## 2 Materials and Methods
### Methodology  
The overall methodology is presented in Figure 2. Its rationale is to set-up a monitoring framework using no prior knowledge about the field and no models available to draw upon for active samples selection. A completely data-driven active sampling procedure  
Figure 1: An orthomosaic of the study area. Colored rectangles indicate the plots. Each color refers to a fertilization treatment. allowing a prediction starting from scratch is proposed for the retrieval of calibration data necessary for PLSR. The prosed active sampling method is based on the concept of entropy \(H\) as defined by [PERSON] (1954)  
\[H=\sum_{i=1}^{N}-P_{n}\log_{2}P_{n}, \tag{1}\]  
where \(P_{n}\) is the normalized probability of the \(n\)-th histogram quantization level and \(N\) is total number of bins. Entropy is a measure of the quantity of information carried by a signal. The higher the entropy, the higher its information content. In the literature, entropy is usually exploited as selection criterion for query by bagging (EQB). In this technique, the samples were selected based on the maximum disagreement between a committee of classifiers obtained by bagging. First, different training sets were defined by replacement within original training data. Then, each training set was used to train the selected classifier to predict labels for each unlabeled sample. Finally, the entropy of the distribution of the different labels associated to each sample was calculated with the purpose to evaluate the disagreement among the classifiers. The samples showing the maximum entropy, i.e., those with maximum disagreement among the classifiers, were added to the current training set ([PERSON] et al., 2017). For the purposes of this paper, it is particularly of interest as its calculation was very fast, even relative to large datasets. Moreover, being a histogram shape parameter, it is suitable to be used with vectors composed by heterogeneous data, such as spectral measurements and vegetation indices, without projection within an auxiliary homogeneous feature space. According to the diversity paradigm of active learning techniques, the entropy is exploited as parameter to discriminate whether the sample under consideration is adding information to the set already collected. The hypothesis behind the method is that, within a given hypercube, reflectance differences between different areas of the image are due to variations of the biophysical parameter under investigation. These areas are represented by the plots, in which, according to ([PERSON] et al., 2017), the spectral response was averaged in order to extract a single feature vector for each of them (see Figure 3). The histogram was calculated using all the available spectral features, starting from a plot randomly selected. At the time of the first acquisition, all the components of the feature vector were considered for the calculation of the histogram. Figure 2: Proposed workflow. The active sampling procedure is fed by any observation available. Regression is implemented using all the data available at time \(t_{i}\) to generate the prediction of the biophysical variable of interest. The histogram entropy was calculated according to Equation (1). A new plot was added by appending its spectral content to the vector constituted by the one previously considered. In other words, the vectors representing the spectral response of the plots were concatenated to form a longer one of \(k\times n\) elements, where \(k\) is the number of available spectral features and \(n\) the number of plots considered. The entropy of the new histogram was calculated and, if higher than the previous value, the plot was marked as selected for field sampling. The procedure was repeated up to the end of available plots. Marked plots are ideally sampled to retrieve ground data. They can be used to tune future sampling campaigns. In particular, the Pearson linear correlation coefficient [31] between the average plot response and ground data is computed in order to guide the successive active sampling procedure.