9th International Conference on Urban Drainage Modelling
Belgrade 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.
Swiss Federal Institute of Technology Zurich (ETHZ), Switzerland.
3
Swiss Federal Institute for Aquatic Science and Technology, Switzerland.
2
E-mail: sylvain.coutu@epfl.ch
ABSTRACT
Sewage 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.
KEYWORDS
Modeling, Sewer basin, Urban hydrology
1
INTRODUCTION
Urban 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
(Delleur 2003). Zoppou (2001) made a large review of both quantity and quality aspects of urban
stormwater 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
(Elliott and Trowsdale 2007). Yet, water science abounds with mathematical tools designed for
conceptual lumped hydrological studies, including stochastic and deterministic approaches (see e.g.
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Singh and Woolhiser (2002) for a review). But so far, these models have been mostly experimented on
rural areas where a parsimonious approach is more evident (Basu, Rao et al. 2010; Jacobson 2011).
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.
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2.1
METHODOLOGY
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 (Fenicia, Savenije et al. 2007). 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 (Botter, Bertuzzo et al. 2010).
2
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 Qsub. 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 [L3T-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:

I  Ap Min( j , K sat (10  9 ))
n
(1)
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 jAi.
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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:
dS s (t )
 R(t )  Ai j (t )  Qsup (t )
dt
(2)
where R  Ap j  I and Qsup  ksup S s .
2.3
Modeling of subsurface flow
Infiltrated flow, I, is considered to fill the root zone storage, whose water volume is:
Su  Z Ap
(3)
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 (Botter, Bertuzzo et al. 2010).
Consistently with Nicotina et al. (2011), water vapor flux is modeled as:
ET  Ap ETmax f ( )
(4)
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:
 0
if   w

   w
f ( )  
if  w     *
 *  w if  *  n
 1
(5)
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% (Nicótina, Tarboton et al. 2011).
Maximum evapotranspiration is computed through a modified version of the Blaney-Criddle equation
(Fooladmand and Ahmadi 2009):
ETmax  a  b[ p(0.46  8.13)]
(6)
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 (Botter, Bertuzzo et al. 2010) the leaching from the root zone is computed
as:
 
J e  Ap K sat  
n
c
(7)
More detail of the mathematical model can be found in Coutu et al. (submitted).
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3
3.1
RESULTS
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 (Rieckermann, Anta et al. 2011), 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. (submitted).
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 timespan, 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.
(submitted).
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DISCUSSION
To 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
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and predicted flow dynamic. Conversely, models focusing on large scale diffuse processes such as
climate change commonly use a lumped approach and parsimonious approach (Jacobson 2011).
Cantone and Schmidt (2009) 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. (2010) 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. (2002) and in most
situation modelers face too limited data availability for complex model uses (Grayson, Blöschl et al.
2002). In addition, to quantify spatial variability or parameters necessary in distributed models is
subject to other sources of uncertainties (Maheepala, Takyi et al. 2001).
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 (Muleta and Nicklow 2005). The challenges
of calibration in urban environment are greater as impervious surfaces intensify episodic flow
(Ackerman, Schiff et al. 2005) and simplified models allows the use of complex and computation
demanding calibration techniques.
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CONCLUSION
Issue 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.
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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
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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
REFERENCES
Ackerman, D., K. C. Schiff, et al. (2005). "Evaluating HSPF in an arid, urbanized watershed." Journal
of the American Water Resources Association 41(2): 477-486.
Basu, N. B., P. S. C. Rao, et al. (2010). "Parsimonious modeling of hydrologic responses in
engineered watersheds: Structural heterogeneity versus functional homogeneity." Water
resources research 46(4).
Botter, G., E. Bertuzzo, et al. (2010). "Transport in the hydrologic response: Travel time distributions,
soil moisture dynamics, and the old water paradox." Water Resour. Res. 46(3): W03514.
Cantone, J. P. (2009). "Potential Dangers of Simplifying Combined Sewer Hydrologic/Hydraulic
Models." Journal of Hydrologic Engineering 14(6): 596.
Coutu, S., D. Del Giudice, et al. (submitted). "Parsimonious hydrological modeling of urban sewer and
river catchments." Journal of Hydrology.
Delleur, J. W. (2003). "The evolution of urban hydrology: Past, present, and future." Journal of
Hydraulic Engineering-Asce 129(8): 563-573.
Elliott, A. H. and S. A. Trowsdale (2007). "A review of models for low impact urban stormwater
drainage." Environmental Modelling & Software 22(3): 394-405.
Fenicia, F., H. H. G. Savenije, et al. (2007). "A comparison of alternative multiobjective calibration
strategies for hydrological modeling." Water Resour. Res. 43(3): W03434.
Fooladmand, H. R. and S. H. Ahmadi (2009). "Monthly spatial calibration of Blaney–Criddle equation
for calculating monthly ETo in south of Iran." Irrigation and Drainage 58(2): 234-245.
Grayson, R. B., G. Blöschl, et al. (2002). "Advances in the use of observed spatial patterns of
catchment hydrological response." Advances in Water Resources 25(8–12): 1313-1334.
Jacobson, C. R. (2011). "Identification and quantification of the hydrological impacts of
imperviousness in urban catchments: A review." Journal of environmental management 92(6):
1438-1448.
Leon, A. S., L. S. Nania, et al. (2010). "Discussion of "potential dangers of simplifying combined
sewer hydrologic/hydraulic models" by J.P. Cantone and A.R. Schmidt." Journal of
Hydrologic Engineering 15(7): 587-588.
Maheepala, U. K., A. K. Takyi, et al. (2001). "Hydrological data monitoring for urban stormwater
drainage systems." Journal of Hydrology 245(1–4): 32-47.
Muleta, M. K. and J. W. Nicklow (2005). "Sensitivity and uncertainty analysis coupled with automatic
calibration for a distributed watershed model." Journal of Hydrology 306(1–4): 127-145.
Nicótina, L., D. G. Tarboton, et al. (2011). "Hydrologic controls on equilibrium soil depths." Water
resources research 47(4).
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Rieckermann, J. r., J. Anta, et al. (2011). "Assessing Wastewater Micropollutant Loads with
Approximate Bayesian Computations." Environmental Science & Technology 45(10): 43994406.
Singh, V. P. and D. A. Woolhiser (2002). "Mathematical Modeling of Watershed Hydrology." Journal
of Hydrologic Engineering 7(4): 270-292.
Zoppou, C. (2001). "Review of urban storm water models." Environmental Modelling & Software
16(3): 195-231.
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