# Object-Based Time-Constrained Dynamic Time Warping Classification of Crops Using Sentinel-2
## 2 Materials and Methods
### Study Areas and Datasets
#### 2.1.5 Temporal Patterns of Reference Samples  
The two test areas present complex phenological patterns of the crops. For simplicity, we will detail here the temporal characteristics of a crop based on the NDVI time series. All five vegetation indices have values between \(-1\) and \(1\), with NDVI and GNDVI having predominantly higher values than NDRE, SAVI, and NDVI for both test areas, while the lowest values are mainly for NDRE and NDWI. Although the five vegetation indices follow similar patterns, there are variations dictated by their sensitivity to vegetation characteristics, i.e., biophysical properties of the classified crops. Temporal patterns of crops for all five vegetation indices are shown in Figure 4 for TA1 and Figure 5 for TA2. For TA1, winter wheat, sugarbeets, and onions have a single cropping cycle with different temporal length, with onions having the shortest (January to May 2017) and sugarbeets having the longest cropping cycle (October 2016 to June 2017). Vegetables have 2-3 cropping cycles, similar to the grass seed. Fallow/idle cropland have values of NDVI between 0 and 0.1 throughout the whole year, while water class presents negative values of NDVI, with shorter peaks of positive values during the summer. Alfafla have the highest diversity of temporal patterns for TA1, with two main types of patterns. In order to account for this, we used two reference temporal patterns for alfalfa, one with 5 cropping cycles and one with 7-8 cropping cycles over the timeframe analyzed (Figure 4). The other hay/non-alfalfa class presents 3 cropping cycles per year, shorter during the summer period. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **California (TA1)** & \multicolumn{4}{c}{**Texas (TA2)**} \\ \hline
**Class** & **Ref.** & **Valid.** & **Class** & **Ref.** & **Valid.** \\ \hline Wheat & 3 & 48 & Corn & 3 & 287 \\ Alfafla & \(3,3\) & 569 & Cotton & 3 & 122 \\ Other hay/non-alfalfa & 3 & 116 & Winter wheat & \(3,3\) & 171 \\ Sugarbeets & 3 & 70 & Alfafla & 3 & 34 \\ Onions & 3 & 98 & Fallow/idle cropland & 3 & 41 \\ Sod/grass seed & 3 & 82 & Grass/pasture & 3 & 129 \\ Fallow/idle cropland & 3 & 76 & Double crop & 3 & 60 \\ Vegetables & 3 & 47 & & & \\ Water & 3 & 30 & & & \\
**Total** & **30** & **1136** & **Total** & **24** & **844** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The number of reference (ref.) and validation (valid.) samples for TA1 and TA2, respectively. For alfalfa in TA1 and winter wheat in TA2, two distinct temporal patterns were identified, as detailed in Section 2.1.5. Figure 4: The temporal patterns of the classes analyzed for TA1, with values of five vegetation indices shown on the vertical axis. We analyzed a single agricultural year, the horizontal axis shows the day-of-the-time-series, namely from 23 September 2016 to 23 September 2017 (365 days). Two temporal patterns were identified for alfalfa (1 and 2). The vegetation indices are the Normalized Difference Vegetation Index (NDVI), Green Normalized Difference Vegetation Index (GNDVI), Normalized Difference Red-Edge (NDRE), Soil Adjusted Vegetation Index (SAVI), and Normalized Difference Water Index (NDWI), derived as shown in Table 1.  
For TA2, winter wheat presents two temporal patterns, with single crop in spring or double cropping cycles in late autumn and spring (Figure 5). Corn is a summer crop, similar with the cotton, but with longer cropping cycle and higher NDVI values than cotton. The temporal pattern of alfalfa shows 5 cropping cycles, longer during the cold season and shorter during the summer. The grass/pasture class shows two cropping cycles during spring and summer, but with values of  
Figure 5: The temporal patterns of the classes analyzed for TA2, with values of five vegetation indices shown on the vertical axis (NDVI, GNDVI, NDRE, SAVI, and NDWI). We analyzed a single agricultural year, the horizontal axis shows the day-of-the-time-series, namely from 18 October 2016 to 2 November 2017 (380 days). Two temporal patterns were identified for winter wheat (wheat 1 and 2).