation of this variable could prove valuable when imple-menting rainwater infiltration techniques that help deter-mine the zones where rainwater infiltration could bebeneficial. These results constitute an initial illustration ofthe possibilities offered by such a distributed urban model-ing approach and will be subsequently validated by compar-ison with distributed saturation level observations using anapplication on various case studies.

Conclusion

This study has presented a distributed hydrological modeladapted for urban areas. This model has been designed tofurnish a more thorough description of the hydrological

Figure 14 Total simulated cumulated evapotranspiration (in

percentage of the total rainfall depth) versus natural soil

fraction of each UHE on catchment Les Gohards.

250 m

270 - 526

220 - 270

176 - 220

136 - 176

20 - 136

Figure 15 Spatial distribution of the storage capacity of the soil (in mm), simulated by URBS-MO on July 1, 2002 on catchment Les

Gohards. Dark parcels are characterized by high storage capacity.



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behavior of urban catchments, thanks to an estimation ofthe various fluxes contributing to the water budget; theseinclude: evapotranspiration, infiltration, runoff, and soilwater drainage through the sewer network. This first appli-cation of URBS-MO has confirmed the effectiveness of ahighly detailed distributed hydrological model based on ur-ban databank records and devoted to urban areas. URBS-MOtakes advantage of the spatial variability of land use, as

characterized by the urban databank content managed byGeographical Information Systems. The model has beentested at two different scales: a small and homogenous ur-ban catchment, representative of an urban hydrological ele-ment; and a medium-sized and more heterogenous urbancatchment. Accordingly, the relevance of both water bud-get modeling and the whole distributed modeling chaincould be evaluated by using long and continuous series ofatmospheric forcing spanning several years. The modelshows that evapotranspiration, water infiltration into sew-ers are indeed capable of generating a significant compo-nent of the water budget, in agreement with previousexperimental studies (Belhadj et al., 1995; Berthier et al.,2004).

This study has confirmed the importance of urban soiland soilatmosphere interaction on the hydrological pro-cesses at work in urbanized areas once focus is placed onthe continuous hydrological modeling over longer periods:years, seasons. The results obtained indicate that someuncertainties still remain, regarding both the set of model-ing principles pertaining to water circulation in the soil andthe estimation of some model parameters, particularlythose controlling how the water budget gets processed.The following modeling principles need to be further exam-ined: (i) the assumption according to which water circula-tion within the saturated zone is fully controlled by thedrainage network; (ii) parameterization of the exchanges

between groundwater and sewer network; (iii) the assump-tion according to which the water supply system leakage isneglected. Interactions between the sewer system and thesaturated zone remain a very current topic of researchwhich deserves detailed investigation Moreover, taking intoaccount the water supply system leakage could be a newchallenge in hydrological modelling of urban catchments.This phenomenon can prove significant (Lerner, 2002; Zhangand Kennedy, 2006) and should be investigated by introduc-ing a new source term of water in the soil; it induces newdata requirements, such as the private water consumption.In the end, channeling all of the runoff produced by naturalsurfaces directly into the sewer system may ultimately beinappropriate in many urban configurations, where built

obstacles block runoff and force the soil surface contribu-tion to infiltrate.

The evaluation of such a distributed model makes it nec-essary to develop new observation strategies. Observationof the groundwater drainage component might, for exam-ple, be pursued in the stormwater or wastewater systemduring wet periods, by measuring the low flow rates. Anevaluation of the spatial distribution in saturation level con-stitutes another area of interest: the model is able to simu-late a very dense distribution of this variable, yet suchinformation remains impossible to validate. The ultimategoal is to evaluate hydrological fluxes from the surface tothe atmosphere. At the present time, we are unable to

judge whether or not the simulated evapotranspiration isrepresentative; nonetheless, a set of well-adapted experi-mental methods are needed to better estimate both energyand hydrological budgets in urban areas.

The objectives of urban stormwater management haveevolved over the previous decades and introduction of theconcept of sustainable development has sparked a newstage of evolution (Delleur, 2003) towards an integrated ap-

proach of urban water management. A detailed modelingapproach, as illustrated in URBS-MO, could contribute toupdating urban models.

Acknowledgement

This study received a financial support from the French re-search program in hydrology (PNRH) of the ANR-ECCO.

Appendix

The vadose zone is represented by a simplified parameteri-

zation of the water movement, which assumes that Darcyslaw can be applied between the saturation level and sur-face, respectively, and a point V indicative of the globalbehavior of the vadose zone. The validity of this set-up mustbe established prior to proceeding with model application.This validity step can be assessed by comparing the pro-posed parameterization with Richards equation being con-sidered as the reference solution. This comparison has beenperformed under the following conditions. The comparisonpertains to a natural UHE, covered by vegetation and 5 mthick. Surface interception is neglected and this UHE isnot drained by a lateral trench. The test then focuses onthe vertical fluxes between the atmosphere, the vadose

zone and the saturated zone. The hydraulic conductivityat UHE saturation is constant with depth, and a high valuehas been set for parameterMin Eq.(8)in order to verify thisassumption. The UHE is submitted to atmospheric forcingthat combines rainfall and potential evapotranspiration dur-ing a one-year period, discretized with a 5-min time step.The meteorological data have been extracted from a casestudy (presented in the accompanying paper) and are typi-cal of French oceanic climate, with an annual rainfall depthof 722 mm, composed mainly of low-intensity precipitationevents. The reference water fluxes and quantities in theground have been calculated by means of the NSAT finiteelement code that solves Richards equation and representsthe flux of water in the soil (Berthier et al., 2004). The val-

ues of model parameters adopted for this evaluation exer-cise are listed in Table 11. The hydrological variablestargeted by the validity test are: saturation level, transpira-tion flux, infiltration flux in the vadose zone, and meanmoisture content of the vadose zone. A sensitivity analysisof the simplified parameterization has been performedand reveals that the best accuracy is obtained for valuesof av included in the interval [0.5, 0.7]; this finding led usto adopt a value of av = 0.5. The results obtained withav= 0.5 are displayed in Fig. 16, along with the comparisonbetween the reference solution and the simplified parame-terization. It appears that the proposed parameterizationprovides for a good simulation of the transpiration, surface



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infiltration and fluxes between the vadose and saturatedzones, with coefficients of determination in excess of 80%.The mean moisture content of the vadose zone has beenrather accurately reproduced, despite a slight bias affectingthe simulation of temporal evolution in the saturated level.

In summary, the comparison between the reference solu-

tion yielded by Richards equation and the simplified pro-posed in this paper confirms the validity of such aparameterization in reproducing the water flux in UHEs forthe considered application.

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Table 11 Values of the model parameters of one UHE

Parameter Unit Value

KnatS m/s 1.3E5

hS 0.43

We 0.20

b 5

M 10,000

aV 0.5zroot m 1.3

k 0

l 2

Figure 16 Comparison of (a) the infiltration flux into the

vadose zone I, (b) the transpiration flux T, (c) the saturationlevelzSand (d) the mean moisture content of the vadoze zone

h.X-axis represents the reference simulation with NSAT and Y-

axis represents the simplified parametrization with URBS-MO.

The simulation has been realized on a natural UHE during a

hydrological year; each star correspond to a time step of 1 h.



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