# Hydraulic Characterization of Green Roof Substrates by Evaporation Experiments
## 2 Materials and Methods
### Evaporation and UHG Experiments  
Given the evaporation method yields the drying branch of the unsaturated hydraulic functions (Figure 1a), the UHG experiment was performed prior to the evaporation experiment and following a descending sequence of applied pressure heads. A device similar to the one described by [26] was used (Figure 1b). Samples were saturated from the bottom on the porous plate of a glass funnel, with an air entry value of \(-40\) cm, connected to an outflow tube that could be moved in height to establish a given \(h\) value at the bottom of the sample. A pressure head at the top of the sample was applied using a tension infiltrometer with an \(8.5\) cm diameter porous disk (Soil Measurement Systems, Tucson, AZ, USA). A thin layer of \(2\) mm sieved material was spread on the surface of TMT and ATV to ensure a good and stable hydraulic connection with the infiltrometer plate. The same \(h\) value was applied at both the upper and lower boundaries in order to establish and maintain a downward unit gradient flux. Under the assumption that the hydraulic gradient is a unit, the unsaturated hydraulic conductivity is equal to the measured downward steady-state flux. Steady-state conditions were considered to be achieved when the infiltration rate, at each imposed pressure head value, was constant with time. A sequence of pressure head values of \(-6\), \(-12\) and \(-18\) cm was applied in succession.  
At the end of the UHG experiment, the sample bottom was sealed and three micro-tensiometers were horizontally inserted into holes drilled at \(2\), \(6\) and \(10\) cm heights in order to measure pressure head profiles during the evaporation experiment. The ceramic cups of \(3\) cm length and \(0.6\) cm outer diameter were connected to pressure transducers (SDEC, Reignac sur Indre, France). The soil core was then placed on a scale (maximum load \(4000\) g, resolution \(0.1\) g) and the evaporation process was allowed to start. Data from scales and tensiometers were automatically acquired and recorded by a CR1000 datalogger (Campbell Scientific, Shepshed, UK) at \(1\) min time intervals until the upper tensiometer stopped working properly. A bluer was used to enhance the soil evaporation rate. For the entire duration of the evaporation experiments, the laboratory temperature was maintained at \(22\pm 1\)\({}^{\circ}\)C.  
Figure 1: Experimental setup for the Wind evaporation method (**a**) and apparatus for measuring unsaturated hydraulic conductivity with UHG method (**b**).  
Depending on the characteristics of the tested substrates, the duration of evaporation experiments was from 72 to 170 hr for TMT, from 141 to 324 hr for ATV and from 222 to 489 h for MIX. The range of the explored pressure head values was rather limited, with the minimum measured \(h\) value equal to -282, -87 and -439 cm for TMT, ATV and MIX, respectively, but in line with the results obtained by [14] for TMT and [40] for coarse textured green roof substrates.  
At the end of the experiment, the tensiometers were removed and the final water content of the substrate was determined by weighing the sample after oven drying at 105 \({}^{\circ}\)C. The average water contents of the soil sample at different times were backward calculated from recorded weights and final water content. For the calculation of hydraulic properties with the Wind iterative method [21], the soil core was divided into three compartments, centered on the tensiometer positions, with a constant thickness of 4 cm.  
The volumetric water contents at a \(h\) value of \(-\)150 m, \(\theta_{150}\), were determined by the pressure plate extractors on three replicated samples of 5-cm diameter by 1 cm height [25].