Green Roof Water-Balance Model: Experimental and
Model Results of a Case Study of the Alexadriumdaken,
in Rotterdam.
Louwrens Timmer
UvA ID: 10668470
0. Abstract
Urban areas are dominated by impervious soils, which prevent the infiltration of rain. A problem amplified by the short term prediction, made by the IPCC, of more intensified rainfall events in big cities. Green roofs have the potential to reduce the peak discharge of (extreme) rainfall which in turn would prevent sewer system floods. There are further advantages of green roofs besides reducing the runoff. In this research the evapotranspiration (ET) runoff and soil moisture content are analysed with a water-balance model. This Green roof water-balance model based on the VR-WBM, developed by Sherrad & Jacobs, is implemented in Matlab and the simulation results are evualated. This model requires five paramters and operates on a daily basis. The model’s runoff and soil moisture storage predictions were evaluated using the Nash-Sutcliffe efficiency framework. The model ran smoothly in Matlab and the experimental results look realistic. However, the model’s ability to accurately quantify the evapotranspiration, runoff and soil moisture storage was not verified. As evaportranspiration was not measured on the green roofs, while runoff and discharge measurements appear to be inaccurate. For future green roof modelling accurate measurements are required and parameter optimization deserves more attention in future research with this water-balance model.
1. Table of Contens
0. Abstract ... 2
1. Table of Contens ... 3
2. Introduction ... 4
3. Technical aspects of a green roof ... 7
4. Study area ... 9
5. Green roof water-balance model ... 10
6. Methodology ... 13
6.1 Refererence-crop evapotranspiration equation ... 13
6.2 Data collection ... 14
6.3 Data processing ... 15
6.4 Parameters estimation ... 16
6.5 Statistics and model validation ... 16
7. Results ... 19
7.1 Soil Moisture Content measurements ... 19
7.2 Analysis KNMI data & Weather station data ... 20
7.3 Model validation ... 22
7.4 Parameter estimation & sensitivity ... 27
8. Discussion ... 29
8.1 Discussion of results ... 29
8.2 Recommendations for future research ... 30
9. Conclusions ... 31
10. References ... 32
11. Appendices ... 34
Appendix I – Data sheet vegetation green roof ... 34
Appendix II – Data sheet drainage board ... 35
Appendix III – Data sheet substrate type ... 36
Appendix IV – KNMI Makkink equation ... 37
Appendix V – Matlab scripts data processing ... 38
Appendix VI – Nash-Sutcliffe efficiency and coefficient of determination ... 40
Appendix VII – Matlab data script ... 41
Appendix VIII – Matlab model script ... 49
2. Introduction
‘’When man thinks he has to correct nature, it is an irreparable mistake every time’’ (Hundertwasser 1990/2011). According to Hundertwasser, it is important to live in harmony with nature and give back to the earth what you use (Hundertwasser 1990/2011). Hundertwasser was among the first architects to design buildings with green roofs and vegetated walls, and did so in the early seventies. The rapid rate of expansion of the human population has forced people to to live in small communities and cities. Cities are expanding exponentially, and so too are the vast areas of impervious surfaces (Bengtsson, 2010). Stormwater cannot escape through the impervious surfaces and stormwater runoff becomes a greater issue in urbanized areas (Getter & Rowe, 2006). A consequences of which is flooding of the sewers in urban areas (Getter & Rowe, 2006).
According to the Intergovernmental Panel on Climate Change report (2014) extreme weather events are likely to occur on a global scale (IPCC, 2014). Urban areas in particular will endure higher temperatures and extreme rainfall events (IPCC, 2014). This is often associated with urban heat island (UHI) effect (Susca, Gaffin & Dell’Osso, 2011). The UHI effect relies upon the modification of the energy balance in urban areas, which depends on certain factors; thermal properties of building materials, the substitution of green areas for impervious surfaces that limit evapotranspiration, and the decrease in urban albedo (Susca, Gaffin & Dell’Osso, 2011). These predicted extreme precipitation events in urban areas will cause more stormwater runoff and will eventully exceed sewer capacities (Getter & Rowe, 2006).
Considering, 30-50% of the urban surface area is comprised of roofs (Oberndorfer et al., 2012; Sherrard & Jacobs, 2012), one can assume green roofs could help mitigate the flooding of urban areas (Voskamp & van de Ven, 2015). Green roofs reduce stormwater runoff through the water retention properties of vegetated roofs and their subsequent evapotranspiration (Sherrard & Jacobs, 2012). Research shows that 30 to 80% of stormwater can be reduced depending on the type of green roof construction (Getter & Rowe, 2006; Oberndorfer et al., 2010; Sherrard & Jacobs, 2012). A study conducted by Berndtsson (2010) shows that water retention decreases with increasing roof slope.
Although many studies have described the precipitation and runoff relationship in water-balance models, only a few water-balance models are able to quantify evapotranspiration (ET), runoff and soil water storage (Sherrard & Jacobs, 2012). This is because limited data exists on ET, runoff and storage values. However, there are some studies that estimated ET rates. A study conducted by Lazzarin, Castellotti and Busato (2005) predicted that ET rates range from 0.69 to 6.9 mm/day with an average of 1.6 mm/day, applying the Penman-Monteith equation and derived crop coefficients. Greenhouse research done by Berghage et al. (2007) found out that on average ET rates range between 1.9 mm/day and 0.4 mm/day, two and ten days after watering. Voyde et al. (2010) found averages between 1.9 mm/day and 2.2 mm/day in his research on evapotranspiration of green roofs. Although these studies provide extensive data on ET rates, storage and runoff data, both studies were performed in greenhouses, and hence aren’t directly comparable with ET losses from a rooftop. ET rates are relevant for green roof designers and researchers. Green roof construction could be adjusted to the local climate, for example what substrate layer thickness and vegetation are required in specific climates. Better understanding of evapotranspiration processes adds to the optimization of green roofs for the future. For water-balance models evapotranspiration is an indispensable input argument as it is a dominating factor in green roof hydrological processes (Sherrard & Jacobs, 2012). Green roofs also provide shade and
insulation for buildings reducing indoor temperatures 3 to 4 degrees Celsius (Getter & Rowe, 2006). Substrate thickness and subsequently evapotranspiration have a large influence in reducing this energy conservating process (Getter & Rowe, 2006).
Several hydrological models have been developed to calculate the runoff of green roofs. Models such as the curve number method were used to estimate green roof runoff but are limited in their ability to account for former soil moisture content conditions. The HYDRUS-1D model designed by Hilten et al. (2008) uses precipitation, potential evapotranspiration, soil field capacity, wilting point, density and sand, silt and clay fractions as inputs. Most models require too much physical input and need detailed soil profile information to estimate the ET, runoff and soil water storage (Sherrard & Jacobs et al., 2012). There is still no commonly accepted green roof water-balance model that accurately predicts ET, storage and runoff rates.
Accordingly, this research will review the former green roof models and evaluate the water-balance model that is implemented based on the vegetated roof water-balance model (VR-WBM) developed by Sherrard & Jacobs (2012). ET rates will are predicted using the equation for reference-crop evapotranspiration according to Makkink. The underlying reason for using the Makkink equation for the ET calculation is explained in section 5.1 and the methodology. The goal of this research is to run and evaluate a water-balance model based on Sherrard & Jacobs (2012) for a green roof with readily available data in MatLab2015b. Parameters of the model have to be estimated to get acceptable predictions. The parameters will be optimized according to previous literature and the relevant calculations. Thereafter, experimental results will be compared with modelled results using the Nash-Sutcliffe efficiency and the coefficient of determination to assess the models performance. A further objective of this research is to examine if a water-balance model can be implemented on two alternative green roofs. Even though there is no experimental data on actual ET rates of the investigated green roofs. Model results of ET rates are checked to determine if they are realistic compared to previous studies. Thus, the research question is:
‘’To what extent can the VR-WBM of Sherrard & Jacobs (2012) predict evapotranspiration, soil water storage and runoff rates of an experimental roof at Alexdrium over the period of May and June 2015?’’
The research question can be divided into the following sub questions:
‘’To what extent do the measurements conducted by the Municipality of Rotterdam correspond with the KNMI measurements?’’
‘’How sensitive is the model to the five soil and vegetation parameters?’’
‘’How accurate are the predictions of the green roof water-balance model based on the VR-WBM of Sherrard & Jacobs (2012)?’’
Green roofs are being adopted worldwide, yet their performance is still based on assumptions. Their still lacks closure and consensus on the effect that green roofs have on the water-balance of urbanized areas, except for the fact that some water is retained and evapotransirated back to the atmosphere. The exact process by which greenroofs mitigate the effets of heavy rainfall is still not accurately described by existing models. Quantative analyses of specific green roof processes have been developed but a general model is yet to be
deveoped. A general green roof water-balance model is desperately needed to quantify the efficiency of vegetated roofs. This research will further highlight the need of such a hydrological model.
3. Technical aspects of a green roof
Green roofs hve been used for centuries in Nordic countries for the prupse of insulation (Berndtsson, 2010). Hundertwasser designed buildings and maquettes with green roofs and vegetated walls in the early seventies, later that decade a green roof movement begun/ in Germany (Berndtsson, 2010). Green roofs generally consist of four layers: (1) vegetation layer, (2) substrate layer, (3) drainage buffering layer, (4) membrane protection layer (Figure 1) (Optigreen, 2016). The lightweight green roof is one of the simplest solution that Optigreen has to offer and is most suitable for roofs with small slopes and limited structural strength (Figure 1). Furthermore, green roofs are usually divided in two categories, extensive and intensive. Intensive green roofs typically have a deeper soil layer for larger plants, trees and bushes. Extensive green roofs have a thin soil layer for small vegetation. Extensive green roofs are more common because of their low maintenance, and other, costs.
Figure 1. Cross-section of the extensive green roof on the Alexandrium shopping centre (Optigreen, 2016)
The vegetation on an extensive roof develops itself into a self-sustaining plant community (Broks & Luijtelaar, 2015). Intensive green roofs have a roof construction thicker than 150 mm (Broks & Luijtelaar, 2015). They are planted with a wide variety of plants including trees and shrubs requiring deeper substrate layers (Getter & Rowe, 2006). In contrast, extensive roofs can be built on a sloped surface (Getter & Rowe, 2006). Extensive green roofs have a roof construction smaller than 150 mm and the maximum height of the vegetation cover is 500 mm (Broks & Luijtelaar, 2015). Usually extensive roofs are planted with herbs, grasses, mosses and drought-tolerant succulents (Getter & Rowe, 2006).
Conventional (black) roofs are designed to drain the stormwater as fast as possible, whereas green roofs are created to retain the rainwater in the soil layer. After a while the layer becomes saturated and runoff occurs (Getter & Rowe, 2006). While evapotranspiration is at the core of this research, some aspects of green roofs are related to evapotranspiration. Green roofs appear to reduce the heat flux by evapotranspiration by physically shading the roof and augmenting the insulation mass (Oberndorfer et al., 2007). Furthermore, evapotranspiration rates are much higher when water is readily available on vegetated roofs than on roofs with only a growing medium (Oberndorfer et al., 2007). Therefore, storage for rainwater is essential for evapotranspiration rates. Evapotranspiration also depends on vegetation type, vegetation height, soil properties and climate conditions. Hence, evapotranspiration depends on water storage capacity, vegetation and climatic conditions (Getter & Rowe, 2009). However, the runoff will be delayed with a certain time lag, this delay can prevent sewer
systems from overflowing (Oberndorfer et al., 2007). The extent of that time lag depends on several factors: slope/length of slope, media thickness, soil type, vegetation cover, area of green roof, precipitation intensity, location of roof (e.g. face direction) and roof age (Berndtsson, 2010). Other advantages of green roofs are their cooling effect, sound insulation, mitigating air pollution, reducing UHI, increasing life span of roofing membranes, increasing biodiversity and improving aesthetic value (Broks & Luijtelaar, 2015; Getter & Rowe, 2006; Oberndorfer et al., 2007).
4. Study area
The study area of this research was on the Alexandrium shopping centre (latitude 51°56’54 N and longitude 4°33’19 O) in the Municipality of Rotterdam (Figure 2.). Rotterdam has a maritime temperate climate with average precipitation of 52 and 72 mm in May and June respectivly (KNMI). It is approximately 27 km from the North Sea and 5.5 meters below sea-level. The experimental site is divided into two green roofs (15 & 17) and a black roof (17). Green roof 15 is situated 8.6 meter above ground level and green/ black roof 17 is 13.4 meters high. The weather station was located on the latter. The roofs have different surface areas, green roof 15 has a surface of 710 m2 while green roof 17 only has a surface of 150 m2 and the black roof is just 49 m2. According to T. van Hille, personal communication (2016), green roof 15 has a slight slope. Rotterdam, according to the Royal Netherlands Meteorological Institute (KNMI), in May and June has on average minimum temperatures ranging from 7°C to maximum average temperatures of 19°C (KNMI).
The Alexandrium shopping center lightweight green roofs were provided by Optigreen and were planted, approximately two years before the experiment started, in 2014. The roofing modules are 2 by 1 meter (2 m2) and made of recycled HDPE (Highly-density polyethylene). The substrate within the modules used as drainage and growing medium was pumice. When dry, the total weight of the green roof was 53 kg/m2 and the soil porosity was 86%. The substrate layer is only 50 mm thick and vegetation cover constitutes of various types of Sedum album (see Appendix I). According to Optigreen, this green roof has a water retention potential of 40-50% and can store 18 l/m2 (18mm).The vegetation growing on the green roofs are various species of Sedum album (see Appendix I). More information on the vegetation, substrate and drainage board are in the appendices (Appendix I, II and III).
Figure 2. Site map of Alexandrium shopping centre, experimental site indicated with the black star icon (Downloaded from Google Earth Pro).
5. Green roof water-balance model
Modelling in this case is used to assess the environmental benefits and hydrological effects of green roofs. For example, the total runoff reduction and peak flow attenuation and delay could be modelled. Modelling is based on empirical relations identified by the researchers and aims to represent reality as accurately as possible (Palla, Gnecco & Lanza, 2012). The model looks at the relationship between rainfall and antecedent soil moisture content, runoff and soil moisture. The relationship between evapotranspiration and soil moisture content was identified. The water-balance in this model was based on a model designed by Sherrard & Jacobs (2012), which uses daily time steps. The model was slightly adjusted to make it more suitable to this scenario.
S
t+1=S
t+ 𝑃 + 𝐷 − 𝐸𝑇 − 𝐷𝑟 − 𝑅Where St+1 = final soil moisture (mm); St = initial soil moisture (mm); P = precipitation (mm); D = nighttime dew formation (mm); R = runoff from unsaturated soils, between soil medium saturation and field capacity (mm), Dr = direct runoff from saturated soil medium (mm); and ET = Evapotranspiration (mm). So, the total runoff of the green roof is the sum of runoff and direct runoff.
The evapotranspiration is calculated on the basis of a potential Evapotranspiration (ETp) and the soil water content. For this calculation the equation according to Guswa et al., (2002) was applied. Here, it is assumed that the amount of evapotranspiration during the daytime varies, but that there is a relationship between the ETp and the soil water. It is assumed that if the soil water content is lower than the hygroscopic saturation (mm) (Sh) there is no evapotranspiration. If the soil moisture content lies between the Sh and the Ssc (mm) (soil water content at stomatal closure).
0 if S ≤ Sh ET = [𝑆−𝑆ℎ
𝑆𝑠𝑐−𝑆ℎ]
𝐸𝑇
𝑝 if Sh < S < Ssc𝐸𝑇
𝑝 if S ≥ SscETp is calculated with the help of the Makkink equation for reference-crop evapotranspiration (ETr) and proportioned with the crop coefficient (de Bruin et al., 1987).
𝐸𝑇
𝑝=𝐸𝑇
𝑟∗ 𝑐Where c = the crop coefficient; and ETr is calculated accordingly.
𝐸𝑇
𝑟= 𝐶 𝑠 𝑠 + 𝛾𝐾 ↓ 𝜆
Where ETr = reference-crop evapotranspiration (mm/day); C = the Makkink constant (0.65); s = slope of saturation water vapour temperature curve at Ta (hPa/°C); 𝛾 = psychrometric constant (hPa/°C); K = global radiation (J/m2). The values of K are imported from the KNMI database since the small weather station on the rooftop did not measure the global radiation. Furthermore, the equation, as presented above, is a simplified version of the Makkink equation. In the model the equation calculates the parameters for each time step, according to the Manual for evapotranspiration of the Royal Netherlands Meteorological Institute (see
Appendix IV) (handbook KNMI, 2005). In the methodology this will be explained extensively.
To determine the infiltration, the model uses the relationship between available soil storage and precipitation (Sherrard & Jacobs, 2012). This is essential to calculate the runoff later on. Hence, infiltration is calculated as follows.
𝐼 = 𝑀𝑖𝑛(𝑃,
𝑆
𝑀𝑎𝑥− 𝑆
𝑜)Where I = infiltration (mm); SMax = maximum water storage available in de module (mm). based on the infiltration the runoff was calculated with a simple equation.
0 if I + So ≤ Sfc R = 𝐼 +
𝑆
𝑜−𝑆
𝑓𝑐 if I + So > SfcWhere Sfc = soil field capacity, this is the point at which the suction force of the soil is equal to the gravitational force (FAO chapter 2, 2016). If there is more precipitation than the soil medium can store i.e. soil saturation, a direct runoff from the surface will occur.
0 if P < I Dr = 𝑃 − 𝐼 if P > I
Where Dr = direct runoff from saturated surface (mm). In Sherrard & Jacobs’ (2012) model the input of dew is suggested. Nighttime dew formation was based on the change of minimum storage observed after sunset and the maximum storage observed the next morning (Sherrard & Jacobs, 2012).
𝐷 = 0.0085
𝑆
𝑅+ 0.0046Where D = nighttime dew formation (mm); SR = daily solar radiation (MJ/m2). According to Sherrard & Jacobs (2012) daily solar radiation was the best predictor for dew formation based on atmospheric variables and dew forming. Dew occurs when the surface temperature is lower than or equal to the dew-point temperature (Agam & Berliner, 2006). At that point water vapor from the air in contact with the cold surface condenses (Agam & Berliner, 2006). The equation was formulated in the model however the results were not of any significant improvement. As the formula was based on the climate conditions of New Hampshire it was not incorporated in the water-balance. In addition, Sherrard & Jacobs (2012) advised that future studies should focus on this subject as condensation differs locally. Therefore dew was not incorporated in this green roof water-balance model.
To summarize, the model is based on empirical relationships between soil water content and evapotranspiration. The model assumes that everything infiltrates until the soil is saturated. Subsequently, runoff is based on soil water storage and the soil field capacity. Thus, the model requires five parameters. Sh, Ssc and c are the three vegetation parameters and SMax and Sfc are the soil parameters. To find the correct parameters, a lab analysis of soil samples is necessary to determine the field capacity and soil water content at stomatal closure. However, in this research and that of Sherrard & Jacobs (2012) parameters were optimized to predict better results. In the next paragraph the methodology will be elaborated
on. In the methods certain decisions are justified, such as the choice to use the Makkink formula instead of the ‘standard’ Penman-Monteith formula.
6. Methodology
This research will be performed by using MatLab2015b, in which the water-balance model can be designed and run on the loaded data to model the water-balance for the green roofs in Rotterdam. These results will then be statistically analysed to assess the predictive performance of the model. The first paragraph will outlines the data collection process, thereafter the data processing is described. Lastly the model operations are explained.
6.1 Refererence-crop evapotranspiration equation
When it comes to evapotranpiration various calculation alternatives are given. Penman developed a method to calculate the evaporation from open-water in 1948 (De Bruin et al., 1987). Which is presented in the famous equation below:
𝐸 =1 𝜆
𝑠(𝑄∗− 𝐺) + 𝜌𝑐𝑝[𝑒𝑠(𝑇𝑎) − 𝑒𝑎]/𝑟𝑎
𝑠 + 𝛾
Where E = evaporation [kg/m2/s]; 𝜆 = specific heat of evaporation of water [J/kg]; s = slope of the curve of saturation water vapor pressure versus temperature at Ta [mbar/K]; Q* = net radiation [W/m2]; G = soil heat flux density [W/m2]; 𝜌 = density of air [kg/m3]; c
p = heat capacity of air [J/kg/K]; es = saturation water vapor pressure at temperature Ta [mbar]; Ta = air temperature [K]; ea = water vapor pressure [mbar] and 𝛾 = psychrometric constant [mbar/K]. Moreover, Penman developed an empiral method to estimate the evapotranspiration from a well-watered short grass cover with the crop coefficient approach (De Bruin et al., 1987). Penman (1948) was one of the first scientist, who discovered that radiation was one of the important factors in the evapotranspiration process (Hooghart & Lablans, 1987). Monteith (1965) derived a equation that described the transpiration from a dry vegetated surface, using the same physiscs as Penman in 1948 (De Bruin et al., 1987). The equation is shown below:
𝐸𝜆 = 𝑠(𝑄
∗− 𝐺) + 𝜌𝑐 𝑝 𝐷/𝑟𝑎
𝑠 + 𝛾(1 + 𝑟𝑠/𝑟𝑎 )
Where D = es(Ta) – ea. The Royal Netherlands Meteorological Institute used this equation for evaporation and evapotranspiration calculations since 1965 (De Bruin et al., 1987). Micrometeorological observations suggest that temperate arable crops stongly depend on net radiation for their evapotranspiration (Hooghart & Lablans, 1987). Priestley and Taylor (1972) discovered that the second term in the Penman-Monteith equation is usually one-fourth of the size of the first term. This led to the equation suggested by Priestley and Taylor (1972):
𝐸𝜆 = 𝛼 𝑠 𝑠 + 𝛾 (𝑄
∗− 𝐺)
Here α is a coefficient with values between 1.2 and 1.3; G = soil heat flux [W/m2]; Q* = net radiation [W/m2]; s and 𝛾 are the same as in the previous equation. It appears that G is usually small for grassland (De Bruin et al., 1987). Furthermore, the net radiation is about 0.5 times the incoming short wave radiation in summertime in the Netherlands (De Bruin et al., 1987).
Therefore, Makkink found the following equation for well-watered grassland as early as 1957.
𝐸𝑇
𝑟 = 𝐶1 𝑠 𝑠 + 𝛾 𝐾 ↓ 𝜆 + 𝐶2Where C1 and C2 are the Makkink constants. Evapotranspiration of well-watered short crops is primarily determined by the net radiation and air temperature (Hooghart & Lablans, 1988). Factors such as wind speed and saturation deficit seem to be less important when evapotranspiration of short crops are considered (De Bruin et al., 1987). Therefore the choice for the Makkink equation was made. Comparing the Makkink- and the Penman-Monteith equation it appeared to be a better option for this research. The literature supported this statement as will be explained next. The Penman-Monteith equation is the most well-known method to estimate the evapotranspiration from a well-watered short grass cover. However, in this study the choice for Makkink was evident since the equation performs nearly as accurate as the Penman-Monteith equation (Hooghart & Lablans, 1988). The second argument to choose for the Makkink formula is that the equation is remarkably simple: only air temperature and global radiation are required as input. Both are measured directly and very accurately by the KNMI. The Royal Netherlands Meteorological Institute already started measuring global radiation in 1965 on different stations (e.g. De Bilt, Eelde, Den Helder and Vlissingen) (Hooghart & Lablans, 1988). The last argument is that the Makkink equation appears to have a better performance than the Penman-Monteith equation under dry conditions (De Bruin et al., 1987). The Makkink equation was not calculated as presented in the former formula but calculated using the Handbook of the KNMI. Where each parameter is calculated for each new time step in the model. The complete formula is visualized in appendix IV.
Figure 3. Weather station and rain gauge on green roof 17.
6.2 Data collection
A major part of the experimental data was obtained from the Municipality of Rotterdam, who started their research project on green roofs in the summer of 2013. However some required data had to be imported from the KNMI database. Since global radiation was not measured on the green roof, an hourly global radiation data sets was obtained from the KNMI database. In addition, an hourly precipitation and temperature data sets were acquired from the KNMI database. In co-operation with Stadsontwikkeling Rotterdam the Municipality of Rotterdam would like to ‘quantify’ the hydrological and thermal effects of green roofs, which is ambitious but possible with the correct data and knowledge. The Municipality was assisted by
the water board of Schieland en de Krimpenerwaard in their runoff measurements. The devices that were installed for discharge measurements measured the discharge between 0.3 and 10 m/s. For the other measurements a small weather station established on green roof 17 measured over a time period of 12 months: air temperature, relative humidity, precipitation and wind speed. The wind speed device did not operate for some reason. But the rest of the data was collected properly except during a power outage for a couple of days in July and October. Soil moisture content was obtained with two devices per green roof measuring m3 moisture per m3 substrate. The soil moisture content sensors were calibrated in the laboratory using a substrate sample. The sensors were tested at 40 °C. All data was sent to an Argus-data logger, which saved the information every minute (see Table 1).
The data acquisition period was 12 months and 2 months were needed for data processing. The data was processed in an excel-file which was sent by the Municipality after personal communication (2016) with T. van Hille (hydrologist at the Municipality of Rotterdam). Additional data was acquired from the KNMI database as global radiation was not measured by the weather station. In addition, air temperature and precipitation duration and hourly precipitation amount, combined the precipitation (mm/hour), were downloaded. Even though the small weather station measured all those values a comparison was made to check whether the measured data by the Municipality corresponds with the KNMI data. In the next paragraph the process of data structuring is elaborated.
Variables Measuring device Measuring period Measuring frequency Location Air temperature [°C] - 27th of April -14th of December
1 min interval Weather station SMC-1 [mm] Campbell CS 616 27th of April -14th
of December
1 min interval Green roof 15 & 17
SMC-2 [mm] Campbell CS 616 27th of April -14th of December
1 min interval Green roof 15 & 17 Discharge [L/hour] JUMO 406020 (paddlewheel), DN30 27th of April -14th of December
1 min interval Green roof 17
Discharge [L/hour] JUMO 406020 (paddlewheel), DN15 27th of April -14th of December
1 min interval Black roof 17
Discharge [L/hour] WATERFLUX 3000 by Krohne 27th of April -14th of December
1 min interval Green roof 15 Precipitation [mm Campbell ARG-100 rain gauge 27th of April -14th of December 1 min interval (0.2 mm resolution) Weather station Table 1. Overview of required variables measured by the Municipality of Rotterdam.
6.3 Data processing
The acquired data sets were obtained from two different institutions therefore the data sets were not corresponding. The KNMI data was hourly and the green roof data was stored as minutely data. Considering that the model runs with daily time steps interpolation was necessary to fit the data for modelling. Firstly, the data set from the green roof was imported and structured into the relevant vectors. The period between May and June will be modelled and analysed therefore the vectors have to be shortened to obtain only the essential data for the research. While examining the data extensively borders for the vectors were chosen. Since the model works with whole days we started on 28th of April and ended the simulation period on the 30th of June. As the data starts on 12:00 on the 27th of April the first 12 hours were cut out of the vectors. The data ended on 14:00 on the 14th of December therefore the last 5.5
months were also cut out. Now vectors of 28th of April to the 30th of June are left. However the data was stored per minute, which delayed the progress data processing. In Matlab2015b the data was processed with some Matlab functions. The script is denoted and explained in appendix V.
6.4 Parameters estimation
The model needs five parameters to run these have to be estimated and optimized for the model performance. The model requires three vegetation parameters, Sh, Ssc and c, and two soil parameters SMax and Sfc. The soil characteristic SMax was determined by calculation as the storage capacity of the study roof is known. The other parameters had to be estimated on the basis of literature and previous models. The vegetation characteristics Sh, Ssc and the crop coefficient were referenced to the soil moisture content values and literature review. The soil field capacity was estimated as it was not investigated in the laboratory or found in the literature of similar studies. The parameter value Sfc was optimized for the model’s performance.
The crop coefficient was based on the literature and the VR-WBM of Sherrard & Jacobs (2012). Although they based their crop coefficient on the evapotranspiration that was measured in their experiment. While, ET was not measured during my experiment the crop coefficient in based on literature. According to Lazzarin, Castellotti and Busato (2005) the crop coefficient varies depending on the relative humidity of the soil. The crop coefficient approaches 0.50 in well-watered conditions and 0.30 in stressed water conditions (Lazzarin, Castellotti & Busato, 2005). Therefore the crop coefficient was optimized on 0.4 for the model simulation.
The vegetation parameters Sh and Ssc are very important as they determined the rate of evapotranspiration when there is not enough water available for evapotranspiration equal to potential ET. These values were based on the soil moisture content in the green roofs. Taking into account that the Sh and Ssc determine the relationship between the soil moisture content and the ET rate. When optimizing the Sh and Ssc the values have to be adapted to the soil moisture content. As there is almost no information and knowledge about these parameters on green roofs no reference were used for the estimation of these parameters. Therefore, the parameters were estimated Sh = 0.1 mm and Ssc = 1.25 mm for the simulation.
The soil characteristics were determined by a calculation and estimation. The SMax was calculated as the maximum storage capacity is 18 L/m2 resulting in 18 mm. And the soil’s field capacity was determined based on the runoff calculation. Runoff occurs when infiltration plus soil moisture storage exceeds the soil field capacity at a specific time step (see Runoff equation). Based on the infiltrated volume and the capacity the soil drains to field capacity on a daily basis. When estimating the field capacity the value cannot be to high or to low. Considering that runoff will occur on the basis of the sum of the infiltration and soil moisture content minus the field capacity negative values could appear as the Sfc is too high. Therefore the parameter was estimated at 1.8 for model simulation. These parameters values were used to simulate the model. In the next chapter the results will be presented
6.5 Statistics and model validation
In this paragraph the methods of the data sets evaluation will be explained, the applied statistics and model validation method will also be clarified. Before the statistics will be applied the data sets will be evaluated. First, the soil moisture content measurement will be assessed. The data will be visualised for each roof to verify the measurements of each device
thereafter the figures will be evaluated. To assess the model’s predictive power the Nash-Sutcliffe method is applied (Nash & Nash-Sutcliffe, 1970). The method developed by Nash and Sutcliffe is usually applied to assess the predictive power of hydrological models (Krause, Boyle & Bäse, 2005). The observed soil water storage and runoff will be compared to the predicted values. The green roof water-balance model also gives ETr as an output however there are no observed values to compare them to. Therefore the reference-crop evapotranspiration will be compared to the ETr calculated by the KNMI on weather station 344 in Rotterdam. Additionally, the air temperature and precipitation data from the green roof weather station will be compared to the KNMI data. To check whether observations by the weather station were accurate.
According to Allen, Pereira, Raes & Smith (1998) the relationships between two weather data sets from two weather stations can be tested with a linear regression model. In this research Matlab2015b is used for modelling and analysing therefore the function fitlm is applied. The reference observations Xi are the observations of the KNMI and are considered homogeneous Yi are the observations of the green roofs.
ŷ
𝑖=𝛼
𝑓+𝛽
𝑓𝑥
𝑖 (𝑖 = 1,2, … , 𝑛)Where f refers to the full set; i refers to the number of observations. The homoscedasticity hypothesis is accepted when the residuals of the dependent variables to the regression line can be considered to be independent random variables (Allen, Pereira, Raes & Smith, 1998). The coefficient of determination r2 is analysed to examine how much of the observed dispersion is explained by the prediction (Krause, Boyle & Bäse, 2005). The value of r2 lies between 0 and 1 where a value of zero means no correlation and a value of 1 means that the scattering of the prediction is equal to that of the observation (Krause, Boyle & Bäse, 2005). Furthermore, xi, yi and the regression line are plotted to visually verify whether the homoscedasticity can be confirmed. The linear regression analysis will be applied on air temperature, precipitation and reference-crop evapotranspiration.
The performance of the green model is assessed with the Nash-Sutcliffe efficiency E (Nash & Sutcliffe, 1970). The range of E lies between -∞ and 1.0, which is a perfect fit and an efficiency below zero indicates that the mean value of the observed time series would been a better predictor than the model (Krause, Boyle & Bäse, 2005). It is calculated as:
𝐸 = 1 − (∑ (𝑂𝑏𝑠𝑖− 𝑃𝑟𝑒𝑖) 2 𝑁 𝑖=1 ∑ (𝑂𝑏𝑠𝑖− 𝑂𝑏𝑠̅̅̅̅̅𝑖)2 𝑁 𝑖=1 )
Here N = number of observations; Obs = observed value; Pre = predicted value; and 𝑂𝑏𝑠̅̅̅̅̅ = average observed values. The theory was implemented in Matlab to perform the calculations. The script is visible with explanations in appendix VI.
The biggest disadvantage of the Nash-Sutcliffe method is that it not very sensitive to over- or underprediction during low flow periods (Krause, Boyle & Bäse, 2005). For runoff predictions this leads to overestimations during peak flow and underestimation during low flow. The coefficient of determination r2 can also be used to calculate the correlation with the same MatLab function. It is calculated as:
𝑟2= ( ∑𝑁𝑖=1(𝑂𝑏𝑠𝑖− 𝑂𝑏𝑠̅̅̅̅̅)(𝑃𝑟𝑒𝑖− 𝑃𝑟𝑒̅̅̅̅̅) √∑ (𝑂𝑏𝑠𝑖− 𝑂𝑏𝑠̅̅̅̅̅)2 𝑁 𝑖=1 √∑ (𝑃𝑟𝑒𝑖− 𝑂𝑏𝑠̅̅̅̅̅) 2 𝑁 𝑖=1 ) 2
Where 𝑃𝑟𝑒̅̅̅̅̅ = the average predicted value. This method will also be used to assess the models predictions together with the Nash-Sutcliffe efficiency the model will be evaluated. In this chapter, the methods of this research were elaborated. The following chapter will look into the results according to these methods.
7. Results
In this chapter, the results of the MatLab analysis of the green roof data, KNMI data and the green roof water-balance model are explained. First, the soil moisture content measurements will be assessed. Secondly, showing the results of the analysis between the KNMI data and the weather station data thereafter the results of the model analysis will be shown.
7.1 Soil Moisture Content measurements
The soil moisture content was measured with the Campbell CS 616 device on two locations on each green roof. The measurements of each roof are presented in one figure. The results are visually interpreted.
Figure 4. Soil moisture content on green roof 15 & 17.
Above the soil moisture content is visualized and what immediately stands out is the first peak in both figures is significantly higher than the other peaks. The peaks in the soil moisture content fairly correspond with the precipitation peaks (see Figure 5). Later on in the measuring period rainfall events of the same intensity does not seem to correspond with the soil moisture content. Hence, there appears to be a problem with the measurements. The first peaks measured on the two roofs seem to realistic soil moisture content values (5.0 – 5.5 mm). Thereafter the peaks fluctuate between 1.0 and 2.0 mm. One hypothesis is that the measuring device used was detached from the soil after the first heavy rainfall event. When the sensors are not compacted within the soil the measurements could not be as accurate as when they are firmly put in the soil. Therefore the results of the model could significantly delineate from the observed values, which will be discussed later on.
Figure 5. Soil moisture content of green roof 15 & 17 plotted with the KNMI precipitation.
7.2 Analysis KNMI data & Weather station data
Temperature and precipitation measured on the weather station are visualised in figure 6. This will give an overview of the similarities and dissimilarities of the measurement devices. In this section the results of the analysis between the KNMI data and the weather station data are explained. This will be done with visual verification and a regression analysis.
Figure 6. Precipitation and temperature at the weather station on the green roofs and of the Royal Netherlands Meteorological Institute.
As visualised above, the precipitation data appears to deviate significantly from the KNMI precipitation data or could contain measuring errors. Although local rainfall intensity could differ but such a large discrepancy will be unlikely. The KNMI precipitation data was taken as reference and in the regression analysis will become clear that the precipitation measured by the green roof was significantly different. The average temperature over the measuring period was 14 °C while the KNMI measured a temperature of 13.8 °C therefore the measurements seems to be accurate (see Figure 6). Nevertheless, a regression analysis will be conducted to confirm the hypothesis that the green roof air temperature data is correlating with the KNMI air temperature data.
There is a significant difference expected between the two precipitation data sets and this was confirmed with the regression analysis. The coefficient of determination r2 was determined at 0.610 this indicates that there is correlation between the two precipitation data sets however the dispersion of the predictions significantly differs to that of the observations. The p-value 0.221 of the predictor term suggests that the changes in the predictor are not associated with changes in the response. Furthermore, in figure 7 the homoscedasticity hypothesis can be visually rejected.
Figure 7. Regression between the KNMI daily precipitation data and the green roof daily precipitation data. Considering the air temperature data sets appear to correlate over the measuring period. The mean of the two data sets corresponded fairly, however with the mean a correlation between the data sets cannot be scientifically be verified. Therefore, a regression analysis was performed. A correlation is expected between the two variables and the regression confirmed the relationship. The coefficient of determination r2 was determined at 0.986, which indicates that the observed dispersion is significantly explained by prediction. The p-value of the predictor term is 0.035, which indicates that changes in the predictor are associated with changes in the response. In addition, the regression is visually analysed to verify the homoscedasticity hypothesis (see Figure 8)
The first sub question can be answered: the precipitation data appears to significantly differ from the measurements of the KNMI. Local rainfall intensity could be an argument for the difference in measurements considering that the distance between the two locations is 7.3 km. Another explanation is possibly be that the tipping bucket could not handle have rainfall intensities, although this seems not likely. Therefore the precipitation data set of the KNMI was used to improve model prediction.
Figure 8. Regression between the KNMI air temperature data and the green roof weather station data.
7.3 Model validation
In this section the green roof water-balance model predictions will be evaluated. First time series of the model output will be visualised. Secondly, ETr and KNMI ETr will first will compared by a regression analysis. Considering that the air temperature and the global radiation are correctly measured the reference-crop evapotranspiration by KNMI would be similar to the computed reference-crop evapotranspiration according to Makkink. In figure 9 the regression between KNMI ETr and calculated ETr to check the model performance on the applied equation.
In the former section time series of the precipitation and the are temperature were shown. Here all other time series of the green roof water-balance model is shown. Firstly, potential ETr according to Makkink, actual ETr with the estimated crop coefficient and the predicted ETr are presented. Secondly, the Storage results are presented thereafter the (direct) runoff are visualised. Lastly, the nighttime dew formation is visualised although this was not incorporated in the water-balance.
Figure 9. Time series of Potential Eref (red), Eref with c (green) and the predicted Eref (blue).
Next the final soil moisture content and the runoff are displayed in one figure to show the correlation between soil moisture content saturation and runoff as explained by the model’s formulas. The direct runoff is also visualised together with the soil moisture storage (see Figure 10).
Lastly, the nighttime dew formation is visualised. This variable was not incorporated in the water-balance as the calculation was customized for the local climate of the research of Sherrard & Jacobs (2012). The dew formation was visualised to show what the variable theoretically adds to the water-balance (see Figure 11). Dew formation variables ranges from 0.4 mm/day to 0.26 mm/day. However the dew equation in this model was not adjusted for the climatic conditions on the green roofs. Therefore the dew formation was excluded from the water-balance model.
Figure 12. Regression between KNMI ETr and calculated ETr with KNMI data being homogeneous. In the figure above the regression analysis is visualised (see Figure 12). The hypothesis that the there is a correlation between the two data sets is confirmed. The r2 was determined at 0.99 which means that the dispersion of the predictions is equal to that of the observations. It can also be assumed that the equation was applied correctly in MatLab2015b.
The model outputs runoff and soil moisture storage results are presented in this paragraph. The soil moisture storage 1 for green roof 15 was predicted rather badly as visualized in the figure below (see Figure 13). The coefficient of determination r2 0.006 is nearly zero, which means that there is nearly no correlation at all (see Table 2).
SMC Coefficient of determination r2
SMC-1 Green Roof 15 0.0060
SMC-2 Green Roof 15 0.0102
SMC-1 Green Roof 17 0.0043
SMC-2 Green Roof 17 0.0016
Table 2. Coefficients of determination r2 for each soil moisture content measurement.
The Nash-Sutcliffe efficiency is another approach to assess a model’s performance. The following values for the efficiency E were found using Matlab2015b (see Table 3). The range of the E values range from -∞ to 1.
SMC Nash-Sutcliffe Efficiency E
SMC-1 Green Roof 15 -104.78
SMC-2 Green Roof 15 -272.71
SMC-1 Green Roof 17 -63.47
SMC-2 Green Roof 17 -74.65
Table 3. Nash-Sutcliffe Efficiency E for each soil moisture content measurement.
The runoff was predicted rather badly as visualized in the figure 14. The coefficient of determination r2 0.0657 is nearly zero for the modeled discharge of green roof 15, which means that there is nearly no correlation at all (see Table 4). The coefficient of determination r2 are visualized.
Figure 14. Regression between observed runoff and observed runoff.
Runoff Coefficient of determination r2 Runoff Green Roof 15 0.0657
Runoff Green Roof 17 0.0104
The Nash-Sutcliffe was also used to determine the efficiency of the model regarding the runoff predictions for the green roofs (see Table 5).
Runoff Nash-Sutcliffe Efficiency E
Runoff Green Roof 15 -37.89 Runoff Green Roof 17 -2.10
Table 3. Nash-Sutcliffe Efficiency E for each roof’s discharge
The runoff was probably measured inaccurate while there was visually no runoff. When the discharge of green roof 15 and 17 and black roof 17 are plotted with the precipitation the probable measuring error is visualised (see Figure 15). There are remarkable distinctions observed between the discharge of the three green roofs. The significant differences between the measured discharge could be the results of measuring only when the drainpipe is filled. The drainpipe of green roof 15 has a diameter of 110 mm and the other two roofs have drainpipes with a diameter of 30 mm. The flow meter was obviously calibrated for these measurements. Another reason could be that the drainpipes are blocked with dead leaves or debris (personal communication, T. van Hille, 2016).
Figure 15. The discharge of green roofs 15, 17 and black roof 17 with the KNMI precipitation.
7.4 Parameter estimation & sensitivity
The model required five parameters to run properly. First the vegetation parameters were estimated. According to Lazzarin, Castellotti and Busato (2005) the crop coefficient for sedum in general ranges between 0.3 and 0.5 depending on the relative humidity of the soil. However if the evapotranspiration was measured on the green roofs the crop coefficient could be calculated on the bases of the reference-crop evapotranspiration which is much more accurate. The resulting parameters for Sh = 0.1 mm, Ssc = 1.25 mm and c = 0.4 for this model. The vegetation parameters are now estimated and the soil characteristics SMax and Sfc need to be optimized. The modules in the green roof can store up to 18 L/m2, with this information the SMax can be determined on 18 mm. Taking into account that the substrate
layer is 50 mm thick and the storage is therefore 0.018 m3 / 0.05 m3, which means that there is 36% maximum storage. Sfc was set on 1.8 to prevent predicted runoff values below zero. This results indicate that the soil’s field capacity is low and parameters estimation is very difficult when operating with a short research period.
These values were chosen as they predicted the most realistic values. For example, when the parameters Sfc and the crop coefficient were varied with a significant increase or decrease, the model predicted unrealistic values for runoff and storage variables. Sfc and the crop coefficient are the most sensitive parameters of the model. While, the parameter Ssc has a significant influence on the ET rates there parameter is not very sensitive. There model is not very sensitive for the Sh and SMax parameters as the hygroscopic saturation is low enough that it will not occur and the SMax is only sensitive when decreasing it by 50-100% which is unrealistic.
In this next chapter the results presented above are discussed. Furthermore, recommendations for future green roof water-balance model research and design are specified. The measurements are discussed as many data sets were inaccurate. Suggestions for future research and model analyses are given.
8. Discussion
In this section the research is discussed in order to lay a foundation for further and future research on green roof water-balance models. In the first section, the results and measurements are discussed. In the second section, recommendations for future research are suggested.
8.1 Discussion of results
The soil moisture content measurements were measured with a Campbell CS 616, which is a small device consisting of two sensitive pins that are put in the soil. The results visualised a probable deviation in the soil moisture content, while in the first period the peaks range to 4.5-6.0 mm, the latter periods show no values higher than 2.0 mm. In the results there was already suggested that a measurement error was recognized. The two pins of the two measuring pins are positioned under the vegetation layer in the substrate layer. It was suggested that after the first intensive rainfall event, on the 5th of May 2015, the pins were loosened from the soil. Therefore the pins probably did not measure the soil moisture content correctly for the research period. Another reason for the measurements to be incorrect is that the measurements are unrealistically low.
Air temperature and precipitation measured by the weather station on the green roofs were analysed with regression statistics. The precipitation data from the green roof seem to be lacking the high peaks that occur in the KNMI data. It could be that the rainfall intensity differs on location, although this seems highly unlikely as the KNMI weather station and the green roof weather station are only 7.3 km apart. While this distance argument cannot be excluded it appears that the peaks are missing systematically. It could also be discussed that local climate conditions on rooftops could differ with climate conditions on the ground. Therefore it could be discussed if meteorological data measured on ground level could be used as input data for green roof models. Observing the visualized results of the precipitation comparison the KNMI seems more reliable. Therefore the KNMI precipitation data was used for model simulation. The air temperature however did significantly correspond with the air temperature observed by the KNMI.
Unfortunately, the reference-crop evapotranspiration was not measured on the green roof location. Therefore the crop coefficient could not be determined for this research unfortunately. The crop coefficient is an important and interesting parameter not only for this research but also for future research on green roofs. Although the lack of the crop coefficient, the evapotranspiration was calculated correctly and the model simulation for ET seems to work smoothly. However, the choice for the Makkink equation could be discussed, as the Makkink equation has no room for the wind variable, which can play an important role in the process of evapotranspiration. In the methodology the Penman-Monteith formula and Priestley-Taylor equation were discussed but found inappropriate for this research as too many input arguments where required. The Priestley-Taylor equation requires soil heat flux as an input argument therefore it was not an option for this research as the soil heat flux was not known in this research. The Penman-Monteith formula requires measurement of net radiation, soil heat flux, air temperature, relative humidity and wind speed. Like the Priestley-Taylor equation it requires soil heat flux as an input argument however it also requires wind speed which is another unknown factor in this research. A wind speed meter was incorporated in the small weather station but did not operate during the measuring period for an unidentified reason. The KNMI weather station of Zestienhoven measures wind speed and the variable could be imported from their database. However, there could be argued that the wind
speed was measured on ground level and the climate conditions on a rooftop are probably different from the ground level. Therefore the final decision was the Makkink equation as it did not require wind speed and soil heat flux. According to the literature it is suggested that the Makkink equation performs better under dry conditions. Furthermore its behaviour is similar to the Penman-Monteith equation. The choice for the Makkink equation was therefore justified.
The results of the first model runs are not promising as the statistics are suggesting that the model predicts both the runoff and final soil moisture storage inaccurately. However, the results could also be interpreted the other way around, assuming that the observed soil moisture content as well as the runoff were measured incorrectly. Consequently the model could have predicted the realistic results of the two variables. However, such a hypothesis cannot be proven without the correct data on soil moisture storage and runoff.
The parameters were optimalized during the model development. Except for one all parameters were estimated for an optimal model simulation. However, the crop coefficient was determined on the basis of current literature, while there was no experimental evapotranspiration data of the green roofs available. The other three parameters were chosen on model prediction power. Unfortunately, this did not go smoothly as the input data was inaccurate. Therefore, the model simulation was disturbed and the output was not significantly corresponding with the observations. However, the model appears to operate smoothly and the output seems to be realistic.
8.2 Recommendations for future research
Measurements obtained for this research were inaccurate and that significantly disturbed model calibration. Although the crop coefficient was missing, the literature provided satisfying options. Due to unreliable measurements the model parameters were difficult to optimize. For future research, a lysimeter is therefore recommended for soil moisture content measurements. This will give a much more detailed and accurate measurement. A small-scale lysimeter experimental set up was conducted by DiGiovanni, Gaffin and Montalto (2010). Usually the green roof is separated in small squares, which support the vegetation, substrate and drainage layer and the lysimeter is installed underneath.
For the precipitation measurement on the roof regular checks are advised or the installation of a second device or rain gauge. Also one rain gauge located on ground level close to the building is recommended. The differences between discharge measurements on roof 15 and 17 were also remarkable. The report of the municipality suggested that the discharge was only measured when the whole drainpipe was full. Maybe this led to underestimated discharge values and subsequently to the significant difference between the predicted and experimental model results. Although the Municipality of Rotterdam is not a scientific institution correct measurements are obviously vital for valid research results. The aim of this research was the comparison of the experimental results and the predicted results. Therefore, better measurement techniques are advised for future research.
Extensive research is needed on this topic as green roofs are constructed without knowing exactly how much effect it has on the water balance of urban areas. Furthermore, green roofs play a role in the attenuation of the peak flow to sewer system during extreme rainfall events. Infiltration surface for rainfall are limited in cities as impervious surfaces dominate the urban areas nowadays. Another important characteristic of green roofs is the aesthetic value they add to the city. There is still much to learn about green roofs and how they behave under various (urban) climate conditions.
9. Conclusions
As the world population will keep on growing, more and more people will live in cities. As a result, open land will be exchanged for impervious surfaces such as buildings, streets and parking lots leading to a intensified runoff peak during rainfall events. Previously the water could infiltrate and evapotranspirate on these open lands, whereas now the water will directly flow to the sewage system or river. Besides the IPCC predicts more intensified precipitation events in urban areas in the nearby future due to climate change. This will increase the pressure on the sewage systems. Subsequently the risk of sewer system flooding will significantly increase and will bring many people in danger. Green roofs are design to attenuate the peak flow during heavy rainfall events and retain the water instead of directly draining it to the sewage system. In this research the green roof water-balance model based on a model of Sherrard & Jacobs (2012) was validated with experimental data. Therefore three sub-questions had to be answered. The precipitation data obtained from the Municipality of Rotterdam did not correspond with the KNMI data while the air temperature data greatly corresponded with the KNMI data. The exact reason for the deviation in the measured precipitation cannot be identified however.
The model’s sensitivity for the five parameters was checked to identify the parameters influencing the model output significantly. The model’s runoff predictions appeared to be very sensitive to the field capacity parameters and the crop coefficient parameters. The crop coefficient determines the rate at which water is lost to the atmosphere and the field capacity regulates the runoff quantity. The Ssc parameter is also sensitive for adjustments as it determines the rate of ET. When the Ssc parameters is lower the potential ET rate is increased. Therefore, parameter optimization is very important for these three parameters although the other two cannot be forgotten.
The accuracy of the model’s predictions was also evaluated with the appropriate statistics. There were no experimental results on ET rates therefore only runoff and final moisture storage were evaluated. All Nash-Sutcliffe efficiencies were below zero meaning that the model has no correct predictions at all. The coefficients of determination were also not significant therefore it can be concluded that the predictions of the green roof water-balance model are not accurate at all. Explanations are ranging from measurement errors to faulty parameter optimization though it appears to be a combination of both.
In conclusion, the VR-WBM was implemented successfully in MatLab and all data sets were imported and handled correctly. However the model’s performance was far from optimal and the model results did not correlate with the experimental results. Several reasons for the weak performances were contemplated and discussed. Curious precipitation, soil moisture content and discharge measurements resulted in a tough parameter optimization, which appear to be the biggest obstacle in successfully implementing a green roof water-balance model based on the VR-WMB by Sherrard & Jacobs (2012). While cities are turning into mega-cities with millions of inhabitants, the infiltration of rain water becomes a challenging issue worldwide. It seems that a general water-balance model describing the water flows in a green roof in detail is still to be developed. Therefore, extensive research on an VR-WBM model is essential when assessing the effect of green roofs on urban water system.
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