12nd International Conference on Urban Drainage, Porto Alegre/Brazil, 10-15 September 2011
Simulation of green roof hydrological behavior
with a reservoir model
Emmanuel Berthier1*, David Ramier1, Bernard de Gouvello2
1
CETE d’île-de-France, 12 rue Teisserenc de Bort, 78190 Trappes, France
: Université Paris-Est, Centre Scientifique et Technique du Bâtiment et Laboratoire Eau
Environnement et Systèmes Urbains, 6-8 avenue Blaise Pascal, 77455 Champs-sur-Marne
cedex 2 ; France
*
Corresponding author, emmanuel.berthier@developpement-durable.gouv.fr
2
Abstract
Extensive green roof technique (EGR) is becoming increasingly used for sustainlable
rainwater management, but tools to properly design it need still development. The work
presented herein is a first step to build a simple and robust model of green roof hydrological
behavior, in order to be used to assist in the stage of EGR design. The type of model tested
(reservoir model with the force-restore scheme in the substrate) appears suitable to reproduce
the hydrological behavior of a 146m2 EGR during one year. An original and relevant method
was used to study the sensitivity and the calibration of the model. Such model allows also to
access important information, like the variation of storage water capacity in the EGR, key
variable for runoff retention and regulation.
Keyword
Green roof ; Runoff ; Modelling
Introduction
Vegetated roofs offer a priori advantages, for best management practise (BMP), at the
building level (improving thermal and acoustic insulation, increasing durability of the seal)
and city level (improving air quality and landscape aesthetics, reducing the urban heat island,
increasing urban biodiversity). The technique also contributes to sustainable rainwater
management, helping to get closer to the natural cycle (storage and evapotranspiration).
Green roofing knows a strong growth for the past few years in France, the most widely used
technique is the Extensive Green Roof (EGR) which is less demanding in maintenance and
adaptable to new projects as well as rehabilitation projects because of its low overweight.
In order to properly design and size EGR for rainwater management, studies and research
have been conducted on their hydrological behavior. These studies focus on the amount of
runoff at the outlet of experimental roofs (see Mentens et al., 2006 for a summary and Palla et
al. 2008 ; Uhl and Schiedt, 2008 for recent studies). They show that EGR has a double effect
on runoff: (i) reduction, through storage and evapotranspiration, and (ii) regulation, with
attenuation and delay of peak discharge by retention. All EGR have followed a marked
seasonal pattern, with efficiency (runoff reduction and regulation) much more important in
spring and summer. Only a few recent studies involve modelling (Baraglioli et al., 2008, Palla
et al., 2009) but have not yet opportunities on a robust tool for extrapolating results to other
roofs and other climates.
Our work aims to develop a simple and robust model to reproduce the hydrologic behavior of
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12nd International Conference on Urban Drainage, Porto Alegre/Brazil, 10-15 September 2011
EGR ; the tool developed could be used to assist in the EGR design but also to better assess
the impact of technology on rainwater management at the city scale. The study presented
herein is a first step towards this objective, first step consisting in developing and testing a
model on an existing database. The first section presents the rainfall-runoff database used.
The second section describes the structure chosen for the model. A sensitivity analysis and
calibration of the model is developed in section three. Finally the model results are evaluated
and analyzed for the purpose in section four, before a short conclusion.
The database
Data used for this work comes from a green roof of 146m2 located in the Paris region
(France) on the CSTB building (De Gouvello, 2007). The roof structure consists of a layer of
vegetation with type Sedum (carpet laid sod) and a monolayer of substrate of a 10mm
thickness (mixture of volcanic materials, pozzolana and organic). A sterile area exists on the
perimeter, which represents 13% of the EGR area.
The experimental device includes a weather station, a rain gauge (bucket volume equivalent
to 0.2mm of water) and a runoff discharge measurement at the outlet of the roof by tipping
bucket, with a volume of 3L (equivalent to 0.02mm of water). The measurements were carried
out continuously in 2004 and 2005 at a 3min time-step. After a rigorous review and validation
of data, one year of data from March 20, 2004, 00h is adopted for the simulation work, with a
lack of data for 6 internal non-rainy periods of cumulative duration of 3h. An estimate of
potential evapotranspiration is necessary for the simulation: from the data of the weather
station on site and the nearby station of the French Weather Service, a value of potential
evapotranspiration is calculated for each day with the Penman-Monteith formula (Choisnel,
1988). These daily values are discretized at a 3min time-step by introducing the diurnal cycle.
During the study period, rainfall represented 566mm, a value close to the average annual
value, and observed runoff totalized 251mm (runoff coefficient of 44%).
Figure 1. Picture of the
146m2 CSTB EGR
Development of the model
To simulate the hydrological behavior of such EGR, different types of model could be
investigated. The first one is “physically-based” model which included the resolution of the
diffusion equation in the substrate, via the Richards equation, and adequate boundaries
condition at the atmosphere interface and at the bottom of the structure. It is the approach
retained by Palla et al. (2009) for example. The interest of this type of model is a detailed,
dynamic and rigorous representation of flows in the structure. At the opposite, this type of
model has numerous parameters: some of these parameters require generally calibration due
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12nd International Conference on Urban Drainage, Porto Alegre/Brazil, 10-15 September 2011
to a lack of knowledge and limiting measurements. The well-known problem of overparameterization and equifinality for physically-based model appears (Beven, 2006). To
develop a robust model useful on other climate and other EGR ungauged, this is a real limit.
On the other hand, reservoir model which could be qualified of global or conceptual, are
known to be robust because they need less parameters. The force-restore scheme has been
used to represent water transfer in soil layer: its application on large scale catchment with
limited database has been successful (Noilhan and Planton, 1989). In this context, our study
focused on the development of a reservoir model with the force-restore scheme to reproduce
the hydrological behavior of the CSTB EGR.
The model consists of two reservoirs, one for the vegetation layer and the other for the
substrate layer (Figure 2). Each reservoir stores water and exchanges fluxes at its limits.
Calculation of the different variables, at each time-step t (index i), are sum up hereafter (see
Table 1 for the variables and parameters signification):
Flow calculation at the time-step i, in function of the storage at the time-step (i-1):
if P(i)=0
if Sveg(i-1)>0,
Eveg(i)=min[Sveg(i-1),ETP(i)] ; Esub(i)=0 ;
else
Eveg(i)=0 ; Esub(i)=min[ETP(i),Ssub(i-1)-Csub_wilt].LAIveg/3 ;
else P(i)>0
Eveg(i)=Esub(i)=0 ;
Isub(i)=max[P(i)-(Cveg-Sveg(i-1)),0] ;
R(i)=max[Ksub/(dsub.t).(Ssub(i-1)-Csub_fc),0]
Calculation of the new storage for the time-step i:
Sveg(i)=Sveg(i-1)+P(i)-Eveg(i)-Isub(i) ;
Ssub(i)=Ssub(i-1)+Isub(i)-Esub(i)-R(i) ;
Figure 2. Vertical scheme of the CSTB EGR and of the two reservoirs model developed
It is assumed that during rainy period, evapotranspiration is null. Two key parameters are
important for the hydrological behavior of the substrate: (i) if the stored water is less than the
field capacity Csub_fc, then there is no free runoff toward the substrate bottom, and (ii) drying
the substrate by evapotranspiration takes place as the stored water remains above the wilting
point of vegetation Csub_wilt.
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12nd International Conference on Urban Drainage, Porto Alegre/Brazil, 10-15 September 2011
Table 1. Signification and values of variables and parameters used in the model
1
Name
Unit
P
ETP
mm
mm
Sveg
Cveg
LAIveg
Eveg
mm
mm
mm
dsub
Isub
Ssub
Csub max
Csub fc
Csub wilt
mm
mm
mm
mm
mm
mm
Ksub
mm/s
Esub
mm
R
mm
Designation
Entry data
Observed rainfall
Potential evapotranspiration
Vegetation layer
Storage in the vegetation layer
Storage capacity of the vegetation
Leaf Area Index
Evaporation from the surface of the vegetation
Substrate layer
Substrate thickness
Infiltration in the substrate layer
Storage in the substrate layer
Storage capacity of the substrate layer
Field capacity of the substrate layer
Wilting point of the substrate layer
Parameter for the dynamic of the gravitational
drainage in the substrate layer
Evapotranspiration from the substrate layer
Output variable
Runoff at the outlet of the EGR
Value1
0.2
2.5 [0.2-5]
100
35 [25-45]
20 [10-25]
5 [1-10]
1.6 10-3 [0.1-10 10-3]
: for model parameter only; for parameter to be calibrated, the range of possible values is added in brackets
Model’s parameterization following sensitivity and calibration studies
The model is applied continuously throughout the selected period at the time-step of
15s: this low value of time-step allows a simplified temporal discretization. The input data,
available at the 3min time-step, are averaged every 15s. For analysis, the simulated results are
expressed at different time-step.
Calibration proves useful because of certain unknown parameters and of the limited
observations (focusing only on runoff discharge). After an examination of the information
available from the CSTB EGR and from the literature, 5 parameters need to be calibrated:
LAIveg, Csub_max, Csub_fc, Csub_wilt and Ksub. The range of their possible values has been defined
from physical consideration, as the values for the non-calibrated parameters (see Table 1).
Calibration is carried out using a multicriteria method, in conjunction with a sensitivity study.
This method has been presented in detail by both Gupta et al. (1999) and Bastidas et al.
(1999). The aim of this method is to conduct a set of simulations using parameters randomly
chosen from the range of their possible values (5000 simulations are performed in our case).
The quality of these simulations has been estimated on runoff discharge with the well-known
Nash and Budget criteria. The values of these criteria allow splitting the simulation into two
subsets according to Pareto rank (Yapo et al., 1998): one subset of ‘acceptable simulations’,
i.e. simulations for which the two criteria are considered ‘good’, and the other subset
regrouping the ‘unacceptable simulations’. From these two subsets, the cumulative
distributions of each parameter are then computed. A parameter will be considered sensitive if
a significant difference can be identified between the distribution of the ‘acceptable
simulations’ and the ‘unacceptable simulations’. Figure 3 contains these distributions for the
five parameters tested and shows that only LAIveg and Ksub are sensitive.
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12nd International Conference on Urban Drainage, Porto Alegre/Brazil, 10-15 September 2011
Figure 3. Cumulative distribution of the five parameters tested in the sensitivity study:
dashed line is for the entire simulation, continuous line only for the ‘acceptable simulations’
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12nd International Conference on Urban Drainage, Porto Alegre/Brazil, 10-15 September 2011
Model calibration stems from this sensitivity study: the subset of ‘acceptable simulations’
provides the best parameter set according to the selected criteria and the final values of the
various parameters are chosen from among the subset of ‘acceptable simulations’. The value
adopted for LAIveg is situated in the middle of the possible range value (2.5) and the value for
Ksub is in the first part of the possible range value (1.6 10-3 mm/s). For the other non-sensitive
parameters, a value in the middle of the possible range is adopted (see Table 1 for the final
value).
Performance and results of the model
The performance of the calibrated model is acceptable: Nash criterion reaches the
value of 0.77 (good value is considered from 0.80) and budget criterion is close to zero (6%).
The scattergram between observed and simulated runoffat a 1hour time-step is satisfactory
(Figure 4) with a determination coefficient, R2, of 0.85: it appears difference for some low
values, the model slightly overestimates the middle values and underestimates the few highest
values.
Figure 4. Scattergram between observed and simulated runoff
(1h time-step and for the whole year of simulation)
Figure 5 illustrates these results during a selected rainy period of about 17 days during fall
season. It can be observed a good agreement between observed and simulated runoff
discharges. The model encounters difficulties to reproduce the beginning of low rain event,
the simulated runoff being over-estimated. The tail end of hydrograph is also slightly underestimated by the model. To improve this result, a linear reservoir model has been tested to
better represent the transfer of runoff through the 146m2 green roof. Despite the attempt of
calibration of the time-response parameter, the result are not convincing (not shown). It also
can be noticed that the observed runoff value are in increment of 0.02l/s about, which
corresponds to a tipping of the 3L bucket: this value is a bit high for representing the runoff
dynamic during usual rain event.
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12nd International Conference on Urban Drainage, Porto Alegre/Brazil, 10-15 September 2011
Figure 5. Comparison of the observed and simulated runoff discharged at a 3min time-step
during a fall period (duration of 17day about)
Such model allows also to have information on the hydrologic behavior of the EGR, and
especially the variation of water storage in the substrate layer, key variable in perspective of
runoff reduction and regulation. The variation of water amount stored in the substrate during
the year is represented in Figure 6.a: for the first part of the year, the substrate is entirely
unsaturated during the dry periods and the storage is equal to the wilting point value of 5mm.
In contrary, during the second part of the simulation, rainier, substrate storage never reaches
the unsaturated condition and stays all time above 10-15mm. It has to be noticed that the
maximum storage value of 35mm is never reached. Figure 6.b shows the histogram of the
water amount available for storage in the substrate for the whole year: for almost one third of
the year, the water amount available for storage in the substrate is around 30mm, which is an
interesting value for runoff reduction and regulation. At the opposite for 40% of the year, the
available storage is less than 18mm.
(a)
(b)
Figure 6. (a): water amount stored in the substrate layer during the simulated year; (b):
histogram of the water amount available for storage in the substrate during the year simulated
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Conclusion and outgoing
The work presented herein is a first step to develop a robust model of green roof hydrological
behavior. After a stage of validation and calibration, the model tested (reservoir storage model
with the force-restore scheme in the substrate layer) presents rather good performance: in
comparison with an one-year rain-runoff database on a 146m2 EGR, the Nash criterion is 0.77
at a 3min time-step and Budget criterion is +6%. This model allows also to study the variation
of water storage capacity and our results show that the maximum water storage capacity is
never reached. Thus, such a model seems able to be used to assist in the design of EGR in the
aim of rainwater management.
In term of prospects, the actual limit of the work is certainly the limited database used to
develop and calibrated the model. If the objective is to develop a robust model allowing
extrapolation to other EGR structures and climates, the work must take into account more
important database in term of duration, EGR structure, climate, and also measured variables
(especially water storage in the EGR). It is the subject of an important experimental ongoing
program, called TVGEP.
References
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Emmanuel Berthier