## 4 Results
### Calibration of Thermal Inertia Based on TLHS under Controlled Conditions--The Indoor Experiment
Images were characterized by the shadows of trees moving within the scene during the field acquisition that partially extinguish the incident irradiance reaching the soil; thus, we assumed reliable values of \(\alpha_{SW}\) only over sunlit areas. Shadowed areas were identified through a K-means algorithm [48] and removed from the further calculations. Figure 5 shows two thermal images (pseudo color composite) acquired at 13:21 (left panel) and 18:34 (right panel) solar time. Thermal and VIS/NIR images allowed the assessment of spatial distributions of \(Kp\) (Equation (5)), and thus the remote assessment of SWC values, SWC\({}_{\text{RS}}\). Daytime thermographs were characterized by high spatial variability, whereas the homogeneity of the thermal images increased between sunset and sunrise (night-time images). At night, the vegetation exhibited a higher temperature than the surrounding bare soil, while the dry basket exhibited higher temperatures than the wet one both during the day and at night. Figure 4: Canon optical image (true color composite, left panel) and Tetracam’s Agricultural Digital Camera (ADC) multispectral image (Color-infrared, CIR, composite, right panel), acquired at 13:21 (solar time) on the 30 July 2013. Wet and dry baskets are highlighted by blue and red boxes respectively (left panel). Vegetation cover is distinguishable by the reddish color (near infrared) in the CIR composite (right panel). Figure 5: Thermal images (pseudo color composite) acquired at 13.21 (left panel) and 18.34 (right panel) solar time. Bare soil was, on average, characterized by a lower albedo than the soil covered by vegetation. Moreover, wet soil was slightly darker than dry soil. As expected, the white and black reference markers exhibited the extreme values (the highest and lowest albedos). The irradiance dropping during the daytime, due to the orchard olive trees, affected the sensed albedo; thus, the estimated noon albedo spatial distribution had reliable values out of shaded areas. These latter pixels were removed in SWC elaborations (Figure 6, right panel), by classifying optical and multispectral images through a K-means algorithm. The _ATI*_ spatial distribution shown in Figure 6 (right panel), retrieved according to Equation (6), is considered a proxy variable of the actual SWC (Figure 6, left panel): the lower the _ATI*_, the lower the SWC (see dry basket). The tree canopy within the scene exhibited high _ATI*_ values. Although the model was not able to retrieve the SWC below dense vegetation [49], vegetated pixels were not removed from the image to highlight their outlier behavior. The final Remote-sensing soil water contents were masked through a Boolean operator (based on the K-means classification) to remove shadowed pixels or covered by vegetation. On the other hand, the simulations of soil water content in two plastic baskets were performed using the one-dimensional physically-based model Hydrus-1D. Figure 7 shows the temporal dynamic of SWC simulated by Hydrus-1D (\(SWC_{HID}\)) and the measurements acquired by TDR sensors in both the dry (\(TDR_{d}\)) and wet (\(TDR_{w}\)) baskets. Moreover, SWCs estimated for the three acquisition days (Table 2) by means of the RS-based TLHS model (\(\text{SWC}_{\text{RS}}\)) are also shown. Analysis of the data showed the good performance of the Hydrus-1 Dmodel if compared to the measured soil water contents, \(\text{SWC}_{\text{TDR}}\), with _RMSE_ values equal to 0.01 and 0.005 m\({}^{3}\) m  
Figure 6: Apparent thermal inertia (ATI)* spatial distribution (left panel) and pseudo color composition of \(\text{SWC}_{\text{RS}}\) (right panel); shadowed pixels are in white highlighted masked. Figure 7: Temporal dynamics of soil water contents simulated and measured during the experimental field trial. respectively for the wet and the dry conditions. However, with reference to the model efficiency, E, good performance can be ascertained only in wet conditions (\(E\) = 0.98).