## 2 Methodology
### Sentinel-1 Time Series Preprocessing  
Only descendent orbits were found suitable for monitoring the ROI due to the S1 acquisition configuration over the study site. Two relative orbits are thus available for EO purposes: orbits 68 for S1-A and S1-B and 141 for S1-A. A detailed overview of the S1 acquisition over the BVCR at multiple incidence angles is provided by [PERSON] et al. [25]. In the case of S1, the acquisitions are equally spaced. One S1-A or S1-B descendent pass is available every 6 days over the study site for the relative orbit 68 approximately at 6.20 a.m. local time. The S1-A acquisitions for the relative orbit 141 have a revisit time of 12 days. Radar data was collected from the GEE catalog accessing the COPERNICUS/S1_GRD_FLOAT dataset. It provides S1 Interferometric Wide Swath (IW) Ground Range Detected (GRD) scenes in dual-polarization VH\(+\)VV, that have been processed using the Sentinel-1 Toolbox to generate radiometrically calibrated, ortho-corrected products. For each BVCR crop campaign, two completed collections of S1 images were created for the two observation geometries, covering a time span of more than 3 years. From December 2018 to January 2021, there were 64 S1-orbit 141 and 103 S1-orbit 68 images (21 S1-orbit 68 images and 11 S1-orbit 141 images correspond to the 2020 winter wheat crop campaign) and 66 S1-orbit 141 and 115 S1-orbit 68 images from November 2019 to January 2022 (21 S1-orbit 68 images and 10 S1-orbit 141 images correspond to the 2021 winter wheat crop campaign). For each S1 scene, the dual-pol Radar Vegetation Index (RVI) [PERSON] et al. [44], was initially generated as follows:  
\[RVI=\frac{4 VH}{VH+VV} \tag{12}\]  
The coherent integration of signals backscattered from different targets in the resolution cell induces the speckle noise to be generated in the S1 data. The use of local statistics is one of the simplest ways to reduce the speckle noise in SAR data [65]. Spatial speckle filtering 7 \(\times\) 7 Refined Lee [66] as coded in [[https://github.com/senbox-org/s1](https://github.com/senbox-org/s1) tbx/]([https://github.com/senbox-org/s1](https://github.com/senbox-org/s1) tbx/) (accessed on 11 January 2023), was applied. The refined Lee approach makes use of local gradient data. It does not blur the edges and minute details, and it does not require picture modeling. Depending on how the edge is oriented, the local mean and variance for both the additive and multiplicative noise instances are calculated from a smaller number of pixels. As a result, the edge becomes sharper and the noise around it is reduced [66]. [PERSON] et al. [28] analyzed the temporal trend of the cross-polarized ratio VH/VV for a variety of winter and summer crops (wheat, rapeseed, maize, soybean and sunflower) in southwest France. They suggested a 7 \(\times\) 7 window size for filtering the speckle of the cultivated region observed by S1. To recover the essential curve shape, S1 time series smoothing is required [67]. Smoothing has the dual objectives of removing random noise and, ideally, maintaining the true spectral signal. For signal denoising purposes, RVI temporal profiles were filtered using an additional Savitzky-Golay (S-G) smoother [68] (window length = 9, polynomial order = 2) at the pixel level. The S-G smoother whit these predefined parameters, fits a polynomial of order 2 to the 9 RVI samples in the window length to locally smooth a noisy signal employing the least-squares concept. Regarding the S-G parametrization, lower values of the polynomial order can cope with low-rate changing phenomena such as crop rotation in the BVCR. The size of the windows is related to the frequency of the S1 acquisitions. The S-G parameters selection methodology was based on the analysis of the power spectrum associated with the S1-RVI signal. High-frequency components in the power spectrum result from the noise's (if it's genuinely random) ability to shift unpredictably from pixel to pixel. On the other hand, the lower frequency range has a greater concentration of signal power [69].