A Conceptual Model for Simulating the Hydrologic

The 7th International Conference of SuDBE2015, Reading, UK; 27-29 July, 2015

Topic: T2.3 Performance Evaluation

Reference number: 2057

A Conceptual Model for Simulating the Hydrologic Performance of Extensive Green Roof Systems Xi Liu, Ana Mijic and Cedo Maksimovic Department of Civil and Environmental Engineering, Imperial College London, London SW7 2AZ, UK

Abstract: Green roofs are a classic example of a multifunctional, sustainable urban drainage system, which can mitigate the adverse effects of the increase in impervious surfaces associated with urbanisation. This paper describes a simple linear reservoir (SLR) conceptual model developed to predict the hydrologic response of extensive green roof systems for event based simulations. The SLR model was calibrated and validated by comparing the outputs with observations from two extensive modular green roof systems in London, UK. The assessment focuses on three aspects: reduction of the total runoff volume, delay in the initiation of runoff and reduction of the peak runoff rate. The main results show that the SLR model shows good potential for an accurate estimation of the runoff hydrograph from modular extensive green roof systems. However, the applicability of the SLR model decreases with higher rainfall intensity and larger drainage storage capacity. Also, the validation results show that SLR is able to capture the temporal dynamics of the observed runoff, but clearly underestimates the peak of discharge. Key words: Modular green roof systems, hydrologic performance, simple linear reservoir (SLR) model

1 Introduction Climate change is now the dominant threat to cities, with the increased likelihood of extreme weather events posing a grave risk to human life and urban infrastructure. By creating green space on unused building facades, it is well documented that green roofs can provide a wide range of benefits to the urban environment including stormwater attenuation, thermal insulation, enhancement of biodiversity, etc. [1,2]. Green roofs are a multi-layer vegetated roof covers with plants and growing media, installed on regular concrete roofs. In terms of design, green roofs can be clustered into two categories: extensive and intensive. Extensive green roofs are the most common type with a thinner substrate layer (60 mm to 150 mm), lighter 2

weight (about 100 kg/m ) and less construction costs [3]. Most of the early green roofs were made from simple, locally available materials including stones and earth with a simple structure drainage layer to create an environment for plants to survive [4]. In the 1970s, in response to calls by planners and architects for a green roof build-up that would require considerably less maintenance work, the modular green roof system was developed in Germany [5]. The drainage layer of modular systems can store water during wet periods, and some are equipped with water retention elements that can return moisture to the substrate during dry weather via the capillary effect and evaporation. Another benefit is the additional water storage provided by green roof drainage elements, which can improve overall system performance for stormwater management [5]. Many studies have quantified the stormwater benefits of green roofs, either through experiments or by developing conceptual and physically based models [2,6,7,8]. However, most of the studies carried out were based on data collected from lab experiments or green roof systems with a simple drainage layer. Thus, to gain knowledge of the modular hydrological performance, there is a growing need to conduct full-scale


experiments with widely used commercial modular green roof systems. For practical implementation of the green roof technology, green roof models are often required to be embedded within catchment-scale runoff modelling to predict their hydrological performance. The main objectives are predicting the reduction in the total runoff volume, and total peak runoff volume and also, the delay in the initiation of runoff [6]. The conceptual model approach is recommended when the interest of the modeller is limited to the runoff profiles and not to the water content profile inside the green roof system [9]. Therefore, the objective of this study is firstly, to design and develop a full-scale experimental site for data acquisition and creation of a database for model development. Secondly, to develop a conceptual model that will be able to predict the stormwater retention and detention performance of the experimental extensive modular green roof systems.

2 Full-scale Experimental Testing of Green Roof Systems The rooftop at Eastside Halls of Residents, Imperial College London, consists of three adjoining flat roofs, 2

with an overall surface area of 480 m . Originally, in 2008 a low maintenance solution extensive sedum green roof was installed with aesthetic, thermal and stormwater management functions. As from April 2014, the center part of roof has been replaced by two typical extensive green roof systems (3m by 4m each), which are the most commonly utilised in the market (Figure 1), and differ in the type of the drainage layer and in the usage of the wicking mat.

Fig. 1 Cross section of green roof systems: 1. Vegetation; 2. Substrate; 3. Drainage layer (with filter sheet on top); 4. Protection layers (consists of root-resistant and waterprooﬁng layers); 5. Roof insulation foam; 6. Wicking mat;

From the top to the bottom, plot A consists of pre-cultivated sedum plants growing on 70 mm depth 2

substrate, a filter layer, an ‘egg box’ shape drainage layer (storage capacity of 3 L/m ), a protection mat layer, a root-resistant waterproofing layer and finally a protection layer. Plot B has the same generic system as the 2

plot A but with 32 mm depth drainage layer (storage capacity of 7.5 L/m ) in combination with wicking mat layer. The wicking mat layer is a water distributing polyester fleece with capillary-effective fibers on one side positioned between the substrate and the drainage layer. The system B is expected to provide a longer detention effect by allowing the wicking mat to empty the water stored in the drainage element after an event. The Eastside green roof experimental site is fully equipped with sensors for on-site meteorological and flow rate measurements. A weather station has been installed to measure rainfall, air temperature, humidity, wind speed and global radiation since June 2013. Each plot is hydraulically isolated, and the runoff volume has been recorded by a tipping counter at 5 minutes time resolution. No irrigation was applied during the data collection period. The soil moisture is recorded using a set of two TDR sensors installed at a depth of 2cm and 4cm from the green roof surface.


3 The Conceptual Model A simple linear reservoir (SLR) conceptual model was developed to simulate the hydrologic behavior of experimental green roof systems as a modification of Kasmin [10] and Palla’s [9] conceptual models. The evapotranspiration process and the drainage flow have been considered in the SLR model to reflect the characteristics of the experimental modular green roof systems. The SLR model considers the green roof systems as divided into three layers, each one corresponding to a storage or reservoir. The first layer represented in the model accounts for the evapotranspiration process is the upper soil of the green roof system, namely the layer corresponding to the root depth of the vegetation. The evapotranspiration process occurs if there is enough soil moisture available in the upper soil to satisfy the needs of the vegetation, i.e. if the soil moisture deficit does not reach the permanent wilting point (𝑊𝑃 [𝐿/𝐿]). The potential soil moisture deficit 𝑃𝑆𝑀𝐷 [𝐿/𝑇] is given by equation (1), where 𝑆𝑀𝐷 [𝐿/𝑇]) is the soil moisture deficit value, 𝑃𝐸 [𝐿/𝑇] is the potential evapotranspiration term

calculated using the

Hargreaves-Samani method [11] and 𝑃 [𝐿/𝑇] is the precipitation term.

𝑃𝑆𝑀𝐷𝑖 = 𝑆𝑀𝐷𝑖−1 + 𝑃𝐸𝑖 − 𝑃𝑖

(1)

The input flux is the precipitation (𝑃 [𝐿/𝑇]) and the output fluxes are the actual evapotranspiration ( 𝐴𝐸𝑃 [𝐿/𝑇] ) and the effective precipitation ( 𝐸𝑃 [𝐿/𝑇] ). 𝐸𝑃 can be defined as the actual precipitation

infiltrating into the substrate, after evapotranspiration occurs. The actual evapotranspiration is formulated by equation (2). 𝐴𝐸 = 𝑊𝑃 − 𝑆𝑀𝐷𝑖−1 + 𝑃𝑖 { 𝑖 𝐴𝐸𝑖 = 𝑃𝐸𝑖

𝑃𝑆𝑀𝐷𝑖 > 𝑊𝑃 𝑃𝑆𝑀𝐷𝑖 ≤ 𝑊𝑃

(2)

Effective precipitation proceeding from the upper soil infiltrates vertically in the substrate and is stored in the pores of the soil matrix. This infiltration process within the substrate layer is modelled by the second layer of the SLR model. The resulting outgoing flux 𝑄𝑠 [𝐿/𝑇] is given by equation (3) where 𝑇𝑠 [𝑇] represents the substrate residence time. 𝑄𝑠𝑖 = 𝑄𝑠𝑖−1 + (𝐸𝑃𝑖 − 𝑄𝑠𝑖−1 )⁄𝑇𝑠

(3)

The third reservoir of the SLR model describes the drainage lateral flow process and is regulated by a pair of equations (4) and (5). 𝑆𝑡𝑒𝑚𝑝𝐴[𝐿/𝑇] is the water stored in the drainage layer. The overflow 𝑄𝑚𝐴[𝐿/𝑇] from drainage layer will be generated after the water stored reaches the maximum drainage capacity 𝑆𝑎[𝐿/𝑇]. The final runoff 𝑄𝐴[𝐿/𝑇] from the green roof plot is then calculated from the drainage layer overflow, using a routing function. 𝑇𝑎[𝑇] is the horizontal routing time. The pair of equations (4) and (5) considers the plot A and analogous calculations can be carried out using the parameters for plot B. 𝑄𝑚𝐴𝑖 = 0 , { 𝑄𝑚𝐴𝑖 = 𝑄𝑠𝑖 + 𝑆𝑡𝑒𝑚𝑝𝐴 − 𝑆,

𝑄𝑠𝑖 + 𝑆𝑡𝑒𝑚𝑝𝐴 < 𝑆𝑎 𝑄𝑠𝑖 + 𝑆𝑡𝑒𝑚𝑝𝐴 ≥ 𝑆𝑎

𝑄𝐴𝑖 = 𝑄𝐴𝑖−1 + (𝑄𝑚𝐴𝑖 − 𝑄𝐴𝑖−1 )⁄𝑇𝑎

(4) (5)


4 Model Calibration and Validation To simulate the runoff from a green roof system using the SLR, model requires mainly three groups of input data namely climate data, initial conditions and model parameters (Table 1). The climate data and initial soil moisture conditions were obtained by measurements from the Eastside experimental green roofs. In the cases where soil moisture data are not available, A.palla proposed an approach to determine initial soil moisture conditions by antecedent dry weather period (ADWP) [9]. However, the determination of the initial soil moisture conditions for the SLR model is outside of the scope of this study. The initial water content of the drainage layer (𝑆𝑡𝑒𝑚𝑝𝐴 and 𝑆𝑡𝑒𝑚𝑝𝐵) is set to zero at the beginning of the simulation. This corresponds to the actual conditions of the storage layer, which was nearly empty at the beginning of the monitoring period either through evaporation or capillary processes. Table 1 The input data, initial conditions and parameters of the green roof SLR conceptual model Type

Parameter

Value

Precipitation (P)

Various from events

data

Potential evaporation (PE)

Various from events

Initial

Soil moisture deficit (SMD)

Various from events and systems

Drainage layer water content (𝑆𝑡𝑒𝑚𝑝𝐴 and 𝑆𝑡𝑒𝑚𝑝𝐵)

Various from events and systems

Climate

conditions

Model parameters

Wilting point (WP [mm])

7.60

Substrate residence time (T [hr])

1.19 Sa = 8.82

Drainage layer maximum storage capacity [mm]

Sb = 17.33 Ta = 6.81

Drainage layer horizontal routing time [hr]

Tb = 7.65

The model parameters were optimised using the Monte Carlo calibration approach [12] with a multi-events optimisation algorithm [13,14] based on selected five events. The Nash-Sutcliffe-Efficiency (𝐍𝐒𝐄) [15] was chosen as the objective function to assess how well the observed runoff (Qobs ) and the simulated runoff (Qsim )

profiles fit. For a single event, the Nash-Sutcliffe-Efficiency (𝐍𝐒𝐄) of each system is given by

equation (6). 𝐍𝐒𝐄 = 𝟏 −

𝐭 𝐭 ∑𝐧 𝐭=𝟏(𝐐𝐨𝐛𝐬 −𝐐𝐬𝐢𝐦 )

𝟐

(6)

𝟐

𝐭 ̅ ∑𝐧 𝐭=𝟏(𝐐𝐨𝐛𝐬 −𝐐𝐨𝐛𝐬 )

For multi-events and two systems (NSEA and NSEB ) calibration, an overall Nash-Sutcliffe-Efficiency (NSEoverall ) can be computed by equation (7). j

j

NSEoverall = ∑N j=N αj (ωA NSEA + ωB NSEB )

(7)

where ωA and ωB are the weighting factor for system A and B, respectively, while αj is the weighting factor for event j. A higher weight indicates higher priority and the sum of weights must be one. In this study, systems

The 7th International Conference of SuDBE2015, Reading, UK; 27-29 July, 2015 1

and events are equally important. Therefore, ωA = ωB = 0.5 and αj = N , N is the total events number. The value of NSEoverall ranges from -∞ to 1 and the value one indicates the simulated runoff matches perfectly with the observed runoff for both systems. In order to assess the SLR model with different type of rainfall in terms of rainfall depth and duration, a combination of small events (with return period less than one month) and relatively extreme events (with up to 1.54 year return period) were chosen for the calibration and validation processes. The hydrologic characteristics of the rainfall events are listed in the Table 2. Table 2 Hydrologic characteristics and overall Nash-Sutcliffe Efficiency (NSEoverall ) index of the observed rainfall events used for calibration and validation. C represents the calibration events while V denotes the validation events Rainfall depth

Rainfall duration

[mm]

[h]

10 Aug (C)

29.6

15 Oct (C)

ADWP [h]

Return period

NSEoverall [-]

13.2

23.3

1.54 year

0.86

7.2

6.8

36.8

< 1 month

0.78

2 Nov (C)

20.0

14.2

419.4

< 1 month

0.79

6 Nov (C)

14.2

6.0

24.9

1.01 year

0.86

11 Dec (C)

12.6

6.9

433.6

< 1 month

0.89

Mean_Calibration

16.7

9.4

187.6

25 Aug (V)

38.4

14.5

351.9

14 Nov (V)

12.8

4.6

21 Nov (V)

32.2

16.9

16 Dec (V)

9.0

26 Dec (V) Mean_Validation

Rainfall event

-

0.84

2.90 year

0.66

127.7

1 year

0.68

135.8

1.61 year

0.75

8.2

111.0

< 1 month

0.85

9.8

16.4

226.1

< 1 month

0.88

20.4

12.1

190.5

-

0.76

5 Results In the Table 2, the NSEoverall values for the calibration (C) and validation (V) events are reported. The hyetographs, observed runoff profiles (grey area) and simulated hydrographs (dash line) for plot A and plot B of four selected calibration and validation events are illustrated in Figures 2 and 3. The calibration results, as shown in Table 2 and Figure 2, confirm the SLR model is able to reproduce a good match of the measured runoff for both plots, with an average NSEoverall value of 0.76 for five selected calibration events. However, the SLR model slightly underestimates the peak runoff rate for both systems, especially for the event with higher rainfall intensity such as the one from 6/11/2014. Note that the optimal value for the parameters Sa and Sb are larger than the values of maximum storage of drainage layer provided by manufacture. This is because of the presence of filter sheet and wicking mat add more water holding capacity to both plots.


In Figure 3, simulated and observed runoff profiles for two validation events are reported. The hydrographs show that the SLR model can reproduce the initial small discharges accurately for both systems and provide a fairly good prediction for the runoff hydropath profiles. The lower NSEoverall

values of the

heavy rainfall events reveal that the applicability of the SLR models decreases with higher rainfall intensity. Although, the SLR model is still underestimating the peak runoff rate (errors range from -10% to -40%), the cumulative volume of runoff proceeding from the both green roofs is well simulated with relative error values less than 10% for all events. Focusing on plot B, for the small event dated at 16/12/2014, the observed runoff was slowly generated even until few days after the rainfall event. The SLR model fails to reproduce the small discharges from plot B, especially for the heavy rainfall events with an underestimation of the total runoff volume of 7 mm on average. However, in general, the SLR model is able to provide a good fit to the measured runoff profile, the total runoff volume and the peak timing, with an average NSEoverall value of 0.76 obtained for validation events.

Fig. 2 The Hyetographs, observed runoff profile and the comparison of the simulated runoff for two calibration events started at 06/11/2014 (with a return period of 1.01 year) and 11/12/2014 (with return period less than one month)


Fig. 3 The hyetographs, observed runoff profile and the comparison of the simulated runoff for two validation events started at 21/11/2014 (with a return period of 1.61 years) and 16/12/2014 (with return period less than one month)

6 Conclusions This study combines experimental studies and model development of the hydrologic performance of two different modular extensive green roof systems installed on a student residence building in London. A simple linear reservoir (SLR) conceptual model for green roof hydrologic behaviour simulation was developed to describe the main processes occurring within modular extensive green roof systems, including the evapotranspiration process in the upper soil layer, the infiltration process within the substrate layer and the lateral flow within the drainage layer. The SLR model is then calibrated using the Monte Carlo calibration approach with a multi-events optimisation algorithm to obtain the best parameter set for both plots. The results obtained from calibration and validation confirm the suitability of the SLR model to describe the hydrologic performance of both green roof systems in terms of the runoff profile, the total runoff volume and the peak timing. However, the suitability of the SLR models decreases with higher rainfall intensity and larger drainage storage capacity. Also, the validation results show that SLR clearly underestimates the peak of discharge. A longer dataset is however needed to confirm the model applicability to a wider spectrum of meteorological conditions. The main advantages of the SLR model are that it requires a minimum input of data and being relatively simple in its conception. Therefore, the SLR model can be implemented, adapted and customized by the user


to reflect the characteristics of specific green roof systems based on various needs.

Acknowledgements The authors wish to acknowledge the financial support of the European Institute of Technology, Climate KIC funded project: Blue Green Dream - http://bgd.org.uk/ (Grant No. APIN0022).

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