# Hydraulic Characterization of Green Roof Substrates by Evaporation Experiments
## 1 Introduction  
Green roofs are low-impact development measures aimed at mitigating the effects of flooding in urban areas [1]. Green roofs are able to reduce and delay the peak rate into the sewage system through two mechanisms: (i) the retention of rainfall and (ii) the detention of runoff. The retention capacity is the volume of rainfall that is stored by the growing medium and lost via evapotranspiration. Detention refers to the temporal delay occurring between rainfall that is not retained and emerges as runoff [2]. Considering that roofs may represent a large portion of the total impervious surfaces in urban areas, green roofs are one of the key options for hydrologic restoration and stormwater management [3]. Conceptual models for green roof hydrologic functioning, e.g., [4], include lumped parameters that are case sensitive and need to be calibrated against experimental data, thus limiting their general applicability [5, 6]. Physically based models such as Environmental Protection Agency (EPA)'s Storm Water Management Model (SWMM) [6, 7], Soil Water Atmosphere and Plant (SWAP) model [8] and Hydrus model [9, 10, 11, 12] in either one-dimensional [13, 14], two-dimensional [15, 16] and three-dimensional versions [5] weresuccessfully applied to simulate the water balance and the hydrologic response of a vegetated roof. Knowledge of the hydraulic properties, i.e., the relationships between the soil water pressure head, h, the volumetric water content, \(\theta\), and the soil hydraulic conductivity, \(K\), is necessary to apply simulation models based on the numerical solution of the Richards equation [8; 14]. However, few studies have provided a comprehensive hydraulic characterization of green roof substrates. In most cases, the hydraulic properties of green roofs were highly simplified or limited to some specific soil characteristics (e.g., field capacity, wilting point, or particle size distribution) and generally focused only on the soil water retention curves. For example, in [13], only field capacity and wilting point were measured. These data, in conjunction with the bulk density and particle size distribution, were used to estimate the hydraulic properties of substrates using a pedotransfer function. Similarly, Refs. [8; 17] assumed water retention parameters from the literature. [PERSON] and [PERSON] [15] acquired the shape parameters (\(\alpha\) and \(n\)) of the van Genuchten model for water retention [18] from the hanging water column and saturated hydraulic conductivity from laboratory falling head experiments. A comprehensive estimation of both \(\theta\)(\(h\)) and \(K\)(\(h\)) functions for a mineral green roof substrate was conducted by [5] and [14] who used a simplified version of the evaporation method with an extended measurement range [19; 20]. However, they assumed the saturated soil hydraulic conductivity, \(K_{s}\), as a fitting parameter and their estimations of soil hydraulic conductivity function basically relies on measurements conducted in the dry range between 10 and 30% of volumetric water content. In the range of \(\theta\) values near to soil saturation, an accurate determination of \(K\)(\(h\)) (or \(K\)(\(\theta\))) is critically important for highly permeable porous media, like green roof substrates, given they must ensure rapid drainage and avoid water ponding on the surface even during intense precipitation. However, the high non-linearity of hydraulic functions represents a major difficulty as a small change in \(\theta\) may change \(K\) by several orders of magnitude. A very effective and rapid transient laboratory method for simultaneous determination of both \(\theta\)(\(h\)) and \(K\)(\(h\)) relationships for the same sample is the evaporation method, firstly proposed by [PERSON] [21]. The water retention characteristic \(\theta\)(\(h\)) is first estimated from the average water content and pressure head readings at several locations of the soil sample by an iterative procedure.