## 2 Materials and Methods
### Data Preparation  
Given the time-intensive nature of collecting grazing calendars and the resulting acquisition of a limited reference dataset, this study leveraged unsupervised learning to explore the potential for identifying the moving status of a parcel based on the temporal variation of predicted CSH. The central working hypothesis posits that moving events can be discerned from abrupt differences in CSH or related descriptive statistical parameters within the grazing period. To facilitate the identification of these potential patterns, the dataset underwent initial processing. Therefore, we investigated three data aggregation strategies (DAS) grounded in the distribution and variation of MEAN_DAY and SD_DAY over the grazing period. These strategies were tested both in combination and separately, with a reduction method applied to these features. The primary objective was to optimize computational resources and address concerns related to model overfitting. Specifically, the three DAS applied per parcel and year were the following: In Strategy 1, we aggregated MEAN_DAY and SD_DAY to compute the mean, standard deviation (sd), skewness (sk), and kurtosis (ku) for the considered grazing period (yearstats dataset: 8 features (4 \(\times\) 2 features)). In Strategy 2, as the temporal density of data was not the same per parcel and year, we standardized MEAN_DAY and SD_DAY weekly (31 features as there are 31 weeks during the grazing season) for each studied trait (week_std dataset: 62 features (31 \(\times\) 2 features)) by subtracting the mean and dividing by the standard deviation. Finally, in Strategy 3, fast Fourier transform (FFT), a dimensional reduction method, was applied to the week_std dataset to reduce the number of components to 10, which is a good compromise to limit the mirror effect of this kind of modeling (week_fft dataset: 20 features (10 \(\times\) 2 features)). To optimize computational resources, all values in the datasets underwent rescaling before dimension reduction. This was achieved by dividing each value by 250, the maximum value within the calibration set used to construct the Cubist model for predicting CSH. For the daily standardization outlined in Strategy 2, the recording days were organized in a daily-spaced dataset covering the period from 1 st April to 3 rd November (e.g., 217 days). The choice of 3 rd November was made to evenly divide the dataset into seven segments, facilitating comparison with other time-standardized datasets. Subsequently, date gaps \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Year** & **Nparels 1** & **Pixel CSH** & **MEAN_DAY** & **SD_DAY** \\  & **(mm)** & **(mm)** & **(mm)** & **(mm)** \\ \hline
2018 & 86,218 & 56.0 \(\pm\) 19.9 & 56.2 \(\pm\) 17.5 & 7.0 \(\pm\) 5.3 \\
2019 & 86,617 & 63.8 \(\pm\) 21.6 & 62.8 \(\pm\) 17.6 & 8.1 \(\pm\) 6.2 \\
2020 & 91,224 & 60.1 \(\pm\) 20.1 & 59.6 \(\pm\) 16.6 & 7.5 \(\pm\) 6.0 \\
2021 & 136,892 & 59.2 \(\pm\) 18.5 & 58.8 \(\pm\) 15.7 & 7.3 \(\pm\) 5.0 \\ \hline \hline \end{tabular} 1  
\end{table} 
Table 2: Summary statistics (mean \(\pm\) SD) for predicted compressed sward height (CSH) at the pixel level, and aggregated averages per parcel and date (MEAN_DAY) with corresponding standard deviations (SD_DAY) across the 4-year period. (highlighted in red in Figure 2) where MEAN_DAY and SD_DAY were unavailable due to meteorological reasons were filled using linear interpolation, as we made the hypothesis that grass growth is linear within a short period, summarized as follows:  
\[CSH_{i}=CSH_{prev}+\left(CSH_{next}-CSH_{prev}\right)\times\frac{dt}{ndays}\]  
where \(CSH_{i}\) = the interpolated date, \(CSH_{prev}\) = the previous date of CSH prediction, \(CSH_{next}\) = the next available date of CSH prediction, \(dt\) = the number of days between the previous prediction and the interpolated date, and \(ndays\) = the length of the time gap between the previous and next predictions.