## 2 Materials and Methods
### Agricultural Operations and Remote Sensing Data  
In this study, the data regarding the detection of soil tillage operations were provided by the Instituto de Financiamento da Agricultura e Pescas (IFAP--in English: National Paying Agency for Agriculture and Fisheries). Its mission is to validate and make payments resulting from the financing of the application of measures defined at the national and community levels within the scope of agriculture, rural development, fisheries, and related sectors. It also proposes information and communication technology policies and strategies in the field of agriculture and fisheries. For this work, the field notebooks of 73 subsidized farmers for the agricultural year of 2020-2021 (between October 2020 and September 2021) were used. Figure 1 shows the location of the farms considered. These field notebooks recorded real soil tillage operations performed on each farm. The notebooks were filled out by the farmers and verified by a third-party certifier. All field notebooks were digital and provided by the farms to the IFAP under different subsidy schemes. From these field notebooks, it was possible to identify all the agricultural operations, including the soil tillage operations, recorded with the following information: the parcel ID (a unique numerical identified for each parcel), land cover (crop type class), and date of the operation. The identification of farmers was excluded from this paper for confidentiality reasons. The geographic limits of the parcels with identified soil tillage operations were collected using the Portuguese Land Parcel Identification System (LPIs), which is also managed and made publicly available by the IFAP [26]. The LPIs is updated annually and provides  
Figure 1: Spatial distribution of the parcels used to detect soil tillage operations. information on the geographic location and delimitation of each agricultural parcel, as well as the crop type declared by farmers during their CAP subsidy application. For this study, we considered the 2021 version of the LPIS provided by the IFAP. Using the geographic limits of the identified parcels, the remote sensing times series data were collected. We utilized remote sensing data from two satellite sensors: Sentinel-1 (SAR data) and Sentinel-2 (multi-spectral optical data). The data acquisition for both Sentinel-1 and Sentinel-2 was conducted through Google Earth Engine (GEE) [27]. For Sentinel-1, we used C-band Level 1 Ground Range Detected images provided by GEE, acquired on a descending orbit in interferometric wide swath (IW) mode. The analysis incorporated VV and VH polarization bands, and we also calculated the cross-ratio (CR) VV/VH, which has been demonstrated in previous studies to be effective for identifying agricultural operations [20]. For Sentinel-2, we used Level 1C Bottom-Of-Atmosphere (BOA) scenes, also sourced from GEE (Appendix A). To ensure minimal cloud interference, only images with less than 30% cloud cover were selected. Additionally, any remaining cloudy pixels were identified and masked using the Sentinel-2 \"quality_cloud_confidence\" masks. Spectral data from Sentinel-2 were utilized to calculate the Normalized Difference Vegetation Index [28], which has also proven useful in identifying agricultural operations [23; 29; 30]. Appendix A presents the dates of all images used and not used due to cloud coverage. For both Sentinel-1 and Sentinel-2 data, a 15-day average was computed for each parcel throughout the study period, from October 2020 to September 2021. This timeframe aligns with the agricultural year in Portugal, capturing the full cycle of cultivation activities, which typically begins in the autumn. In total, 24 bi-monthly data periods were considered for each parcel. For 15-day periods without available Sentinel-2 data due to cloud cover, 'NaN' values were assigned. To address gaps due to cloudy images, a linear interpolation method was employed, based on [PERSON] et al. [31]. To ensure dataset consistency, we computed the mean pixel value at the parcel level.