## 2 Materials and Methods
### Models and Analysis
#### 2.2.2 Crop Type Classification and Regional Per-Parcel Grain Yield Estimation  
We performed a pixel-based supervised random forest (RF) classification to differentiate wheat fields from fields of other crops. The classified area was stratified in three zones: II, V, and VI, corresponding to three of Navarre's agricultural zones shown in Figure 1. Each one located in Montana, Media, and Ribera Alta areas, respectively. Following [PERSON] [50] and [PERSON] [27], which state that for RF classifications the training sample should correspond to around 0.25% of the total area, 513 points of parcels of the ground dataset in Zone II (33,345 pixels), 927 in Zone V (58,401 pixels), and 1050 in Zone VI (60900 pixels) formed the training dataset. Figure 3 indicates the points of the parcels from which the pixels from the various analyzed classes were obtained. The points collected were classified into three classes: wheat, bare soil, and other crops. As mentioned before, the target classification areas were delimitated with the available rain-fed and herbaceous crops polygons mask from SIGPAC.  
Considering that the majority of cropland under study (83%) is either bread wheat or barley, we took advantage of the later ripening of bread wheat in order to differentiate it from other crops. After considering both preliminary results and phenological characteristics, differences between wheat and barley were clearer late in the season. This is a consequence of the shorter crop duration of barley, which makes it reach maturity and change color before wheat. Hence, late season Sentinel-2 images (24-05-2018, 03-06-2018 and 18-06-2018) were used for the classification as the moment of greatest contrast.  
Due to their better spatial resolution (10 m) and contrasting capacities in comparison with its other bands, Sentinel-2 B3 (green), B4 (red), and B8 (near infrared) bands were used for the crop type classification. Crop classifications [26; 51] and field boundary delimitation [52] were successfully mapped using B3-B4-B8 images in previous studies with Sentinel-2 data. The trained datasets were divided as follows, 2/3 for training the model and 1/3 for validation. The number of trees was 500 [53]. RF classification and object filters were computed with ArcGis Pro 2.3.0. We applied majority voting of the classified pixels within the agricultural parcels (SIGPAC), as field crops are exclusively grown in monocultures in the region of Navarre, which we confirmed during farmer visits. The pixel's majority from the zonal statistics tool was then used to object filter the classification. With the validation data and the output of classification, a confusion matrix was computed at parcel level in order to obtain classification accuracies. At parcel level, the Fscore of each class was calculated with the Equation (2), where PA refers to producer's accuracy while UA refers to user's accuracy.  
\[Fscore=\frac{2*PA*UA}{PA+UA} \tag{2}\]  
The most suitable multilinear stepwise regression model was extended into all the classified parcels of bread wheat in order to estimate grain yield per field for the three agricultural sub-regions. The resulting wheat cropland and grain yield average per zone were compared to the Navarre regional government's official statistics (www.navarra.es).