# Best Practices for Applying and Interpreting the Total Operating Characteristic
## 2 Materials and Methods  
Figure 2 gives a flow diagram of the procedure, which begins with maps that show the presence or absence of crop at three time points: 2000, 2010, and 2020. Overlays generate maps of crop change during 2000-2010 and 2010-2020. A spatial filter converts some isolated pixels from crop presence to crop absence so the result has crop presence only in large patches. A distance operation generates four maps that feed into the TOC Curve Generator, which also reads a map of crop gain during 2010-2020 and a mask to focus exclusively on pixels that are candidates to gain crop after 2010. The outputs are four TOC curves in one TOC parallelogram. Figure 1: Maps of the study area showing the nine municipalities in western Bahia, Brazil. Figure 2: Flow diagram of the methods. Black rectangles represent maps. Dark blue polygons are GIS operations. The data derive from MapBiomas ([[https://brasil.mapbiomas.org/](https://brasil.mapbiomas.org/)]([https://brasil.mapbiomas.org/](https://brasil.mapbiomas.org/)) accessed 1 January 2024), which formed in 2015 as a collective of non-governmental organizations, universities, laboratories, and technology startups. MapBiomas has hundreds of experts in remote sensing and landscape ecology who produce annual maps of land cover for each of Brazil's biomes. MapBiomas, via its collection 7.1, provides 30 m resolution raster maps where each pixel shows the presence or absence of temporary crops at 2000, 2010, and 2020 [27]. Temporary crops are crops that have a growing cycle of less than one year, which includes soybean, cotton, and corn. For brevity, this manuscript uses the single word \"crop\" to refer to this class. MapBiomas conducts many steps for quality control. MapBiomas collected 85 thousand sample points at each year from 1985 to 2022 using three visual interpreters per point. The commission error rates for the crop class in the Cerrado biome are 18%, 14%, and 8% at 2000, 2010, and 2020, respectively. The omission error rates for the crop class in the Cerrado biome are 9%, 6%, and 4% at 2000, 2010, and 2020, respectively. These error rates indicate an overestimation of the size of crop at the three time points but do not indicate the data quality concerning temporal change. MapBiomas has started to analyze data quality concerning change but has not yet published their results. Figure 3 shows the trajectories of how crop is stable or not during the two time intervals of 2000-2010 and 2010-2020. The three upper case letters in the name of each trajectory indicate a pixel's status at 2000, 2010, and 2020, where P indicates the presence and A indicates the absence of crop. Pixels are candidates to gain crop during the second time interval when the middle letter is A. The black polygon is the union of the nine municipalities of western Bahia. Figure 3 shows the regions outside the black polygon because these regions will contribute to the computation of the distances to crop. Agriculture in the west tends to be on large industrial farms that use pivot irrigation more so than in the southeast. Agriculture in the southeast tends to be on smaller farms. Individual isolated pixels of crop presence or crop change surrounded by crop absence are so small that they are not visible in Figure 3.  
The spatial filter defines a crop patch as a cluster of 1000 or more touching pixels. The spatial filter eliminates crops that appear in clusters of fewer than 1000 touching pixels by converting those pixels from crop presence to crop absence. The spatial filter keeps the crop that resides in patches. The spatial filter uses 1000 pixels because that is the size of a typical irrigation pivot. The western region within the black polygon includes many crop patches. The southeast has fewer crop patches but includes many isolated crop pixels that do not form patches. The crop's gross gain is 9.89 million pixels during 2000-2010 and 7.75 million pixels during 2010-2020.