Guido Petrucci
email: guido.petrucci@leesu.enpc.fr

Bruno Tassin

Hydrographs' attenuation in sewers. Effects on stormwater source control regulation

Keywords: Attenuation, BMP, peak flow-rate, source control, stormwater sewer, urban runoff

In this paper we propose an empirical approach to quantify the hydrographs' attenuation in sewers. The purpose is to evaluate attenuation's consequences for the scale-transfer between the parcel and the catchment in urban settings, and in particular for stormwater source control (SC) regulation. In fact, SC regulation practices often consider this scale-transfer by a linear approach. We draw a formulation for the attenuation of peaks in partially full pipes, and we assess, by a sensitivity analysis, the respective weights of the different pipes' and hydrographs' characteristics on attenuation. We found that the driving factors of the peak attenuation vary according to the distance from the outlet, and we draw possible guidelines for SC regulation.

INTRODUCTION

In urban hydrology, a scale-gap exists between the parcel-scale (~10 3 m²), where runoff is produced, and the city-scale (~10 km² = 10 7 m²), where global hydrological effects are observed. As an example, total imperviousness area of the catchment (TIA, a city-scale data) has been considered for years as a driver of urban impact on water bodies (a city-scale effect). Now, many researchers consider that the urban impact is not directly linked to the total imperviousness, but to the effective one (EIA, e.g. [START_REF] Brabec | Impervious Surfaces and Water Quality: A Review of Current Literature and Its Implications for Watershed planning[END_REF]. "Effectiveness" of an area is defined by the connection to the sewer system, which is a parcel-scale characteristic and should be measured at that scale [START_REF] Lee | Estimation of Urban Imperviousness and its Impacts on Storm Water Systems[END_REF].

More in general, a scale-transition is necessary when catchment-wide hydrographs characteristics (in this paper, peak flow-rate and volume but also, for example, runoff pollutant load) are to be traced back to elementary runoff production.

The regulation of stormwater source control (SC) is a typical application "making the jump": SC consists in managing stormwater runoff at the city-scale by using small facilities diffused in all the catchment, typically at the parcel-scale. These parcel-scale facilities are usually called Best Management Practices (BMPs) in the US, or Sustainable Urban Drainage Systems (SUDS) in the UK. Terms like Low Impacts Development (LID) or Water Sensitive Urban Design (WSUD) are used, today, to identify the application of this principle to the design of new developments, which is typical of an intermediate scale (~10 4 -10 5 m 2 ). [START_REF] Revitt | The Best Management Practice catalogue developed within the DayWater project[END_REF][START_REF] Morison | Understanding the nature of publics and local policy commitment to Water Sensitive Urban Design[END_REF].

Often, in SC regulation practice, the transfers between scales are supposed to be linear (as described in next section or, for example, by [START_REF] Cantone | An innovative approach for modelling large urban hydrologic/hydraulic systems[END_REF]. This approach, oversimplifying physical processes, can bring to unsuitable regulations of SC. Consequences will be a lack of efficiency of SC at the city-scale (i.e. more BMPs, and with higher capacities, will be necessary to obtain a same global effect) and, in some cases, even a worsening of the catchment hydrologic behaviour [START_REF] Goff | The Influence of Watershed and Development Characteristics on the Cumulative Impacts of Stormwater Detention Ponds[END_REF].

In this paper we analyse the transport process in the sewer system, and in particular hydrographs' attenuation. The purpose of the analysis is to understand how this physical process intervenes on the scale-transition and how, taking it into account, SC regulation could be improved.

We focus our study on the sewer system, considering that sewers provide the link between scales in most urban settings, particularly those urbanised typically during the XX th century. These networks are in charge of collecting surface runoff at the small-scale and draining it to the catchment outfall. Recent approaches may lead in the future to the disappearance of the stormwater sewer but today most of the stormwater flowpath, in many urban catchments, occurs in the sewers.

In this perspective, after an overview of current practices in SC regulations, we present and validate a formulation of hydrographs attenuation in sewers. We base our formulation on empirical results obtained by [START_REF] Ackers | Attenuation of flood waves in part-full pipes[END_REF] and we evaluate the implications for SC through an analysis of attenuation's sensitivity to sewer's and hydrograph's characteristics.

Stormwater source control regulation and the linear approach.

In the last four decades, SC has gained relevance in many countries (e.g. France, UK, USA, Brazil, Australia), mainly for its potential to reduce negative impacts of fast urbanization and imperviousness increase.

In hydrologic literature, increases of runoff volumes and peak flow-rates due to urbanization, are well documented (e.g. [START_REF] Dunne | The control of surface water runoff from new development -UK national policy'in need of review? Urb[END_REF]. So it is the capacity of BMPs to reduce these effects at the local scale (e.g. Chocat, 1997). What is less known is the effect, at the catchment-scale, of a large number of BMPs (i.e. SC implementation). Although some recent studies begin to provide field data-based analyses on the topic at various catchment sizes (Petrucci et al., submitted;[START_REF] Meierdiercks | Heterogeneity of Hydrologic Response in Urban Watersheds[END_REF], they are still too scarce to provide practical guidance for SC regulation.

Today, the main instruments in SC strategy are regulation policies. They mainly belong to two categories:

• A constraint for new developments to maintain a (or to reduce to a given fraction of) predevelopment peak runoff for a series of rain events (for US examples, see [START_REF] Balascio | A survey of storm-water management water quality regulations in four Mid-Atlantic States[END_REF]; for UK ones, see Faulkner, 1999). • A constraint to limit area-specific peak runoff from a new development, for a given rain event, to a given value. For example 5 l/s/ha for a 10 year return period rain event.

UK examples are presented by Faulkner (1999), while in France most local regulation follow this scheme, in some cases with extremely low limits (e.g. 1 l/s/ha). The limit value is based on sewer capacity (e.g. [START_REF] Vuathier | Limitation des rejets d'eau pluviale à la parcelle en milieu urbain[END_REF] or on a predevelopment runoff regime (e.g. Régions Aquitaine et Poitou-Charentes, 2007).

Both these categories represent regulations based on runoff flow-rate. In some cases, volume or infiltration specifications are joined to the flow-rate regulations in order to improve runoff quality. In facts, small runoff events contribute for most of the annual pollution load, and are virtually unaffected by regulations concerning the runoff peak (Pitt and Clark, 2008).

Both the two forms of regulation are based on an implicitly linear approach to scale-transition.

The rationale behind the first form of regulation can be summarized as: "if every parcel of the catchment does not produce a runoff peak higher than the pre-development one, the whole catchment too will not produce a runoff peak higher than the pre-development one". But, also if every parcel of a catchment produces a runoff limited to the pre-development peak level, it will anyway produce a higher runoff volume because of its increased imperviousness. The pre-development peak level from every parcel will then be maintained for an increased time [START_REF] Booth | Urbanization of aquatic systems: degradation thresholds, stormwater detection, and the limits of mitigation[END_REF]. Thus, it becomes more and more probable, with increasing imperviousness and despite the regulation, that contributions arriving from different parcels could superpose, producing at the catchment outlet a runoff peak higher than the predevelopment one (as showed by [START_REF] Goff | The Influence of Watershed and Development Characteristics on the Cumulative Impacts of Stormwater Detention Ponds[END_REF]. For the second form of regulation, linear addition of flow-rates is also implicit, but the reasoning is inversed: an admissible catchment flow-rate is determined, and the parcel-scale limit is obtained dividing this catchment flow-rate by the catchment's area.

A first consequence of this linear approach is that to limit catchment-scale peak flow-rate all authorities use parcel-scale flow-rate-based regulations. [START_REF] Booth | Urbanization of aquatic systems: degradation thresholds, stormwater detection, and the limits of mitigation[END_REF] and [START_REF] Goff | The Influence of Watershed and Development Characteristics on the Cumulative Impacts of Stormwater Detention Ponds[END_REF] suggested that limiting parcel-scale runoff volume could be more efficient.

A second consequence is that all parts of a catchment are considered equivalent by the regulations: uniform regulations are in fact the standard. By an hydrologic point of view, the contribution to catchment-scale runoff from, for example, upstream and downstream parts of a catchment are not the same. The differences are generated by the catchment physical processes that participate to the scale-transition.

In this perspective, we analyse hydrographs' attenuation in sewers as a major process involved in the scale-transition in urban settings. This allows to determine how catchments' physics introduces actual distinction among catchments' parts, and to provide useful guidance to improve SC regulations.

METHODOLOGY

An hydrograph peak flowing through a channel or pipe is attenuated [START_REF] Chow | Open-channel hydraulics[END_REF]. De Saint Venant's equations and their approximations describe this phenomenon [START_REF] Hingray | Hydrologie 2. Une science pour l'ingénieur[END_REF].

In particular, the diffusive wave model presents a diffusion coefficient that defines hydrographs' attenuation. It is thus possible, in theory, to study this process using one of these theoretical models. However, no analytical solution exists, in general, for these models. If inflows are slowly varied, a solution exists -the Hayami model [START_REF] Chow | Open-channel hydraulics[END_REF] -but this hypothesis is not consistent with rapidly varying hydrographs for storm events. Thus, using this approach requires performing numerical simulations on specific sewer systems and does not allow finding general guidance for SC regulation.

Another approach, alternative to consider the whole flow routing problem, but just the attenuation in sewers, is that used by [START_REF] Ackers | Attenuation of flood waves in part-full pipes[END_REF]: they performed a series of experiment on a controlled setting to measure the attenuation entity for peaks superposed to a uniform baseflow. Their result is an empirical equation linking inlet hydrograph height and pipes characteristics to the outlet hydrograph height.

In order to find an approximated model of the process, useful for a general estimation of its effects on SC, we will base our approach on Ackers and Harrison results, and use an approximation of their original formula. Then, in order to evaluate implications for scaletransition and SC, we perform a sensitivity analysis of the resulting equation.

Remark: we always refer, in this work, to the case of free surface flow in circular pipes, with no backward effect.

Peak attenuation.

In order to quantify attenuation, we consider the empirical results obtained by [START_REF] Ackers | Attenuation of flood waves in part-full pipes[END_REF] for peak attenuation in partially-full circular conduits (notation in table 1). They observe that the attenuation of a peak superposed to a permanent, constant baseflow, depends on the peak's volume. They also observe that a relationship subsists between the peak height at a distance x from the inlet, and the dimensionless distance

f VQ gD x ∆ 9 .
In [START_REF] Ackers | Discussion. Attenuation of flood waves in part-full pipes[END_REF], a formula is suggested for this relationship, for 0 ≤ h 0 /D ≤ 0.5 and

D h D h ) ( 2 1 ) 0 ( * 0 - = ∆ : D h f VQ gD x x h 0 5 . 1 1 9 15 2 1 ) ( * +         ∆ + = ∆
(eq. 1)

4 ; 4 ; 1 2 2 / 1 3 / 2 D S D R S i R n Q h h f π = = = h 0 m Baseflow height h(x) m Height of the perturbation at position x ∆h*(x) - Relative height of the perturbation at position x D h D x h x h 0 ) ( ) ( * - = ∆ ∆V m 3
Volume of the peak If we consider the whole length L of the conduit, we can define the term C (m 3 ), depending only on the conduit's characteristics,

f Q gD L L C 15 ) ( Substituting D h 0 5 . 1 1 + = α , eq. 1 can be rewritten: α       ∆ + = ∆ V L C L h ) ( 2 1 ) ( * (eq. 1b)
It is possible to show that Eq.1 and Eq.1b are not consistent for, respectively, x = 0 and L = 0, unless h 0 = 0. A second issue is that the two equations are defined for a specific value of ∆h*(0). We can solve these two issues adopting an approximation of Eq.1b, explicitly involving ∆h*(0) and consistent for L = 0. A possible approximation, having these characteristics is:

α α       ∆ + ∆ = ∆ - V L C h L h ) ( ) 0 ( * 1 ) ( * / 1 ⇔ ⇔ V L C h L h ∆ + ∆ = ∆ - - ) ( ) 0 ( * ) ( * / 1 / 1 α α (eq. 2)
Numerical tests showed that the difference between Eq.1b and Eq.2 is less than 1% for h 0 /D ≤ 0.2 (i.e. for low baseflow and high perturbations) and less than 10% for C/∆V > 1.3 (i.e. for long flowpaths). Thus, Eq.2 can be considered globally satisfying, considering that it approaches well Eq.1b in the most significant cases (long flowpaths, high perturbations) and it differs from Eq.1b where the latter shows consistency problems (short flowpaths). The peak's attenuation -the difference between the peak's height at the inlet ∆h*(0) and its height at the outlet ∆h*(L) -does not appear explicitly in Eq.2. However, considering that 1 ≤ α ≤ 2.5, and thus -1/α < 0, it is possible to infer from Eq.2 that the attenuation grows with the C/∆V term.

Remark: physical interpretation of C. As underlined by [START_REF] Ackers | Attenuation of flood waves in part-full pipes[END_REF], the dimensionless term C/∆V has a physical interpretation. In fact, it can be rewritten as:

f f Q gD V LD VQ gD L V C 5 2 9 15 1 15 ⋅ ∆ ⋅ = ∆ = ∆
The factor V LD ∆ 2 is proportional to the ratio between pipe's volume ( 4

2 π ⋅ LD
) and peak's volume (∆V). The other factor,

f Q gD 5
, is proportional to the inverse of the Froude number ( 2

5 π ⋅ gD Q f
,for a full circular pipe). Thus, the effect of attenuation is influenced by both the volume and the characteristic flow conditions of the pipe.

SENSITIVITY ANALYSIS

To assess the orders of magnitude of the attenuation process, we plot in Figure 1 the values of ∆h*(C) for different values of ∆h*(0) and ∆V. We observe that attenuation is strongly dependent on the C/∆V term: considering the ∆V=100m 3 set of curves,

• for C=100m 3 (C/∆V=1), peaks' height (∆h*(C)) are about halved (0.5 0.22; 0.3 0.16; 0.1 0.07);

• for C=200m 3 (C/∆V=2), peaks are strongly attenuated, for ∆h*(0)=0.5, ∆h*(C)=0.125;

• for C=300m 3 (C/∆V=3), even for ∆h*(0)=0.5, ∆h*(C)<0.1;

• for C=500m 3 (C/∆V=5), the values of ∆h*(C) are extremely close, comprised between 0.025 and 0.045. Attenuation makes nearly undistinguishable the initial differences in peaks' height.

The same observations can be done on the other sets of curves, for the same values of C/∆V. High peaks are thus halved for C/∆V ≈ 1, reduced to a quarter for C/∆V ≈ 2 and to a tenth for C/∆V ≈ 5. Smaller peaks incur in a slower attenuation, but approximately we can consider that attenuation is weak for C/∆V < 1 and strong for C/∆V > 2.

The additional x-axes in Figure 1 show the conduits lengths corresponding to C values in the main axis, for two diameters (1 and 2 m) of classical sewer pipes. It is possible to notice that the lengths' orders of magnitude correspond well to typical lengths for a city-wide sewer system (~10 3 -10 4 m).

IMPLICATIONS FOR SOURCE CONTROL REGULATION

To analyse the implications for SC regulation, we can consider the case of a typical urban catchment in which each parcel is connected to a "uniform" sewer network (constant D, i, n).

The hydrograph generated from each parcel is routed to the outfall, and the corresponding C value depends only on the parcel position in the catchment (i.e. the distance from the outlet).

We search the best SC regulation to minimise the hydrograph's height at the outfall.

The first case that we consider is that of a parcel close to the catchment's outlet. In this case, the hydrograph routing will occur over a small distance, and the corresponding C will be small. To minimise the peak's height at the outfall, it is necessary to keep its volume extremely low, or to limit the peak's height at the sewer inlet. In this case, a parcel-scale flowrate-based regulation is a pertinent option, while a volume-based one should be too restrictive.

The second case is that of a parcel in the upper part of the catchment, for which the hydrograph routing in sewer occurs for several km, with a high C value. In this case, if the hydrograph volume is not of the same order of magnitude of C, the peak height at the parcelscale is completely negligible at the catchment-scale. To minimise the peak's height at the outfall, reducing hydrograph volume makes unneeded to control hydrograph' peak at the parcel-scale. In this second case, a volume-based regulation seems more pertinent than a flowrate one.

In a real catchment, the pertinence of a given regulation over an area depends on the catchment's characteristics. However, these simple examples show how, as a consequence of transport processes, the contribution of different part of the catchment to its global output can vary. We can draw two general implications for SC regulation:

• Uniformity of the regulation: inside of a catchment, differences actually exist among its different parts. A hydrologically-sound regulation should consider this fact. Uniform regulations are not "wrong", as they can be justified in specific situations, but the initial framework of any SC regulation should be spatially varied. • Volume-based regulations. At our knowledge, when these regulations are used, they are usually justified by water quality and natural water-cycle concerns. On the contrary, flow-rate-based limits are justified by overflows concerns. Our results on the attenuation process show that, except in proximity of the outlet (or of an overflow point), flow-rate regulations are poorly effective to solve overflow concerns, while runoff volume regulations can be. This seems to reduce the scope of flow-rate-based regulations to a relatively small set of situations and, conversely, to extend the scope of volume-based regulations.

CONCLUSIONS

In this paper, we studied the hydrographs' attenuation in sewers. Although the results obtained take into account just one aspect of the water routing process in urban settings, and should be extended to more complex situations, like ramified sewers, they provide some guidance on how to regulate SC.

We derived a formulation for the attenuation of peaks and perturbations in partially full pipes. Smaller the volume of the peak or perturbation, stronger the attenuation. Then, we performed a sensitivity analysis to assess the weight of the different factors on attenuation. The analysis highlighted a strong link between the C/∆V factor and the attenuation. Studies about the scope and applicability of a simplified rule to estimate attenuation in practical situations can make the object of further research.

We found that the driving factors of the attenuation for an hydrograph drained by a sewer system are different according to the distance from the outlet: if this distance is small, attenuation is mainly driven by hydrograph height, while for a large distance by hydrograph volume.

These results are clearly contrasting with the linear approach that most SC regulations follow today: transport processes create actual differences among the different parts of a catchment and their contributions to the catchment hydrological behaviour. If future SC regulations will integrate this fact, they could become more effective.

Figure 1 .

 1 Figure 1. Plot of ∆h*(C) for different values of ∆h*(0) (0.1; 0.3; 0.5) and of ∆V (10; 100; 1,000 m 3 ; respectively the dotted, continue and dashed lines). Additional axes show the corresponding length for two concrete conduits (n = 0.013) with slope i = 0.01 m/m and varying diameters (1; 2 m).

Table 1 . Notation. In the first and second part, respectively, conduit's and hydrograph's characteristics

 1

	Symbol	Units	Description	Notes / Calculation
	L	m	Length of the conduit
	x	m	Position in the conduit	x=0 for the inlet, x=L for the outlet
	D	m	Diameter of the conduit
	i	-	Slope of the conduit
	n	-	Manning coefficient
				Manning formula:
	Q f	m 3 /s	Maximal flow in the unpressurized conduit


Guido Petrucci
email: guido.petrucci@leesu.enpc.fr

José-Frédéric Deroubaix

Bruno Tassin

Stormwater source control regulation: a hydrological comparison of alternative policies

Keywords: Catchment scale, regulation, runoff volume, sewer overflows, source control, urban drainage

Stormwater source control regulations are rapidly diffusing in many countries. Most of these are provisions that limit runoff rates at the parcel-scale, although some references indicate some negative side effects, at the catchment-scale, for this form of regulation. In this paper, we compare, at that scale, the effects of several runoff rate and runoff volume provisions, using a hydrological model calibrated on a real catchment in the Paris region. We considered two main objectives: to avoid sewer overflows and to preserve receiving waters. The results show that runoff volume provisions are more effective in terms of receiving waters preservation than the runoff rate ones. In terms of sewer overflows, both can reach the same performances.

INTRODUCTION

In the last four decades, stormwater Source Control (SC), has gained relevance in many countries, mainly for its potential to mitigate negative impacts of fast urbanization and imperviousness increase. Many local authorities in several countries (e.g. France, USA, UK), formulate policies to generalize SC implementation. Yet, choosing a locally "good" policy, able to solve the specific problems of the catchment, is a hard task.

Authorities use several policy instruments from two main groups: voluntary instruments, including both financial and technical support, and compulsory instruments like runoff regulation or taxation [START_REF] Parikh | Application of market mechanisms and incentives to reduce stormwater runoff: An integrated hydrologic, economic and legal approach[END_REF][START_REF] Morison | Understanding the nature of publics and local policy commitment to Water Sensitive Urban Design[END_REF]. The first instruments' group is likely to produce a more punctual development of SC, in comparison with the second group that can have a more generalized effect. In this paper we are interested on the global hydrological effects of policies, and thus we focus on compulsory instruments.

From the hydrological point of view, regulation or taxation are similar: both require to find a global level of performance and the appropriate technical means to achieve it. Then, the actual mechanism of implementation of these technical means (i.e. a constraint or a tax) does not make a significant difference. Therefore, we can study hydrological effects of regulation only, knowing that, with some adaptations, the results could be applied to a tax instrument.

No theoretical framework is available for the catchment-scale effects of SC, and this makes difficult to find a link between a global objective and a corresponding SC implementation. As

BACKGROUND

Many researchers (e.g. [START_REF] Emerson | Watershed-Scale Evaluation of a System of Storm Water Detention Basins[END_REF] and environmental authorities (Agences de l'Eau in France, EPA in the US) argue that SC effects should be analyzed at the catchment-scale, because policy goals are set at that level. Still, while we know the effects of BMPs at the local scale, we do not have a precise insight of what is their global effect at the catchment-scale. As it is impossible to create actual-scale experiments, our knowledge of global effects of SC provisions is mainly based on ex-post analysis of actual SC implementations (Petrucci et al., submitted;[START_REF] Meierdiercks | Heterogeneity of Hydrologic Response in Urban Watersheds[END_REF]. As this kind of studies is, today, too scarce to develop a consistent foundation for SC provisions, policy-makers and researchers have followed two different approaches.

Policy-makers were in the need to develop SC as rapidly as possible to solve urgent concerns (mainly urban floods and receiving waters degradation). Thus, they generally adopted policies with the purpose of promoting the implementation of as many BMPs as possible. The implicit assumption is that if BMPs are effective locally, they will be effective at the catchment-scale. The two general forms of provisions are (i) to set a parcel-scale runoff rate value, valid for all the parcels of the catchment, or (ii) to set a formula to calculate pre-development peak runoff rate for any parcel, to be maintained after development. The first option is generally adopted in France, while the second one is common in the US [START_REF] Balascio | A survey of storm-water management water quality regulations in four Mid-Atlantic States[END_REF]. In the UK, examples of both are in use [START_REF] Faulkner | The control of surface water runoff from new development -UK national policy'in need of review?[END_REF].

Researchers tried to compensate the absence of large-scale datasets by attempting modelling approaches, both on real and on "synthetic" catchments, in order to find general rules to guide SC regulation. [START_REF] Konrad | Hydrologic mitigation using on-site residential storm-water detention[END_REF], [START_REF] Fennessey | Changes in Runoff due to Stormwater Management Pond Regulations[END_REF], [START_REF] Fang | Using a Distributed Hydrologic Model to Evaluate the Location of Urban Development and Flood Control Storage[END_REF], tried approaches based on real catchments, finding that runoff rate provisions are not always effective in reducing catchment-scale runoff for extreme rain events and that, for current rain events, runoff rates can be heavily distorted. In general, water balance at the catchment scale is not preserved. [START_REF] Emerson | Watershed-Scale Evaluation of a System of Storm Water Detention Basins[END_REF] found that volume-based provisions can be effective in reducing peak flow-rate at the catchment-scale. [START_REF] Goff | The Influence of Watershed and Development Characteristics on the Cumulative Impacts of Stormwater Detention Ponds[END_REF] simulated ponds implementation on a synthetic catchment varying 6 parameters describing both watershed and urban development. They confirmed that, for fully developed watersheds, even if all the parcels maintain pre-development peak runoff rate, it is impossible to maintain it at the catchment-scale, and they suggested to emphasize the use of volume provisions.

The effect of SC on a catchment will depend on both the characteristics of the catchment (topography, geology, climate, urban development) and of the provision (type, level of constraint). Most of the studies cited focus on catchments' variability, while provisions' variability is seldom considered in depth (only Fennessey et al. compare five US stormwater ordinances). These studies provide, thus, a growing support to the idea that runoff rate provisions can be ineffective and even harmful for some catchment. However, they do not help defining the specific provisions that can be effective, ineffective or harmful. Similarly, there are evidences that runoff volume provisions can be effective for peak flow-rate reduction at the catchment-scale, but we do not know the link between constraint level and effectiveness.

Because of the dependence on catchment's characteristics, generalization of results obtained on a single catchment should be done carefully. Nevertheless, the analysis of specific casestudy can provide information about the possible behaviour (or type of behaviour) that a catchment can have when submitted to SC, and thus orient subsequent research and policymaking efforts. With this purpose we consider, in this paper, a periurban catchment in the Paris region, representative of the regional 1950-2000 urbanization. We test, on the catchment model, a series of runoff rate and runoff volume provisions with different levels of constraint, in order to check how the catchment response to SC is sensitive to provision's characteristics.

EXPERIMENTAL CATCHMENT

In this research, we study an urban catchment in France, 20 km south of Paris, object of several measurement campaigns over the last 10 years. The catchment area is 451 ha -a relevant scale for SC policy-making -and is divided in four municipalities (Figure 1). Each municipality is in charge of collecting stormwater, but an inter-municipal authority (Syndicat mixte de la Vallée de l'Orge Aval, SIVOA) is in charge of its transport and treatment. Thus, municipalities own proximity collectors on their territories (not modelled in the current study), drained by a major collector managed by the SIVOA. The latter is also in charge of catchment-wide policies, including SC regulation. After the enforcement, in 2003, of a very strict provision -i.e. all the stormwater has to be infiltrated at the parcel level or, if it is impossible, to be stored and released at very low rates (1 l/s/ha) -SIVOA is currently revising its policy.

Topographically, the catchment is on a plateau (see box in figure 1): its upstream two thirds have really small slopes (<0.5%), while the downstream part -on the hillside -is much steeper (5-6%). The catchment was rural until 1960 and drained by small creeks. Since the construction of the main collector from the SIVOA (1968/69), many urban developments took place and were connected to it. The development occurred both as large planning operations (the "Zone opérationnelle d'habitat" -ZOH -is a public housing plan that gives its name to the collector and the catchment) and as gradual urban development. Impervious cover in the catchment is approximately 31%, and urbanization of the area is still in progress. This type of plateau development is typical of the urbanization of the Paris region and of the villes nouvelles in the second half of the 20 th century.

The stormwater outlet is connected to a group of small sand-pit lakes linked to the Seine river. The outlet is equipped ( 2003) with a settling unit to protect the lakes from suspended solids and eutrophication.

METHODOLOGY

As the purpose of the study was the assessment of different future scenarios of SC implementation over a catchment, we used a distributed physically-based model. The distribution feature is necessary to take into account the spatial effects due to SC application [START_REF] Fang | Using a Distributed Hydrologic Model to Evaluate the Location of Urban Development and Flood Control Storage[END_REF], while the physical base allows to describe explicitly the scenarios' characteristics. The chosen model is SWMM 5 (Rossmann, 2004), a widely-used model allowing both traditional and SC drainage simulations [START_REF] Elliott | A review of models for low impact urban stormwater drainage[END_REF]. A useful feature of SWMM is that it can run continuous simulations over long periods (years) with short timesteps (5' in our study). In this way it is possible to evaluate, using the same model, both water-balance indicators (e.g. yearly runoff volumes) and peak flow-rates for extreme events on short time-scales.

Model setup, calibration and validation.

First step of the procedure presented in Figure 2, model setup includes the division of the catchment in sub-catchments, the corresponding data-analysis to define each sub-catchment characteristics, the definition of calibration parameters, criteria and algorithm. Calibration and validation phases where performed on data issued from two measurement campaigns operated

CALIBRATED MODEL

RESULTS

MODEL SETUP CALIBRATION VALIDATION

DEFINITION OF SCENARIOS

DEFINITION OF INDICATORS

SIMULATION by the local sanitation authority in 2009 and 2010. Further details of the procedure followed are presented in [START_REF] Petrucci | Rainwater harvesting to control stormwater runoff in suburban areas. An experimental case-study[END_REF].

Performance indicators.

We consider that SC provisions have two main objectives: avoid sewer overflows and preserve receiving waters. The SIVOA fixed, as the reference rain event for BMP dimensioning, a triangular hyetograph with 55 mm of precipitation in 4 hours (return period T=20 years). Thus, to evaluate the first objective, the indicator chosen is the peak flow-rate for this rain event, normalized on the impervious area of the catchment (141 ha). This indicator is noted q peak (l/s/ha).

For the second objective, we consider two indicators: one catchment-specific and one more general:

• In the ZOH catchment, the outfall settling unit has a limited capacity (0.8 m 3 /s). It is important, thus, to minimize the annual runoff volume that bypass the treatment. This indicator is noted V 0.8 (m 3 ). • The presence of the treatment unit is catchment-specific: often, stormwater is directly routed to a natural creek or river. In this case, the stability and ecological status of the receiving waters depend on low-flow regimes [START_REF] Fennessey | Changes in Runoff due to Stormwater Management Pond Regulations[END_REF]. A performance indicator for low-flow regimes is the frequency of flow: the fraction of time during which a flow is detected at the outlet. This indicator is noted f flow (-). These two indicators are computed for a 23-month rainfall series (1/1/2009 to 1/12/2010). The series is not long enough to give statistically relevant results for extreme rain events (T > 1 year), but it is sufficient for current ones (T < 6 months).

Scenarios of SC implementation.

We made 34 simulations: one reference case, corresponding to the calibrated model; 15 peak runoff rate provisions, ranging from q*=0.5 l/s/ha to q*=50 l/s/ha; 18 runoff volume provisions, ranging from i*=0.01 mm to i*=50 mm. We do not test provisions using predevelopment formulas (see background) as there is no reference available for the experimental catchment considered.

Runoff rate provisions are modelled through a reservoir for each subcatchment (32 in total), draining runoff from impervious areas. Reservoir and outfalls dimensions are defined through the rainfalls design method [START_REF] Chocat | Encyclopédie de l'hydrologie urbaine et de l'assainissement[END_REF]. Resulting capacities are reported in Table 1. For values of q*≥15 l/s/ha, the model incurs in numerical instabilities for low flows (~10 -2 m 3 /s). For these cases, thus, computation of f flow is unreliable and will not be presented. Runoff volume provisions are modelled as filter strips downstream of each subcatchment. If the subcatchment has an impervious area A s , the strip stores (as initial losses) a runoff volume of V=A s •i*. This water is then infiltrated and can be replaced by further runoff. The infiltration model used is Green-Ampt, with parameters corresponding to a silt loam (Rossmann, 2004).

RESULTS AND DISCUSSION

The simulations results, for the three considered indicators, are plotted in Figures 3 to 5. In each figure the x-axes are plotted in the sense of "increasing implementation efforts": moving from left to right the runoff volume to infiltrate increases (lower x-axis) and the maximal runoff rate decreases (upper x-axis). However, as we do not consider "efforts" or costs in the analysis, two vertically aligned points should not be interpreted as having an equivalent cost of implementation. In Figure 3 is plotted the normalized peak flow-rate for the reference rain event (q peak ). For both types of provisions, q peak decreases with efforts. This is positive, as it shows that there are no risks to worsen actual situation for the catchment considered. A second observation is that, for runoff rate provisions, q peak is always greater than q*. The reason is that, for intense rain events, pervious areas (not controlled by reservoirs) contribute to the peak flow-rate. An important remark is that the range of resulting q peak for both types of provisions is the same (from 50 to 8-10 l/s/ha). Thus, for a given target value of the objective in this range (e.g. 20 l/s/ha), it is always possible to find two corresponding provisions, one runoff rate-based (in the example q*=5 l/s/ha) and one volume-based (i*=35 mm).

Figure 4 shows flow frequencies at the catchment outlet (f flow ). As it was expected, runoff rate provisions never improve the reference situation, while runoff volume ones always do. More in detail, runoff rate provisions do not affect the indicator for q*>2 l/s/ha, while for lower values they worsen the situation. With regard to this indicator and this specific catchment, thus, provisions distort low-flow regimes only if they are extremely strict. Runoff volume provisions, on the contrary, rapidly improve the indicator value for i*<20 mm. This indicator is affected even for extremely small storage values (i*=0.01 mm): this corresponds to the infiltration effect of filter strips providing no storage (see Scenarios of SC implementation).

In Figure 5 is plotted the runoff volume exceeding the treatment unit flow capacity (V 0.8 ). Also for this indicator, runoff volume provisions show a continuous improving behaviour, slowing down with increasing constraint values. As in the previous case, a small constraint (e.g. i*=5 mm) is enough to nearly half the reference value of the indicator. Runoff rate provisions have a more complex behaviour, with 4 different ranges:

• q* < 5 l/s/ha. Catchment flow-rate is always below 0.8 m 3 /s, and thus V 0.8 =0.

• 5 l/s/ha < q* < 15 l/s/ha. In this range the provisions show a "good" behaviour: increasing efforts improve values of the indicator. • 15 l/s/ha < q* < 30 l/s/ha. In this range, the effect of provisions is a worsening of the indicator values. The reason of this fact is that, during reservoir emptying, the catchment flow-rate is above 0.8 m 3 /s for longer durations than in the reference case. • q* > 30 l/s/ha. No significant variation from the reference case.

Comparing the results for the three indicators, we observe that runoff volume provisions have a simpler behaviour than runoff rate ones. In fact, in the three cases, volume provisions show always a monotonous trend: increasing efforts generate improvements in the indicators value. On the contrary, runoff rate provisions have threshold-effects and, for some ranges, can produce degradation of some indicators value. These thresholds and the existence of critic ranges are catchment specific: for example, for f flow , provisions do not change the indicator value if the emptying time of the reservoirs for a rain event is shorter than the duration of the corresponding hydrograph in the reference situation. In the same way, we find no aggravation ranges for q peak while other researchers did, for other catchments (see Background).

In terms of preserving receiving waters (i.e. the two last indicators), volume provisions perform well even for small constraint values. As expected, this form of provision seems much more effective, toward this objective, than the other. With regard to avoiding sewer overflows (i.e. the first indicator) the results are more surprising: the same values that can be obtained through runoff rate provisions are accessible through runoff volume provisions.

CONCLUSIONS

In this research, we developed a model of a real catchment in the Paris region in order to compare several levels of constraint for both runoff rate and runoff volume provisions. We considered two objectives: to avoid sewer overflows and to preserve receiving waters. To measure the performance of each provision we adopted three indicators: peak flow-rate for a reference design storm for the first objective; flow frequency and volume bypassing the treatment unit during a 23-month simulation for the second one.

The results show that runoff volume provisions are more effective than runoff rate ones for receiving waters preservation. For sewer overflows, both can reach the same performances. Thus, is it possible to replace all runoff rate provisions with more environmental-friendly runoff volume provisions? In theory yes, but two observations are needed: 1. While runoff rate provisions can be realized almost everywhere, infiltration is not always possible. Even if other possibilities to deplete stormwater exist (e.g. rainwater harvesting and reuse) they do not seem, today, capable to reduce runoff volume systematically over an entire catchment. In some catchment, thus, volume provisions are not applicable. 2. We did not consider, in our research, any form of implementation cost. Then, even if we find an equivalence of runoff rate and runoff volume provisions in terms of peak flow rate reduction, it is possible that, in terms of costs, this equivalence is not valid. A promising solution, that deserves further research, is an integration of both runoff volume and rate provisions. It seems possible that this approach could gather the global advantages of both, involving smaller local costs.

Figure 1 .

 1 Figure 1. Catchment's and administrative borders. In the box, profile plot of the stormwater collector.

Figure 2 .

 2 Figure 2. Modelling and simulation procedure.

Figure 3 .Figure 4 .Figure 5 .

 345 Figure 3. Simulation results for q peak .

Table 1 .

 1 Peak runoff rate provisions and corresponding storage volumes.

	q* (l/s/ha) 0.5 v (m 3 /ha) 658 565 485 447 377 323 299 262 252 231 205 184 168 155 145 1 2 3 5 8 10 15 20 25 30 35 40 45 50


Guido Petrucci
email: guido.petrucci@leesu.enpc.fr

José-Frédéric Deroubaix

Bernard De Gouvello

Jean-Claude Deutsch

Philippe Bompard

Bruno Tassin

Rainwater harvesting to control stormwater runoff in suburban areas. An experimental case-study

Keywords: rainwater harvesting, source control, BMP, runoff, rainfall-runoff analysis, sewer overflows

On a 23 ha urban watershed, 10 km East of Paris, rainwater tanks have been installed on 1/3 of the private parcels to prevent stormwater sewer overflows. This paper investigates the macroscopic effect of rainwater harvesting on runoff, and thus the potential of this technique for stormwater source control. The analysis is performed using the SWMM 5 model, calibrated on rainfall-runoff measures from two measurement campaigns, before and after the equipment. The availability of two data-sets allows to point out changes in the catchment's behaviour. The main findings are that: (1) catchment's evolution, mainly caused by individual land-cover modifications, produces non-stationarity of the hydrologic behaviour; (2) the rainwater tanks installed, although they affect the catchment hydrology for usual rain events, are too small and too few to prevent sewer overflows in case of heavy rain events.

Introduction

Today, problems of urban runoff excess are addressed not only through traditional systems but also through stormwater "source control" (SC). Traditional systems, like sewer networks and downstream detention basins, concentrate stormwater from the catchment before managing it. SC, on the opposite, tries to manage small quantities of rainwater, as close as possible to its falling point, through small devices to store and/or to infiltrate it. These devices, widely known as Best Management Practices (BMP), are distributed over the catchment (Chocat, 1997).

A posteriori design of SC (i.e. on previously urbanised area) is rather difficult as, on the one hand, the available public areas are seldom and, on the other hand, installing SC on previously occupied private lots needs the final acceptance of the present owners (Marsalek and Chocat, 2002). Moreover, SC design requires not only a good knowledge of the hydrologic behaviour of the catchment, but also the capacity to forecast the urban planning of the area. Appropriate hydrologic models may be used to combine these different aspects and test the impact on runoff of different SC alternatives. Nowadays, this is successfully applied for BMPs' design or project, at the building or housing estate scale, but we still miss reliable tools and procedures for largescale planning (Niemczynowicz, 1999, Bethany, 2006, Chang et al, 2009).

Rainwater Harvesting (RH) is an ancient reviving practice. The possibility i) to reduce potable water consumption, ii) to reduce the water uptake outside of the catchments, iii) to participate to the restoration of the local water balance makes it sustainable. RH is not only diffusing in arid and semi-arid climates, but also where water shortages are extremely rare, like in northern France (de Gouvello, 2005), where it is often considered as a symbol of environmental involvement. From a SC point of view, rainwater tanks work as BMPs: during storm events, they fill up and store part of the rainfall. This water is definitely abstracted from the runoff component of the water cycle and used for local external or internal consumption.

However, two relevant characteristics distinguish rainwater tanks from usual BMPs: the direct advantage to the owner and the uncontrolled available capacity. The fact that the landowner takes advantage from the rainwater tanks makes this practice suitable in all the situations where it is not possible to oblige him to install a classical BMP on his property. This is in general the case for areas which are already completely urbanized and which experience stormwater management problems. Installing or subsidizing rainwater tanks can frequently represent one of the few SC options available.

The second characteristic is that water abstraction from the tanks is not controllable, as it is demand-driven. Then, the available rainfall storage capacity for a given rain event is even more uncertain for rainwater tanks than for usual BMPs. Moreover, the only collection surfaces are roofs, which represent a quite small fraction of land occupation in detached housing areas, where RH is better suited. This disadvantage causes a limited efficiency of rainwater tanks in reducing runoff.

Recently, experimental balances of RH have been studied at the building scale (de Gouvello et al, 2005, Kyoungjun andChulsang, 2009); theoretical and modelling approaches have been used to quantify the effects on runoff (Guillon et al, 2008 ;Vaes et Berlamont, 2001); at the catchment scale, assessments have been done extrapolating small scale data (Coombes et al., 2002). To our knowledge, there is no analysis of macroscopic real-scale experimental results on runoff effect of stormwater tanks.

This paper presents a hydrological analysis based on a case study, where a significant number of rainwater tanks have been installed on the private parcels of a district, to prevent stormwater sewer overflows. Two rainfall-runoff measurement campaigns have been conducted before and after the tanks' installation, enabling the assessment of the effect of the tanks on runoff. The purpose of the analysis is to verify if RH is able to significantly reduce sewer overflows in the district. Moreover, the analysis points out that the catchment undergoes slow but sensible changes in its land cover and occupation, with hydrological consequences, even if no major change in the urban structure took place in the period considered.

Material and methods

Methodology

In this research, all the available data about the case-study catchment and its hydrological response are integrated in a rainfall-runoff model. To point out the evolution of the catchment's hydrological behaviour, an approach is to calibrate the model separately before and after the tanks' installation, using the two available data-sets from the measurement campaigns. In this way, evolutions in the catchment behaviour can be traced by differences in the model parameters and can be analyzed through model's simulations.

However, as the model relies on a large set of parameters, two completely independent calibrations will result in a large set of hardly interpretable differences. In order to generate through calibration two comparable sets of parameters, it is possible to define a limited number of parameters that can represent catchment's evolution. The selection of these parameters is made on the basis of available data's analysis (section 3), to depict expected or observed evolutions of the catchment.

The first step of this approach is to calibrate the whole model on one of the two data-sets. Then, a second calibration is done on the second data-set, but only for the few parameters selected. The results of this procedure are two calibrated models, one for each data-set, differing only for a limited set of physically interpretable parameters (par. 4.1). Comparisons between the two models can be done both on parameters' value (par. 4.2) and through simulations. To assess the impact of RH tanks on sewer overflows, simulations are focused on rain events likely to produce failures of the sewer system. Both real rainfall records (par 4.3) and synthetic hyetographs of given return periods (par 4.4) are used for the analysis.

Description of the district and of the experimentation

The "Village Parisien" is a district occupied mainly by detached housing, in the city of Champigny-sur-Marne, 10 km east of Paris (France). The current urban development dates back to the 70's, and corresponds to the demolition of an adjacent slum (1971). The parcels have an average size of about 400 m 2 ; they host private houses, parking areas and/or garages. The remaining parcels' surface is generally used for ornamental gardens. Most of the population is newly urban, and has a developed water awareness.

The catchment area corresponding to the district is 22.9 ha (figure 1), with a maximum length of 750 m and an average slope of 2%. The sewer system is separate. The main collector (diameter D = 0.8 m, average slope = 1%) borders the Eastern side of the catchment, under the avenue Thorez. This avenue, and then the collector, does not follow the topographic thalweg of the catchment, which lies 50-100 m to the East. The streets perpendicular to the avenue Thorez are equipped with smaller collectors (0.3 m < D < 0.6 m) which feed the main one. The final segments of these secondary collectors, link the lowest points of the catchment to the main collector, and have very small slopes (≈1‰). For this reason, in case of intense rain events, water overflows over the road surface in these lowest points.

Inhabitants reported overflows (up to 0.4 m over the road level) for intense storms in 2001 and 2007. The storm of the 25th of May 2007 was classified as an event with a return period between 5 to 10 years.

The environment and sewer service of the county (Direction des Services de l'Environnement et de l'Assainissement du Valde-Marne, DSEA) decided, also because of the limited flooding consequences, to experiment SC instead of classical pipe-based techniques (enlarging or doubling the sewer, etc.). Thus, DSEA installed for free RH tanks (figure 2) to a group of volunteers in the district. The tanks are external, with a size of 0.6 m 3 or 0.8 m 3 . Each volunteer could choose size and number of the tanks (1 or 2). The main expected use for the harvested water is gardening.

At the end of the installation (spring 2008), 157 parcels out of approximately 450 were equipped, for a total volume of 173 m 3 .

To perform the current study, the DSEA provided two runoff time series in the sewer at a 5-minute time step, both measured during the summer period:

(1) from the 29 th of July to the 30 th of October 2005, before tanks' installation;

(2) from the 25 th of June to the 23 rd of October 2008, after the installation.

Rainfall series are available from a rain gauge 200 m South-East of the catchment, in place since the 29th of July 2005. Other data available are sewer and parcels cartography, a list of the equipped parcels, and two orthophotographs of the catchment, one taken in 1998, and the other in 2007.

Model and calibration

The model used to integrate the available data and perform the analysis is SWMM 5 (Rossmann, 2004). It is a widely diffused urban hydrology model, flexible and well suited to represent BMPs (Elliott and Trowsdale, 2007).

In SWMM 5, both rainfall-runoff transformation on subcatchments and flow in the sewer network are modelled.

Each subcatchment is considered as a non-linear reservoir, with an outflow equation given by the kinematic wave approach (Singh, 1988). The corresponding equations, whose terms are listed in table 1, are:

dV/dt = A (p -% imp i -e) -Q(V) (eq. 1) Q(V) = k W n -1 (d -d p ) 5/3 s -1/2 (eq. 2)
Some of the parameters can be defined differently for the pervious and impervious parts of a unique subcatchment, in particular the surface characteristics dp and n.

It is worth to remark the role of initial losses: they constitute, for a given subcatchment, the amount of rainfall that can be stored on it before the beginning of the outflow. This parameter will be used to describe the tanks' effect on the roofs equipped with them (see paragraph 3.3). The SWMM 5 model performs routing in channels and pipes by numerical solution of De Saint-Venant 1-D equations, under dynamic wave assumption. Manning friction formula is used (Graf and Altinakar, 2000). In this equation, the Manning's n for conduits plays a role of "velocity factor", like the analogous parameter in equation 2. Even if this parameter affects the hydrograph shape, considering the size of the catchment and the corresponding length scale, it will mainly contribute in slowing down or accelerating the runoff. This is equivalent to a time translation of the hydrograph at the outfall.

The model calibration is performed through a genetic algorithm. This type of algorithm has been used on hydrologic models during the last 20 years (e.g. Franchini et al., 1998). For each calibration, the first two-thirds of the rain events of a data-set are used for the calibration itself, while the remaining one-third for validation. The data-set parts are always used as continuous time-series, and not as discontinuous collections of rain events. This approach allows the model to simulate the initial conditions for each rain event.

The objective function used in the optimization is the Nash-Sutcliffe criterion (Nash and Sutcliffe, 1970):

N = 1 -∑ t (Q o,t -Q s,t ) 2 / ∑ t (Q o,t -Q o,mean ) 2 (equation 3)
Where Qo,t and Qs,t are respectively the observed and simulated values at time t, and Qo,mean is the observations' mean value. This indicator, ranging from -∞ to 1, is higher for a more accurate model. A value of 1 denotes a model perfectly matching the observed data, while a value of 0 denotes a model as accurate as the observations' mean value. This criterion is well suited for applications, like the current one, where the focus is on instant flow values and not on integrated values (e.g. daily runoff volume).

A complementary robustness test was performed, based on calibrations on synthetic time series obtained by randomly mixing the rain events available. The results of this process are poorer (i.e.: lower Nash criteria) than using the actual time series, because the consequentiality of the rain events is lost. In fact, the model estimates the initial conditions for a rain event simulating the preceding dry period. For the actual time series, simulated dry periods correspond to the actual ones, providing a coherent estimation of initial conditions. Conversely, for the synthetic time series with randomly mixed events, dry periods do not correspond with actual ones and provide, thus, poorer estimations. However, the parameters obtained by these calibrations sensibly confirm the robustness of those obtained with the actual time series. In fact, in 70% of the test calibrations, resulting parameters' values are in a ± 10% interval around the ones obtained by calibration over the actual time series. analysis

Catchment land-use and evolution

The catchment area has been analyzed through orthophotographs, maps analysis and direct observations. It has been divided in 5 land-use categories: roads, equipped roofs (i.e. with tanks), non-equipped roofs, green areas and "others" (see data in table 2).

A visual inspection of the two available orthophotographs (1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007) shows an evolution of land cover. Even if nearly no new houses have been built, there is a slight increase in impervious areas (private driveways, garages, terraces; see for instance figure 3). This imperviousness increase is quite surprising for an already urbanized area and is taken into account in the hypotheses setting (paragraph 3.3).

It is noticeable, in table 2, that the "others" surface category covers 21% of the total catchment area. These unclassified surfaces represent a heterogeneous set of landuses. These areas are considered as partially paved (driveways, etc., parameterised like roads) and partially pervious (bare soil, etc., parameterised like green areas); partition, through the %imp parameter, is object of calibration.

Rainfall-runoff analysis

Both measurement campaigns took place in summer. All the results presented here are therefore valid only for this season. This fact, however, does not reduce the interest of the study, as the rain events producing sewer overflows are concentrated in summer. In facts, storms in that region are typically shorter and more intense in summer than in other seasons (Roux, 1996). The small size of the catchment makes this kind of rain event the more critical.

The hydrological conditions of the two campaigns are similar: the cumulative rainfall in the three months preceding the measurements where of 135 mm and 131 mm in 2005 and 2008 respectively.

The global runoff coefficient, estimated as the ratio of total runoff volumes and total rain volumes for 22.91 ha, is higher in 2008 than in 2005: 0.16 instead of 0.13.

An event-based analysis was conducted. Two rain events were considered separated if a period of 4 hours with less than 2 mm of precipitation occurred between them. 21 events were identified in 2005, 17 in 2008. This analysis shows that no heavy rainfall events occurred in 2005. The strongest rain in the 2005 recording period is the one of the 11th of September 2005, with a maximal average intensity on 30' (I30') of 15.6 mm/h and I15' = 31.2 mm/h. In comparison, the rain event of the 7th of August 2008 had I30' = 38 mm/h and I15' = mm/h. This absence of strong events in 2005 suggests to perform the complete calibration (paragraph 2.1) on the 2008 data-set, in order to obtain a parameter set based on a larger spectrum of events variability.

Figure 4 represents the distribution of the catchment's concentration time for the two data-sets. Even if the number of recorded events is too small to perform a significant statistical test, it seems that the concentration time increased between 2005 and 2008. This phenomenon can be interpreted in several ways. For example, it could be an effect of inlets and pipes obstructions, of the lengthening of flow paths in the catchment, or eventually of a bad synchronization between the rain gauge and the flow meter clocks. This effect is taken into account in the hypotheses setting (paragraph 3.3).

Hypotheses setting

To analyse the evolution of the catchment in the 2005-2008 period, three hypotheses are made about the catchment change. They are based on changes both expected (tanks' installation) and observed in the available data (imperviousness increase and flow slowdown).

(1) Tanks' installation: the effect of this change is that, during rain events, the rainfall on equipped roofs does not produce runoff until the tanks are filled. The choice made is to transpose this effect in the model by a variation of the initial losses for equipped roofs areas. This choice is close to reality at the event-scale, because initial losses provide storage of rainfall until fulfilment. At a longer time-scale, however, this formulation can be less realistic: the abstraction from the tanks is, in fact, strongly simplified and described as a daily evaporation rate. This description of tanks will behave well only if the emptying time is generally shorter than the interval between two rain events.

In "Village Parisien", considering a specific average capacity of the tanks of 12.7 mm (see paragraph 4.2), a gardening surface double than the roof area, and a gardening demand of 2 mm/day, it is possible to estimate the actual emptying time in: T actual = 1/2 • 12.7 mm / 2 mm/days = = 3.18 days

The model simulates the abstraction as a monthly-based daily evaporation rate ranging between 1.9 mm (October) and 3.2 mm (July). The average over the simulation period is 2.63 mm/day. The model emptying time is: T model = 12.7 mm / 2.63 mm/days = = 5.04 days These two emptying times must be compared with the average dry period between two rain events. For the available time-series, T dry = 6.16 days. On first approximation, thus, at the beginning of a rain event both real and modelled tanks will be empty. The simple description chosen appears to be acceptable in the specific conditions. The advantage of this description is that it does not require formulating any assumption on water demand, as the tanks are globally described by a single parameter, which could be calibrated.

(2) Imperviousness increase: the effect of this change is an increase in runoff volume, especially for small to medium rain events (i.e.: when pervious areas do not contribute significantly to runoff). This change, described in paragraph 3.1, does not concern roofs or roads but only driveways, terraces, etc. Thus, it is transposed in the model as a variation of the impervious area ratio for "other" areas.

(3) Flow slowdown: the effect of this change is a delay in the hydrograph. As explained in paragraph 3.2, this phenomenon is noticeable in the data and could be physically interpreted in different ways.

The available information about the catchment is not sufficient to provide a reliable explanation of it. Then, the process is just translated in the model through a parameter having a similar effect: the Manning's n for the pipes (see par. 2.3).

Results and discussion

Calibration

Table 3 shows the results obtained by the calibration process.

For 2008, the calibration was performed for the whole set of model's parameters. The Nash criteria values obtained, both in calibration and validation, are high (>0.8) and confirm, thus, the capability of the model to represent correctly the catchment's observed behaviour.

The calibration on the 2005 data-set was performed on the three parameters (initial losses for equipped roofs, imperviousness ratio for "other" areas, Manning's n for pipes) described in paragraph 3.3. Also in this second case, Nash criteria values are high. The calibration value, however, is lower (0.59) than the other values obtained. This is linked to the first events recorded: the robustness test with random series showed that including these first events always produce lower Nash values. However, it showed also that the parameter estimated considering or not these events do not vary significantly. Thus, these "bad" events were kept anyway in the data-set: as the number of recorded rain events is small, it is more appropriate to use the highest number of events available. A likely explanation of this poorer quality is that the rain gauge was just installed.

Analysis of catchment evolutions' effect

Observing the parameters' variation obtained by the calibration (table 3), an interesting result is the variation on initial losses for equipped roofs. Considering the total storage volume available (173 m 3 ) and the total equipped roofs' area (13601 m 2 ), it is possible to estimate the maximum variation in initial losses (i.e.: if the tanks were always empty at the beginning of a rain event): d p,max = V tot / A tot = 173 m 3 / 13601 m 2 = = 12.7 mm

The value obtained by the calibration (11,3 mm) shows that the observed effect of the tanks is about 90% of the maximum expectable effect. A reasonable conclusion is that in summer, when ornamental gardening demand is high and rain events infrequent, it is reasonable to assume that the tanks are empty at the beginning of the rain events.

appreciate the relative effect of each of the three parameter's variations, the system is simulated for a given rain event (21/10/2005, total rainfall of 8.8 mm, I30'=13.2 mm/h), with 2005 and 2008 values, and also with each parameter varying alone (figure 5). The overall behaviour change (peak attenuation and delay) between 2005 and 2008 is noticeable in graph a). The graph b) shows the strong attenuation effect of the rainwater tanks, and the opposite effect of the imperviousness increase.

Sensitivity analysis to tanks installation

To evaluate the efficacy of the tanks in reducing sewer overflows, the simulations of two rain events, one small (21/10/2005, 8.8 mm, I30'=13.2 mm/h) and one large (25/05/2007, 31.6 mm, I30'= 44.9 mm/h) are compared. During the latter, that has a return period between 5 and 10 years, overflows have been reported. Four different scenarios are ineffective. The cause is that, with increases in the rainfall, the effect of rainwater tanks is progressively reduced. It is interesting to verify if, in the "Village Parisien" case, the effect of the actual equipment is sufficient to avoid sewer overflows for at least some rain-events.

Then, it is possible to consider a set of increasing return periods (from 2 to 5 years) for a given duration (30 minutes) and the corresponding synthetic hyetographs (double triangle hyetographs, widely used in France (Desbordes, 1974)). Intensities are based on the Paris-Montsouris weather station I-D-F curves. The simulations of the first three scenarios described above are presented in figure 7.

With increasing return period, tanks' effect becomes smaller, while peak flow rate increases. Let's consider the overflow threshold of 0.5 m 3 /s. For the two smaller rains, the threshold is not reached by any scenario. For a 1-in-4-years rain (c), the threshold is reached by both the full and empty scenarios, while the hydrograph for the complete equipment scenario is barely under it. For a 1-in-5-years rain (d), the three scenarios reach the threshold.

In conclusion, the effect of the existing tanks becomes negligible for a 1-in-3-years rain event, too small to produce any overflow. The current equipment is then ineffective in avoiding any overflow in the district. An equipment of all the parcels of the catchment with rainwater tanks analogous to the ones actually in use will not improve results significantly.

Conclusions

In the case study discussed in this article, a consistent number of rainwater harvesting tanks was distributed in an urban catchment in order to avoid sewer overflows. About 30% of the roofs in the catchment were equipped with an average specific capacity of 12.7 mm. The analysis is based on two rainfall-runoff measurement campaigns, and performed using the SWMM 5 model. The main purpose of the analysis is to evaluate, on a real-scale experimental setting, the impact of RH on runoff.

The data analysis shows that the catchment undergoes significant evolutions despite its urban characteristics did not change. A model setting and calibration methodology were then developed to compare both the catchment evolution and the tanks installation.

Catchment evolutions, and in particular diffuse imperviousness increase, have similar but opposite hydrological effects than the tanks' installation, even on the short period considered (3 years). The consequences on SC practices and planning are relevant:

(1) The time-scales involved in the evolution of urban catchments are small, also when no major changes occur. Using old data about a catchment without any updating procedure involves a risk.

(2) Symmetrically, CS planning must take into account the physical and urban context as a dynamical variable, especially on long term scenarios.

the impact of RH tanks on runoff, the results show that the equipment installed on the "Village Parisien" is not able, alone, to prevent any stormwater sewer overflow. Its effect on runoff, in facts, become negligible for rain events smaller than the ones generating sewer overflows.

Another finding is that the inefficacy of the equipment is linked to the tanks' volume and not to the harvesting area: according to simulations, installing the same size of tanks on every parcel of the catchment will not provide better results. On the contrary larger tanks, at least theoretically, could prevent overflows for rain events with return period between 5 and 10 years.

It is important to point out that RH is considered as the only SC technique applied in the catchment. Even if, alone, this technique proved to be ineffective without large investments (i.e. large tanks in all the parcels), in practice it could be usefully integrated in a series of cascading BMPs installed both on private and public areas.

In conclusion, on an already developed urban catchment, rainwater harvesting subsidizing can prove to be a socially acceptable and reasonably-priced SC solution, but its hydrologic effectiveness can be poor without a wise planning and implementation. An effective solution needs to take into account both the parcel-scale and the catchment-scale. At the parcel-scale, this is possible through a balance of the ratios among tanks' volumes, roofs' areas and rainwater demand; at the catchment-scale, through an analysis of the different contributions to runoff.

Figure 1 -

 1 Figure 1 -Plan of the ''Village Parisien'', with catchment limits and stormwater sewer.

Figure 2 -

 2 Figure 2 -A rainwater harvesting tank installed by the DSEA.

Figure 4 -

 4 Figure 4 -Concentration time distribution for 2005 and 2008.

Figure 3 -

 3 Figure 3 -Aerial views of a catchment detail in (a) 1998 and (b) 2007.

Table 1 -

 1 Terms of the subcatchment model

	Term	S.I.	Description	Ter	S.I.	Description
	V	m 3	Volume stored over the	Q	m 3	Outflow
			subcatchment
	A	m 2	Subcatchment area	W	m	Average width of the
						subcatchment
	p	m	Rainfall	d	m	Water level (V/A)
	% imp	%	Impervious area ratio	d p	m	Initial losses
	i	m	Infiltration, estimated by	n	/	Manning's n, depending on
			Green-Ampt model			surface characteristics
	e	m	Evapotranspiration, assumed	s	/	Average slope of the
			as a monthly constant			subcatchment

Table 2 -

 2 Catchment's surface analysis

		Green	Roads	Others	Equipped	Non-equipped	Total
		areas			roofs	roofs
	Area	119896	22852	47701	13601	25050	229100
	(m²)
	%	52	10	21	6	11	100

Table 3 -

 3 Nash criteria and parameters' values from the calibrationThis document is an authors' version of the article: Guido Petrucci, José-Frédéric Deroubaix, Bernard de Gouvello, Jean-Claude Deutsch, Philippe Bompard and Bruno Tassin. Rainwater harvesting to control stormwater runoff in suburban areas. An experimental case-study. Urban Water Journal, Vol. 9(1), 2012.

			Nash	Init. losses	Imp. area ratio
		(calibration)	(validation)	(equip. roofs)	("others")	Pipes' n
		(-)	(-)	(mm)	(%)	(-)
	2005	0.59	0.81	2.76	2.6	0.02
	2008	0.84	0.83	14.06	13.4	0.03
	Variation	-	-	+11.3	+10.8	+0.01

Acknowledgements

The authors wish to acknowledge the support given by the Conseil Général du Val-de-Marne, and would like to thank particularly the DSEA for the precious help provided.

 considered:(1) All the tanks are full. This scenario is equivalent to the absence of tanks.

(2) All the tanks are empty. This scenario is the most favourable under the present equipment: the initial losses increase on equipped roofs is set to 12.7 mm. (3) All the roofs are equipped with empty tanks (volume limited scenario). This scenario is intended to show the maximal effect of this size of tanks on the considered catchment. An initial losses increase of 12.7 mm is applied to all the roofs of the catchment. (4) All the roofs are equipped with "large" tanks, i.e. all the roofs are disconnected from the sewer (harvesting surface limited scenario). This scenario is intended to test the potential effect of larger tanks on runoff. It tests, more generally, if it is possible to avoid sewer overflows through actions on the roofsgenerated runoff alone. It is then simulated only for the largest rain.

Simulations are shown in figure 6. For the small rain event (a), a consistent reduction in runoff is obtained with the current equipment when the tanks are empty. It is possible to obtain further consistent reduction of runoff through the equipment of other roofs.

For the strong rain event (b), the situation changes: the rainfall exceeds the tanks storage capacity (scenarios 1 to 3) and even the infiltration capacity of the soil (i.e.: pervious areas contribute to runoff). In that case the tanks' effect on runoff is negligible: passing from the first to the third scenario, the peak flow is just shortened of a few minutes, and then the trajectories are superposed. The peak flow is not reduced.

However, in the fourth scenario the hydrograph peak is reduced of about 10%. This is enough to make it lower than 0.5 m 3 /s, which can be considered as an overflow threshold. Even if this scenario is extreme and, probably, unfeasible, this simulation shows that it is theoretically possible to avoid sewer overflows (for the considered rain event) acting just on roofs-generated runoff.

Sensitivity analysis to return period

The analysis showed that, for the rain-event considered, the actual equipment is rapidly