## 2 Methodology
### Sentinel-2 Time Series Preprocessing  
The COPERNICUS/S2_SR image collection over the ROI was assembled using GEE, where the S2 multispectral surface reflectance (S2-L2A) images are available in the form of tiles from December 2018 to current. The cloudy pixel percentage (CPP) was configured to 5 % and the bitmask QA60 band with cloud mask information was used to filter the S2 image collection. The cloud mask permits cloudy and cloud-free pixels to be identified. The 60 m resolution QA60 band includes both cirrus clouds and dense clouds with an indicator specifying the cloud type. Bits 10 and 11 are clouds and cirrus, respectively. The standard GP regression model presented in [PERSON] et al. (2018) was tailored to be scalable into the GEE framework to generate VWC time series at 10 m using the methodology proposed by [PERSON] et al. (2018). The S2 GP VWC hybrid model was trained with in situ measurements collected in the BVCR during the 2020 crop campaign using Gaussian Processes as a core machine learning regression algorithm (MLRA) and an active learning technique (AL) ([PERSON] et al., 2018) to estimate VWC of irrigated winter wheat (R\({}^{2}\) = 0.75, RMSE = 416 g m\({}^{-2}\)). With AL strategies, the number of samples in hybrid modeling can be effectively decreased. Therefore, using an \"optimal\" statistical technique, the MLRA selects the most representative samples from the training dataset, which leads to the GP hybrid model reaching superior accuracies ([PERSON] et al., 2018). Several research efforts have successfully used AL to intelligently reduce the training dataset's size ([PERSON] et al., 2018; [PERSON] et al., 2018; [PERSON] et al., 2018). The in situ VWC values considered the total amounts of water stored in all wheat plant organs including leaves, fruits, flowers, and stalks. The _VWC_ values were then obtained by calculating the difference between the fresh (_FW_) and dry (_DW_) organic matter and referring it to the sowing area (_A_) implicated in the field data collection process. Additionally, seeking to integrate the bare soil contribution, we introduced the fractional vegetation cover (_FVC_) in situ measured values to the calculations of _VWC_:  
\[VWC=\frac{(FW-DW)}{A}\times FVC\ \left[g\ m^{-2}\right] \tag{11}\]  
_FVC_ is defined as the ratio of green vegetation's vertical projected area to the considered land surface extension ([PERSON] et al., 2018; [PERSON] et al., 2018; [PERSON] et al., 2018; [PERSON] et al., 2018). This approach arises as a necessity for the improvement of the concept of canopy water content (CWC) defined as the total mass of water in all plants' leaves per surface unit (see Section 2.5.1 of [PERSON] et al. (2018) for a thorough explanation of the formulas used to determine the _VWC_ values). The S2 GP VWC hybrid model accepts as input the S2 spectral bands at 10 m and 20 m and predicts VWC along with associated uncertainties. The availability of S2 images strongly depends on sky conditions  
Figure 1: Overview of BVCR test sites (ROI) for the winter wheat campaigns of the years 2020 and 2021. The red and orange dotted rectangles delimit the MOGP subsets analyzed in Section 3.3. Reference system: WGS84 (EPSG 4326). (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article).  
over the study site and differs from one crop campaign to other. A total of 44 and 52 cloud-free atmospherically corrected S2 scenes were collected unequally spaced between December 2018 and January 2021 (11 S2 images correspond to the winter wheat 2020 crop campaign from 29 August to 12 December 2020) (see also [PERSON] et al. [54] for details), and between November 2019 and January 2022 (8 S2 images correspond to the winter wheat 2021 crop campaign from 24 August to 22 December 2021), respectively.