## 1 Introduction
The performance of an SGS combined with a PPS was simulated in laboratory experiments [26] but lacked a validation tool such as numerical modeling. The state of the art shows studies focusing on the hydraulic performance and pollutant mitigation capacity of these systems but leaving the thermal performance aside [27; 28]. On the other hand, other studies conducted field experiments under real conditions, centering their efforts in the analysis of PPSs in combination with an SGS [18; 24]. These studies helped in paving the way towards the understanding of how \"grey\" SuDS design can be improved to integrate SGS and energy conservation. However, they showed the need to further develop the so-called \"green\" SuDS (those with a vegetative base including in NBS) and their potential to house SGS. Following up from these initial steps in the scientific literature, vegetated swales were incorporated into the scientific narrative, outlining the viability of geothermal utilization in other SuDS with a higher ecosystem potential (see Figure 1) [29]. Swales are one of the most promising SuDS techniques due to its simplicity of design and versatility for implementation both in urban environments and transport infrastructures such as roads [30]. There are mainly three types of vegetated swales based on their geometry and hydraulic behavior: dry, wet, and conveyance and attenuation swales [31]. Among these three typologies, the dry swale is considered the most suitable for the potential combination with SGS [29]. These type of swales, due to their geometry, are constructed at a greater depth, making them compatible with the minimum ones required for the installation of GHEs [32; 33]. Before designing a shallow geothermal installation, studying and determining the thermal properties of the materials beneath the point where the heat exchanger will be located is essential (see Figure 1) [34]. These properties can be estimated from the scientific literature, as well as through in situ and laboratory tests. On-site tests, such as the Thermal Response Test (TRT) [35], are a popular tool to measure the ground thermal conductivity in situ. The main drawback is that it is essential to ensure a minimal thermal interference between the surface and the GHE in order to obtain a correct interpretation of long-term results [10], which introduces further complexity to the test. Moreover, laboratory tests have been developed to determine the thermal properties of the soil under controlled scenarios. These include the guarded-hot-plate (GHP), the transient-hot-wire (THW) [36], the box probe, the dual-needle, and the single-needle methods [37]. These methods allow the direct measurement of the thermal properties of materials under both controlled temperature and humidity conditions. The difficulty in determining thermal properties within a SuDS lies in the fact that it is a porous medium, as well as a multilayer heterogeneous system made of varying materials, and therefore, governed by different and rather specific physical processes. As a consequence, determining the effective or equivalent thermal conductivity values of the SuDS technique should be one of the main objectives when working with such complexity in varying layers and physical processes [34]. In addition, previous research in the literature on the potential geothermal utilization of SuDS neither fully accounted for the physical thermal processes associated with the materials analyzed in the studied SuDS techniques, nor considered their energy-oriented design to include energetic parameters in the overall design exercise [14; 34; 35]. As a result, real-world field tests combining ground source heat pumps (GSHP) with PPSs have not performed as well as they should have as the hydrologic and water quality aspects ruled the design scheme and main targets. In this vein, the GHE was unduly influenced by  
Figure 1: Schematic diagram of the proposed system outlined under a standard green swale.