# Monitoring of Sugarcane Harvest in Brazil Based on Optical and SAR Data
## 3 Methodology
### SAR + Optical Data
The checking is based on the following assumptions:  
* harvest is carried out in terms of _NDVI_ descending trend;
* on the harvest completion, _NDVI_ should be low. The _NDVI_ trend construction consists of three stages (Figure 7):  
\begin{table}
\begin{tabular}{l l l l l l} \hline \hline i & **T** & **C** & \(\Delta\)**C** & **DC** & \(\mathbf{D^{2}C}\) \\ \hline
1 & \(T_{1}\) & \(C_{1}\) & & & \\
2 & \(T_{2}\) & \(C_{2}\) & \(\Delta C_{1}\) & \(DC_{1}\) & & \\
3 & \(T_{3}\) & \(C_{3}\) & \(\Delta C_{2}\) & \(DC_{2}\) & \(D^{2}C_{1}\) \\... &... &... &... &... &... \\ M & \Harvest condition on the descending _NDVI_ trend:  
\[trend(NDVI)_{l}-trend(NDVI)_{l-1}<0 \tag{8}\]  
where \(l-1\) and \(l\) are the numbers of optical images before and after the potential harvest date. After the harvest, _NDVI_ should be low. \[trend(NDVI)_{l}\leq NDVI_{hd}. \tag{9}\]  
That condition is similar to the second condition from (3) for the algorithm based on the optical data. Gradual coherence growth before harvest (Figure 6a) may be caused not only by the plant drying-out but by the partial field harvest. The harvested part is empty, and it has high coherence, while the rest of the field is of low coherence. Along with the increasing harvest area, average field coherence grows gradually so that one cannot observe the fast coherence growth upon the harvest completion. As a result, the harvest date is not determined from the conditions (5)-(7). Irrespective of that, high coherence is observed within the parcel upon the harvest completion. Single out the members of time series \(C_{h}\) (\(h\in 1,\ldots,M\)) with high coherence  
\[C_{h}>C_{hi}. \tag{10}\]  
High coherence values correspond to the sparse vegetation or bare soil. Consequently, harvest may be carried out only after a long period from the last date with high coherence \(T_{h}\). Denote the potential harvest date by \(T_{I}\) and introduce the checking  
Figure 7: Stages of the _NDVI_ time series trend construction for a cell: (**a**) the initial _NDVI_ time series; (**b**) the series after filtration (1) with window width \(k=3\); (**c**) the series after averaging by the sliding median filter with window width \(k=9\); (**d**) the series after spline-smoothing. \[T_{I}\leq T_{h}\text{ OR }T_{I}>T_{h}+\Delta T_{hi}. \tag{11}\]  
where \(\Delta T_{hi}\) is the minimum time period required for the plant growth. Finally, if the harvest dates are not determined from the patterns of coherence time series (5)-(7) and conditions (8)-(11), check the dates of high coherence (10) as for their meeting the conditions (8), (9), and (11). Thus, the algorithm of harvest monitoring in terms of the SAR and optical data consists of the following steps:  
1. Searching for the rapid changes in coherence corresponding to types 1 and 2 (5)-(7). 2. Checking the dates determined from _NDVI_ (8), (9). 3. Checking the potential harvest dates, left after step 2, as for their following the high coherence dates (11). 4. If no harvest dates are found in steps 1-3, perform steps 2-3 for high coherence dates (10). The algorithm parameters are: \(\varepsilon\), \(\theta\), \(NDVI_{hd}\), \(C_{hi}\), \(\Delta T_{hi}\). It should be noted that the use of _NDVI_ trend does not mean the determining of harvest dates from optical data. Comparing to the data used in the optical algorithm, the _NDVI_ trend may derive from the data of much lower spatial resolution and/or periodicity: MODIS, Landsat, etc. (Figure 8).