## 2 Materials and Methods
### Materials
#### 2.1.1 Crop Field Parcels and Annotations  
We are interested in six categories to gauge the variety of land use and management over winter. The first class of _conventional ploughing_ means mould-board ploughing in  
Figure 1: Foreground polygons: Autumn tillage operations annotated to six classes (colors). Background raster: Red-green rendering of a VH+VV dual polarization Sentinel-1 SAR image. Note: Due to data protection regulations, the polygons are from publicly open similar data from 2016 instead of our actual data, and the classes are randomized.  
autumn to a depth of 20-25 cm. The second class of _conservation tillage_ comprises tilling methods that mechanically disturb the soil to a depth less than 15 cm while retaining most of the crop residues on the surface. The last four classes include cases where the soil is either covered with crop residues (_stubble_), or with vegetation (_autumn crop_, _grass_). Soil with autumn crop has typically sparse plant cover before the growing season, and the soil surface is rough after seedbed preparation, whereas grass vegetation is typically rather thick, and the soil is covered. Stubble fields are covered with stalks and crop residues. In autumn spontaneous regrowth and weeds typically start to re-vegetate the soil. A special category of _stubble field growing catch crops_ means crop fields where a companion crop (catch crop) re-vegetates the soil after the harvest of the main crop.  
The region of interest (ROI) is illustrated in Figure 2 and was chosen on agrometeorological grounds: autumn tillage operations can span over many autumn months depending on the soil moisture conditions up until the soil is frozen and covered with snow. Therefore, the optimal time window to acquire images to monitor winter-time tillage status is shortly after snowmelt and before seedbed preparation in the spring. This time window is typically quite short; from two to four weeks. During this time, the soil dries out fast, but also there may occur sudden snow showers. To select the ROI, we used the regional starting dates of the thermal growing season in 2018. In this region, by mid April, the mean daily temperature permanently exceeded 5 \({}^{\circ}\)C, and snow had melted from open areas. The ROI was used to mask the underlying field parcels for reference data.  
Reference data were annotated as follows. Information on agricultural land use in agricultural registers from two preceding growing seasons--2017 and 2018--were compared. The soil cover class was decided based on the variables of the winter-time vegetation cover related parcel-wise agri-environmental measures declared by farmers. Conservation tillage and vegetation cover are subsidised and subscribed to parcels. The different types of vegetation and crop residue cover were inferred from comparing the preceding years crop types with expertise in crop management. If a parcel was not subscribed to any measure, it was considered ploughed.  
The intersection of the area of the satellite images shown in Figure 2 and of the parcel polygons yields a total of 127,757 annotated parcels. Annotations across the six classes are distributed as follows:  
Conventional tillage, that is, ploughing 46,765; Conservation tillage 15,211; Autumn crop 2681; Grass 24,503; Stubble with no tillage 37,750; and Stubble with companion crop 847. We assigned each parcel exclusively to training and test sets by random sampling in a proportion of 80% for training and 20% for testing, resulting in total of 102,206 samples available for training and 25,551 for testing. However, in the computational experiments we mostly used considerably smaller subsets for studying the accuracy of models trained on less data.