## 3 Materials and Methods  
### Description of Laboratory and Field Experimental Setup  
A laboratory experiment was initially carried out on a disturbed soil sample (0.20 m in diameter and 0.18 m in height) filled with soil collected in the same field where the trial was implemented. The soil was oven-dried at 40 \({}^{\circ}\)C, sieved at 0.5 mm and then placed into a Plexiglas cylinder after sealing the bottom side. During the gradual filling of the cylinder, two KD2 Pro Thermal Properties Analyzer (Decagon Devices Inc., Pullman, WA, USA) and one ML3-ThetaProbe soil moisture sensor (Delta-T device Inc., Cambridge, UK) were installed. The commercial KD2 Pro allows the evaluation of the thermal conductivity through two phases, a heating phase which lasts for 30 s, followed by a cooling phase for the subsequent 30 s.  
The measurement of thermal inertia and SWC via the TLHS method and ThetaProbe respectively, allowed the calibrating of the relationship between P and SWC (Equation (2)), using only indoor data. Once the relationship between P and SWC was retrieved, the spatial distribution of SWC was determined in situ via remote sensing, using only shortwave and thermal images. Remote-sensing-derived SWCs were then validated using independent measures. ML3-ThetaProbe soil moisture sensors were placed vertically along the cylinder axis at 0.03 m depth. A high precision balance (model Orma-BC) with a resolution of 0.1 g was used for the continuous monitoring of the cylinder weight, whose values were registered on a data logger every thirty minutes. The sensors provided measures of SWC of a small sampling volume (\(\approx\)7 \(\times\) 10\({}^{1}\) cm\({}^{3}\) around a central rod), whereas the precision balance provided the SWC of the whole soil sample (\(\approx\)2 \(\times\) 10\({}^{5}\) cm\({}^{3}\)). Both SWCs are indirect estimations: the ML3-ThetaProbe allows the conversion of the electromagnetic permittivity of the soil into SWC; the sample SWC using the balance is determined via ponderal measurement and visually estimating the height of the sample (thus the volume). Due to the different sampling volumes and soil-water content distribution within the sample some differences are expected. However, independently of the accuracies of the two measurements, SWC obtained via ML3-ThetaProbe was used to calibrate Equation (2), as the ML3-ThetaProbe and KD2 Pro sampling volumes were of the same order of magnitude (\(\sim\)10 cm\({}^{3}\)). The soil sample was saturated from the bottom. After reaching a soil water content near saturation, the installed sensors started to acquire and to store the data during the subsequent drying process. After 30 days, soil drying was forced by using an air heater, until the soil sample was completely dry. Sensor based measurements of soil water content and thermal properties were collected after water re-distribution. Water and temperature re-distribution started after turning off the heater which was operated for about 10 h each day. Valid measures were assumed by restricting the analysis to temporal windows where the standard deviation of the soil temperatures, provided by KD2 Pro and ML3-ThetaProbe sensors, was under an imposed threshold (0.2 \({}^{\circ}\)C). This also minimized differences in the SWC measures provided by the balance and the ML3-ThetaProbe. A field experiment was also carried out in the south-west of Sicily, Italy, in an area where table and oil olives (Olea europaea L., cv. Nocellara del Belice) are the main crop. The investigated area is located at a latitude of 37\({}^{\circ}\)38\({}^{\prime}\)35\({}^{\prime}\) N and longitude of 12\({}^{\circ}\)50\({}^{\prime}\)50\({}^{\prime}\)50\({}^{\prime}\) E, at an elevation of 123 m a.s.l. The trees are planted on a regular grid of 8 \(\times\) 5 m (250 plants/ha), with mean canopy height of about 3.7 m and a crop fraction coverage equal, on average, to 0.35.