2.2.1 Large-scale assessment using the surface energy balance

On green roof surfaces, most radiative energy comes from solar shortwave radiation and, to a lesser degree, from longwave radiation provided by the ground, the leaves, and the sky. This energy can be partially absorbed or reflected by the vegetation and the soil of the roof. Thus, the net radiative flux (R_n) is the difference between the incident and reflected radiative fluxes. R_n represents the main input of the surface energy balance (SEB), which is exchanged with the green roof, the surrounding atmosphere, and the building structure (see Fig. 2) via the sensible heat flux (Q_h) produced by convection, the latent heat flux (Q_e) due to evapotranspiration from vegetation and soil, and the heat conduction into the soil substrate (Q_g) (de Munck et al., 2013; Marasco et al., 2015). In this way, the energy balance on a green roof can be defined as follows:

All terms of the energy balance are expressed in terms of energy transfer per unit area (W m⁻²). The terms on the right-hand side of Eq. (1) can be either positive or negative, representing losses or gains of heat with respect to the surface, respectively. Conversely, the sign of R_n is positive when there is a heat gain and negative when there is a heat loss (Oke, 1987). Additional heat fluxes transferred by advection, anthropogenic sources, photosynthesis process, and heat stored in the substrate matrix are neglected.

Figure 2Surface energy balance on a green roof.

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As R_n, Q_h, and Q_g are measured by radiometers, scintillometer, and thermocouples, respectively (see Sect. 2.3), Q_e can be deduced like the residual component of SEB:

2.2.2 Small-scale assessment using an evapotranspiration chamber

A portable evapotranspiration chamber built by Cerema (Centre D'études Et D'expertise Sur Les Risques, L'environnement, La Mobilité Et L'aménagement) was installed at specific points across the BGW vegetation to measure Q_e. This device (see Fig. 1) consists of a 1 m² enclosed Plexiglas chamber with a total volume of 0.3 m³ (1 m² × 0.3 m). Gas exchange, specifically water vapour (absolute humidity), H₂O, and carbon dioxide, CO₂, was monitored inside the chamber using a LI-COR LI-7500 gas analyser. The chamber was also equipped with two small rotating fans (to homogenize the air sample inside the chamber), two T107 temperature sensors, and an NR Lite radiometer (Kipp & Zonen), in order to control the variation in microclimate parameters inside the ventilated chamber.

The latent heat flux rate of the volume enclosed by the chamber is deduced from the rise in the absolute humidity (Coutts et al., 2013). Measurements of absolute humidity are made each second over a 2 min period. A linear regression is then carried out on the first minute of measurement (assumed to be short enough to not generate microclimate changes inside the chamber and to attain the saturation vapour pressure; see Fig. 3). The latent heat flux rate is then obtained by the slope of the linear regression (Ramier et al., 2015; Ouédraogo et al., 2023) as follows:

where Q_e is the latent heat flux (W m⁻²), L_v is the latent heat of the vaporization of water, V_ch and A_ch correspond to the respective volume and area of the chamber (0.3 m³ and 1 m², respectively), $\mathrm{d}q/\mathrm{d}t$ represents the absolute humidity variation during the first minute of measurement (g m⁻³ s⁻¹), and 10⁻³ is a conversion factor.

Figure 3Time series of absolute humidity variation (blue) for 2 min (start and end times are shown by the dotted red lines) and the linear regression on the first minute (black).

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2.2.3 Point-scale assessment using the water balance

In a green roof, water input fluxes (precipitation or irrigation) can be released to the discharge/sewage network as runoff or to the atmosphere as ET (see Fig. 4). Therefore, the water balance in a green roof can be expressed as follows:

where P represents the precipitation, I is the irrigation, Q_r is the runoff, and ΔS corresponds to the variation in the stored water in the soil. All of the terms in Eq. (4) are expressed in millimetres per hour (mm h⁻¹).

In extensive green roofs, where no irrigation system is usually implemented (i.e. as is the case for BGW), there is no water infiltration in the substrate nor runoff during long dry periods without precipitation. Therefore, during these periods, the ET flux can be estimated from the water balance equation using the soil water content variations:

ET can then be converted in Q_e as follows:

where L_v (2.45×10⁶ J kg⁻¹ at 20 °C) is the latent heat of the vaporization of water and ρ_w (1000 kg m⁻³ at 20 °C) is the water density.

Figure 4Water balance for a green roof without irrigation.

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2.3.1 Radiometer

To analyse the main components that supply energy to the BGW, a CNR4 radiometer from Kipp&Zonen^® (Kipp&Zonen, 2014) was installed close to the scintillometer receiver unit and 1.5 m above the ground. The objective was the measurement of R_n, the ratio between the incoming and outgoing short- and longwave radiation (see Eqs. 1 and 2). The CNR4 radiometer includes two pyranometers to measure incident (Sw_in) and reflected (Sw_out) solar or shortwave radiation as well as two pyrgeometers to estimate longwave radiation from the sky (Lw_in) and the ground (Lw_out). Due to the energy gain for the surface from incident radiation, Sw_in and Lw_in are positive, whereas the energy reflected, Sw_out and Lw_out, is negative. All radiation components are used to calculate the net total radiation on the BGW as follows:

As a temperature sensor (Pt100) is incorporated in the CNR4, air temperature was also recorded.

2.3.2 Scintillometer

A scintillometer is an instrument that consists of a transmitter that emits an electromagnetic wave signal (with a specific wavelength λ_s) to a receiver which records the intensity variations in the signal (Yee et al., 2015). The variations in signal intensity are caused by the fluctuations in the refractive index of air (n) along a propagation path (see Fig. 5), due to eddies created by variations in temperature, humidity, or pressure in the planetary boundary layer. The magnitude of the variations in a scalar, the refraction index of air n for this case, can be described by the structure function parameter of the scalar $C_n^{\mathrm{2}}$.

Figure 5Operational principle of a scintillometer.

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In this experiment, a large-aperture scintillometer (LAS) MkI produced by Kipp&Zonen^® (Kipp&Zonen B.V, 2015) was installed at the highest levels of the BGW. The path length range of an LAS is from 250 m up to 4.5 km; however, shorter distances of between 100 m to 1 km can be measured if the aperture diameter (D) is reduced to 10 cm using a diaphragm. Another specification of the LAS is the λ_s, which corresponds to 850 nm. An LAS MkI provides spatially averaged measurements of $C_n^{\mathrm{2}}$. Indeed, the LAS MkI measures the variance in the intensity fluctuations' natural logarithm $\left({\mathit{\sigma }}_{\ln I}^{\mathrm{2}}\right)$, which is related to the path-averaged refractive index structure parameter $C_n^{\mathrm{2}}$ as follows:

where D is the aperture diameter of both the transmitter and receiver and R is the path length between both LAS units.

When the intensity of $C_n^{\mathrm{2}}$ is too elevated, the signal becomes saturated and the intensity fluctuations in the scintillometer ${\mathit{\sigma }}_{\ln \left(I\right)}^{\mathrm{2}}$ are no longer proportional to $C_n^{\mathrm{2}}$. This phenomenon is known as the “saturation effect”. To avoid this, the pathlength, the aperture diameter, and the wavelength are used to evaluate the criterion of $C_n^{\mathrm{2}}$ for saturation-free conditions using the following formula: $C_n^{\mathrm{2}}<\mathrm{0.18}{D}^{\mathrm{5}/\mathrm{3}}{R}^{-\mathrm{8}/\mathrm{3}}{\mathit{\lambda }}_{\mathrm{s}}^{\mathrm{2}/\mathrm{6}}$.

The spatial fluctuations in n along the path length are associated with fluctuations in temperature (T), humidity (Q), and (to a lesser extent) air pressure (P). Hence, the structure parameter $C_n^{\mathrm{2}}$ can be related to the thermodynamic structure parameters of air temperature $C_T^{\mathrm{2}}$, humidity $C_Q^{\mathrm{2}}$, and the covariant term C_TQ (ignoring pressure fluctuations):

where A_T and A_Q are constants (functions of the beam wavelength), $\overline{T}$ is the mean value of air temperature, and $\overline{Q}$ is the mean humidity.

Nevertheless, as demonstrate by Moene (2003), $C_T^{\mathrm{2}}$ can be considered to be directly proportional to $C_n^{\mathrm{2}}$, as this is more influenced by the temperature than humidity:

From $C_T^{\mathrm{2}}$, it is then possible to estimate Q_h by applying the Monin–Obukhov similarity theory (MOST) in combination with the following additional meteorological data: air temperature, relative humidity, wind speed, and air pressure (Kipp&Zonen B.V, 2015). MOST derived the universal dimensionless relationship for $C_T^{\mathrm{2}}$:

and

Here, d is the zero-plane displacement height (the height to which the roughness length is added to define the height at which the logarithmic wind profile is equal to zero due to obstacles such as buildings or the canopy), z_LAS is the effective height of the scintillometer beam above the surface, L_MO is the Monin–Obukhov length, T_∗ is the temperature scaling variable, and f_T corresponds to the universal stability function.

In this way, from $C_n^{\mathrm{2}}$ measurements, meteorological and terrain parameters, and the application of MOST relationships, T_∗, L_MO, and the friction velocity u_∗ are iteratively estimated. Finally, Q_h can be computed as follows:

where ρ_a is air density (∼1.12 kg m⁻³ at sea level) and C_p is the specific heat capacity of air at constant pressure (∼1005 J K⁻¹ kg⁻¹).

2.3.3 Thermocouples

According to Fourier's law, the conduction of heat flux into the soil is linearly proportional to the soil temperature gradient $\partial T/\partial z$ of the soil layer (expressed in K m⁻¹) and the capacity of the soil to transfer heat, a property known as soil thermal conductivity k (W m K⁻¹):

During the energy balance measurement campaigns, four thermocouples were placed in the BGW substrate, between the LAS receiver and the CNR4. They were vertically separated by 1–2 cm, aiming to estimate the soil thermal gradient as a direct application of the one-dimensional form of Fourier's law and to quantify the heat flux transfer (Q_g) by means of Eq. (14).

The experimental temperature data gathered by the thermocouples placed in the deepest and most superficial soil locations (z₁=6 and z₄=2 cm, respectively), as shown in Fig. 6, were used to calculate the temperature gradient in the substrate layer profile. (Note that z₃=3 and z₄=2 cm can also be used to compute Q_g closer to the surface.)

Figure 6Time domain reflectometry (TDR) sensor and K-type thermocouple set-up on the BGW.

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As k is a function of several factors, such as the soil density, porosity, water content, or thermal conductivity of individual particles (Vera et al., 2018), there is a great difficulty in obtaining accurate k measurements under field conditions. In this experiment, a value of k was set according to a literature review (Vera et al., 2017) based on the soil moisture conditions of green roofs. Two values corresponding to dry conditions (0.15 W m K⁻¹) and wet conditions (0.85 W m K⁻¹) have been used, but these values can be modified in the Python script to better account for this variability.

As already mentioned, two additional thermocouples were used with the evapotranspiration chamber (see Section 2.2.2) to measure the air temperature in and outside of the chamber.

2.3.4 TDR water content sensor

The space–time variability in the local water content and soil temperature (T_soil) was monitored on the BGW by means of a wireless network of 16 CWS665 sensors (produced by Campbell Scientific^®) placed at different locations on the roof. The sensors use the time domain reflectometry (TDR) technique to measure the propagation time of an electromagnetic (EM) pulse. This pulse is applied to a pair of 12 cm metallic rods inserted into the soil. The time necessary for the incident EM to reach the end of the rods and its reflection will depend on the dielectric permittivity (k_a) of the soil. An empirical universal relationship between k_a and the volumetric water content (VWC) for a homogeneous mineral soil was established by Topp et al. (1980):

From VWC (m³ m⁻³) measurements, variations in the soil water content were determined as follows:

where z_s is the soil layer thickness and Δt is the time step of soil water storage variation.

ET in the BGW was then deduced from Eqs. (5) and (16). It represents the water loss due to soil evaporation and plant transpiration over a dry period.

2.3.5 Gas analyser

The concentration of absolute humidity within the evapotranspiration chamber was monitored using a LI-COR LI-7500 CO₂/H₂O gas analyser (by LI-COR^®; see Li-COR Biosciences, 2017, for details).

Measurement consists of a broadband infrared light source, band-pass filters to select a wavelength range that spans absorption lines for CO₂ and water vapour, and a detector. Light is absorbed by CO₂ and H₂O in the light path, and the reduced intensity observed by the detector is a nonlinear function of the molar concentration of CO₂ and H₂O. The LI-7500 is an open-path analyser that has a sample cell in open air.

Concentration data of H₂O in millimoles per mole measured by the LI-COR LI-7500 were directly converted to grams per cubic metre for the deduction of ET from Eq. (3).