9th International Conference on Urban Drainage ModellingBelgrade 2012

Ignoring the complexity of drainage network in drainage modeling: an efficient step towards integrated modeling

Sylvain Coutu1 , Dario Del Giudice2,3, Luca Rossi1, David Andrew Barry1

1 Ecole Polytechnique Fédérale de Lausanne (EPFL), Switzerland.2 Swiss Federal Institute of Technology Zurich (ETHZ), Switzerland.3 Swiss Federal Institute for Aquatic Science and Technology, Switzerland.

E-mail: sylvain.coutu@epfl.ch

ABSTRACTSewage networks and river networks are known to have very different characteristics. In this study, we present a modeling framework that allows modeling of rainfall/runoff processes in both sewage network and urban rivers. The originality of the model stands in the fact that the pipe network is absolutely not considered. It is instead replaced by a linear box reservoir. The efficiency of this simplification is illustrated by the validation of the basin on two overlapping basins: a sewage basin with endpoint the local WWTP, and urban river, with endpoint a natural Lake.

KEYWORDSModeling, Sewer basin, Urban hydrology

1 INTRODUCTIONUrban hydrology has been subject to intense and various researches and has now reached a state of maturity in terms of prediction of the hydrologic response of urban or partially urban watershed . Zoppou made a large review of both quantity and quality aspects of urbanstormwater models where a concise mathematical description of common methods for flow routing and contaminant generation was provided.

Most popular urban hydrological models used in research and engineering (e.g. MOUSE, SWMM) are spatially distributed with link-node drainage network. If some of them (e.g. PURPS, RUNQUAL, SLAMM, StormTac and WBM) treat the catchment in a lumped fashion, ignoring the drainage network, they are nonetheless unfit for routing of the drainage network and baseflow simulation . Yet, water science abounds with mathematical tools designed for conceptual lumped hydrological studies, including stochastic and deterministic approaches (see e.g. Singh and Woolhiser for a review). But so

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far, these models have been mostly experimented on rural areas where a parsimonious approach is more evident .

This paper proposes to derive river basin scale exiting theory and shows for the first time the applicability of a parsimonious approach in highly engineered catchment at WWTP basin scale. A mathematical framework relying on a combination of linear and non linear reservoir is presented and adapted to particularities of urbanized catchment which are (i) high proportion of impervious surfaces, (ii) complex drainage system, (iii) presence of combined sewer overflow, (iv) artificial water inputs. To achieve this in a parsimonious manner, the detail of the drainage network (pipes) is ignored and replaced by a linear box-reservoir.

As evidence of the utility and efficiency of the designed hydrological model, we apply the derived equations to two real case studies. Simulated flow at WWTP of the city of Lausanne (Switzerland) is calibrated and validated. Similarly, the model is validated on an urban river basin overlapping the sewer network. Results show that the proposed methodology, despite its apparent simplicity, turns out to be very efficient for prediction of flow in highly engineered systems.

2 METHODOLOGY

2.1 Conceptual model developed

In this study, the drainage basin is modeled as a set of four reservoirs, each one characterized by a state variable representing the water storage in the compartment (Figure 1). The two meteorological forcings to the hydrosystem are the precipitation and air temperature Γ , assumed uniformly applied on the whole watershed.

The water is considered to flow on surface and in subsurface. The surface compartment, responsible for surface runoff, is modeled as a fast-reacting (transient) storage characterized by a water volume of Ss . The subterranean layer is represented as composed of two reservoirs: the upper soil (or root zone) region and the groundwater region, respectively with a storage of Su and Sg .

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Figure 1. Schematic representation of the hydrological processes occurring in urbanized catchments. The watershed is divided into a pervious Ap and impervious Ai zone. In Ap inltration I and percolation Je fluxes recharge the aquifer, responsible for a slow out flow Q sub. Rainfall j on Ai, on the contrary, provokes a rapid system response in terms of runoff Qsup.

2.2 Modeling of surface runoff

Since modeling intensively managed (i.e. engineered) watersheds, the presence of fast flow bypassing the complex subsurface has to be taken into account. Being in an urban environment this effect is considered by dividing the catchment area into pervious and impervious surfaces. The flux j [L 3T-1] of precipitation falling on each part is respectively jAp and jAi, where Ap and Ai represent the permeable and impermeable areas [L2]. It is important to notice that on an urban basin equipped with a partially separate sewer system, Ai comprises just the fraction of the impermeable area actually contributing to the discharge of studied catchment.

When falling on pervious fraction of the basin, the rain can either infiltrate or give origin to overland flow. The infiltration flux I is described by a highly simplified law derived from a linearization of Horton function:

where Ksat is the saturated hydraulic conductivity [LT-1], _ the soil moisture content [ ] and n the effective porosity of the medium [ ].

In case the rainfall intensity exceeds the soil infiltration capacity, the surplus of precipitation becomes overland flow. This mechanism of generation of surface runoff from pervious zones is named `infiltration excess overland flow'. This conceptualization implicitly assumes that the compartment to which infiltration flux is directed is large enough to not become full (i.e. limiting). When the infiltration capacity of the soil is surpassed, the excess of precipitation is transferred to a surface storage. This reservoir is also directly filled by the rain flux arriving on the impervious surfaces jA i.

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The output Qsup of this linear box represents the fast component of the total streamflow. The water budget equation for the surface storage is:

where and .

2.3 Modeling of subsurface flow

Infiltrated flow, I, is considered to fill the root zone storage, whose water volume is:

with Z the depth of the active soil layer [L]. Two types of outputs from this region are considered: evapotranspiration ET and deep percolation (or leaching) Je.

Evapotranspiration represents the sum of the output fluxes due to soil evaporation (affected by climatic features and soil water availability) and plant transpiration . Consistently with Nicotina et al. , water vapor flux is modeled as:

where ETmax [LT-1] is the maximum (potential) flux of water that can be lost as vapor and f(θ) represents a moisture extraction function describing moisture restrictions on water extraction from the soil:

where θw represents the permanent wilting point and θ* the critical soil moisture level at which the plant begins to close stomata in response to water stress. The dryness state is assumed to be reached when the relative soil water content is below 65% .Maximum evapotranspiration is computed through a modified version of the Blaney-Criddle equation :

with a and b fitting parameters and p the mean annual percentage of daytime hours, only depending on latitude.

The second loss from upper soil region is due to percolation, a vertical movement of water deep toward the phreatic zone (i.e. the groundwater region). According to a widely used parameterization of vertical gravity-driven flow the leaching from the root zone is computed as:

More detail of the mathematical model can be found in Coutu et al. (submitted).

3 RESULTS

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3.1 Case study

The mathematical model presented in the previous chapter is applied to study the rainfall/runoff mechanism of two overlapping mid-size scale drainage basins (~20 km2). The two studied basins are fundamentally different. One, predominantly made up of storm sewers and semi natural creeks, is an urban river (the Vuachère) discharging into the Lake Geneva. The second, consists mainly of pipes, galleries, sewers overflows and pumps, collects wastewater and part of stormwater and transports them to the local WWTP.

Figure 2: Lausanne urban area with the two studied catchments. Modified from Margot et al. (2011).

3.2 Validation of flow dynamics in the sewer catchment

The model reproduces well sewage cycles as well as peak discharges. In the presented case, the flow rate arriving from Lausanne sewer to STP during severe storm events in attenuated by the presence of CSOs; this behavior is well captured by the simulator. Due also to the inherent stochastic nature of wastewater production , to measurement errors and rain measurements not always representative, the model exceptionally does not manage to reproduce perfectly certain variation of discharge time series. However, the efficiency metrics adopted (NS=0.72, NB=-0.0011) confirms the overall satisfactory predictive power of the model. The capability to fit well observed hydrograph data is confirmed during cross validation phase (Figure 3).

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Figure 3: Response of Waste Water Treatment Plant to rain triggers at WWTP inlet. Adapted from Coutu et al. .

3.3 Validation of flow dynamics at urban river outlet

After validation on the sewer basin, the model is tested on the urban river watershed. Figure 4 shows the comparison between measured and simulated discharges during the validation period (Spring 2011). This `split sample test' illustrates that the calibrated model satisfactorily reproduces flow rates observed at the outlet of the river basin, with correct Bias (NB=-0.0057) index. A slight overestimation of some peaks is observable, and, since time series has low variability in this time-span, this has an important effect on Nash error function (NS=0.73).

Figure 4: Response of urban river basin to rain triggers at Vuachère outlet. Adapted from Coutu et al. .

4 DISCUSSIONTo model every component of a large combined drainage network is impractical due to the extreme complexity of the system, time constraint and very often availability of relevant data. Thus all hydrological models are built upon certain simplification, whom degree can be extremely various from one model to another. Distributed models are built for developing sizing rules for devices, planning or flood controls. They consider the spatial variability of many factors that influence run-off production and predicted flow dynamic. Conversely, models focusing on large scale diffuse processes such as climate change commonly use a lumped approach and parsimonious approach .

Cantone and Schmidt discussed the potential danger of simplifying sewer hydrologic/hydraulic models and concluded that to lump together interacting non linear processes of the system may affect the outfall hydrograph. If we agree in this statement, we believe that the inclusion of elements of the system can lead in over parametrization of the system and increase uncertainties as discussed by Leon et al. in a discussion paper that followed the publication of Cantone and Schmidt (2009). Indeed, depending on data availability, there is an optimum model complexity beyond which the predictive performance decrease has it is nicely illustrated in Grayson et al. and in most situation modelers face too limited data availability for complex model uses . In addition, to quantify spatial variability or parameters necessary in distributed models is subject to other sources of uncertainties .

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Finally, the use of parsimonious approach reduces demanding computation time necessary for calibration procedures. It has been noted that the high number of parameters used in distributed approach make more complex the calibration procedure . The challenges of calibration in urban environment are greater as impervious surfaces intensify episodic flow and simplified models allows the use of complex and computation demanding calibration techniques.

5 CONCLUSIONIssue in urban hydrology and planning are multiples and varieties of hydrological models proposed by scientists and engineers shall be at least as numerous. The modeling approach presented here, inspired by existing models designed for water quality modeling in rural areas and adapted to the specificities of the urban environment, does not stand in opposition to classical distributed models which have their own advantages. Rather, it has been designed taking advantages of the parsimony concept that has proven his efficiency in the past, and that allows light computation techniques and thus the implementation of functions for more integrated models.

6 QUESTIONARY

1. Name of the author that will present the paper: _Sylvain Coutu_

(please note that one author can have only one oral and one poster presentation at the Conference)

2. Is the first author an young researcher (according to IWA, under the age of 35): Yes

3. Have you submitted the extended abstract yet: Yes

If Yes, give the file name of extended abstract: “141-60-1-SP-1.docx”

4. Have you previously published this paper at another conference or Journal: Yes

5. Do you want to have the full paper offered for the Journal:

Water Science and Technology: No

Journal of Hydraulic Research: No

Other Journal: __No_______________________________________

6. Have you checked your paper for style, formatting and English language: Yes

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