Simulation of green roof runoff under different substrate depths and vegetation covers by coupling a simple conceptual and a physically based hydrological model

Journal of Environmental Management 200 (2017) 434e445

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Journal of Environmental Management journal homepage: www.elsevier.com/locate/jenvman

Research article

Simulation of green roof runoff under different substrate depths and vegetation covers by coupling a simple conceptual and a physically based hydrological model Konstantinos X. Soulis a, *, John D. Valiantzas a, Nikolaos Ntoulas b, George Kargas a, Panayiotis A. Nektarios b a

Department of Natural Resources Management and Agricultural Engineering, Division of Water Resources Management, Agricultural University of Athens, 75, Iera Odos Str., 11855, Athens, Greece Department of Crop Sciences, Lab. of Floriculture and Landscape Architecture, Agricultural University of Athens, 75, Iera Odos Str., 11855, Athens, Greece

b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 16 December 2016 Received in revised form 26 May 2017 Accepted 6 June 2017

In spite of the well-known green roof benefits, their widespread adoption in the management practices of urban drainage systems requires the use of adequate analytical and modelling tools. In the current study, green roof runoff modeling was accomplished by developing, testing, and jointly using a simple conceptual model and a physically based numerical simulation model utilizing HYDRUS-1D software. The use of such an approach combines the advantages of the conceptual model, namely simplicity, low computational requirements, and ability to be easily integrated in decision support tools with the capacity of the physically based simulation model to be easily transferred in conditions and locations other than those used for calibrating and validating it. The proposed approach was evaluated with an experimental dataset that included various green roof covers (either succulent plants - Sedum sediforme, or xerophytic plants - Origanum onites, or bare substrate without any vegetation) and two substrate depths (either 8 cm or 16 cm). Both the physically based and the conceptual models matched very closely the observed hydrographs. In general, the conceptual model performed better than the physically based simulation model but the overall performance of both models was sufficient in most cases as it is revealed by the Nash-Sutcliffe Efficiency index which was generally greater than 0.70. Finally, it was showcased how a physically based and a simple conceptual model can be jointly used to allow the use of the simple conceptual model for a wider set of conditions than the available experimental data and in order to support green roof design. © 2017 Elsevier Ltd. All rights reserved.

Keywords: Urban water management Extensive green roofs Hydrology Modelling HYDRUS Lysimeter

1. Introduction Among a variety of recently developed management practices aiming to ameliorate the environmental problems and hydrological risks associated with urbanization (Booth and Jackson, 1997), green roofs are emerging as one of the most promising alternatives (Carbone et al., 2014, 2015; Gnecco et al., 2013; Guo et al., 2014). Green roofs, also known as vegetated rooftops, eco-roofs, or living roofs, normally consist of three major components: a vegetation layer, a lightweight substrate medium, and a water storage/ drainage layer placed on top of a waterproof membrane (Carbone

* Corresponding author. E-mail address: [email protected] (K.X. Soulis). http://dx.doi.org/10.1016/j.jenvman.2017.06.012 0301-4797/© 2017 Elsevier Ltd. All rights reserved.

et al., 2015; Carson et al., 2013; Yang et al., 2015). One of the most important advantages of green roof systems is related to their ability to retain a portion of the precipitation and to gradually release the remaining part, distributing storm runoff over a longer period of time. The retained precipitation is eventually released back into the atmosphere through evapotranspiration. In this way, green roofs facilitate storm water management in urban regions. The hydrologic performance (i.e. precipitation amount retained and runoff release rate) depends on many factors, such as storm characteristics, anteceded rainfall conditions, substrate depth and its hydraulic characteristics, storage/drainage layer characteristics, vegetation cover characteristics, and slope of the green roof (Carbone et al., 2015; Speak et al., 2013; Stovin et al., 2015a; Teemusk and Mander, 2007; Wong and Jim, 2014). Green roofs are commonly classified as extensive or intensive

K.X. Soulis et al. / Journal of Environmental Management 200 (2017) 434e445

depending on the depth of the growing substrate layer. Green roofs with substrate depth less than 15 cm are classified as extensive and their vegetation consists of shallow rooting, drought resistant plants. Intensive green roofs with substrate depth more than 15 cm may support deeper rooting plants including shrubs and trees. Generally, extensive green roofs are lighter, cheaper, and require less maintenance. Accordingly, they have wider applicability, especially on older buildings where rooftop weight is an important limiting factor (Carson et al., 2013; Nektarios et al., 2011, 2015; Yang et al., 2015). In spite of the significant and well-known green roof benefits, their widespread adoption in the management practices of urban drainage systems requires the use of adequate analytical and modelling tools (Carbone et al., 2015; Elliott and Trowsdale, 2007; Stovin et al., 2015b). Therefore, apart from the numerous studies focusing on the experimental investigation or the long-term monitoring of green roof hydrological performance, increased attention has recently been given in predicting their hydrologic effects at a watershed scale using hydrological models (Palla and Gnecco, 2015; Trinh and Chui, 2013) or analyzing their hydraulic functioning at a system scale (Carbone et al., 2014, 2015; Hilten et al., 2008; Palla et al., 2011, 2012; Stovin et al., 2013; Vesuviano and Stovin, 2013). Normally, the followed approach consists of two steps: a) estimation of the green roof runoff response and b) integration and routing of the estimated runoff response in the urban system using various methods. Many studies aimed at modelling the hydrological behavior of green roofs using physically based numerical models that described the unsaturated flow in the porous matrix of the substrate such as HYDRUS software (Hilten et al., 2008; Palla et al., 2012) or other similar models (Carbone et al., 2015; Palla et al., 2009, 2011) based on numerical solutions of the Richards' equations. Other researchers utilized methodologies based on empirical relationships like curve number (CN) and rational coefficient (Getter et al., 2007; Moran et al., 2005; Fassman-Beck et al., 2016) or conceptual models based on cascades of reservoirs (Carbone et al., 2014; Locatelli et al., 2014; Palla et al., 2012; Stovin et al., 2013; Vesuviano et al., 2014). Physically based models like HYDRUS are very well suited for green roofs planning and design and are generally more accurate than the conceptual and empirical models (Carbone et al., 2015; Palla et al., 2012). However, they are not widely used due to their prohibiting computational requirements as the numerical schemes used in these models require very fine temporal and spatial scales (De Munck et al., 2013). Palla et al. (2012) compared the performance of a mechanistic model based on HYDRUS-1D and a simpler, conceptual, linear reservoir model. They reported that even though the mechanistic model was more accurate, the conceptual model closely matched its performance. Several other studies presented efficient conceptual models simulating the hydrological functioning of several green roof configurations (Carbone et al., 2014; Locatelli et al., 2014; Palla et al., 2012; Stovin et al., 2013; Vesuviano et al., 2014; Vesuviano and Stovin, 2013). Accordingly, conceptual models seem to represent the best feasible alternative for the development of modeling tools for green roof planning, design, and management. However, conceptual models confront an important obstacle due to the lack of a clear physical meaning. As a result, the required parameters are generally difficult to be estimated without calibration while the calibrated models cannot safely be applied in other conditions or other locations. In this context, the main objectives of this study were the following. Firstly, to investigate whether simplified model conceptualizations are still able to simulate extensive green roof hydrologic behavior. Secondly, to attempt to overcome the above hurdles by using a simple conceptual model jointly with a physically based numerical simulation model using HYDRUS-1D. This

435

approach aims at combining on one hand the advantages of conceptual models, namely simplicity, low computational requirements, and ability to be easily integrated in decision support tools and on the other hand the capacity of physically based simulation models to be easily transferred in conditions and locations other than those used for calibrating and validating them. Thus, a physically based numerical simulation model based on HYDRUS-1D and a simple conceptual model able to simulate the hydrological functioning of extensive green roofs were developed and tested using experimental data. Subsequently, the models were compared and possible relationships between their parameters were investigated. Finally, the physically based model was used to create a set of synthetic runoff data for various conditions. The conceptual model was calibrated using the synthetic data in order to thoroughly compare the two models and to investigate whether the simple conceptual model can reproduce the results of the physically based model for a wider set of conditions than the available experimental data. In this way, it was attempted to demonstrate that the physically based model may act as the basis for calibrating the simple conceptual model for a wider set of conditions than that of the available experimental data (e.g. climatic conditions, green roof configurations, substrate properties) in order to combine the advantages of both models. 2. Methodology 2.1. Experimental setup and data acquisition The outdoor study was conducted from December 1, 2014 to April 5, 2015. Twenty two (22) orthogonal lysimeters having dimensions of 110 cm wide
210 cm long
35 cm height were placed on the roof of the library building at the Agricultural University of Athens, Greece (37 590 lat., 23 420 long). The lysimeters were set at an inclination of 5 . Each lysimeter was thermally insulated at the bottom and from all four sides by 5 cm extruded polystyrene slabs. Taking into account the width of the polystyrene slabs, the remaining space within each lysimeter was 100 cm wide
200 cm long
30 cm in height. On top of the polystyrene slabs a waterproofing membrane was lined. An outflow opening was constructed in the middle of their lowest part. The outflow opening was lined with the same waterproofing material and was connected to a pipe leading the runoff to a tipping bucket system. The size of the opening was sufficiently large to avoid the possibility of bottleneck effect even at extreme rainfall intensities. A complete extensive green roof layering system was simulated within each lysimeter, starting with a protection mat placed on top of the water proofing membrane. The 3 mm protection mat was able to retain 3 L m2 water as manufacturing instructed. A 25 mm high drainage board with 11.8 L m2 water storing capability was laid over the protection mat. Then, the drainage layer was covered by a non-woven geotextile. The substrate for plant growth was placed on top of the non-woven geotextile. Half of the 20 lysimeters were filled with 8 cm substrate depth, while the other half with 16 cm substrate depth. The substrate comprised of pumice, attapulgite clay, zeolite and grape marc compost at volumetric proportions of 65:15:5:15 respectively, according to the patent 1008610. The physical and chemical capacities of the utilized substrate are listed in Table 1. Each lysimeter was equipped with autonomous automated subsurface drip irrigation system; however, during the study period no irrigation was applied. The lysimeters were planted with two different vegetation types 8 months before the initiation of the study period. Eight (8) lysimeters were planted with 18 plants of Origanum onites L. each (Fig. 1c), and 8 more lysimeters were planted with 18 plants of Sedum sediforme (Lacq.) Pau each (Fig. 1b). During the study period

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Table 1 Physical and chemical properties of the substrate comprised of pumice (65% v/v), attapulgite clay (15% v/v) clinoptilolite zeolite (5% v/v), and compost from grape marc (15% v/v). Values represent the mean values of three replications (±SE). Measurement pH Electrical conductivity Weight at saturation Weight at maximum field capacity Dry weight Total porosity Maximum water holding capacity Hydraulic conductivity

Unit

Value (±SE)

mS$m1 g$cm3 g$cm3 g$cm3 % % vol. mm$min1

7.2 (±0.02) 60 (±2.10) 1.30 (±0.05) 1.20 (±0.03) 0.80 (±0.02) 63.8 (±2.30) 54.2 (±1.65) 7.62 (±0.67)

the green cover ranged between 56% and 90%. Each plant species occupied 4 lysimeters with a substrate depth of 8 cm and 4 more with a substrate depth of 16 cm. In addition four lysimeters were left unplanted with bare substrate from which two had a substrate depth of 8 cm and two more had 16 cm substrate depth. These lysimeters were used as controls to compare the effects of vegetation between planted and non-planted green roofs (Fig. 1a). The reported data from the current study is the average of the available replications of each treatment. In addition, two lysimeters were left empty without any green roof layering over the water proofing membrane in order to simulate a common building roof top without any green roof technology (Fig. 1d). During the study period, rainfall was recorded with a tipping bucket rain gauge. The data series obtained from the two empty control lysimeters were compared with the rain gauge data series and it was found that they were almost identical. The runoff from each lysimeter was guided towards the outflow opening and through a pipe into a tipping bucket system that recorded continuously the runoff volume. The volume needed to turnover each tipping bucket was predetermined to correspond to 0.08 mm/tip (160 cm3/tip) in order to secure high accuracy in low rainfall intensities. For the same reason the tipping bucket systems were separately calibrated for each lysimeter. During the study period rainfall and runoff data were recorded at 10 min time intervals. Monitoring of substrate moisture and temperature fluctuation was performed with Turfguard® dielectric wireless sensors (The TORO Co). In most cases the accuracy of the soil water content sensors ranges between ±0.03 cm3/cm3 and ±0.04 cm3/cm3, when the factory calibration equations are utilized and it can improve to ±0.01 cm3/cm3 if soil specific calibration equations are used (Kargas and Soulis, 2012). Therefore, Turfguard® sensors were specifically

calibrated for the utilized substrate according to the methodology described by Kargas et al. (2013). During the study period substrate moisture and temperature were recorded at 1 h time intervals. 2.2. Physically based simulation model At the first level of the current analysis a physically based numerical simulation model was developed to predict the green roof runoff response (Fig. 2a). For the purposes of this study, it was attempted to keep the model conceptualization as simple as possible. Accordingly, the following described reasonable assumptions were made. Firstly, it was assumed that the incoming water enters green roof system from the surface of the substrate as precipitation. Then, water leaves the green roof system either as evaporation from the substrate surface or as plant transpiration (collectively evapotranspiration) or as runoff through the green roof drainage layer. However, the outflow towards the drainage layer can be considered as the only runoff source due to the increased hydraulic conductivity of the coarse-textured substrates utilized in extensive or semi-intensive green roofs. This assumption is well justified by comparing the saturated hydraulic conductivity of the specific substrate with the maximum observed rainfall intensities and by comparing it with several other relative studies (Hilten et al., 2008; Palla et al., 2012; Yang et al., 2015). Specifically, in the current study the saturated hydraulic conductivity of the substrate was much higher than the maximum observed rainfall intensity in all cases. Once the runoff generated from the green roof reaches the drain, it can be routed in the same way as if the green roof did not exist. For this reason and due to the small size of the green roof blocks it is assumed that the delay in the drainage layer of the green roof is negligible. In this approach, the total amount of water, which outflows from the green roof system, is simulated by means of the HYDRUS-1D
 code, version 4.15 (Sim unek et al., 2012). It is assumed that water flow through the substrate profile is one dimensional (vertical). As it was previously described, HYDRUS-1D has been used in previous studies for modelling the hydrological behavior of green roofs with very promising results (Hilten et al., 2008; Palla et al., 2012). Furthermore, HYDRUS-1D has also been used in studies investigating the hydrological functioning of natural watersheds and many other similar hydrological cases (Diamantopoulos et al., 2011; Soulis et al., 2009, 2015; Valiantzas, 2010). As it was described in the “Experimental setup and data acquisition” section a uniform substrate is used in extensive green roof

Fig. 1. Photographical depiction of the four lysimeter types: a) Lysimeter filled with substrate without vegetation cover; b) Lysimeter planted with Sedum sediforme; c) Lysimeter planted with Origanum onites; d) Lysimeter without green roof system simulating a conventional roof top. In all cases the tipping bucket system is visible. The photos were taken at the end of the studied period (5 Apr. 2015).

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Fig. 2. Graphical representation of: a) the physically based model and b) the conceptual model concerning water routing through an extensive green roof system. The parameters a, n, qs, qr, and Ks describe the water retention characteristics and the saturated hydraulic conductivity of the substrate according to the van Genuchten (1980) model. The parameters of the conceptual model WHC and c are the water holding capacity and the runoff release coefficient of the substrate, respectively.

systems. Accordingly, a simplified uniform substrate profile was simulated for all the scenarios examined. In this way, the calibration and validation of the model was facilitated due to the limited number of the involved parameters. The depth of the simulated profile varied between 8 cm and 24 cm (8 cm, 12 cm, 16 cm, 20 cm, and 24 cm) according to the examined scenario. In this way both extensive and semi-intensive green roof systems were covered by the simulation. To solve Richards' equation, the upper and lower boundary conditions and the initial conditions need to be specified. In this study, the upper boundary condition was defined as an atmospheric condition where potential water fluxes across the substrate surface are controlled by the external (atmospheric) conditions. However, the actual fluxes also depend on the prevailing (transient) substrate moisture conditions. In this case atmospheric conditions are defined as the 10-min recorded or estimated precipitations for the measured or the synthetic storm events. In the scenarios that included vegetation cover, interception was also considered (Fig. 2a). Evapotranspiration was not considered in the simulation runs, which is acceptable during storm events. However, it is included in the physically based model development and can be taken into account during continuous simulations. Test runs of both considering and neglecting evapotranspiration were also carried out to examine the validity of this assumption. At the lower boundary of the simulated profile, a seepage face boundary condition was defined. This type of boundary condition is applied when the bottom of the substrate column is exposed to the atmosphere (gravity drainage of a finite substrate column). The condition assumes that the boundary flux will remain zero as long as the pressure head is negative. However, when the lower end of the substrate profile becomes saturated, a zero pressure head is imposed at the lower boundary and the outflow is calculated accordingly. It is also possible to specify a value other than zero pressure head for triggering flux across the seepage face according to the actual setting. In this case this pressure head was defined equal to 1.5 cm to consider the storage capacity of the green roof drainage layer (Fig. 2a). The initial conditions were given in terms of substrate moisture. The initial substrate moisture was defined based on the substrate moisture sensors readings for the studied storm events. A fine discretization of the simulated profile was applied in all cases to enhance the numerical stability and the accuracy of the solution. Finally, in addition to the initial and boundary conditions, the water retention characteristics [q(j)], and the hydraulic conductivity curve [K(q) or K(j)], must be specified. In this study the empirical closed-form analytical model of van Genuchten (1980) was used to describe the water retention characteristic q(j) and the relationship K(q), respectively. The parameters of the van

Genuchten (1980) model, a and n, as well as the saturated hydraulic conductivity (Ks), were initially evaluated based on laboratory measurements and the final values were obtained during the model calibration. Based on the laboratory measurements and initial model runs, the remaining two parameters of the van Genuchten (1980) model namely, the saturated water content (qs) and residual water content (qr), were set equal to 0.65 cm3 cm3 and 0.001 cm3 cm3 respectively, to facilitate the calibration procedure. The Mualem (1976) model pore connectivity parameter (L) was also set equal to its typical value of 0.5.

2.3. Conceptual model In the graphical representation of the physically based model (Fig. 2a) green roofs normally consist and therefore can be conceptually divided into a series of three elements: a) the vegetation layer, b) the substrate medium layer, and c) the storage/ drainage layer. The proposed conceptual model (Fig. 2b) simulates these elements using a cascade of two reservoirs. The first one accounts for the rainfall interception by the vegetation layer and the second one for the infiltration process through the substrate layer and the storage at the storage/drainage layer. The main goal of this conceptualization is to develop a conceptual model as simple as possible. If this is achieved, then the involved calibration parameters will be minimal facilitating calibration and validation and avoiding the common problem of over-parameterization. A second key goal was to follow a conceptualization similar to that of the physically based model in order to facilitate their integration. For these reasons, the same assumptions described for the physically based model were also utilized for the conceptual one. Specifically, the interception in the vegetation layer was simulated as an overflowing reservoir (Fig. 2b) as follows:

Int i ¼ Int i1 þ P  ETp 9 ETint ¼ ETp = i ¼ Int  Intmax ; Int i ¼ Intmax ETint ¼ ETp qiint ¼ 0 9 ETint ¼ ETp þ Int i = qiint ¼ 0 ; Int i ¼ 0

qiint

(1)

if

Int i > Intmax

if

0  Int i  Intmax

if

Int i < 0

(2)

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ETpsub ¼ ETp  ETint

(3)

where P is the precipitation depth, ETp is the potential evapotranspiration depth, Int i is the interception depth in the current step, Int i1 is the interception depth in the previous step, Intmax is the interception reservoir capacity, qiint is the outflow to the next reservoir, ETint is the evapotranspiration depth of the vegetation layer, and ETpsub is the remaining potential evapotranspiration depth for the next reservoir. The infiltration process in the substrate layer and the storage in the storage/drainage layer are simulated simultaneously as a linear reservoir (Fig. 2b):

Si ¼ Si1 þ qiint  ETpsub ETsub ¼ ETpsub 9  = Q ¼ c Si  TAWC ; Si ¼ Si  Q i 9 ETsub ¼ Kst ETpsub = i i S ¼ S þ ETpsub  ETsub ; Qi ¼ 0 9 ETsub ¼ 0 = Qi ¼ 0 ; Si ¼ 0 i

ETa ¼ ETsub þ ETint

(4)

if

Si > TAWC

if

0  Si  TAWC

if

Si < 0

(5)

(6)

where Si and Si1 are the second reservoir's storage depths in the current and in the previous step respectively, TAWC is the sum of water holding capacity of the substrate (WHC) and of the storage layer (St), ETsub is the evapotranspiration depth of the second layer, ETa is the total actual evapotranspiration, c is the runoff release coefficient, Kst is the plant stress coefficient according to FAO (1998), and Qi is the runoff depth of the green roof at the current step. The proposed conceptual model can operate in both continuous and single event basis, because it directly considers evapotranspiration. However, in the current analysis only storm events were analyzed and therefore evapotranspiration was neglected.

2.4. Models application The calibration and validation of both physical and conceptual models were made by comparing the predicted and the measured runoff. Model performance was evaluated statistically based on the Nash and Sutcliffe (1970) efficiency (NSE, ∞ to þ1, values close to þ1 indicate better model performance) and the percent bias (PBIAS, indicator of under- or over-estimation, values close to 0 indicate better model performance). The performance was considered satisfactory if NSE >0.5 and PBIAS < ±25% (Moriasi et al., 2007). At the first step of the analysis, both models were calibrated independently for each event and for each studied case. Based on the obtained results the stability of the models' parameters and possible relationships with the substrate depth or with initial and boundary conditions (i.e. relationships between initial moisture or rainfall intensity with the model parameters) were investigated. In all cases, the initial substrate water content was defined based on the substrate moisture sensors readings at the beginning of each storm event. The estimation of the interception capacity of the two examined vegetation covers was attempted in this stage of analysis as well.

The estimation of the interception capacity was based on the conceptual model because its calibration is much easier and computationally efficient compared with the physically based model, as it is described in more detail in the results and discussion section. For this purpose, the conceptual model was calibrated with the interception capacity of the two examined vegetation covers as an additional calibration parameter using the experimental data corresponding to each vegetation cover. The interception capacity of each vegetation cover was considered to be equal in both models. At a following step, the models were calibrated and validated for each substrate depth as well as for each vegetation cover (for the conceptual model only) to further investigate the above referred relationships. For this reason, the split sample test method was used. The examined events were divided into two groups; i.e. events with odd numbering (1, 3, …, and 11) were used for calibration while events with even numbering (2, 4, …, and 10) were used for validation. Finally, global calibration and validation of both models was attempted to investigate if adequate performance was achievable with a common set of parameters for all the examined cases. HYDRUS-1D was calibrated for each event using a MarquardtLevenberg type parameter optimization algorithm for inverse estimation of soil hydraulic parameters which is included in the
 software (Sim unek et al., 2012; Marquardt, 1963). The method is considered to be very effective and has become a standard in nonlinear least-squares fitting among soil scientists and hydrologists (Kool et al., 1987). The calibration parameters were a, n, and Ks. In order to perform the global model calibration, the resulted parameter values for each event were compared and a new set of initial values and ranges for the involved parameters were manually defined. HYDRUS-1D was calibrated again using the new initial values and ranges. This procedure was repeated again until a common set of parameters providing acceptable performance for all the examined events was identified. The conceptual model was calibrated in a similar way using a simple custom-made spreadsheet application that automatically executed the model code for a user defined variation range of the corresponding calibration parameters in order to minimize the primary performance criterion (NSE). A final check was performed using a trial and error approach to examine if any further improvements on the model performance could be achieved with fine tuning the calibration parameters values considering also the second performance criterion (PBIAS). Finally, it was examined whether the obtained parameters values coincident with the limits of the defined variation ranges. In cases of coincidence, the calibration was repeated using a wider variation range. In all cases TAWC was set equal to the sum of the water holding capacity of the substrate (WHC) and of the storage layer (St). WHC was estimated as follows:

WHC ¼





qfd  qr SD

(7)

where SD is the substrate depth, qfd is the remaining substrate moisture after free drainage, and qr is the residual water content. St was estimated in a similar way supposing an equivalent substrate depth of 1.5 cm in an analogues way with the conceptualization of the physically based model and considering that water overflows the drainage layer when it is fully saturated.

St ¼ ðqs  qr ÞDED

(8)

where DED is the equivalent drainage layer depth. As it was described in the “Physically based simulation model” section the saturated water content (qs) and residual water content (qr), were

0.23 0.13 0.18 0.07 0.04 0.01 0.00 0.01 0.03 0.05 0.03 34.7 15.5 69.6 11.7 2.5 6.7 0.0 2.6 12.7 15.8 8.3 0.17 0.09 0.15 0.04 0.00 0.01 0.00 0.01 0.03 0.05 0.03 32.5 14.3 65.7 10.4 0.0 6.7 0.0 2.6 12.7 15.8 8.3 0.18 0.10 0.18 0.07 0.04 0.01 0.00 0.02 0.04 0.05 0.06 32.4 14.9 69.6 11.7 2.5 6.3 0.0 5.5 14.3 17.5 12.4 0.17 0.10 0.16 0.03 0.00 0.00 0.00 0.00 0.01 0.04 0.02 33.9 15.0 68.1 8.1 0.0 0.0 0.0 0.0 6.3 12.2 5.7 0.16 0.10 0.1 0.070 0.16 0.03 0.04 0.14 0.07 0.11 0.17 37.0 16.5 74.1 13.4 5.4 11.5 6.8 10.0 16.3 23.3 19.7 0.13 0.08 0.13 0.07 0.11 0.02 0.01 0.12 0.05 0.08 0.12 34.3 15.4 68.5 12.5 3.6 10.4 2.8 9.1 15.1 16.2 17.8 0.29 0.14 0.30 0.25 0.73 0.11 0.11 0.40 0.22 0.18 0.23 600 290 2640 400 50 1050 1070 380 700 1090 770 1 2 3 4 5 6 7 8 9 10 11

38.8 17.6 74.2 15.6 13.1 13.9 22.6 14.4 17.5 29.6 25.2

Peak Rate

(mm/min) (mm)

Total Depth Peak Rate

(mm/min) (mm)

Total Depth Peak Rate

(mm/min) (mm)

Total Depth Peak Rate

(mm/min) (mm)

Total Depth Peak Rate Total Depth

(mm) (mm/min) (mm)

Peak Rate Total Depth

(mm/min) (mm)

(mm/min)

Sedum 8 cm Sedum 16 cm Origanum 8 cm No Vegetation 16 cm Peak Intensity Total Depth

Origanum 16 cm No Vegetation 8 cm Runoff

The characteristics of the rainfall events and the observed hydrographs for all the studied cases are presented in Table 2. Observed total rainfall depths ranged between 13.9 mm and 74.2 mm and peak 10 min rainfall intensities ranged between 0.11 mm min1 and 0.73 mm min1. The duration of the studied events ranged between 50 min and 2640 min. The higher total runoff depth (74.1 mm) was observed for the case of 8 cm substrate depth without vegetation cover. In this case almost all rainfall was released as runoff. It should be also noted that in this case the initial moisture content of the substrate was very high (55.4%). However, even in this case the peak runoff rate was reduced from 0.3 mm min1 to 0.13 mm min1 (56.3%). In contrast, 100% reduction of both runoff depth and peak runoff rate was observed in smaller rainfall events and drier initial substrate moisture conditions (Table 3). Overall, the observed runoff reduction ranged between 0.1% and 100% with an average value of 42.8% for the total runoff depth and between 8.7% and 100% with an average value of 70.2% when the peak runoff rate was considered. In contrast, the observed delay of the runoff peak ranged from negligible (below the 10 min time discretization step) to over 30 min. The generally low peak delay values could be attributed mainly to the generally high hydraulic conductivities in combination with the low substrate depths of extensive green roofs. Furthermore, due to the small size of the green roof blocks the delay in the block drainage layer of the green roof is negligible. It should be noted that it is not always possible to securely estimate the delay of the runoff peak, especially for the multi peak events due to the smoothening of the outflow hydrographs. Several other studies have reported that green roofs can retain up to 90% of the total storm depth when individual storm events are considered, with the observed retention being reduced as the storm depth increased (Carson et al., 2013; Carter and Rasmussen, 2006; Getter et al., 2007; Mentens et al., 2006; Morgan et al., 2013; Simmons et al., 2008; Spolek, 2008; Stovin et al., 2012; Teemusk and Mander, 2007; Van Woert et al., 2005; Wong and Jim, 2014). Furthermore, reductions of 60% to 80% have been reported in peak flow rates from green roof systems compared with conventional roof tops (Bliss et al., 2009; Carter and Jackson, 2007; Palla et al., 2012; Villarreal et al., 2004). In contrast, the observed delay of the runoff peak was not as impressive.

Rainfall

3.1. Experimental data

Duration (min)

3. Results and discussion

439

Event

set equal to 0.65 cm3 cm3 and 0.001 cm3 cm3 respectively, to facilitate the calibration procedure. Finally, qfd was set equal to 0.55 cm3 cm3 based on the laboratory measurements and the analysis of the substrate moisture data. At a third step of the analysis, the results of the two models were compared. Furthermore, possible relationships between the parameters of the two models were also examined. Following, as a final step, the physically based model was used to create a set of synthetic runoff data for a range of substrate depths (8, 12, 16, 20, and 24 cm) and for various conditions (for three sets of hydraulic parameters and for all the studied rainfall events). Then, the conceptual model was calibrated using these synthetic data. The purposes of this final step were: a) to further investigate possible relationships between the conceptual model parameters, the hydraulic parameters of the substrate, and the substrate depth, b) to investigate the applicability range of the simple conceptual model (hydraulic properties, substrate depth), and c) to demonstrate how the physically based model may act as the basis for the empirical parameters of the simple conceptual model in order to facilitate the broader use of the simple conceptual model.

Table 2 Rainfall and runoff characteristics of the studied events. Substrate depth is indicated by either 8 cm or 16 cm while plant coverage is indicated as Sedum (Sedum sediforme) or Origanum (Origanum onites) or No Vegetation (bare substrate).

K.X. Soulis et al. / Journal of Environmental Management 200 (2017) 434e445

70.4 42.7 79.1 62.0 22.8 32.8 Average

67.1

56.9

16.4 15.0 6.1 24.7 80.7 54.5 100.0 61.7 18.4 41.1 50.7 41.6 28.8 47.7 87.0 100.0 100.0 100.0 100.0 93.8 79.3 91.3 12.5 14.6 7.6 47.8 100.0 100.0 100.0 100.0 63.9 58.7 77.3 4.5 5.8 0.1 14.0 58.7 17.2 70.0 30.9 7.0 21.3 21.8 11.4 12.1 7.7 19.9 71.4 25.1 87.6 36.7 13.7 45.3 29.6 1 2 3 4 5 6 7 8 9 10 11

57.1 40.0 56.9 73.7 85.1 84.6 88.5 70.1 76.0 57.1 49.1

45.9 29.5 56.3 71.5 78.5 76.8 69.1 64.6 67.8 40.1 26.0

Event 11 Rainfall Depth = 25.2 mm

46.2 76.7 50.4 71.2

%

43.4 34.6 49.6 81.9 100.0 92.0 100.0 97.8 85.6 71.6 87.4 16.2 18.4 11.4 33.4 100.0 51.5 100.0 81.8 27.3 46.7 67.3 39.8 25.3 41.3 72.9 94.2 90.0 100.0 94.6 80.8 71.3 73.6

22.9 8.7 41.3 72.9 94.2 92.0 100.0 97.8 85.6 71.6 87.4

% %

10.4 11.6 6.1 24.7 80.7 51.5 100.0 81.8 27.3 46.7 67.3

Total Depth Peak Rate

%

Peak Rate

Total Depth

% %

Total Depth Peak Rate

% %

Total Depth

%

Peak Rate Total Depth

% %

Total Depth

Peak Rate

%

Sedum 8 cm Sedum 16 cm Origanum 8 cm Origanum 16 cm No Vegetation 8 cm No Vegetation 16 cm

Runoff Reduction Event

Table 3 Runoff reduction statistics. Substrate depth is indicated by either 8 cm or 16 cm while plant coverage is indicated as Sedum (Sedum sediforme) or origanum (Origanum onites) or no vegetation (bare substrate).

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Peak Rate

440

Fig. 3. Observed runoff hydrographs for all the examined cases for event 11 (26/03/ 2015). Substrate depth is indicated by either 8 cm or 16 cm while plant coverage is indicated as Sedum (Sedum sediforme) or Origanum (Origanum onites) or No Vegetation.

The observed runoff hydrographs for all the examined cases for the last studied event (event 11) are illustrated in Fig. 3. This event was selected because it presents average rainfall depth and initial moisture conditions. Smaller substrate depth and no vegetation cover resulted in very low runoff retention and peak runoff rate reduction. In contrast, higher runoff retentions and peak runoff rate reductions were observed in the case of origanum vegetation cover and 16 cm substrate depth. The higher delay of the runoff peak for the same case (origanum, 16 cm), as well as the smoothening of the outflow hydrographs can be also observed in Fig. 3. An important observation was that the vegetation cover had a profound effect on initial substrate moisture conditions probably due to higher evapotranspiration rates. Significant differences in evapotranspiration and soil moisture losses between vegetated and non-vegetated roof gardens were also observed in previous studies € et al., 2015). Generally, the most densely (Berretta et al., 2014; Poe vegetated cover yields higher evapotranspiration and storm water retention as well as lower outflow volumes at the annual scale (Bengtsson, 2005; Palla et al., 2010; Stovin, 2010; Yilmaz et al., 2016). Furthermore, many researchers reported seasonal variation in green roofs runoff reduction, with runoff reduction potential being larger during summer periods (Mentens et al., 2006; Stovin et al., 2012, 2013; Villarreal and Bengtsson, 2005). In addition, previous studies reported that substrate depth influences green-roof runoff reduction capacity, which is in agreement with the results of this study and the general understanding (Mentens et al., 2006; Monterusso et al., 2004; Van Woert et al., 2005; Yilmaz et al., 2016). In contrast, Wong and Jim (2014) were unable to determine any statistical significance in performance difference between the studied substrate-depth treatments. 3.2. Conceptual model At a first step of the analysis, the conceptual model was calibrated independently for each event and for each studied case. A comparison of the simulated and the observed runoff for the cases of 8 cm substrate depth and no vegetation cover, for events 1, 5, 6, and 7 are illustrated in Fig. 4 as an indicative example. It was found that the performance of the conceptual model was very good in most cases. The average NSE value was 0.82, the median 0.87, the maximum 0.98, and the minimum 0.46. Concerning PBIAS the average value was 1.9%, the median 3.6%, the worst 45%, and the

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a

c

Event 1

Event 6

b

d

441

Event 5

Event 7

Fig. 4. Estimated runoff hydrographs using either the physically based model (HYDRUS) or the conceptual model in comparison with the observed runoff hydrographs for the case of 8 cm substrate depth without vegetation cover for events 1 (a), 5 (b), 6 (c) and 7 (d).

best 0.2%. It should be noted that inadequate performance (NSE < 0.5 and PBIAS > ±25%) was observed only in two cases (event 6 for substrate depth of 8 cm planted with origanum and for substrate depth of 16 cm planted with sedum). In most cases that were characterized by low performance, the peak rainfall intensity and the corresponding peak runoff rates were very low (Table 3). Therefore, even if the volume corresponding to each tip was very low and the total volume measurement accuracy was very high, the noise introduced by the tipping bucket measuring device due to the stepping effect is still a limiting factor. An example of the influence of the stepping effect on the obtained accuracy is presented in Fig. 4. Specifically, in Fig. 4c, where an event characterized by low runoff rates is presented, although the conceptual model reproduces very closely the observed hydrograph the obtained NSE value was only 0.82. The stepping effect on the recorded runoff can be clearly seen in this case. In contrast, in Fig. 4a, the conceptual model also reproduces very closely the observed hydrograph but in this case, the obtained NSE value was as high as 0.98. Furthermore, in Fig. 4b, the results of the conceptual model for a very short event (event 5) are illustrated, while in Fig. 4d the results of the conceptual model for an event (event 7) characterized by low initial substrate moisture are illustrated. In both cases the model performance was sufficient. The calibrated c parameter values ranged between 0.03 and 0.32, however in most cases c parameter ranged between 0.05 and 0.2. The average value was 0.12 and the median 0.11. Since, the retention coefficient c represents the runoff release coefficient of the entire substrate, higher c parameter values were obtained for the lower substrate depth (8 cm) compared to the deeper ones of 16 cm. Concerning the estimation of the interception capacity (Int) for the two studied vegetation covers the obtained results characterized by a considerable variability. More specifically, the interception capacity ranged between 1.4 mm and 6.8 mm for origanum and between 0.5 mm and 6.1 mm for sedum. The interception capacity may vary due to variations on the development, density, and

general condition of the vegetation covers or due to differences in the prevailing conditions (e.g. wind or rainfall characteristics). This variability can be also attributed to the limitations posed by the accuracy of the initial substrate moisture measurements especially for those cases characterized by lower initial moistures. For this reason the final estimation of the interception capacity was based on the events with high initial substrate moisture (events 1, 2, 3, 6, and 9). The resulted interception capacity was 2.1 mm for origanum € et al. (2015) indicated that the dense and 1.2 mm for sedum. Poe Sedum foliage may result in greater interception capacity than equivalent configurations with a mix of ‘Meadow Flowers’. However, in most studies the interception capacity is collectively considered in the green roof storm runoff retention capacity and hence there are no specific figures concerning the interception capacity of various green roofs vegetation covers in order to perform any valid comparisons. Carter and Jackson (2007) provided a general figure for green roofs interception for all storms of about 3.1 mm based on the results of studies on the interception of urban forests. A general outcome is that the estimation of the interception capacity is challenging and more thorough study is needed in order to provide conclusive results. Following, the conceptual model was calibrated and validated simultaneously for each substrate depth and then for each vegetation cover. The c parameter values obtained during the calibration for each substrate depth were 0.11 for 8 cm and 0.07 for 16 cm. The corresponding NSE values were 0.81 for calibration and 0.76 for validation in the first case and 0.78 for calibration and 0.77 for validation in the second case. Concerning the results obtained for each vegetation cover, c parameter value for no vegetation was 0.1 (NSE ¼ 0.76 for calibration and 0.72 for validation), for sedum was 0.09 (NSE ¼ 0.85 for calibration and 0.79 for validation), and for origanum was 0.08 (NSE ¼ 0.80 for calibration and 0.76 for validation). Finally, the conceptual model was globally calibrated and validated. The performance of the conceptual model with globally calibrated c parameter (c ¼ 0.08) was still sufficient (NSE ¼ 0.73 for

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calibration and 0.70 for validation). However, in this case the model considerably overestimated runoff response in specific events having very low runoff. Therefore, it was suggested that this parameter should be calibrated separately for each depth. This decision was further supported by the fact that there is a clear relationship between c and substrate depth, as it is further analyzed in the last section. Overall, the performance of the conceptual model was sufficient for the most cases. Other studies proposing conceptual models based on cascades of linear reservoirs (Carbone et al., 2014; Palla et al., 2012; Stovin et al., 2013; Vesuviano et al., 2014; Vesuviano and Stovin, 2013) concluded that such models represent adequate solutions for modelling the hydrological behavior of green roofs. The outcomes of this study support this general conclusion as well. Furthermore, it was found that a much simpler model is still capable of describing the hydrological behavior of extensive green roofs, at least in the cases that the assumptions posed in the current study are met; i.e. small size of the green roof blocks and a uniform substrate profile. As an example, Palla et al. (2012) reported that a conceptual model based on a cascade of three linear reservoirs also performed sufficiently well (the obtained NSE values for the 10 studied events ranged between 0.52 and 0.985). However, in their study a total of 7 parameters were involved. Vesuviano et al. (2014) achieved adequate performance in rainfall simulator experiments using a two-stage nonlinear storage routing model involving six calibration parameters. Finally, Carbone et al. (2014) also achieved adequate performance in rainfall simulator experiments using a complex conceptual model that separated the green roof system in three individual components and simulated each of them with the Green-Ampt equation, a weir flow equation, and a kinematic wave method correspondingly. From the above analysis, it can be concluded that the performance of the proposed simplified conceptual model is on par with the much more complex models presented up to now; however, the proposed model follows a much simpler conceptualization involving only one calibration parameter avoiding thus the problem of equifinality, which may arise in multi-parameter models, and facilitating model setup, calibration, and validation. Accordingly, the main advantage of the proposed model is its simple and compact algorithm that can be easily integrated in DSS tools applicable even on mobile devices such as smartphones and tablets. 3.3. Physically based simulation model Similarly to the conceptual model, the physically based model was initially calibrated independently for each event and for each studied case. A comparison of the simulated and the observed runoff for the cases of 8 cm substrate depth and no vegetation cover, for events 1, 5, 6, and 7 are illustrated in Fig. 4 as an example. Similarly to the conceptual model, the performance of the physically based one was also very good in most cases. The average NSE value was 0.71, the median 0.76, the maximum 0.98, and the minimum 0.41. Concerning PBIAS, the average value was 9.3%, the median 10.1%, the worst 27.1%, and the best 4.2%. In the case of the physically based model there was not a clear justification of the event characteristics related to lower performance. Inadequate performance (NSE ¼ 0.41) was observed only in one case while in two other cases the PBIAS value was a little higher than the performance criterion of 25%. However, in several cases the model performance was only marginally better than the criteria posed. As it is reported by De Munck et al. (2013) the high computational requirements of physically based models is a common problem as the numerical schemes used in these models require very fine temporal and spatial discretization. Therefore, in order to facilitate

the calibration of the physically based model and to secure that the obtained results were not influenced by the initial parameter estimations, careful selection of the parameters' initial values and ranges as well as many repetitions of the calibration process with different initial parameter values were performed. Furthermore, as it was described in the “Materials and Methods” section, special care was taken to keep the number of the calibration parameters to a minimum in order to facilitate the calibration procedure and to avoid the problems of over-parameterization and multiple solutions. As it was previously described, the estimation of the interception capacity was based on the conceptual model. Concerning the main calibration parameters, Ks values ranged between 3 mm min1 and 15 mm min1 (average ¼ 7.3 mm min1, median ¼ 6.5 mm min1, standard deviation ¼ 3.2 mm min1), a values ranged between 0.157 cm1 and 0.315 cm1 (average ¼ 0.237 cm1, median ¼ 0.221 cm1, standard deviation ¼ 0.04 cm1), and n values ranged between 3 and 8.6 (average ¼ 6.38, median ¼ 7.24, standard deviation ¼ 1.3). Based on the reported data, there was a considerable variability in the hydraulic parameters values. However, the average Ks value was very close to the laboratory measurements (Table 1). Certainly, temporal and spatial variability of substrate hydraulic parameters is a significant but common issue for natural soils (Kargas et al., 2016) as well as for substrates (Yanling, 2014) and therefore further study is needed. The substrate hydraulic parameter values obtained during the simultaneous calibration for each substrate depth were: Ks ¼ 4.7 mm min1, a ¼ 0.275 cm1, and n ¼ 6.0 for substrate depth of 8 cm and Ks ¼ 10.6 mm min1, a ¼ 0.210 cm1, and n ¼ 7.2 for substrate depth of 16 cm. The corresponding NSE values were 0.60 for calibration and 0.56 for validation in the first case and 0.66 for calibration and 0.61 for validation in the second case. These results indicate a link between substrate depth and hydraulic parameters. The same link was also observed in the independent calibration results. This relation, which is very difficult to justify, may indicate that the substrate profile is not completely uniform, but there is a stratification on the substrate hydraulic properties due, for example, to uneven compaction or fine material movement in the substrate profile. Furthermore, the growth of the plants' roots may also affect the hydraulic properties of the substrate. A more complicated conceptualization could probably consider these effects but it could also cause over-parameterization problems. However, it was attempted to keep the model conceptualization as simple as possible in order to investigate if simplified model conceptualizations are able to simulate extensive green roofs hydrologic behavior. Finally, the performance of the physically based model with globally calibrated hydraulic parameters (Ks ¼ 6.9 mm min1, a ¼ 0.216 cm1, and n ¼ 6.9) was generally poor but acceptable (NSE ¼ 0.54 for calibration and 0.51 for validation). However, it should be noted that due to the above described difficulties of the physically based model calibration, further performance improvements could be possibly achieved with further effort. Furthermore, as it is also discussed in more detail in the previous paragraphs, in the current study, due to the examination of different substrate depths and vegetation covers, it is reasonable to have variation in substrate hydraulic parameters resulting in poorer performance of global calibration and validation. In the study of Palla et al. (2012) a mechanistic model based on Hydrus 1D performed also sufficiently well for both calibration and validation. However, in their study the mechanistic model concerned a more complex system comprised of two substrate layers. Therefore a total of 12 parameters were involved (5 hydraulic parameters and 1 rooting parameter for each layer). In other previous

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studies, Palla et al. (2009, 2011), applied a two-dimensional physically based model at the same experimental green roof system and they concluded that mechanistic models may suitably describe the hydrologic performance of a green roof, which is typically realized with high hydraulic conductivity and coarse-textured porous media. Finally, Hilten et al. (2008) reported that HYDRUS-1D accurately predicted total runoff for small rainfall events but it overestimated total runoff at larger rainfall depths. Overall, the results of this study also support the general conclusion of the previous studies that physically based simulation models using numerical solutions of the Richards' equations may sufficiently describe the hydrologic behavior of green roofs. Furthermore, the performance of the proposed simpler physically based model can be considered as sufficient to describe the hydrological behavior of extensive green roofs, at least in the cases that the assumptions posed in the current study are met; i.e. small size of the green roof blocks and a uniform substrate profile. However, some common weaknesses of physically based models were also noticeable in this application, namely high computational requirements, difficulties in the calibration procedure, and variability of the calibrated parameters. In HYDRUS-1D, the governing equations are numerically solved using Galerkin type linear finite element schemes, while integration in time is achieved using an implicit finite difference scheme. Furthermore, additional measures are taken to improve solution efficiency for transient problems, including automatic time step adjustment and adherence to preset ranges of the Courant and Peclet numbers. However, in specific cases convergence limitations may arise such us problems associated with the numerical solution near saturation or when sharp fronts occur (Vogel et al., 2001). Accordingly, the computational efficiency of the physically based model was generally high, however, run times significantly varied according to the porous medium hydraulic properties, the event characteristics as well as the initial conditions. Specifically, in the current study, the average run times were normally below 5 s for the direct solution and below 30 min for the inverse solution. However in specific cases, much higher run times were required, while in rare cases the algorithm failed to converge. In contrast, the very simple explicit conceptual model runs almost instantly and does not have convergence limitations. These weaknesses in combination with the difficulties involved in the integration of the more complex physically based models in decision support tools may represent significant obstacles in the broad use of physically based models and may balance with the capacity of physically based simulation models to be easily transferred in conditions and locations other than those used for calibration and validation.

443

closely the shape of the observed hydrographs compared with the physically based model. However both models describe the hydrologic response of the green roof adequately well. Palla et al. (2012), in a similar study, reported that the physically based model performed better than the conceptual model which followed closely its performance. However, in their study the physically based model concerned a more complex system as it was described in the previous sections. Many other studies concerning either physically based models (Palla et al., 2009, 2011; Hilten et al., 2008) or conceptual models (Carbone et al., 2014; Palla et al., 2012; Stovin et al., 2013; Vesuviano et al., 2014; Vesuviano and Stovin, 2013) for various green roof setups reported that the respective models used in each study may sufficiently describe the hydrologic behavior of studied green roofs. Following the calibration and evaluation of both models, possible relationships between their main parameters were examined. The interception capacity and drainage storage were reasonably assumed to be the same in both models, as it was previously described. In contrast, no specific relationship was identified between c parameter and Ks or any other substrate hydraulic parameter. Further investigation revealed that a relationship between c parameter and a combination of a, n, and Ks parameters is possible to exist for each depth. However, more events are needed to be examined to draw a definite conclusion. The final step was to use the physically based model to create a set of synthetic runoff data for a wider range of substrate depths. The three sets of hydraulic parameters used, corresponded to the hydraulic parameters obtained during the global calibration of the physically based model as well its calibration for each substrate depth. These sufficiently cover the range of the hydraulic parameters variability in the obtained results. The three sets are referred as “Low” (Ks ¼ 4.7 mm min1, a ¼ 0.275 cm1, and n ¼ 6.0), “Mid” (Ks ¼ 6.9 mm min1, a ¼ 0.216 cm1, and n ¼ 6.9), and “High” (Ks ¼ 10.6 mm min1, a ¼ 0.210 cm1, and n ¼ 7.2). The results of the conceptual model calibration using the synthetic data are presented in Fig. 5. The conceptual model perfectly fitted the synthetic data for lower substrate depths but its performance deteriorated for larger depths and especially for depths greater than 20 cm. An indicative example is presented in Fig. 6. In this figure the synthetic runoff data generated for the first rainfall event, for the “Mid” hydraulic parameters set, and for substrate depths of 12 and 24 cm are plotted in comparison with the simulated runoff by the conceptual model. Furthermore, improved performance was observed for the “High” hydraulic parameters set

3.4. Models comparison and combined application The previously presented results concerning the performance of the conceptual and the physically based model reveal that the conceptual model performed generally better than the physically based model; however, the performance of both models was adequate in most of the studied cases. The obtained NSE values of the conceptual model were higher than 0.70 in most cases. As regards to the physically based model the obtained NSE values were higher than 0.6 in most cases, which can be considered adequate taking also into account the physical meaning of the involved parameters allowing the formulation and investigation of various scenarios. Graphical representations of the comparison between the observed hydrograph and the hydrographs simulated by the two models for 4 characteristic cases (8 cm substrate depth, no vegetation cover for events 1, 5, 6, and 7) are illustrated in Fig. 4 as an example. In these cases the conceptual model followed more

Fig. 5. Results of the conceptual model calibration using the synthetic data for different green roof substrate depths.

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Fig. 6. Estimated runoff hydrographs using the conceptual model in comparison with the synthetic runoff hydrographs produced by the physically based model for the first rainfall event, for the “Mid” hydraulic parameters set (Ks ¼ 6.9 mm min1, a ¼ 0.216 cm1, and n ¼ 6.9), and for substrate depths of 12 and 24 cm.

compared to the “Low” set. Accordingly, it can be concluded that the simple conceptual model is able to reproduce the results of the more complex and more computationally intensive physically based model and to sufficiently describe the hydrologic behavior of extensive green roof systems for substrate depths up to 20 cm. In the case of the synthetic data, there was a clear relationship between c parameter and substrate depth with c parameter value reducing as the depth increases, which is in accordance with the model conceptualization (Fig. 5). Accordingly, as it was already indicated in the “Conceptual model” section, c parameter should be calibrated separately for each substrate depth. Furthermore, a relationship between the substrate hydraulic parameters and c parameter can also be observed with c parameter being higher in the case of the “High” hydraulic parameters set and lower for the “Low” hydraulic parameters set. However, this relationship is observed only for substrate depths of 8 and 12 cm. It should be noted that substrate depth is a very important design parameter influencing the weight, cost, and performance of the green roof. Based on the above results it can be concluded that a physically based and a simple conceptual model can be jointly used in order to facilitate the broader use of the simple conceptual model to support green roof design. However, the high computational requirements, the difficulties in the calibration procedure, and the observed variability of the calibrated hydraulic parameters of the physically based model are important remaining issues that should be addressed.

4. Conclusions In this study a physically based numerical simulation model based on HYDRUS-1D and a simple conceptual model able to simulate the hydrological functioning of extensive green roofs were developed and tested using experimental data for various vegetation covers and green roof substrate depths. Furthermore, it was investigated whether the simple conceptual model can reproduce the results of the physically based model for a wider set of conditions than the available experimental data in order to test if the two models may be jointly used. Concerning the experimental data, the observed runoff reduction ranged from 1% to 100% for the total runoff depth and from 26%

to 100% for the peak runoff rate. Higher reductions were observed for the deeper substrates, the origanum vegetation cover, lower initial water contents, and smaller rainfall depths. Concerning the modeling of green roof hydrological behavior, both the physical and the conceptual models matched very closely the observed hydrographs. In general, the conceptual performed better than the physically based model and its overall performance was sufficient in most cases. The performance of the physically based model can also be considered as sufficient, especially when taking into account the physical meaning of the involved parameters that allows the formulation and investigation of various scenarios. However, the high computational requirements, the difficulties in the calibration procedure, and the observed variability of the calibrated hydraulic parameters of the physically based model represent significant obstacles that should be addressed. Considering the results obtained using the synthetic data generated by the physically based model, it can be concluded that, the proposed simple conceptual model can be sufficiently utilized for modeling the hydrological behavior of extensive green roofs for substrate depths up to 20 cm. Furthermore, it was demonstrated how the simple conceptual model can be transferred in a wider set of conditions than the available experimental data (e.g. climatic conditions, green roof configurations, substrate properties) through its calibration based on synthetic data generated by an analogous physically based model. In this way, the advantages of the conceptual model, namely simplicity, low computational requirements, and ability to be easily integrated in decision support tools were combined with the capacity of the physically based simulation model to be easily transferred in conditions and locations other than those used for calibrating and validating. With such an approach, the broader use of the simple conceptual model to support green roof design is facilitated. Acknowledgments This project was co-funded by National Funds (General Secretariat of Research and Technology - GSRT) and by European Funds, under the call of Bilateral Cooperation between Greece and China with grand number 12CHN136. The donation of the Turf Guard® wireless moisture sensors by the TORO Co. and of the attapulgite clay by GeoHellas SA is greatly appreciated. The authors wish also to sincerely thank the editor and the anonymous reviewers for their constructive comments and suggestions, allowing us to improve the final version of the paper. References Bengtsson, L., 2005. Peakflows from thin sedum-moss roof. Nord. Hydrol. 36, 269e280. €, S., Stovin, V., 2014. Moisture content behaviour in extensive green Berretta, C., Poe roofs during dry periods: the influence of vegetation and substrate characteristics. J. Hydrol. 511, 374e386. http://dx.doi.org/10.1016/j.jhydrol.2014.01.036. Bliss, D.J., Neufeld, R.D., Ries, R.J., 2009. Storm water runoff mitigation using a green roof. Environ. Eng. Sci. 26 (2), 407e417. DOI:10-1089/ees.2007-0186. Booth, D., Jackson, C.R., 1997. Urbanization of aquatics systems: degradation thresholds, stormwater detention, and the limits of mitigation. J. Am. Water Resour. As 22 (5), 1e20. Carbone, M., Brunetti, G., Piro, P., 2015. Modelling the hydraulic behaviour of growing media with the explicit finite volume solution. Water 7 (2), 568e591. Carbone, M., Garofalo, G., Nigro, G., Piro, P., 2014. A conceptual model for predicting hydraulic behaviour of a green roof. Procedia Eng. 70, 266e274. Carson, T.B., Marasco, D.E., Culligan, P.J., McGillis, W.R., 2013. Hydrological performance of extensive green roofs in New York City: observations and multi-year modeling of three full-scale systems. Environ. Res. Lett. 8 (2) http://dx.doi.org/ 10.1088/1748-9326/8/2/024036. Carter, T., Jackson, C., 2007. Vegetated roofs for stormwater management at multiple spatial scales. Landsc. Urban Plan. 80, 84e94. Carter, T.L., Rasmussen, T.C., 2006. Hydrologic behavior of vegetated roofs. J. Am. Water Resour. Assoc. 42, 1261e1274.

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