# Monitoring of Sugarcane Harvest in Brazil Based on Optical and SAR Data
## 3 Methodology
### Optical Data  
Each parcel has the time series composed of \(N\) images. \(NDVI_{i}\) is the parcel average _NDVI_ calculated for the \(i\)th image \((i=1,2,\ldots,N)\), \(T_{i}\) is the date of the \(i\)th image.  
The main stage of the sugarcane harvest is stalk cutting in separate stripes according to the terrain features. Depending on the growth process and crop rotation plan, the cut stalks are either left unaffected (ratoon) or harvested completely with the following parcel plowing. In both cases, harvest results in sharp _NDVI_ decrease (Figure 4).  
Figure 3: Sentinel-1 and Sentinel-2 aquisition dates, 2018–2019.  
As a rule, short-term periods of _NDVI_ decrease with its following increase up to the previous values are caused by clouds or cloud shadow. The modified median filter is used to smooth them.  
A standard median filter [43] smoothes the time series fragments with high _NDVI_ located among the dates with dense clouds (in Figure 5 it should be noted the lack of _NDVI_ local peak in the middle of November as a result of median filtering). That may result in the loss of harvest dates. Hence, the filter was modified to use the median data \(\text{med}(NDVI)\) only where they exceed the _NDVI_ values of the initial time series.  
\[NDVI\leftarrow\max\{NDVI,\text{med}(NDVI)\}. \tag{1}\]  
Following conditions should be met for the harvest date \(T_{ik}\):  
\[k=\left\{i|NDVI_{i-1}-NDVI_{i}\geq\Delta NDVI\right\} \tag{2}\]  
\[\left\{i_{k}|NDVI_{i_{k}-1}\geq NDVI_{preve}\ \&\ NDVI_{i_{k}}\leq NDVI_{ harr}\right\}. \tag{3}\]  
\[\left\{i_{k}|\exists T_{j}\in\left[T_{ik};T_{ik}+\Delta T\right],NDVI_{j}\geq \mu\cdot NDVI_{i_{k}-1}\right\}. \tag{4}\]  
Figure 4: Example of a sugarcane parcel before (**a**,**c**) and after harvest (**b**,**d**) in natural colours (**a**,**b**) and _NDVI_ (**c**,**d**).  
Figure 5: Example of the _NDVI_ time series for a cell: (**a**) initial; (**b**) smoothened by the median filter; (**c**) smoothened by the modified median filter.  
Condition (2) means that \(NDVI\) decreases sharply in the harvest date \(T_{i_{k}}\)--not less than by \(\Delta NDVI\) comparing to the previous date. According to condition (3), the before-harvest \(NDVI\) should be rather high. Otherwise, the \(NDVI\) decrease may be caused not by the harvest but by the field plowing. The \(NDVI\) threshold value during the harvest date \(NDVI_{harv}\) takes into account different harvesting technologies. The \(0.3<NDVI\leq 0.4\) values correspond to the parcels with moderate and sparse vegetation [44]. Condition (4) represents the fact that harvest causes long-term \(NDVI\) decrease: if \(NDVI\) is not raised up to the level of \(\mu\cdot NDVI_{i_{k}-1}\) within \(\Delta T\) period, then harvest was carried out at \(T_{i_{k}}\) moment. The \(\mu\in[0;1]\) coefficient compensates insignificant \(NDVI\) fluctuations as well as the effect of clouds during the \(NDVI\) decrease period.  
Thus, the algorithm of determining the harvest dates according to the optical data consists of:  
1. preliminary filtration (1) of time series \(NDVI_{i}\) (\(i=1,2,\ldots,N\));
2. control if conditions (2)-(4) are met.  
The main algorithm parameters are as follows: \(\Delta NDVI\), \(NDVI_{prev}\), \(NDVI_{harv}\), \(\Delta T\), and \(\mu\).  
To check if condition (4) is met for the harvest dates falling on the end of a calendar year, the \(NDVI\) time series should be prolonged by \(\Delta T\) beyond the limits of a harvest monitoring interval.