## 2 Materials and Methods
### Unsupervised Analysis to Detect Moving Events  
The 12 datasets (resulting from 4 years \(\times\) 3 DAS) served as input for two distinct unsupervised algorithms for categorization (UACs): isolation forest (IF) and k-means. The IF algorithm, proposed by [48], employs random partitioning of the dataset to identify anomalies. Given the expectation that mown parcels would exhibit different behavior than grazed parcels, it can be assumed a priori that mown parcels would be detected as an abnormal population. To this end, the contamination threshold was set to 0.2, a value aligned with the prevailing management practices in the Walloon region of Belgium [49]. Indeed, the predominant management modality for permanent pasture, comprising 42.7% of the usable agricultural area, involves either grazing or a combination of grazing and mowing, which is ten times more extensive than temporary pastures in terms of surface area [50]. The second unsupervised algorithm tested was based on a k-means algorithm [51]. The k-means algorithm is a clustering method that segregates a dataset into k distinct, non-overlapping subsets called clusters by iteratively assigning data points to the cluster with the nearest mean and updating the cluster centroids. As this method necessitates specifying the number of clusters beforehand, 2 to 5 clusters were tested to evaluate the partitioning. From the requirement for interpretability, a 5-cluster limitation was chosen to parameterize the k-means.  
The interpretation of the clusters generated by both UACs relied on the following hypothesis: groups exhibiting higher average values for MEAN_YEAR and SD_YEAR should predominantly consist of mown parcels. This was inferred from the expectation that grass height in mown parcels would be significantly higher than in grazed parcels until the mowing event, and the variability in this parameter would be more pronounced. Following the identification and labeling of mown and pasture clusters, all parcels categorized within these groups over the 4-year period were incorporated into three distinct datasets corresponding to week_std, week_fft, and year-stats datasets.  
Subsequently, supervised learning was conducted using partial least squares discriminant analysis (PLS-DA) on the three datasets, where the mown character was designated as \"1\" and the pasture character as \"0\". PLS-DA aims to identify patterns indicative of mowing events by maximizing the correlation between these variables and the occurrence  
Figure 2: Temporal density of the CSH predictions across the four studied grazing seasons. Green marks actual prediction dates, red marks temporal areas with a linear interpolation to fill the gaps, and light blue marks the periods with a closest value replacement to fill the gaps.  
of moving events. To address the imbalanced proportion between mown and pasture modalities, the up-sampling technique from the caret package was applied before the PLS-DA. Outputs from the stratified ten-fold cross-validation informed the determination of the number of components in the PLS-DA model, mitigating overfitting and providing an assessment of the overall accuracy of the obtained classification. In addition to cluster predictions, PLS-DA enabled the prediction of the probability of being in the mown cluster. To evaluate the similarity in signals produced by these different models, correlations between the probabilities obtained from the six constructed PLS-DA models were calculated. Furthermore, for the three types of datasets, we examined the number of occurrences that would be labeled as mown with a probability exceeding 50% for k-means and IF.