# Monitoring of Sugarcane Harvest in Brazil Based on Optical and SAR Data
## 3 Methodology
### SAR + Optical Data  
The satellite derived observations for sugarcane show a dynamic pattern similar to wheat and other crops [24; 45]:  
1. Slow increase of coherence when the crop gradually dries out (Figure 6a, 12 April-29 July 2018). Then, it drops due to harvest (Figure 6a, 29 July-22 August 2018). Intermittent growth of coherence (Figure 6a, 22 August-3 September 2018) shows that the field is harvested. 2. Low and practically unchangeable coherence (Figure 6b, 6 January-11 June 2018), characteristic for dense sappy vegetation cover, drops to low coherence at harvest. High coherence values (Figure 6b, 11 June-29 July 2018) show that the field is harvested. It should be noted that optical sensors are capable to determine the harvesting operations immediately at the surveying moment while the SAR data help identify the fact of harvest completion, and determine high coherence peculiar for the bare soil, sparse vegetation, and harvest residues. Nevertheless, both cases deal with the algorithm for harvest date determination. The algorithm for determining the sugarcane harvest date from SAR data is based on the algorithm from [PERSON] et al. [24]. It searches for the patterns of coherence time series of types 1 and 2, and assessing the vegetation cover density after possible harvest from the backscattering coefficient \(\sigma^{0}\). In contrast to [24], the study uses \(NDVI\) to estimate the vegetation state. Use of Statistics API to generate \(NDVI\) time series helped save the disk space and time required before to store and  
Figure 6: Coherence time series: (**a**) type 1, harvest (red line): 11 August 2018; (**b**) type 2, harvest (red line): 12 June 2018.  
process \(\sigma^{0}\) data. Moreover, other improvements are introduced in the algorithm [24] representing the features of sugarcane cultivation and harvest. Consider the proposed algorithm in more detail. Take \(M+1\) time-ordered SAR SLC images. Denote the date of the \(i\)th image by \(T_{i}\) (\(i=1,2,\ldots,M+1\)). Calculate the coherences between \(i\)th and \((i+1)\)th images as it is shown in Section 2.4. Generate a time series of the field-average coherence values \(C_{i}\) (\(i=1,2,\ldots,M\)). To search for the time series patterns corresponding to the harvest, calculate the differences of coherences \(\Delta C_{i}=C_{i+1}-C_{i}\) (\(i=1,\ldots,M-1\)) and determine the directions of their changes \(DC_{i}\)  
\[DC_{i}=\left\{ \begin{array}{ll}0,&|\Delta C_{i}|\leq\varepsilon,\\ 1,&\Delta C_{i}>\varepsilon,\\ -1,&\Delta C_{i}<-\varepsilon.\end{array} \right.\]  
The \(\varepsilon\) threshold is chosen so that the coherence change \(\Delta C_{i}\) within the range of \([-\varepsilon;\varepsilon]\) could be considered as insignificant. Harvest either results in coherence drop (\(DC_{i}=-1\)) or does not change it comparing to the previous period (\(DC_{i}=0\)). After harvest, coherence grows (\(DC_{i}=1\)). Thus, harvest corresponds to the transfers \(DC_{i}\to DC_{i+1}\) of type: \(0\to 1\) or \(-1\to 1\). Introducing the second differences \(D^{2}C_{i}=DC_{i+1}-DC_{i}\) write down the conditions of coherence change corresponding to the harvest  
\[D^{2}C_{i}=2, \tag{5}\] \[D^{2}C_{i}=1\ \&\ DC_{i+1}=1. \tag{6}\]  
Condition (5) corresponds to the time series of type 1 coherence; and condition (6) corresponds to the time series of type 2 coherence. Conditional check \(DC_{i+1}=1\) is meant for eliminating from the analysis the transfers \(DC_{i}\to DC_{i+1}\) from \(-1\) to \(0\). The latter may be caused by the beginning of harvest but not by its completion. When the harvest is over, one can usually observe considerable growth of coherence. Thus, introduce the additional condition, when (5) and (6) are checked  
\[\Delta C_{i+1}>\theta, \tag{7}\]  
where \(\theta>\varepsilon\). Table 1 demonstrates connection between the time series indices. Thus, index \(i\), determined from the conditions (5)-(7), corresponds to the harvest date \(T_{i+2}\). Check the identified potential harvest dates using the _NDVI_ time series.