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Parsimonious hydrological modeling of urban sewer and river catchments

25 Sep 2012-Journal of Hydrology (Elsevier)-Vol. 464, pp 477-484

Abstract: Summary A parsimonious model of flow capable of simulating flow in natural/engineered catchments and at WWTP (Wastewater Treatment Plant) inlets was developed. The model considers three interacting, dynamic storages that account for transfer of water within the system. One storage describes the “flashy” response of impervious surfaces, another pervious areas and finally one storage describes subsurface flow. The sewerage pipe network is considered as an impervious surface and is thus included in the impervious surface storage. In addition, the model assumes that water discharged from several CSOs (combined sewer overflows) can be accounted for using a single, characteristic CSO. The model was calibrated on, and validated for, the Vidy Bay WWTP, which receives effluent from Lausanne, Switzerland (population about 200,000), as well as for an overlapping urban river basin. The results indicate that a relatively simple approach is suitable for predicting the responses of interacting engineered and natural hydrosystems.
Topics: Impervious surface (57%), Combined sewer (56%), Subsurface flow (52%), Population (51%)

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Parsimonious hydrological modeling of urban sewer and river catchments
Sylvain Coutu
, Dario Del Giudice
1,2
, Luca Rossi, D.A. Barry
Laboratoire de technologie écologique, Institut d’ingénierie de l’environnement, Faculté de l’environnement naturel, architectural et construit (ENAC), Station 2,
Ecole Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland
article info
Article history:
Received 8 February 2012
Received in revised form 17 July 2012
Accepted 23 July 2012
Available online 1 August 2012
This manuscript was handled by Geoff
Syme, Editor-in-Chief, with the assistance of
Paul Jeffrey, Associate Editor
Keywords:
Urban hydrology
Modeling
Sewer catchment
Case study
summary
A parsimonious model of flow capable of simulating flow in natural/engineered catchments and at WWTP
(Wastewater Treatment Plant) inlets was developed. The model considers three interacting, dynamic sto-
rages that account for transfer of water within the system. One storage describes the ‘‘flashy’’ response of
impervious surfaces, another pervious areas and finally one storage describes subsurface flow. The sew-
erage pipe network is considered as an impervious surface and is thus included in the impervious surface
storage. In addition, the model assumes that water discharged from several CSOs (combined sewer over-
flows) can be accounted for using a single, characteristic CSO. The model was calibrated on, and validated
for, the Vidy Bay WWTP, which receives effluent from Lausanne, Switzerland (population about 200,000),
as well as for an overlapping urban river basin. The results indicate that a relatively simple approach is
suitable for predicting the responses of interacting engineered and natural hydrosystems.
Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction
Catchment modeling is a mature discipline, and much research
and modeling has been carried out on natural catchments. Like-
wise, urban hydrological modeling has now reached a state of
maturity in terms of prediction of the hydrologic response of urban
or partially urbanized basins (Delleur, 2003; Ashley et al., 1999;
Borah, 2011). As discussed in detail by Zoppou (2001), urban
stormwater models are based on detailed spatial descriptions of
the constituent drainage networks. Such models are valuable for
many purposes, of course.
Most popular urban hydrological models used in research and
engineering (e.g., MOUSE (Hernebring et al., 2002), SWMM
3
) are
spatially distributed with link-node drainage networks. Detailed
modeling of drainage systems is often deemed necessary because
of the complexity of flow paths in urban catchments (Cantone and
Schmid, 2011; Gironás et al., 2009). Yet, water science abounds with
mathematical tools designed for lumped hydrological studies,
including stochastic and deterministic approaches (see, e.g., Singh
and Woolhiser (2002) for a review). But, so far, these models have
been mostly tested on rural areas where a parsimonious approach
is more evident (Amin and Campana, 1996; Beven and Kirkby,
1979; Jacobson, 2011; Kelman, 1980; Perrin et al., 2001; Yadav
et al., 2007).
Here, we explore a simplified approach to urban hydrology
modeling based on a lumped approach, as an alternative to de-
tailed network modeling. Lumped models are appropriate when
the focus of the modeling effort is the catchment outlet, which is
the case considered here. The model integrates the main physical
processes in urban catchments (i.e., precipitation, infiltration, soil
moisture, runoff, streamflow and groundwater flow), but without
consideration of the detailed pipe drainage network. The model
is designed to predict the flow (i) at the entrance of a WWTP
(Wastewater Treatment Plant), which is the endpoint of the city’s
drainage system, and (ii) in an engineered urban river basin, which
also receives flow from the city. In urban systems, these two end-
points drain overlapping basins.
The model is based on a small number of storages that account
for the main features of an urban catchment, i.e., (i) high propor-
tion of impervious surfaces, (ii) complex drainage system, (iii)
presence of CSOs (combined sewer overflows), and (iv) artificial
water inputs. In addition, the hydrological model integrates func-
tions that aim to reproduce characteristic daily variations of dry
weather flow to the WWTP. The model is validated for a WWTP
drainage basin and for an urban river. The two considered basins
partly overlap over the city of Lausanne, Switzerland.
0022-1694/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.jhydrol.2012.07.039
Corresponding author. Tel.: +41 (0)21 693 8024.
E-mail address: sylvain.coutu@epfl.ch (S. Coutu).
1
Present address: Eawag, Swiss Federal Institute for Aquatic Science and Technol-
ogy, Ueberlandstrasse 133, CH-8600 Duebendorf, Switzerland.
2
Address: Institute of Environmental Engineering, Swiss Federal Institute of
Technology Zürich (ETHZ), 8093 Zürich, Switzerland.
3
http://www.epa.gov/nrmrl/wswrd/wq/models/swmm/, last accessed December
2011.
Journal of Hydrology 464–465 (2012) 477–484
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2. Design and mathematical description of the model
The basin is modeled as a set of three storages (one surface and
two subsurface), each characterized by a state variable represent-
ing the water stored within it (Fig. 1). The two meteorological forc-
ings considered are precipitation and air temperature, T, both
assumed uniform over the basin. The type of precipitation is deter-
mined based on a temperature threshold (DeWalle and Rango,
2008; Schaefli et al., 2005): when T is above the threshold T
cr
,
precipitation occurs as rain, otherwise precipitation is frozen.
The water is considered to flow on surfaces and in the subsur-
face (c.f., Kirkby, 1988; Musy and Higy, 2010; Quinn et al., 1991;
Rinaldo et al., 2006; Rodriguez-Iturbe and Valdes, 1979). The sur-
face compartment, responsible for surface runoff, is modeled as a
fast-reacting (transient) storage characterized by a water volume
of S
s
cf.(Beven and Kirkby, 1979; Fenicia et al., 2007; Puente
et al., 1993; Todini, 1988). The subterranean layer is represented
as composed of two reservoirs: the upper soil (or root zone) region
and the groundwater region with, respectively, storages of S
u
and
S
g
(Botter et al., 2010). S
s
and S
g
are considered to extend over
the total surface of the catchment, whereas S
u
occupies only the
pervious fraction of the basin (Fig. 1).
2.1. Modeling of surface processes
In urban basins, the rapid run-off response to precipitation is an
important feature (Basu et al., 2010; Deletic, 1998; Elliott and
Trowsdale, 2007; Gupta and Saul, 1996; Jacobson, 2011). This
water bypasses the subsurface flow, and is treated as a separate
component in the lumped model. Physically speaking, this
amounts to dividing the catchment area into pervious and imper-
vious surfaces, with the latter producing the rapid runoff
component.
The flux of precipitation falling on each part is, respectively, jA
p
and jA
i
, where A
p
and A
i
½L
2
represent the permeable and imperme-
able areas (Fig. 1) and j ½LT
1
is the precipitation rate. Note that, for
an urban basin equipped with a partially-separated sewer system,
A
i
comprises the fraction of the impermeable area actually contrib-
uting to the discharge.
When falling on the pervious fraction of the basin, the rain can
either infiltrate or produce overland flow. The infiltration flux, I
½L
3
T
1
, is described by a simplified law derived from the Horton
function (e.g., Hingray et al., 2009; Horton, 1940; Ravi and Wil-
liams, 1998):
I ¼ A
p
Min j; K
sat
10 9
h
n

; ð1Þ
where K
sat
½LT
1
is the saturated hydraulic conductivity, h [–] the
soil moisture content and n [–] the effective porosity.
When the precipitation exceeds the soil infiltration capacity, the
surplus precipitation becomes infiltration-excess overland flow
(Beven, 2004; Cundy and Tento, 1985; Engman and Rogowski,
1974; Evans et al., 1999). In this circumstance, the compartment
to which the infiltration flux is directed is not saturated when run-
off occurs. In the model, the excess precipitation is transferred to a
surface storage. This storage also receives the precipitation flux
falling on any impervious surfaces, jA
i
. The output, Q
sup
, from this
storage produces the fast component of the total streamflow. The
water-budget equation for the surface storage is:
dS
s
ðtÞ
dt
¼ RðtÞþA
i
jðt ÞQ
sup
ðtÞ; ð2Þ
where R ¼ jA
p
I; Q
sup
¼ k
sup
S
s
and k
sup
is the rate discharge of the
impervious surface linear reservoir. When Hortonian infiltration is
exceeded (Eq. (1)), a fraction R of the rainwater is added to the over-
land flow.
2.2. Modeling of subsurface processes
Surface infiltration enters the root zone storage, the total vol-
ume of which is:
S
u
¼ Zh A
p
; ð3Þ
with Z [L] the depth of the active soil layer. Two types of outputs
from this region are considered: evapotranspiration, ET, and deep
percolation, J
e
. The water vapor flux is modeled as:
ET ¼ A
p
ET
max
f ðhÞ; ð4Þ
where ET
max
½LT
1
is the maximum (potential) flux of water that can
be lost as vapor and f ðhÞ represents the restriction on water extrac-
tion due to the soil’s moisture content:
f ðhÞ¼
0; h < h
w
;
hh
w
h
h
w
; h
w
6 h 6 h
;
1; h
< h < n;
8
>
<
>
:
ð5Þ
where h
w
is the permanent wilting point and h
the critical soil
moisture level at which the plant begins to close stomata in re-
sponse to water stress (e.g., Dingman, 1994; Nicótina et al., 2011;
Fig. 1. Schema of the WWTP catchment conceptualization. The pipe and channel network is replaced by a linear reservoir (S
s
). A fraction jA
i
of the rainfall enters this
reservoir. The other part of the rain jA
p
enters the pervious zone (S
u
), where it can evapotranspires or percolates to the subsurface linear reservoir (S
g
). Note that same
framework applies for river basin modeling. In the case where the model is used to simulate flow at the WWTP entrance, the subsurface reservoir discharges into the pipe
network, thereby modeling the drainage effect of the sewer system, which is in addition to artificial inputs from water use (see Section 2.4). In the second case (river), the
WWTP is replaced by the river. Symbols are explained in the text.
478 S. Coutu et al. / Journal of Hydrology 464–465 (2012) 477–484

Rodrìguez-Iturbe and Porporato, 2005). The dryness state is as-
sumed to be reached when the relative soil water content is below
65% (i.e., h
0:65n) (cf., Nicótina et al., 2011).
The maximum evapotranspiration is computed through a mod-
ified version of the Blaney–Criddle equation (e.g., Doorenbos and
Pruitt, 1975):
ET
max
¼ a þ b½pð0:46T þ 8:13Þ; ð6Þ
where a and b are fitting parameters and p is the mean annual per-
centage of daytime hours, which varies only with latitude (Allen
et al., 1998).
The second loss from the upper soil region is due to percolation
to groundwater. According to a widely used parameterization of
vertical gravity-driven flow (e.g., Botter et al., 2010; Rodrìguez-
Iturbe and Porporato, 2005), the leaching from the root zone is
computed as:
J
e
¼ A
p
K
sat
h
n

c
: ð7Þ
The deepest subterranean region is modeled as a linear reservoir re-
charged by the leaching from the upper soil layer. The water flux
from this zone, Q
sub
¼ k
sub
S
g
, is used to simulate the baseflow in
the river, when this model is applied to the natural region. For
application to the sewer catchment, the subterranean flow repre-
sents the transfer of water from soil to the drainage system. Indeed,
a non-negligible part of the infiltrated water can be drained by the
pipe network, principally depending on soil characteristics (Berthier
et al., 2004; Karpf and Krebs, 2011). This infiltration of groundwater
to the drainage network must in consequence be considered in the
water dynamics (Dupont et al., 2006; Göbel et al., 2004).
The mass conservation equations modeling near-surface and
deep soil water dynamics are:
dS
u
ðtÞ
dt
¼ IðtÞETðtÞJ
e
ðtÞ; ð8Þ
dS
g
ðtÞ
dt
¼ J
e
ðtÞQ
sub
ðtÞ: ð9Þ
This formulation of subterranean flow, based on Botter et al. (2010),
is easily extendible to account for interflow (or subsurface runoff)
through shallow soil layers. This ‘‘fast internal flow’’, with drainage
capacity in between overland and deep flow, could be a relevant
component of hydrographic recession curves for anisotropic soils
in which the lateral hydraulic conductivity dominates that in the
vertical (Hingray et al., 2009; Musy, 2005; Raghunath, 2006; Shaw,
1994). In this case, the hydrological model proposed can be en-
hanced by limiting the deep percolation reaching the groundwater
storage and diverting part of it into streamflow (cf., Thomet, 2010).
2.3. Consideration of CSOs
A characteristic feature of hybrid sewer networks are CSOs. In
the drainage network, CSOs divert flows above a certain level di-
rectly to receiving waters, rather than to the WWTP (Butler and
Davies, 2010; Lee and Bang, 2000; Wisner et al., 1981). Although
a sewer network usually consists in several CSOs, we consider in
this study that a single, representative flow delimiter is sufficient
to model the effect of all CSOs of the system in a lumped fashion
manner. This representative CSO is modeled using a diversion
law that follows a linear threshold-limited function (in Fig. 2).
2.4. Dynamics of wastewater production
During dry weather, discharges arriving at the WWTP inlet are
determined mainly by two phenomena: (i) infiltration of ground-
water into the pipe network (see Section 2.2 and Dupont et al.
(2006); Göbel et al. (2004)) and, (ii) water use and consequent
wastewater production. This ‘artificial’ water input, which is not
present in a natural catchment, is modeled based on statistical
analysis presented by Jordan (2010). In this study, monthly, daily
and hourly flow coefficients are extrapolated from temporal series
analysis and considered as characteristic of the system. This in-
cludes direct water consumption in households, and all parasitic
clear water (fountains, street washing, industrial uses, etc).
3. Optimization of hydrological quality index
Model calibration was performed based on the two objective
functions in Table 1, since this combination has been found to yield
better overall fits (Hingray et al., 2009; Perrin et al., 2001). The list
of fitting criteria and the range of prior values given before calibra-
tion process can be found in Table 2.
Similarly to Fenicia et al. (2006) and Seibert (2000), the calibra-
tion approach adopted here is based on a Monte Carlo algorithm
designed to optimize the model performance, using the
Fig. 2. Linear low partitioning function applied to the representative CSO. The
maximum flow reaching the WWTP is limited by the threshold, Q
lim
. The excess is
diverted out of the modeled pipe network.
Table 1
Mathematical expressions of adopted fitting criteria functions e.g.,(Nash and Sutcliffe,
1970; Hingray et al., 2009; Schaefli and Gupta, 2007; Fenicia et al., 2007; Reusser
et al., 2008). Z
sim
and Z
obs
are the modeled and observed values and n is the number of
observations.
Criterion function Expression Optimal value
Nash–Sutcliffe
1
P
n
i¼1
½Z
obs
ðiÞZ
sim
ðiÞ
2
P
n
i¼1
½Z
obs
ðiÞZ
obs
2
1
Normalized Bias
P
n
i¼1
½Z
obs
ðiÞZ
sim
ðiÞ
n
Z
obs
0
Table 2
Calibration parameters and the range of values considered. For the Monte-Carlo
parameter optimization procedure, a uniform distribution was considered.
Parameter Symbol Lower bound Upper bound
Saturated conductivity K
sat
(m s
1
)
1:4 10
6
2:6 10
5
Wilting point h
w
0.14 0.26
Clapp exponent c 120
ET parameter a 4.8 0.84
ET parameter b 0.7 1.19
Subsurface discharge rate
k
sub
(s
1
)
2:8 10
8
3:8 10
7
Surface discharge rate
k
sup
(s
1
)
2:0 10
5
3:8 10
4
S. Coutu et al. / Journal of Hydrology 464–465 (2012) 477–484
479

Nash–Sutcliffe (NS) and the Normalized Bias (NB) criteria (Table 1).
The former places an emphasis on the model’s ability to estimate
large magnitudes (i.e., peak discharge), while the latter weights
more the deviation between simulated and observed water
balance, as follows:
Min1 NSÞþ j NB jg: ð10Þ
4. Case study and results
4.1. Application of the model to an urban basin: Modeling of flow at
the river outlet and WWTP entrance
The same modeling framework is employed to model both the
dynamics of flows at an urban river outlet and inlet of a local
WWTP. The application area is the city of Lausanne in Switzerland,
which has a population of about 200,000 and is characterized by a
steep average gradient towards nearby Lake Geneva. A feature of
Lausanne is that the WWTP catchment and the river catchment
overlap over a fraction of the city (Fig. 3). The model is calibrated
twice on the same time period, once to model the WWTP input,
and once to model the river output to the adjacent Lake Geneva,
which is the receiving water body for both river and WWTP
discharges.
4.2. Application to the WWTP basin
The WWTP catchment under study is the Lausanne hybrid (par-
tially-separate) sewer system, drains to the Vidy Bay WWTP. It is a
typical urban catchment, where much water comes from toilets,
washing, industry and other uses, rather than directly from natural
sources. The channels comprising the WWTP basin consist mainly
of concrete galleries, pipes and overflows, which often do not fol-
low the natural topography and sometimes even move upslope,
driven by pumping stations (Assainissement Lausanne, 2009).
The Vidy Bay WWTP treats about 6 10
4
m
3
of wastewater dai-
ly. Flow data were collected at the entrance of the WWTP (Jean-
bourquin et al., 2011; Nguyen et al., 2009). Rain and temperature
information were extracted from a nearby meteorological station
managed by the Swiss Federal Office of Meteorology and
Climatology.
4
There is significant heterogeneity in the WWTP basin: The old-
est, central part of the catchment is made up of a combined sewer
system, in which wastewater and stormwater flow together,
whereas in newer, surrounding areas, separate drainage systems
have been installed (i.e., wastewater and stormwater are collected
separately). The combined system drains about 30% of the WWTP
basin, while its imperviousness is around 25% (Rossi et al., 2008).
Note that 70% of the WWTP basin consists of separate sewer sys-
tem. A large part of the water is in consequence diverted through
drainage out of the WWTP basin. This fraction of water does not
participate in the flow to the WWTP entrance and was thus re-
moved from the system.
The hydrological model setup for the WWTP basin was cali-
brated over the period July–November 2010. The comparison of
observed and computed hydrographs is satisfactory (Fig. 4), with
a NS coefficient of 0.73 and NB of 0.00041. Good performance
was achieved also for the validation period November 2010–Janu-
ary 2011, as can be seen in Fig. 4, with fitting metrics in the same
range.
The model reproduces well dry weather conditions as well as
peak discharges. In this case, the flow rate at the WWTP entrance
during significant storm events is attenuated by the presence of
CSOs; this behavior is captured by the simulator. As stated above,
all CSO’s in the network are represented by a single CSO and diver-
sion law (Section 2.3), for which a single parameter, Q
lim
, must be
selected. For the latter, we used the Q
lim
value for the CSO at which
most diversion occurs. This CSO, the closest CSO to the WWTP, is
responsible for more than a third of all CSO discharge, and is typ-
ically the first to become operational in storms (e-dric.ch, 2008).
The modeling results in Fig. 4 do not capture perfectly the mea-
sured data. Such differences could arise from the inherent stochas-
tic nature of wastewater production (Rieckermann et al., 2011)or
measurement errors at the WWTP. In addition, rainfall measure-
ments from a single location were used, without any consideration
of possible spatial variations due, for example, to topographic
Fig. 3. Two basins are studied. For the Vidy Bay WWTP (white), the catchment is fully artificial, and is composed of Lausanne’s pipe network. The other is the urban basin of
the Vuachère river (gray). The two basins partly overlap.
4
http://www.meteosuisse.ch, last accessed January 2012.
480 S. Coutu et al. / Journal of Hydrology 464–465 (2012) 477–484

effects (Huff and Vogel, 1978; Kieffer and Bois, 2001). Nevertheless,
the fitting metrics used confirm the overall satisfactory predictive
power of the model (NS = 0.73, NB = 0.0041).
The described modeling approach was also compared with the
distributed model RS-3.0 used by the local authorities to manage
flow the WWTP inlet. This model is a SWMM-type object-oriented
program developed in the VBA environment (Dubois and Boillat,
2000). The model simulates Lausanne’s full routing network (100
sub-basins,12 CSOs and 2 pumping stations), with flow based on
the kinematic wave approximation.
As shown by Fig. 5, the two models closely agree during dry
weather. The lumped model results are somewhat smoother. The
dry weather flow variations at WWTP inlet follow monthly, daily
and hourly variations around the mean base flow. These variations
in our model have been described by assigning to the base flow
corresponding coefficients (monthly, daily, hourly). These coeffi-
cients are taken from local public wastewater management reports
(Assainissement Lausanne (2009)). During rain events, the magni-
tude of the simulated peaks correspond for the two models,
although we observe a faster response time for the lumped model.
Structural differences between the two models are so numerous
that it would be difficult to isolate a specific reason to explain this.
First, slope effects can explain the velocity of the response, but ba-
sin slope is not directly involved in our model, even if slope is indi-
rectly integrated into reservoir discharge rate. Volumes simulated
during the rain events are in the same range (11:1 10
4
m
3
for
RS-3.0 and 9:6 10
4
m
3
for the lumped model). The difference in
the distribution of pervious/impervious areas between the two
models could also explain the shift. Our model considers a uniform
distribution whereas RS-3.0 uses different distributions for the 100
sub-basins that are routed together. Globally, the results in Fig. 5
show satisfactory agreement.
4.3. Application to the river basin
The modeled river, called the Vuachère, is located in the eastern
part of the city of Lausanne (Fig. 3). The total area of the catchment
is about 15 km
2
, of which approximately 34% is impervious.
According to data shown by Jordan (2010), about 60% of the runoff
generated on the Vuachère’s impervious surfaces contributes to
the river discharge, while the rest is considered to flow into the
sewer system.
The flow rate was measured at the outlet of the river basin, just
before discharge into Lake Geneva. The calibration and validation
periods were taken the same as for the WWTP basin modeling.
Close agreement is shown in the comparison of predicted and mea-
sured flow rates (Fig. 6).
Different factors in the model drive the simulated flow dynamics
in the river. The subsurface reservoir discharge constant controls
the river’s base flow. The magnitude of peak discharge during rain
events is controlled by the impervious surface reservoir area. The
volume of water involved in the fast response of the basin during
rainfall, on the other hand, is driven by three factors: (i) the fraction
of impervious area of the basin, (ii) the fraction of water diverted to
the WWTP through the pipe network due to the presence of CSOs,
and (iii) infiltration excess (when the rainfall intensity exceeds
the infiltration rate limit, the excess is diverted to the impervious
reservoir, and is thus transported rapidly to the river).
5. Sensitivity analysis
A sensitivity analysis was conducted to estimate the influence
of the model parameters (Table 2). Each parameter was varied
within the prior range of acceptable values for this parameter,
and the two fitting criteria (Nash–Sutcliff and Normal Bias) com-
puted. Results are presented in Fig. 7.
Precipitation [mm/h]
1
3
5
7
9
11
0
5
10
15
20
Nov/10
Dec/10
(b)
23/07/10 24/07/10 25/07/10 26/07/10 27/07/10 28/07/10 29/07/10 30/07/10
0
1
2
3
4
5
6
7
8
(a)
Fig. 4. Sample of the hydrograph for the calibration period (a) and full validation period (b) for flow modeled at WWTP inlet. Gray dashes are field measurements, solid lines
are model predictions and precipitation rate is on the right abscissa of (b).
01/08 02/08 03/08 04/08 05/08
0
2
4
6
8
10
12
0
20
40
60
80
Precipitation [mm/h]
01/08 02/08 03/08 04/08 05/08
Fig. 5. Comparison of flow modeled at the WWTP with the presented model (black)
and the RS-3.0 model (gray).
S. Coutu et al. / Journal of Hydrology 464–465 (2012) 477–484
481

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Journal ArticleDOI
TL;DR: A structured approach to select, among five variants, the optimal bias de- scription for a given urban or natural case study and results clearly show that flow simulations are much more reliable when bias is accounted for than when it is neglected.
Abstract: . Hydrodynamic models are useful tools for urban water management. Unfortunately, it is still challenging to obtain accurate results and plausible uncertainty estimates when using these models. In particular, with the currently applied statistical techniques, flow predictions are usually overconfident and biased. In this study, we present a flexible and relatively efficient methodology (i) to obtain more reliable hydrological simulations in terms of coverage of validation data by the uncertainty bands and (ii) to separate prediction uncertainty into its components. Our approach acknowledges that urban drainage predictions are biased. This is mostly due to input errors and structural deficits of the model. We address this issue by describing model bias in a Bayesian framework. The bias becomes an autoregressive term additional to white measurement noise, the only error type accounted for in traditional uncertainty analysis. To allow for bigger discrepancies during wet weather, we make the variance of bias dependent on the input (rainfall) or/and output (runoff) of the system. Specifically, we present a structured approach to select, among five variants, the optimal bias description for a given urban or natural case study. We tested the methodology in a small monitored stormwater system described with a parsimonious model. Our results clearly show that flow simulations are much more reliable when bias is accounted for than when it is neglected. Furthermore, our probabilistic predictions can discriminate between three uncertainty contributions: parametric uncertainty, bias, and measurement errors. In our case study, the best performing bias description is the output-dependent bias using a log-sinh transformation of data and model results. The limitations of the framework presented are some ambiguity due to the subjective choice of priors for bias parameters and its inability to address the causes of model discrepancies. Further research should focus on quantifying and reducing the causes of bias by improving the model structure and propagating input uncertainty.

90 citations


Cites background from "Parsimonious hydrological modeling ..."

  • ...Lumped modeling is particularly appropriate when a study focuses on outlet discharge and computation can be a limiting factor (Coutu et al., 2012)....

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Journal ArticleDOI
TL;DR: The results of the case study indicate that the uncertainty in calibration data derived by the rating curve method may be of the same relevance as rainfall-runoff model parameters themselves.
Abstract: Streamflow cannot be measured directly and is typically derived with a rating curve model. Unfortunately, this causes uncertainties in the streamflow data and also in- fluences the calibration of rainfall-runoff models if they are conditioned on such data. However, it is currently unknown to what extent these uncertainties propagate to rainfall-runoff predictions. This study therefore presents a quantitative ap- proach to rigorously consider the impact of the rating curve on the prediction uncertainty of water levels. The uncer- tainty analysis is performed within a formal Bayesian frame- work and the contributions of rating curve versus rainfall- runoff model parameters to the total predictive uncertainty are addressed. A major benefit of the approach is its inde- pendence from the applied rainfall-runoff model and rating curve. In addition, it only requires already existing hydro- metric data. The approach was successfully demonstrated on a small catchment in Poland, where a dedicated monitoring campaign was performed in 2011. The results of our case study indicate that the uncertainty in calibration data derived by the rating curve method may be of the same relevance as rainfall-runoff model parameters themselves. A conceptual limitation of the approach presented is that it is limited to water level predictions. Nevertheless, regarding flood level predictions, the Bayesian framework seems very promising because it (i) enables the modeler to incorporate informal knowledge from easily accessible information and (ii) bet- ter assesses the individual error contributions. Especially the latter is important to improve the predictive capability of hy- drological models.

46 citations


Journal ArticleDOI
Abstract: Given the critical role of the streamflow regime for instream, riparian, and floodplain ecosystem sustainability, modeling the long-term effect of urbanization on streamflow is important to predict possible changes in stream ecosystems. Since flow duration curves are largely used to characterize the streamflow regime and define indices for stream ecosystem health, we present two stochastic models, with different levels of complexity, that link the key physical features of urbanized basins with rainfall variability to determine the resulting flow duration curves. The two models are tested against 11 basins with various degrees of urban development, characterized by the percentage of impervious areas in the basin. Results show that the more complex model needs to be used to reproduce accurately the entire flow duration curve. The analysis performed suggests that the transformation of green (i.e., water used in evapotranspiration) to blue (i.e., streamflow) water in urbanized basins is an important long-term source of ecohydrological alteration. The modeling scheme also provides useful links between rainfall variability, urbanization levels, and some streamflow indices of high and low flows.

39 citations


Journal ArticleDOI
Nathalie Chèvre1, Sylvain Coutu2, Jonas Margot2, Htet Kyi Wynn2  +3 moreInstitutions (3)
TL;DR: In this particular case, ciprofloxacin was found to be the most problematic compound, with a risk quotient far above 1, and a treatment at the WWTP is not sufficient to reduce the risk, and additional measures at the CSO or at the hospital should be considered.
Abstract: Pharmaceuticals constitute an important environmental issue for receiving waters. A holistic approach, taking into consideration the sources of these compounds (hospitals, domestic use), discharges (wastewater effluent, combined sewer overflows) and related risks to the environment, is therefore needed to develop the best protection strategy. The substance flow analysis (SFA) approach, applied, for example, to the city of Lausanne, Switzerland, is an ideal tool to tackle these issues. Four substances were considered: one antibiotic (ciprofloxacin), an analgesic (diclofenac), and two anti-epileptics (carbamazepine and gabapentin). Consumption data for the main hospital of the city (916 beds) and for the population were available. Micropollutant concentrations were measured at different points of the system: wastewater inlet and outlet (WWTP), combined sewer overflows (CSO) and in the receiving waters (Vidy Bay, Lake Geneva). Measured and predicted concentrations were in agreement, except for diclofenac, for which analytical uncertainties were expected. Seven different scenarios were considered (supplementary treatment at the WWTP, at the hospital or at both places, etc.). Based on the results obtained, the supplementary treatment at the WWTP decreases the load of pharmaceuticals reaching surface water by a factor between 2 and 27, depending on the compound and on the technique. The treatment at the hospitals only influences the amount of ciprofloxacin reaching the environment and decreases the release by one third. The contribution of CSO to surface water pollution is low compared to that of the WWTP for the selected compounds. Regarding the risk for the receiving waters, ciprofloxacin was found to be the most problematic compound, with a risk quotient far above 1. In this particular case, a treatment at the WWTP is not sufficient to reduce the risk, and additional measures at the CSO or at the hospital should be considered. SFA is an ideal tool for developing the best strategy for pharmaceutical elimination, but its application depends on data availability and local conditions.

39 citations


Journal ArticleDOI
Dario Del Giudice1, Peter Reichert1, Vojtěch Bareš2, Carlo Albert3  +1 moreInstitutions (3)
TL;DR: The method consists of formulating alternative models with increasing detail and flexibility and describing their systematic deviations by an autoregressive bias process, and shows that a single bias description produces reliable predictions for all models.
Abstract: Oversimplified models and erroneous inputs play a significant role in impairing environmental predictions. To assess the contribution of these errors to model uncertainties is still challenging. Our objective is to understand the effect of model complexity on systematic modeling errors. Our method consists of formulating alternative models with increasing detail and flexibility and describing their systematic deviations by an autoregressive bias process. We test the approach in an urban catchment with five drainage models. Our results show that a single bias description produces reliable predictions for all models. The bias decreases with increasing model complexity and then stabilizes. The bias decline can be associated with reduced structural deficits, while the remaining bias is probably dominated by input errors. Combining a bias description with a multimodel comparison is an effective way to assess the influence of structural and rainfall errors on flow forecasts. We investigate how a random bias process behaves as a function of model complexity.We analyze 5 model structures to simulate a stormwater system.The reduction of systematic deviations is associated with decreasing structural deficits.In this study the remaining bias is likely to be dominated by input errors.The method provides sound probabilistic predictions in a relatively efficient way.

33 citations


Cites background or methods from "Parsimonious hydrological modeling ..."

  • ...These alternative hypotheses with increasing detail aim to represent the typical levels of complexity used in urban hydrological modeling (Coutu et al., 2012; Leitao et al., 2010)....

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  • ...These parsimonious simulators (i.e. deterministic models) usually can be very rapidly calibrated, have easily identifiable parameters and can reproduce the hydrologic response of a simple system well (Coutu et al., 2012)....

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  • ...deterministic models) usually can be very rapidly calibrated, have easily identifiable parameters and can reproduce the hydrologic response of a simple system well (Coutu et al., 2012)....

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  • ...We selected a completely lumped approach as the simplest model, M1 (Coutu et al., 2012), a fullydetailed network modeling as the two most complex structures, M4 and M5, and two simplified network structures in between (Leitao et al., 2010)....

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  • ...We selected a completely lumped approach as the simplest model, M1 (Coutu et al., 2012), a fullydetailed network modeling as the two most complex structures, M4 and M5, and two simplified network structures in between (Leitao et al....

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References
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Book
01 Jan 1998
Abstract: (First edition: 1998, this reprint: 2004). This publication presents an updated procedure for calculating reference and crop evapotranspiration from meteorological data and crop coefficients. The procedure, first presented in FAO Irrigation and Drainage Paper No. 24, Crop water requirements, in 1977, allows estimation of the amount of water used by a crop, taking into account the effect of the climate and the crop characteristics. The publication incorporates advances in research and more accurate procedures for determining crop water use as recommended by a panel of high-level experts organised by FAO in May 1990. The first part of the guidelines includes procedures for determining reference crop evapotranspiration according to the FAO Penman-Monteith method. These are followed by updated procedures for estimating the evapotranspiration of different crops for different growth stages and ecological conditions.

20,634 citations


"Parsimonious hydrological modeling ..." refers background or methods in this paper

  • ...…is computed through a modified version of the Blaney–Criddle equation (e.g., Doorenbos and Pruitt, 1975): ETmax ¼ aþ b½pð0:46Tþ 8:13Þ ; ð6Þ where a and b are fitting parameters and p is the mean annual percentage of daytime hours, which varies only with latitude (Allen et al., 1998)....

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  • ...where a and b are fitting parameters and p is the mean annual percentage of daytime hours, which varies only with latitude (Allen et al., 1998)....

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Journal ArticleDOI
J.E. Nash1, J.V. Sutcliffe1Institutions (1)
Abstract: The principles governing the application of the conceptual model technique to river flow forecasting are discussed. The necessity for a systematic approach to the development and testing of the model is explained and some preliminary ideas suggested.

17,307 citations


01 Jan 1979
Abstract: A hydrological forecasting model is presented that attempts to combine the important distributed effects of channel network topology and dynamic contributing areas with the advantages of simple lumped parameter basin models. Quick response flow is predicted from a storage/contributing area relationship derived analytically from the topographic structure of a unit within a basin. Average soil water response is represented by a constant leakage infiltration store and an exponential subsurface water store. A simple non-linear routing procedure related to the link frequency distribution of the channel network completes the model and allows distinct basin sub-units, such as headwater and sideslope areas to be modelled separately. The model parameters are physically based in the sense that they may be determined directly by measurement and the model may be used at ungauged sites. Procedures for applying the model and tests with data from the Crimple Beck basin are described. Using only measured and estimated parameter values, without optimization, the model makes satisfactory predictions of basin response. The modular form of the model structure should allow application over a range of small and medium sized basins while retaining the possibility of including more complex model components when suitable data are available.

5,714 citations


Journal ArticleDOI
Keith Beven, Mike Kirkby1Institutions (1)
Abstract: A hydrological forecasting model is presented that attempts to combine the important distributed effects of channel network topology and dynamic contributing areas with the advantages of simple lum...

4,163 citations


Journal Article

3,319 citations