Modelling of green roof hydrological performance for urban drainage applications

Journal of Hydrology xxx (2014) xxx–xxx

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Journal of Hydrology

journal homepage: www.elsevier .com/ locate / jhydrol

Modelling of green roof hydrological performance for urban drainageapplications

http://dx.doi.org/10.1016/j.jhydrol.2014.10.0300022-1694/� 2014 Elsevier B.V. All rights reserved.

⇑ Corresponding author. Tel.: +45 4525 1432.E-mail address: [email protected] (L. Locatelli).

Please cite this article in press as: Locatelli, L., et al. Modelling of green roof hydrological performance for urban drainage applications. J. Hydrol.http://dx.doi.org/10.1016/j.jhydrol.2014.10.030

Luca Locatelli a,⇑, Ole Mark b, Peter Steen Mikkelsen a, Karsten Arnbjerg-Nielsen a, Marina Bergen Jensen c,Philip John Binning a

a Technical University of Denmark, Dept. of Environmental Engineering (DTU Environment), Miljoevej, Building 113, 2800 Kgs Lyngby, Denmarkb DHI, Agern Allé 5, 2970 Hørsholm, Denmarkc University of Copenhagen, Rolighedsvej 23, 1958 Frederiksberg, Denmark

a r t i c l e i n f o

Article history:Received 20 December 2013Received in revised form 1 October 2014Accepted 11 October 2014Available online xxxxThis manuscript was handled byKonstantine P. Georgakakos, Editor-in-Chief,with the assistance of Michael Bruen,Associate Editor

Keywords:Green roofsWater Sensitive Urban DesignModellingRainfall–runoffRetentionDetention

s u m m a r y

Green roofs are being widely implemented for stormwater management and their impact on the urbanhydrological cycle can be evaluated by incorporating them into urban drainage models. This paper pre-sents a model of green roof long term and single event hydrological performance. The model includes sur-face and subsurface storage components representing the overall retention capacity of the green roofwhich is continuously re-established by evapotranspiration. The runoff from the model is describedthrough a non-linear reservoir approach. The model was calibrated and validated using measurementdata from 3 different extensive sedum roofs in Denmark. These data consist of high-resolution measure-ments of runoff, precipitation and atmospheric variables in the period 2010–2012. The hydrologicalresponse of green roofs was quantified based on statistical analysis of the results of a 22-year(1989–2010) continuous simulation with Danish climate data. The results show that during single events,the 10 min runoff intensities were reduced by 10–36% for 5–10 years return period and 40–78% for0.1–1 year return period; the runoff volumes were reduced by 2–5% for 5–10 years return period and18–28% for 0.1–1 year return period. Annual runoff volumes were estimated to be 43–68% of the totalprecipitation. The peak time delay was found to greatly vary from 0 to more than 40 min dependingon the type of event, and a general decrease in the time delay was observed for increasing rainfall inten-sities. Furthermore, the model was used to evaluate the variation of the average annual runoff from greenroofs as a function of the total available storage and vegetation type. The results show that even a fewmillimeters of storage can reduce the mean annual runoff by up to 20% when compared to a traditionalroof and that the mean annual runoff is not linearly related to the storage. Green roofs have therefore thepotential to be important parts of future urban stormwater management plans.

� 2014 Elsevier B.V. All rights reserved.

1. Introduction

Urbanization significantly affects the natural landscape turninggreen areas into built environment. This process creates newimpervious surfaces such as roofs, roads, cycling lanes, sidewalks,public squares and parking areas which modify the natural watercycle. Impervious areas increase stormwater runoff peaks and vol-umes and reduce the time delay between peak rainfall and peakrunoff when compared to natural areas (Bengtsson, 2005). Currenturban drainage systems have limited capacity to deal with floodingand climate change will increase the risk of flooding from sewers inurban areas (Larsen et al., 2009; Madsen et al., 2009).

Green roofs are one of the many WSUD (Water Sensitive UrbanDesign; the concept of water sensitive cities was presented byWong and Brown, 2009), LID (Low Impact Development), SUDS(Sustainable Urban Drainage Systems), LIUDD (Low Impact UrbanDesign and Development) techniques aimed to improve storm-water management and address future climatic challenges. Greenroofs have the great advantage of not using new spaces; in factthey can in some cases be retrofitted onto existing traditionalrooftops. The roof area in urban residential areas can be as highas 40–50% of the total impervious area (Palla et al., 2009;Lindblom et al., 2011; Vezzaro et al., 2012). Green roofs are claimedto reduce the risk of urban flooding and to re-establish a morenatural water balance (Bengtsson et al., 2005; VanWoert et al., 2005)and to reduce water and contaminant loads to sewer systems(Buccola and Spolek, 2011).

(2014),

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2 L. Locatelli et al. / Journal of Hydrology xxx (2014) xxx–xxx

The German Guidelines for the Planning, Construction andMaintenance of Green Roofing (FLL, 2008) have suggested a classi-fication of green roofs into two different categories:

� Intensive green roofs have thick soil layers (>15 cm) with largeplants and moderate slopes, these are heavier and require reg-ular watering and fertilization.� Extensive green roofs can have soil covers with a thickness of as

little as few cm and vegetation which requires hardly any main-tenance. When the soil layer is thin and the weight of the greenroof is limited, extensive green roofs can often be placed onexisting buildings without structural reinforcement and theycan reach slopes up to 40–45% (FLL, 2008).

From the 1990s green roofs have become common practice inseveral countries such as Austria, Switzerland and particularly Ger-many where green roofs reached 13% of the flat roofs in 2003(Herman, 2003). Some countries have also released guidelines forimplementation of green roofs like the UK, Germany, United States,New Zealand, Australia, etc.

Green roof performance regarding stormwater managementmay vary among geographic regions due to varying climate, pre-cipitation patterns, building practices and green roof materials.During rainfall events the most important hydrologic mechanismsare the interception of rain by the vegetation layer, infiltration andretention/detention in the soil substrate, and retention/detentionin the drainage layer. Any water in excess to the storage capacitywill be drained into an outlet and during non-rainy periods waterstored in the green roof is lost through evapotranspiration.

Green roofs reduce stormwater runoff compared to conven-tional roofs due to water retention and subsequent evapotranspira-tion. Volume retention depends on rainfall intensity distribution,the initial moisture conditions and green roof characteristics (layerthickness, slope, materials, etc.), including the ability of the greenroof to dry up. Volume retention also contributes to peak attenua-tion and delay. The following examples are based on observationsfrom experimental sites. Experimental sites in Germany showedthat the annual runoff from intensive green roofs was 15–35% ofthe annual rainfall, whereas the performance of extensive roofs isreported to be 20–75% of the annual rainfall (Mentens et al.,2006). In Sweden the runoff observed from thin extensive greenroofs was 46% of the annual precipitation (Bengtsson et al.,2005). In England Stovin et al. (2012) reported an overall retentioncapacity of green roofs of 50%. VanWoert et al. (2005) observed a60% retention in Detroit (Michigan), DeNardo et al. (2005) 45% inPennsylvania, Voyde et al. (2010) 66% in Auckland (New Zealand),Monterusso et al. (2004) 49% and Carter and Rasmussen (2006)78% in Athens (Georgia).

Volume detention, defined as temporary storage and subse-quent release, results in additional attenuation and time delay ofrunoff peaks. Volume detention takes place when the initial mois-ture content is at field capacity (micro- and mesosized pores arewater filled) and additional water percolates through macropores.Peak attenuation and delay due to detention depend on the rainfallintensity distribution and the green roof characteristics, includinglayer thickness, slope, poresize distribution, tortuosity, etc. of thematerials. Observed data recorded from experimental green roofshave been reported by several researchers. Peak runoff delay ofvegetated roofs was found to vary significantly, for the majorityof the observed rain events peak delay was found to be between0 and 30 min when compared to traditional roofs (VanWoertet al., 2005; Carter and Rasmussen, 2006; Simmons et al., 2008).Getter et al. (2007) observed only minimal runoff delay andVillarreal and Bengtsson (2005) found peak delays to be around1 min. DeNardo et al. (2005) showed considerable peak reductionsfor low intensity rains. Stovin et al. (2012) observed a mean peak

Please cite this article in press as: Locatelli, L., et al. Modelling of green roof hyhttp://dx.doi.org/10.1016/j.jhydrol.2014.10.030

flow reduction of 60% for rain events of more than 22 mm accumu-lated rain. Moran et al. (2005) reported 85% peak reductions.

Several models have been developed for the hydrological per-formance of green roofs. Hilten et al. (2008) used the soil moisturesoftware HYDRUS-1D to simulate the single events runoff responsefrom green roofs and validated his results with data collected inGeorgia (USA). Palla et al. (2009) used SWMS_2D based on Richards’equation to simulate the variably saturated conditions within atypical green roof during individual storm events and validatedthe model against data collected in Genoa (Italy). Zhang and Guo(2013) presented a physically based analytical probabilistic modelto evaluate the average long term hydrological response of greenroofs. Villarreal and Bengtsson (2005) analyzed single events run-off from an extensive green roof in Sweden and derived a unit hyd-rograph. Zimmer and Geiger (1997) proposed a linear/non-linearreservoir model to compute the runoff from an experimental greenroof under constant rainfall intensities. Kasmin et al. (2010) used asimple conceptual model, with the runoff described by a non-linearreservoir, in order to evaluate the performance of different meth-ods for modeling evapotranspiration. Sherrard and Jacobs (2012)presented a five parameter water balance model with a daily timestep in order to reproduce the volume runoff on a daily and annualbasis. Jarret and Berghage (2008) presented one model for annualwater balance and one for single event runoff. Stovin et al.(2013) presented a model to quantify long term runoff using con-tinous simulation; results from the model showed volumetricretention values between 0.19 (cool, wet climate) and 0.59 (warm,dry climate) depending on local climate conditions in the UK.

Other studies have derived empirical runoff relations fromexperimental data. Mentens et al. (2006) gathered experimentaldata of green roof hydrological performance on seasonal andannual bases from 18 different publications in Germany.Bengtsson (2005) derived Intensity–Duration–Frequency curvesfor rainfall–runoff prediction from an extensive green roof in Mal-mo in Sweden. Moran et al. (2005) derived the rational coefficientbased on green roof data from North Carolina (USA). Carter andJackson (2007) used the Curve Number method for predictinggreen roof performances at large case studies in Georgia (USA)and Getter et al. (2007) derived the curve number for the studiedgreen roof in Detroit (USA).

A review of available WSUD models was provided by Elliott andTrowsdale (2007). The literature review shows that modelingapproaches vary, from models for single event runoff to conceptualmodels applied to simulate distributed urban runoff. None of thesestudies have presented a single and low computationally demand-ing model that can continuously simulate both single events withfine time resolution and the annual water balance of single greenroofs. The single event hydrological response of green roofs ishighly affected by initial moisture conditions which depends onevapotranspiration rates and can be estimated from a continuoussimulation; at the same time the long term performance is influ-enced by single event runoff and evapotranspiration rates. Thusit is relevant to develop a model that can continuously simulateboth single events and long term response. This paper is basedon the preliminary model results presented in the conferencepaper of Locatelli et al. (2013).

The first aim of this study is to present a simple conceptualmodel for the hydrological performance of green roofs that canbe integrated into urban drainage models for evaluating theimpacts of implementing green roofs at a large scale (e.g. modelingof flood mitigation potential; modeling the potential for reductionof combined sewage volume and combined sewer overflow). Lowcomputational costs and fine time resolutions are thus a require-ment. Many of the previously developed green roof models suchas SWMS-2D and HYDRUS have a high computational cost and soare not suitable for large scale urban water modelling.

drological performance for urban drainage applications. J. Hydrol. (2014),


L. Locatelli et al. / Journal of Hydrology xxx (2014) xxx–xxx 3

The approach used here is based on a deterministic lumpedrainfall–runoff conceptual model applied to a single green roof.The model was calibrated and validated against observed runofffrom three different extensive green roofs installed in Denmark.The second aim of the study is to simulate the hydrological perfor-mance of green roofs in the long term. Statistical analysis of contin-uous simulation results was applied to determine the single eventpeak time delay, peak and volume reductions and mean annualrunoff for a 22 year simulation period exposed to Danish rainfalland climate data. The third aim of the study is to analyze the var-iation of the mean annual runoff as a function of storage capacityand crop coefficient.

The modeling approach developed in this paper is similar tothat employed in several other classical hydrological models, suchas the NAM model of DHI (1999) and Gustafsson et al. (1999). Theemphasis here, is therefore not on presenting a novel hydrologicalmodel. Rather, it is on presenting and testing a modeling approachfor green roofs that is simple, computationally effective and capa-ble of simulating the response to individual rainfall events andlong term runoff. A comparison between the actual model and anexisting rainfall–runoff model included in the commercial softwareMIKE-URBAN was made.

2. Materials and methods

2.1. The experimental data

Three different extensive green roofs were installed in Denmarkand runoff from each test setup was measured. Data from theseinstallations were provided by the different partners. Denmarkhas a cold climate, without a dry season (Peel et al., 2007) and withan average precipitation of 600–700 mm/year (Frich et al., 1997).The first green roof (GR1, Fig. 1 left) is located in the city of Odense.

GR1

Fig. 1. The 3 experimental extensive green roofs (GR1, GR2 and GR3). GR2 and GR3 are cmedia.

Table 1Roofs’ characteristics.

GR1 GR2

Location Odense CopenhagenArea (m2) 9 20Slope (�) 10 4.3Overall thickness (mm) 80 70Vegetation type Sedum and herbs Sedum and herbsSaturated weight (kg/m2) 130 55Drainage (mm) 40 40Drainage material Mineral wool Exapanded foamSubstrate depth (mm) 40 30Substrate material Soil Crushed clay, medium-fineWater holding capacity (l/m2) 53 31

a Drainage holes are placed 1 cm above the bottom.


It has a 3 � 3 m2 surface, east oriented, a slope of 10� and sedumvegetation growing on a 40 mm layer substrate drained by a40 mm of mineral-wool. The roof has a maximum fully wet weightbetween 80 and 130 kg/m2. Runoff data from this roof are availablefrom August 2010 to May 2012. The second green roof (GR2, Fig. 1right) has Sedum vegetation growing on a 30 mm substratedrained by a 40 mm drainage layer made of high porosity oxy-foam mats. This roof has a water saturated weight of 55 kg/m2.The third green roof (GR3, Fig. 1 right) has sedum growing on60 mm high plastic trays filled with substrate soil and drainedthrough raised holes, placed approximately 10 mm above the bot-tom. This has a water saturated weight of 45 kg/m2. A referencetraditional roof was also installed. The latter 3 roofs are connectedto each other and have a surface area of 20 m2 each and slope of4.3� oriented to the south-east and they are located in Copenhagen.Runoff data are available from March 2011 to February 2012. Thecharacteristics of the different roofs are summarized in Table 1.

Each roof has a distinctly separate drainage and runoff cannotmigrate among them. Runoff from the roofs was collected in sepa-rated tanks where the water depth was measured by pressuretransducers to provide a continuous record of runoff. Rainfall wasmonitored using tipping buckets installed at the test sites at a dis-tance of <50 m from the roofs. Meteorological data (wind speed, airtemperature, relative humidity, global radiation and atmosphericpressure) were collected from the nearest available meteorologicalstations which were located 10 km away for one green roof (GR1)and 3 km away for the other two green roofs (GR2 and GR3). Therainfall data were logged by tipping bucket rain gauges with abucket volume of 0.2 mm and runoff data were recorded at1-min time intervals while meteorological data were recordedevery 1-h. Usually small distances (<1 km) are considered to beacceptable for weather stations; however given the lower spatialvariation of hourly averaged climate variables we assume thatthe actual distances are acceptable. Single rain events were defined

GR2

GR3

overed by the same vegetation but have different substrate thickness and drainage

GR3 Reference roof

Copenhagen Copenhagen20 204.3 4.360 –Sedum and herbs –45 –a –Holes in plastic trays –60 –

peat, compost Crushed clay, medium-fine peat, compost –No data –



Surface storage

Subsurface storage

Rmax

PET

h

Peff

R

S

Deten�on storageQssDmax

k1·(h-Dmax)n1

Runoff

Smax

k·hn

ET

ET

Overland flow

a·Rm

axθWP

θFC

θmax

Dmax

Rmax

Soil moisture in the porous media

Fig. 2. Conceptual mass balance model of a green roof.

Fig. 3. Composite scaled sensitivities of the model parameters for the water balance and peak runoff. Long term simulation (left) and a selected single event simulation(right).


as rainfall periods separated by more than an hour. One-hour inter-event period is the definition adopted in Denmark for single rainevents based on the considerations of Arnell et al. (1984). Singleevent runoff was defined to begin with the corresponding rainevent and to end at the beginning of the following rain event. Thisdefinition might cause some runoff events starting with non-zerorunoff values resulting in single event ‘runoff volume > rainfall vol-ume’. This is not considered a problem in the present analysis sincethe observed green roofs cease runoff within 1–2 h meaning thatafter 1 h most of the water is drained. Results from Fig. 8 (Right)show only couple of events with ‘runoff volume > rainfall volume’and the difference in volume is approximately 1 mm.

Rainfall data were corrected according to Allerup et al. (1998) totake into consideration the influence of wind speed, rain intensity,wetting and sheltering effects of the rain gauge.

2.2. The model

A deterministic lumped rainfall–runoff conceptual model wasused. Lumped conceptual models (grey box models), rather thanphysically distributed (white box models) or analytical models(black box models), require lower computational costs and canhave the advantage of easier interpretation of model parameters.The conceptual model divides the green roof into 3 different waterstorages connected to each other and is shown in Fig. 2. A model


based on the mass balance equation for the system was imple-mented in MATLAB. Some of the model parameters can be esti-mated from physical data (Rmax, Smax, Kc), but final calibration tohydrological data is needed.

The mass balance for each of the storages is described as:

dsdt¼ qin � qout ð1Þ

where s is the storage depth [mm], qin and qout are the inflow andoutflow intensities normalized by the roof area [mm/min] and t istime [min].

Rainfall intercepted by the vegetation layer of the green roof isreferred to as surface storage and Smax (see Fig. 2) indicates its max-imum capacity. The capacity of the surface storage is continuouslyre-established through evaporation. When the maximum surfacestorage Smax is exceeded, the effective precipitation Peff is drivenas infiltration into the subsurface storage.

The volume of water that can be stored (retained) both in thegreen roof substrate and in the drainage layer (and eventuallyother built-in layers) is referred to as subsurface storage R. Thedrainage layer is normally constructed to ensure that the roofhas sufficient underdrain and only few commercial productsintroduce storage (retention) elements into the drainage board.The drainage layer of one green roof (GR1) in this study is madeof mineral wool, which has a high retention capacity, and for



Fig. 4. Rainfall–runoff intensity from the 3 extensive green roofs during three different rain events within the calibration period.

Fig. 5. Simulated and observed accumulated rainfall–runoff depth for the summer period (left) and for the winter period (right). Data from GR1.

Fig. 6. Simulated 10 min peak intensities per event as a function of the return period (left). Simulated 10 min peak reductions per event as a function of different returnperiods (right).


this reason we decided to keep the drainage layer to account forthe subsurface storage. Rmax represents the maximum capacity ofthe substrate and drainage layer (and other built-in layers)together; this can be estimated as the difference between thewater content at field capacity hFC (after drainage, macroporesempty) and the permanently retained water content hWP

(comparable to permanent wilting point, mesopores empty).R = 0 represents the permanently retained moisture in the greenroof (it does not correspond to oven dry conditions) and mayvary in response to atmospheric variables. The water contentin the subsurface storage is continuously reduced by evapotrans-piration. From the subsurface storage Qss is diverted into thedetention storage.


The detention storage temporarily stores water up to a maxi-mum volume Dmax. The detention storage represents the excesswater that cannot be held against gravity by the green roof andtherefore will runoff as subsurface flow through the drainage layer.Theoretically the maximum capacity of the detention storage Dmax

cannot exceed the difference between the saturated water contentand the water content at field capacity. When the maximum capac-ity Dmax is exceeded saturation overland flow runoff occurs. Therunoff from the detention storage is described by the non-linearreservoir method:

Runoff ¼ k � hn; h � Dmax

Runoff ¼ k � Dnmax þ k1 � ðh� DmaxÞn1

; h > Dmax

ð2Þ



Fig. 7. Simulated single event runoff volume as a function of the return period (left). Simulated single event runoff volume reductions as a function of different return periods(right).

Fig. 8. Simulated single event intensity as a function of the 10 min rainfall return period (left). Simulated single event runoff volume as a function of the rainfall volumereturn period (right).


where n, k are the routing parameters for subsurface runoff throughthe drainage layer and n1, k1 are the routing parameters for satu-rated overland flow. This method was proposed by Zimmer andGeiger (1997) for the design of multilayered infiltration systems.Due to the high conductivity of the subsurface materials all the rainis assumed to infiltrate and percolate vertically to the drainagelayer. However the water can accumulate in the system up to a cer-tain volume beyond which saturated overland flow occurs.

Evaporation and transpiration continuously restore the capacityof all the storages. Evaporation firstly acts in the surface storage, ifthe surface storage falls below zero then water is withdrawn fromthe detention storage and when the detention storage is emptyevapotranspiration takes place in the subsurface storage. The modelassumes no evapotranspiration during rain events and it does notdistinguish between evaporation and transpiration.

The actual ET rates are calculated based on the FAO Penman–Monteith equation (Allen, 1998):

ET ¼ ET0 � Kc � F ð3Þ

where Kc is the crop coefficient (vegetation coefficient), F is thereduction factor due to water shortage and ET0 is the referenceevapotranspiration. The input parameters for ET0 are the observedwind speed, atmospheric pressure, relative humidity, global radia-tion and air temperature. The clear sky solar radiation used in thecalculation of ET0 (Allen, 1998) was corrected according to


Dingman (2002) in order to take the roof slope and orientation intoconsideration.

The crop coefficient Kc depends on the type of vegetation andtakes into account the differences in stomatal resistance of the leafand aerodynamic resistance through the body of the plant (Allen,1998). The reduction factor F accounts for environmental stress.In the actual model evapotranspiration rates are reduced due towater shortage. The reduction factor F is equal to 1 for both thesurface and detention storages, whereas for the subsurface storageF = 1 for a water content R > w Rmax and then decreases linearly tozero between R = w Rmax and the minimum water content R = 0(0 6 F 6 1). The quantity w Rmax can be interpreted as the watercontent at the stomatal closure point.

The flow recharging the detention storage depends on the fillingratio of the subsurface storage.

Qss ¼ PeffR=Rmax�a

1�a ; R=Rmax > a

0; R=Rmax � a

(ð4Þ

where a Rmax is the threshold water content above which waterstarts draining from the subsurface storage (0 6 a < 1). When thesubsurface storage is full then Qss = Peff. The parameter a is a thresh-old value that changes the hydrograph at the beginning of the rainevent by allowing runoff from the green roof even if the subsurfacestorage still has some capacity.




2.3. Calibration, validation and sensitivity analysis

The model parameters for the green roofs were determined byinverse modeling with a calibration period of approximately2–3 months during the summer period. The calibration procedureused the Shuffled Complex Evolution Metropolis algorithm (Vrugtet al., 2003).

Each of the three extensive green roofs was calibrated accordingto three different objectives:

(1) Peak runoff. The objective function to be minimized was thesum of the squared peak errors. The peak error was calcu-lated for each event as the difference between the observedand the computed peak runoff. Only runoff peaks above4 mm/h were taken into account. The threshold of 4 mm/hwas chosen in order to have at least 4–6 peaks to be cali-brated and still avoiding the influence of small peaks.

(2) Water balance. The objective function to be minimized wasthe sum of the squared water balance error where the errorwas defined to be the difference between the accumulatedobserved and computed runoff. The water balance errorwas calculated for periods with durations of approximately7 days each.

(3) Peak runoff and water balance. The objective function to beminimized included peak runoff and water balance togetherwith different weights and was defined as:

Table 2

XNc

i¼1

wi

m

Xm

t¼1

ðCobsði;tÞ � Csimði;tÞÞ2

r2ði;tÞ

" #ð5Þ

where Nc is the number of objectives considered (in this case Nc = 2,peak runoff and water balance), m is the number of observations foreach objective, Cobs are the observed values, Csim are the simulatedvalues, r is the standard deviation of observations and wi are theweighting parameters.

The reference hard roof was also calibrated using the green roofmodel. Subsurface and detention storage capacities were set tozero (Rmax = Dmax = 0).

The model was validated for each of the three extensive greenroofs and the validation period (3–5 months) made use of all theremaining observation data (data out of the calibration and winterperiods). The standard deviation of the peak error and water bal-ance error during the validation period was calculated.

Sensitivity of the model parameters was analyzed using Com-posite Scaled Sensitivities (CSS) (Hill, 1998). The CSS were calcu-lated considering four different objectives: (1) peak flows duringa single event simulation; (2) runoff volume during a single eventsimulation; (3) peak flows during a long term simulation; (4) run-off volume during a long term simulation.

Calibration results.

Calibration objective k Rmax Kca a Dmax

(mm min)�1 (mm) – – (mm)

GR1Peaks 0.0038 21.2 0.93 0.65 10Water Balance 0.0038 20.4 0.88 0.65 100.60 Peaks; 0.40 WB 0.0040 21.5 0.89 0.53 10

GR2Peaks 0.018 11.0 1.44 0.85 4.2Water Balance 0.018 8.8 0.80 0.85 4.20.60 Peaks; 0.40 WB 0.022 9.7 0.85 0.85 4.2

GR3Peaks 0.065 9.7 0.83 0.90 3.5Water Balance 0.065 10.6 0.90 0.90 3.50.60 Peaks; 0.40 WB 0.075 10.8 0.87 0.90 3.5

a The crop coefficient was calibrated within the period April–October.

2.4. Long term simulations

The long term simulations were based on rainfall and climatedata from Copenhagen in the period 1989–2010. The rainfall datawere taken from a tipping bucket rain gauge in Copenhagen andcorrected as described in Section 2.1. The rainfall data wererecorded for every 0.2 mm of rain. Global radiation, wind speedand temperature were obtained with a daily time step from theDanish national climate grid data (Scharling, 1999,2001). Atmo-spheric pressure and relative humidity were taken from a measur-ing station in Copenhagen. The clear sky solar radiation in thecalculation of ET0 was corrected as explained in Section 2.2. Itwas assumed that the uncertainty in the model predictions is thesame as the uncertainty calculated for the validation period.


The return period T [years] was calculated using the Weibull(1939) plotting position formula:

T ¼ yþ 1r

ð6Þ

where y is the duration of the time series in years and r is the rankof the observed event.

2.5. Annual runoff as a function of storage capacity and cropcoefficient

The variation of the annual runoff as a function of the totalgreen roof retention capacity (total storage capacity = surface stor-age + subsurface storage; detention storage is not considered sinceit is low sensitive parameter (see Fig. 3) for annual runoff) andfor different crop coefficients Kc was simulated. The total storagecapacity was assumed to vary between 2.8 and 40 mm and the cropcoefficient Kc = 0.60; 0.89; 1.20; 1.50.

2.6. Model with MIKE URBAN

The single event and long term hydrological response from thegreen roof (GR1) was also computed using the commercial soft-ware MIKE URBAN (Andersen et al., 2004; DHI, 2009). Mike Urbanincludes a model referred to as NAM (Nedbør-Afstrømnings-Model.In English: rainfall–runoff model), which was developed to computethe runoff from pervious areas and it is furthermore used to simu-late infiltration-inflow to urban drainage systems. It is a determin-istic lumped model with linear reservoirs and threshold functionsthat allow to simulate a range of phenomena. A detailed descrip-tion of the NAM model and its parameters was given by Nielsenand Hansen (1973) and in the manual DHI (1999). The input datarequired for the NAM model are ET rates [mm/day], rainfall inten-sities [mm/min] and the horizontal projected area of the green roof[m2]. The input ET rates had an hourly time step and were obtainedfrom Equation 3. The time step for the NAM model was set to 1 minin order to have a direct comparison to the actual model approach.The chosen simulation period was the month of June 2011. TheNAM model input parameters were calibrated by trial and error.

3. Results and discussion

3.1. Calibration, validation and sensitivity analysis

The calibrated values for the reference roof are Smax = 0.5 mm,k1 = 0.215 mm�1min�1 and n1 = 1.67. The results of the calibrationfor the three extensive green roofs are given in Table 2. The over-land flow from the green roofs was assumed to have the same




routing parameters (k1 and n1) as the reference hard roof. Duringthe observation period few events with overland flow occurredfrom GR2 and GR3, and no overland flow was registered fromGR1. Overland flow was assumed to occur when the observed run-off hydrograph suddenly jumped to the same intensity as theincoming rainfall. The value of Dmax for GR1 was thus assumed tobe just above the maximum simulated detention height duringthe calibration period; this assumption was made in order to avoidoverestimation of the parameter Dmax which could result in higherpeak reductions (simulations will be in the safe side). The Dmax

parameter for roofs GR2 and GR3, was calibrated for a couple ofevents. The parameters k = 2, Smax = 0.8 and w = 0.5 were fixeddue to high parameter correlation. The retention storages Smax

and Rmax were found to be highly correlated meaning that theycould be simplified into a single storage compartment; howeverfor a more flexibility of the model (i.e. one could have a functiondescribing the seasonal variation of the interception storage) theywere kept separated. The calibrated values of Dmax are in the samerange as those reported by Villarreal (2007) for green roofs with30 mm substrates. The sensitivity analysis (Fig. 3) shows that inthe long term hydrological performance (continuous simulations)the most sensitive parameters for the water balance are the cropcoefficient Kc and the subsurface storage Rmax, whereas for individ-ual peaks in the long time series the most sensitive parameters arek, n and Dmax which control the slope of the hydrograph and Kc andRmax, which determine the initial moisture conditions and availablestorage. For the single events (without continuous simulations),the most sensitive parameters to the water balance were the sub-surface storage Rmax and the initial moisture conditions whereasfor the peaks the most sensitive parameters are k, n and Dmax whichcontrol the hydrograph shape, and Rmax and the initial moistureconditions which affect the initial loss.

The non-linear reservoir method was also employed by Kasminet al. (2010) to simulate the runoff from an observed extensivegreen roof and they found routing parameters n = 2 andk = 0.030 mm�1 min�1 which are of the same order of magnitudeas those found in our calibration.

Table 2 shows that peaks had 0.6 weight and water balance 0.4.Several optimizations with different combinations of weights werecarried out and it was observed that reducing the weight on thepeaks would significantly worsen the modeled peaks, whereasthe water balance would keep more stable. This is why peaks weregiven a higher weight.

The model validation results are reported in Table 3. It shouldbe noticed that the retention component was not validated specif-ically for single events, however the observed runoff was shown tobe continuously reproduced by the model (Fig. 5) and the objectivefunction for the water balance considered the runoff volume every7–10 days.

Examples of the computed and observed runoff hydrographsand the corresponding hyetograph for the 3 extensive green roofsare illustrated in Fig. 4. These examples show that the non-linearreservoir routing method adopted in the model suitably describesthe runoff from the 3 observed green roofs. In the present model itwas assumed that, due to the high hydraulic conductivity of thesubstrate materials, all the water infiltrates and percolates down

Table 3Validation results.

GR1 GR2Standard deviation Standa

Calibration target WB (mm) Peaks (mm/min) WB (m

Peaks 2.4 0.024 3.5Water Balance 1.6 0.027 1.8Peaks and WB 1.9 0.026 2.3


to the drainage layer (unless maximum detention storage Dmax

was exceeded) and that interflow through the substrate layer isnegligible (in GR3 interflow is not possible due to trays formingvertical barriers). The latter assumption might not be valid whensubstrate thicknesses become larger than those of the tested roofs(>40 mm) and the interflow through the substrate layer mightbecome larger.

The time delay due to percolation processes was not consideredin the model, nevertheless the time of the observed peaks matchedthe computed one (±1–2 min). This means that percolation is fastthrough the substrate layer due to the highly porous and granularmaterials (presence of macropores, low tortuosity).

Accumulated rainfall and observed and simulated runoff werecomputed for GR1 and shown in Fig. 5. Results show good matchbetween observed and simulated values. Two different graphsare shown in Fig. 5, one for the summer period (April 2011–Octo-ber 2011) and one for winter (October 2011–April 2012). The cropcoefficient for the winter period was assumed to be the same as thecalibrated Kc from Table 2. Proper calibration for the winter periodwas not attempted due to the fact that precipitation as snow wasnot accounted; nevertheless the modelled runoff is shown toapproximate the observed data well (Fig. 5). The annual runoff ofthe green roof GR1 was observed to be 0.47 whereas observationsfrom GR2 and GR3 were not available due to the lack of continuousdata set for a whole year. Fig. 5 shows that there is a seasonal var-iation in retention. Retention is 53% for the period April–Octoberand 35% for the period November–March.

The calibrated crop coefficients for the observed green roofs arein agreement with the range of values found in the literature.Lazzarin et al. (2005) experimentally found crop coefficients forsedum to decrease with decreasing soil relative humidity. Forwell-watered conditions they observed crop coefficients to varybetween 0.42 and 0.65 and for stressed water conditions between0.16 and 0.39. Sherrard and Jacobs (2012) calibrated their modelwith experimental data and obtained a crop coefficient for sedumof 0.53. Rezaei et al. (2005) conducted green-house experimentsand found crop coefficients of 0.74 in winter and 1.97 in fall/spring.Schneider et al. (2011) presented average sedum crop coefficientsbetween 1.1 and 1.9 based on experiments. Seasonal variation ofthe crop coefficient in the present study was assumed not to be sig-nificant due to the limited transpiration of Sedum crop. Actualmodel results (see Fig. 5) showed that using the same crop coeffi-cient for the whole year did reproduce observed runoff for the12 month continuously; this supported the assumption of no sea-sonal effects on the crop coefficient.

Theoretically the crop coefficient should only account for thedifferences in crop canopy and aerodynamic resistance (Allen,1998). However the crop coefficient in this study might be overes-timated due to the effect of roof elevation into the atmosphericboundary layer and the enhanced turbulence generated by the roofslope and neighbouring structures. GR1 might also include theeffect of a possible heat flux from the wooden house below thegreen roof (see Fig. 1).

The parameters presented above are case-specific. In order toestimate some of the parameter values for a previously-unmoni-tored roof the authors suggest the following. The maximum capac-

GR3rd deviation Standard deviation

m) Peaks (mm/min) WB (mm) Peaks (mm/min)

0.028 2.9 0.0430.041 2.2 0.0560.035 2.6 0.051




ity of the substrate and drainage layer Rmax could be calculated asthe difference between a physical measure of field capacity and thepermanently retained water content; the crop coefficient Kc couldbe determined from literature. For the parameters a, Dmax and k,calibration is needed, which could be achieved by use of rainfall,runoff and moisture data collected during controlled experiments.

Fig. 9. Single event peak time delay as a function of the 10 min rainfall returnperiod. Peak time delay above 40 min is simply shown as 40 min value (forillustration purposes).

3.2. Long term simulations

The simulated 10 min runoff intensity as a function of thereturn period is illustrated in Fig. 6 (left). The 10 min intensity isespecially relevant for local sewer surcharge problems, i.e. forsmall catchments with short time of concentration. Extensivegreen roofs are most effective for short duration storms becausethey have a small detention capacity; shorter duration storms(i.e. 1 min) result in higher peak flow reductions and vice versa.The results show that the observed extensive green roofs reducesingle event 10 min peak runoff flow and volume when comparedto the reference traditional roof. Peak runoff flows from GR2 andGR3 approach those of traditional roofs for return periods above7–10 years whereas GR1 has higher peak reductions. Fig. 6 (right)shows the peak reduction for 4 different ranges of return periods. Itcan be seen that peak flow reductions decrease with increasing theevent return period. The 10 min peak reductions are 40–78% forreturn periods between 0.1 and 1 and 10–36% for return periodsbetween 5 and 10. The results show that the best performing greenroof is GR1, which has the thickest substrate and drainage layer.Overland flow during the simulation period was observed twicefor GR1, 9 times for GR2 and 22 times for GR3. Villarreal (2007)observed the 1 min peak intensity runoff to be on average 47% ofthat of a reference hard roof for a real rain event of 2 years returnperiod in Sweden. He also estimated, using the unit hydrographmethod, 1 min peak runoff reductions to be 64% for a 5 yearsreturn period event and 63% for a 10 years events. Peak reductiondepends on many factors such as the initial available storage, rain-fall patterns and the detention capacity of the roof, which dependson the conductivity and thickness of the layers. In general, thehigher the detention capacity the higher the peak intensity reduc-tion and the higher the hydraulic conductivity of the materials thelower the peak reduction. Initial available storage and rainfall pat-terns are more correlated when a rainfall peak occurs at the begin-ning of the event, where initially low moisture content in the greenroof helps reducing the peak; conversely if the rainfall peakoccurred at the end of the event when the green roof had been sat-urated, initial moisture content would not matter.

The simulated single event rainfall–runoff volumes as a func-tion of the return period are illustrated in Fig. 7 (left). These figurescan be used to estimate the stormwater volume reduction duringsingle events. Fig. 7 (right) shows the volume reductions for 4ranges of return period. The single event volume reductionsdecrease with increasing the return period. The reductions are18–28% for 0.1–1 year return period and 2–5% for 5–10 year returnperiod. Similar conclusions were found by Stovin et al. (2012) whoshowed that retention during single 10 year return period eventscould vary between 0 and 80% depending on initial moisture con-ditions. Voyde et al. (2010) also concluded that the single eventretention is likely to decrease with increasing the event return per-iod. The simulated runoff volume reductions only depend on theavailable storage at the beginning of the rain event. NeverthelessGetter et al. (2007) and Sherrard and Jacobs (2012) observed reten-tion to change depending on the rainfall intensity. It is importantto notice that the higher the rainfall depth the lower the potentialfor runoff volume reduction. In fact if we assumed to have a max-imum storage available of 20 mm (similar to GR1) and a rainfallvolume of 50 mm (7–10 years return period according to the


observed time series) the maximum achievable volume reductionwould be 40%.

Fig. 8 shows the single event 10-min runoff intensities and run-off volumes as a function of the rainfall return period (runoff inten-sities and volumes are associated with the corresponding rainevent). Results show that the green roof response to single eventshas a high variability. This highlights the importance of continuousmodelling when forecasting the response of green roofs. Forinstance if we look at the intensity for return periods between 1and 10 years (Fig. 8, left) there is a great variation in the green roofresponse with some of the events that show similar runoff inten-sity as the incoming rainfall and others where the runoff intensityis almost nil.

The peak time delay defined as the time lag between the com-puted runoff peak from the green roof and the one from the refer-ence roof is shown in Fig. 9 as a function of the 10 min rainfallreturn period. The peak time delay is relevant for calculatingreductions in sewer surcharges. Results show that green roofscan delay peak flows from as little as 0 min up to more than60 min (peak delays higher than 40 min were simply shown as40 min, this was done to simplify the figure and to avoid mislead-ing values. Some events where no runoff is observed actually haveno time delay by definition. Other events resulted in more than200 min delay, which is a misleading result because it is an artefactof the method used to calculate peak time delay). Peak time delayvariability depends on initial available storage, rainfall patterns,detention storage capacity and material hydraulic conductivity.An overall trend of decreasing time delay with increasing the rain-fall return period is seen. Nevertheless for some events with returnperiods above 1 year the model indicates delays above 20 min.

The annual runoff defined as the ratio between the runoff andthe incoming rainfall in 1 year period is shown with a box plot inFig. 10. The annual runoff reduction is useful for estimating dis-charge reductions to the sewer system. Results show that annualrunoff ratios vary between 43% and 68% for the given extensivegreen roofs. Fig. 10 also reports the values presented by Mentenset al. (2006) which are based on observations from 121 differentextensive green roofs in Germany. The annual runoff from greenroofs is considerably lower compared to that of traditional roofs.The annual runoff was computed assuming a constant crop coeffi-cient throughout the year even though literature values suggestthat winter crop coefficients might be 0–50% smaller. Neverthelessresults are not expected to vary much since the rainfall depth dur-ing the winter months in Denmark is only 23% of the whole year(Thomsen, 2011) and evapotranspiration rates in this period are



Fig. 10. Simulated average annual runoff over 22 years. The box-whiskers plotindicate inter-annual variation. The figure also includes the results from Mentens(2006) derived from observation of 121 different extensive green roofs.

Fig. 11. Simulated mean annual runoff as a function of the green roof’s total storagecapacity (surface storage + subsurface storage).


about 10% of the ones in summer. Moreover Fig. 5 showed thatusing the same crop coefficient for the summer and winter periodwas a reasonable assumption. It should be noted that crop transpi-ration is not that important for Sedum species; nevertheless itwould become relevant when non-succulent species are used.

Fig. 12. Comparison between the actual model and the NAM model integrated into MIKErainfall-runoff for the month of June 2011 (right). Data from GR1.


GR2 and GR3 have very similar annual runoff volumes. This isbecause the most sensitive parameters to the long term water bal-ance (Rmax and Kc; see Fig. 3) are similar for the two roofs. This isreasonable since these two green roofs have similar substratematerial and vegetation, and are placed on the same structure.

The model results presented in this paper were based onextrapolation of a model calibrated with limited field data. Duringthe observation period the highest 10 min rainfall intensity regis-tered had a return period of T � 2 years whereas the single eventrainfall volume recorded had a return period in the range ofT � 8 years. This means that the modeled runoff associated withhigher return period events might be especially uncertain (a higheruncertainty compared to the one presented for the validation per-iod in Table 3). The modeled single event runoff volume was shownto be only function of the initial moisture content and thereforeresults can be considered reliable even at higher return periods.The modeled single event peak runoff associated with high returnperiod events likely occurs as overland flow; since the modelaccounts for overland flow which was shown to happen even dur-ing the observation period, results can be assumed to be reliableand most likely not overestimating peak reductions.

3.3. Annual runoff as a function of storage capacity and cropcoefficient

Fig. 11 shows the variation of the mean annual runoff as a func-tion of the total green roof retention capacity and for different cropcoefficients. It can be seen that increasing the retention capacityreduces the annual runoff and the relation between the two isnot linear. Even few mm of storage can result in significant reduc-tions in annual runoff as shown by Mentens et al. (2006) whoexperimentally observed annual runoff from gravel-covered roofsto be 70–85% of the total annual rainfall. Similar conclusions werealso found by Berghage and Jarret (2007). Lastly it can be seen thatincreasing the crop coefficient by changing the type of vegetationreduces the mean annual runoff. Changing the crop species mightrequire different substrate depth and composition which could notbe taken into account into the actual simulation.

3.4. Model with MIKE URBAN

A comparison between the computed single event runoff withthe model and the Mike Urban software is shown in Fig. 12 (left).The results show that both models are suitable for reproducingthe observed runoff from green roofs during single rain events.The NAM model integrated in MIKE URBAN routs runoff with the

URBAN. 10 min rainfall-runoff intensity from a single rain event (left). Accumulated




linear-reservoir method whereas the present model uses the non-linear reservoir. The parameter n > 1 changes the curvature of thecomputed hydrograph, during peak flows it gives a steeper shapeand during the descending hydrograph a milder one. Long termaccumulated rainfall–runoff was also compared and shown inFig. 12 (right). Results show that the two models behave similarly.The NAM has a similar conceptual model based on several storageswhich are continuously restored through evapotranspiration. Theactual evapotranspiration rates in the NAM model vary linearlyfrom 100% at R = Rmax to 0% when R = 0. This is the equivalent tosetting w = 1 in the actual model.

4. Future research prospects

The model is designed to be simple so that it can be incorpo-rated into large scale simulations of whole cities. Future researchcould model the impact of retrofitting green roofs at a large scale.The presented model could also be validated for intensive greenroofs. The model is uncertain particularly for peaks resulting fromhigh return period events where data were not available; themodel should be tested when such data becomes available. Itwould also be useful to determine how the model parameters (a,Dmax and k) can be related to roof characteristics such as the slope,thickness and material, pore size distribution, length and width.

5. Conclusion

The presented model for the hydrological response of greenroofs is demonstrated to reproduce runoff data from 3 differentextensive green roofs in Denmark. Both the single event and thelong term hydrological performance can be continuously simu-lated. Model results for runoff peak and volume reductions, andpeak time delay associated with high return period events wereshown. The model is divided into surface, subsurface and detentionstorage. The surface and subsurface storages represent the overallretention capacity of the green roof whereas the detention storagerepresent the amount of water that can be temporarily stored inthe system. All the rainfall is assumed to infiltrate into the sub-strate, unless the maximum detention capacity is exceeded. Runofffrom the model is assumed to occur either as subsurface flow or, incase the maximum detention storage capacity is exceeded, as sat-urated overland flow. Runoff time delay due to percolation throughthe substrate layer and saturated flow in the drainage layer wasnot considered in the model since the simulated timing of peakflows matched the observed ones, suggesting that for such thin lay-ers and high conductivity materials this process is fast. Evapotrans-piration continuously regenerates the capacity of the differentstorages between rainfall events. The model has a fine temporalresolution and low computational costs so that it can be integratedinto urban drainage models to simulate the impact of city-wideimplementation of green roofs.

Intensity-frequency and volume-frequency curves were calcu-lated using a statistical analysis of a 22 year continuous simulationresults with Danish climate inputs. Results showed peak flows andsingle event runoff volumes reductions to decrease with increasingreturn period of the event. Single events 10 min runoff intensitieswere reduced by 10–36% for 5–10 years return period and 40–78% for 0.1–1 year return period; the runoff volumes were reducedby 2–5% for 5–10 years return period and 18–28% for 0.1–1 yearreturn period. The simulated average annual runoff was found tobe 43–68% of the one from reference roofs (runoff coeffi-cient = 0.43–0.68). Retention was shown to be higher in the periodApril–October than November–March and seasonal variation of thecrop coefficient was found to be negligible. The peak time delaywas shown to have a great variability ranging from 0 to more than


40 min, while for 5–10 year return period events the simulatedtime delay was less than 10 min. The mean annual runoff wasfound to decrease with increasing the roof retention capacity andcrop coefficient. Finally a comparison between the developedmodel and the rainfall–runoff model (NAM) integrated into thesoftware MIKE URBAN showed similar results both during singleevents and long term hydrological response of green roofs.

The long-term continuous simulation allowed us to classify theperformance of green roofs for both annual water balance and forsingle events. Annual runoff coefficients were introduced for greenroofs. For single events, variables like initial moisture content andrainfall patterns make runoff analysis quite uncertain and so con-tinuous long term simulations are recommended.

Acknowledgments

The authors thank the Danish Council for Research thatfinanced the present research through the project BIV (Byer I Vand-balance/Cities in water balance), Annette Brink-Kjær from Vand-center Syd who provided the green roof (GR1) runoff data, andNykilde APS and HOFOR for financing green roof experiments inCopenhagen (GR2 and GR3).

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Modelling of green roof hydrological performance for urban drainage applications