2.1 The Blue Green Wave

The Blue Green Wave (BGW) is a large (1 ha) wavy-form vegetated roof located in front of École des Ponts ParisTech (ENPC, Champs-sur-Marne, France). For now it represents the largest green roof of the greater Paris area. From its implementation in 2013, the BGW has been considered to be a demonstrative site oriented to Blue Green Solutions research (Versini et al., 2018). This experimental set-up started during the European Blue Green Dream (BGD) project (http://bgd.org.uk/, last access: 22 April 2020, funded by Climate-KIC) that aimed to promote a change of paradigm for efficient planning and management of new or retrofitted urban developments by promoting the implementation of BGS (Maksimovic et al., 2013). Monitoring was anticipated and the building was adapted for experimental purposes during its construction. It was also supported by RadX@IdF, a regional project that aimed at analysing the benefits of high-resolution rainfall measurement for urban storm-water management. Today the BGW is also part of the Fresnel multi-scale observation and modelling platform created in the Co-Innovation Lab at École des Ponts ParisTech. Fresnel aims to facilitate synergies between research and innovation, as well as the pursuit of theoretical research, the development of a network of international collaborations, and various aspects of data science (https://hmco.enpc.fr/portfolio-archive/fresnel-platform/, last access: 22 April 2020).

From a technical point of view, the BGW is covered by two types of vegetation: green grass that represents the large majority of its area and a mix of perennial planting, grasses, and iris bulbs (see Fig. 1). Vegetation is laid out on a substrate layer of about 200 mm depth (SOPRAFLOR I966), a filter layer made of synthetic fibre (SOPRATEX 650), and a drainage layer made of expanded polystyrene (SOPRADRAIN). The vertical profile of the structure is presented in Fig. 2. The substrate was initially composed of volcanic soil (around 85 %) completed by organic matter. It is worth noting that 50 % of the grains (in mass) are larger than 1.6 mm and 13 % of fine particles are smaller than 80 µm. The main physical properties of the substrate are synthesized in Table 1 (see Stanic et al., 2019, for a detailed description including grain size distribution, water retention, and hydraulic conductivity curves).

Figure 1The Blue Green Wave monitoring site of ENPC: (a) pictures, (b) vertical representation and flow path lengths, (c) aerial representation showing the monitored area, and (d) profile of the section where the water content sensors were implemented indicating the slopes.

From a hydrological point of view, the BGW is connected to three storage units that collect rainwater coming from the roof (with pipes) but also from several impervious parts around the greened building. One of the storage units is preceded by a smaller unit dedicated to irrigation. The water is then routed to a large retention basin to collect excess volumes of water during a rainfall event before being routed to the storm-water management network. This retention basin was designed (and oversized) because it was considered that the green roof (representing 50 % of the total contributive area) was totally impervious without any retention capacity. Until now in France, there have been neither rules nor guidelines devoted to retention basin sizing that take into account the retention properties of green areas. Therefore the follow-up on such infrastructure is particularly important to develop new guidelines or legislations. For this purpose, the three components of the water balance have been monitored on the BGW. This experiment has been particularly focused on a significant drained area collecting only the green roof contribution (3511 m²). The implemented set-up is described in the following.

Figure 2Vertical profile of the green wave structure.

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2.2 Devices

2.2.3 Discharge measurement

Direct discharge measures are difficult to obtain in drainage pipes. For this reason, indirect measures using water level measurements are usually carried out. Here, water level inside the pipes was measured by a UM18 ultrasonic sensor (SICK, 2018) produced by SICK^®. This sensor has been especially developed to perform non-contact distance measurement or detection of objects. The sensor head emits an ultrasonic wave and receives the wave reflected back from the target. Ultrasonic sensors measure the distance to the target by measuring the time between the emission and reception. Implemented with the face to the water surface, it also measures the variation in the water level. The UM18 sensor is characterized by a nominal range of 250 mm and an accuracy of 1 % for this measurement range. For the UM18 ultrasonic sensor, the dead zone is estimated to be 5 mm. As the sensor has been placed on the top of the conduit, only very high values (higher than 240 mm) could be affected by this dead zone. Since its implementation, water levels have never been higher than 120 mm.

One UM18 sensor has been implemented inside a pipe located in the garage in the building basement (see Fig. 1). With a diameter of 300 mm, this pipe collects the water coming from a large part of the BGW (approximately 1143 m²). A standard 4–20 mA current loop is used to monitor or remotely control these analogue sensors. The current is then transformed in voltage by a resistance of 100Ω. The resulting transmitted signal ranges from 400 to 2000 mV. In order to translate the electric signal in water level values, the following relationship has been applied:

$$\begin{array}{}\text{(5)}& H_{\mathrm{0}}=\left(U-\mathrm{460}\right)\times {\displaystyle \frac{\mathrm{250}}{\mathrm{1600}}}.\end{array}$$

H₀ is the water level in millimetres, U the measured voltage in millivolts, 460 the offset, 250 the modified nominal range in millimetres, and 1600 the nominal range in millivolts.

The water level is then transformed into discharge by using the Manning–Strickler equation (Eq. 6). This formula is usually used to estimate the average velocity (and discharge) of water flowing in an open channel. It is commonly applied in sewer design containing circular pipes.

$$\begin{array}{}\text{(6)}& Q_{\mathrm{0}}=V\times S=K\times R^{\frac{\mathrm{2}}{\mathrm{3}}}\times i^{\frac{\mathrm{1}}{\mathrm{2}}}\times S\end{array}$$

Here V is the average water velocity (m s⁻¹), K the friction coefficient (unitless), S the wet surface (m²), R the hydraulic radius (m), and i the pipe slope (m m⁻¹), which is equal to 0.0074 here. R and S are directly linked to the water level.

$$\begin{array}{}\text{(7)}& {\displaystyle }R={\displaystyle \frac{S}{P}}\text{(8)}& {\displaystyle }S={\displaystyle \frac{\left(\mathit{\theta }-\sin \left(\mathit{\theta }\right)\right)\times r^{\mathrm{2}}}{\mathrm{2}}}\text{(9)}& {\displaystyle }P=r\times \mathit{\theta }\text{(10)}& {\displaystyle }\mathit{\theta }=\mathrm{2}\times \arccos \left({\displaystyle \frac{r-H}{r}}\right)\end{array}$$

K has been chosen to be 85. This value corresponds with a cast iron material.

Figure 3Location of the water level sensors in the storm-water management network.

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Two additional UM18 sensors have been implemented in the two consecutive storage units (see Fig. 3) collecting the rainwater drained by a large contributive area of 3511 m² and including the previous monitored area. The first storage unit is a rainwater tank (characterized by a floor area of 32.2 m²) devoted to irrigation. Filled most of the time, the excess water is routed by a pipe toward the second unit (floor area of 22.5 m²). A relationship similar to Eq. (5) between the voltage measurement and the water level has been adjusted for both units:

$$\begin{array}{}\text{(11)}& H_i=\left(U-\mathrm{0.38}\right)\times {\displaystyle \frac{\mathrm{20}}{\mathrm{1.62}}}-\mathrm{d}h.\end{array}$$

Here U is the measured voltage in volts, the nominal range is 20 cm, and dh (equal to 1.06 cm) corresponds to an additional offset due to the elevation of the sensor

By studying both water level variations, a relationship between the water level measured in the first unit (H₁) and the outflow routing to the second unit Q₂ (and related to H₂) has been established (see Fig. 4). Finally, the total discharge reaching the first unit and collecting the downstream rainfall can be assessed by the following equation depending only on H₁:

$$\begin{array}{}\text{(12)}& Q_{\mathrm{1}}=Q_{\mathrm{2}}+{\displaystyle \frac{\mathrm{d}{H}_{\mathrm{1}}}{\mathrm{d}t}}\times A\mathrm{1}=f\left(H_{\mathrm{1}}\right)+{\displaystyle \frac{\mathrm{d}{H}_{\mathrm{1}}}{\mathrm{d}t}}\times A\mathrm{1},\end{array}$$

where Q₁ is the discharge reaching the first unit and Q₂ the second unit; A1=33.2 m² is floor area of the first unit.

Figure 4Relationship adjusted between the water level H₁ and the downstream discharge Q₂.

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Finally, discharge data were recorded with a time step of 30 s for the sensor implemented in the conduit and 15 s for the one in the storage unit.

2.3 Available output, data processing, and period of study

As already presented in detail in Gires et al. (2018), precipitation data are collected in real time and stored through daily files. Here, these files for a 30 s time step rain rate have been gathered with the help of a Python script to create a long time series covering the whole period of study. Each line contains the time step expressed as YYYY-MM-DD HH:MM:SS and the corresponding rainfall intensity (mm h⁻¹) separated by a comma.

Water content and water level data inside the pipe are collected and stored every night on the HM&Co server in two different files. For this purpose, the Loggernet software produced by Campbell Scientific^® has been used. It supports programming, communication, and data retrieval between data loggers and a PC. Concerning the water level file, each line corresponds to a time step for which the following information is recorded (in each line, these values are separated by a comma):

• exact definition of the time step expressed as YYYY-MM-DD HH:MM:SS,

• item number,

• voltage indicator to ensure the quality of the measurement (it should be close to 12 V),

• internal temperature of the data-logger box,

• unused data coming from a non-operational sensor,

• water level measured inside the pipe (U in Eq. 6, expressed in millivolts),

• unused data coming from a non-operational sensor,

• unused data coming from a non-operational sensor.

A similar format has been chosen for volumetric water content data (note that names of the 16 volumetric water content (VWC) sensors are indicated in the header and are also reported in Fig. 1):

• exact definition of the time step expressed in YYYY-MM-DD HH:MM:SS,

• item number,

• voltage indicator to ensure the quality of the measurement (it should be close to 12 V),

• internal temperature of the data-logger box,

• volumetric water content (expressed as k_a) for the 16 TDR sensors,

• STT_B3: summary transfer time for basis, which is related to the total time required for collecting information from all the sensors that are collected to that base.

Water level data inside the storage units have been collected by using the open-source Arduino Uno microcontroller board that works in the offline regime. This Arduino system was chosen because the storage unit was instrumented a few months after the conduit and because the distance was too long to make a connection between the storage unit and the existing data logger. Data are continuously stored on the 64 MB memory card implemented in the board and copied manually to the HM&Co server once per week. Data contain the following information (in each line, these values are separated by a space):

• item number,

• voltage values for the first storage unit – U1 (in millivolts),

• voltage values for the second storage unit – U2 (in millivolts),

• exact definition of the time step expressed in YYYY-MM-DD HH:MM:SS.

By using Eq. (11) U1 values are transformed into H1 as a part of post-processing. Note that U2 data have been used only for a short period of time after the implementation of UM18 sensors, until Q2=f(H1) functionality has been obtained. After that they were no longer necessary.

3.1 Presentation of the available data set

This data set presented in detail in the next section contains the following files:

• a rainfall file, 2018_0219-0507_Data_rainfall.csv;

• a water content file, 2018_0219-0507_VWC.csv;

• a file of the water level inside the pipe, 2018_0219-0507_Data_discharge.csv;

• a file of the water level in the storage, 2018_0219-0507_Data_Arduino.csv;

• a Python script to select the data, transform the raw data in physical measurements, and carry out some initial analysis.

In detail, the Python script is structured as follows.

• Time period selection. This part could be changed to select a study time period by choosing an initial and final date.

• Data selection and transformation. The data corresponding to this time period are selected in the different files. Electric signals measured by the water level sensors are converted in water level (by using Eqs. 5 and 11) and then in discharge by using the Manning–Strickler equation (Eq. 6) for the pipe and Eq. (12) for the storage unit. In order to smooth the erratic 15 s signal produced by storage unit measurements, the computed discharge data are averaged on a moving window, whose number of time steps can be modified. Dielectric constants measured by the 16 TDR sensors are converted in water content by using the Topp equation (Eq. 3).

• Representation of the computed data. Several figures are plotted to illustrate the variation in the hydrological components in time. The first one represents the corresponding hydrographs for both discharges computed inside the pipe and in the storage unit. The second one synthesizes the water content measured by the 16 TDR sensors. In each figure, the precipitation is drawn on an inverted y axis.

• Computation of runoff coefficients. Runoff coefficient is the ratio between the total amount of precipitation (computed by multiplying the rain depth by the corresponding contributive area) and the total volume of water flowing through the monitored pipe or the storage unit. This value ranging from 0 % to 100 % illustrates the capacity of the green roof to retain rainwater.

3.2 Presentation of the time series

During the available time period including half of winter and half of spring, it rained a total amount of 123.1 mm (see Fig. 5). The rainfall file has no missing value, and six rainfall events can be defined. They correspond to periods with cumulative rainfall depths greater than 5 mm (separated by a dry period of at least 6 h) that caused discharge in both the pipe and storage unit: 7 March (9 mm), 11 March (9.7 mm), 17 March (7.5 mm), 27 and 28 March (13.9 mm), 9 April (9.6 mm), and 29 and 30 April (23.5 mm). These events are obviously not representative of the full range of precipitation events in the area. Nevertheless, it has to be mentioned that since the BGW was monitored (2017), intense rainfall has never caused any flooding on the surface or pipe filling (the higher water level measured was about 12 cm).

Concerning the 16 VWC sensors, 5.6 % of the time steps are considered to be missing data. This is essentially due to two particular sensors that were out of service from 16 March to the end of the study time period. The 16 sensors follow the same dynamic, responding to the several rainfall events (see Fig. 6). Water content measurements decrease simultaneously during two long dry periods, at the end of February and from mid-April to the beginning of May. The sensors show a significant spatial variability in terms of absolute values. These differences illustrate the heterogeneousness of the substrate profiles in terms of hydrological behaviour. This is due to the granular composition of the substrate but also to the wavy form of the BGW. Indeed, the lowest values tend to refer to the upstream sensors, whereas the highest values tend to refer to the downstream ones. Note that the grain size distribution time evolution is difficult to assess. Only the loss of some small particles has been noticed in the conduits.

Discharge data are almost complete. Only one measurement is missing in the pipe and 0.2 % of the total number of time steps for the storage unit. These missing data correspond to the short periods during which the manual collection of the data was carried out. Note that in order to avoid the loss of relevant data, this collection was done during a dry period. Over this time period of 78 d, the runoff coefficient computed for both pipe and storage unit is equal to 70.6 % and 71.1 % respectively. These close values demonstrate the suitability of the monitored set-up. The missing water corresponds to the water retained by the substrate and the vegetation. It should be returned to the atmosphere by evapotranspiration. As already mentioned, Topp's equation (Eq. 3) used to convert the dielectric constant to water content could not be adapted to the specific substrate used for the BGW. For this reason, the dielectric constant data are provided, leaving the reader free to use another relationship to convert these data into water content.

Figure 5Rainfall and computed discharges for the whole time period.

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Figure 6Rainfall and volumetric water content (m³ m⁻³) for 16 TDR sensors.

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3.3 Illustration with a particular event

The 29 and 30 April rainfall event is presented in details in this section. It corresponds to the most intense event with a total cumulative rainfall depth of 23.5 mm. Figure 7 shows the corresponding hydrograph from which the delay between rainfall and discharge peaks can be deduced. It reaches 1 h for the first contributive area (drained to the pipe) and 1.5 h for the second one (drained to the storage unit).

Regarding the question of coherency with previous studies (Palla et al., 2009b, for instance), the water content difference was computed with Topp's equation. The water stored in the substrate during this event was assessed according to the difference between initial and final values. For the 16 sensors, this value ranges between 9.8 % and 13.7 %. This corresponds to a water depth of between 19.6 and 27.2 mm and a storage capacity between 83 % and higher than 100 % of the rainfall (note that a range of between 20.6 and 30.0 mm is obtained with the lab relationship presented in Eq. 4). It is clear the larger values are overestimated but the order of magnitude is consistent with the computed runoff coefficients: 15 % for the surface drained to the pipe and 22 % for the surface drained to the storage unit. This result illustrates the retention and detention properties of the green roof. It has to be recalled that these impacts differ from one event to another depending on the precipitation and the initial conditions.

Figure 7Rainfall and computed discharges for the 29–30 April 2018 event.

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Figure 8Rainfall and volumetric water content (m³ m⁻³) for 16 TDR sensors for the 29–30 April 2018 event (sensor references are indicated by an increasing value at the end of the event).

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