# Best Practices for Applying and Interpreting the Total Operating Characteristic
## 3 Results  
Figure 5 shows the four TOC curves for the validation. The presence patches curve derives from the distance to patches of crop presence at 2010. The change patches curve derives from the distance to the patches of crop change during 2000-2010. The presence pixels curve derives from the distance to the presence pixels at 2010. The change pixels curve derives from the distance to the change pixels during 2000-2010. All four TOC curves are above the uniform line and concave down, which indicates that gains during the validation interval are more intensive within segments of shorter distances. The two pixel curves cross near the threshold of the correct quantity. The two patch curves touch through the entire graph. The AUCs of the presence patches, change patches, presence pixels, and  
Figure 4: (**a**) Map for Log base 10 of meters + 1 to change pixels during 2000–2010. (**b**) Map for Log base 10 of meters + 1 to presence patches at 2010.  
change pixels are, respectively, 0.84, 0.84, 0.78, and 0.77. The spatial filter increases the predictive accuracy in both cases of analyzing presence and change. The thresholds at smaller increments show also that the curves are concave down and the AUCs for the patches are greater than the AUCs for the pixels. The change pixels curve has labels on the thresholds at 100 m and 1 km to illustrate how the algorithm selected thresholds at 2 = Log(100 m) and 3 = Log(1000 m). The presence patch curve has thresholds at 2.8 = Log(631 m), 3 = Log(1000 m), and 4 = Log(10,000 m). The first highlighted threshold on those two curves in Figure 5a is the threshold closest to the correct quantity of gain, as indicated by its position below the upper left corner of the bounding parallelogram. The patch curves are above the presence curves at this horizontal position of the correct quantity. A segment on the TOC curve is parallel to the uniform line when the gain intensity in the segment equals the uniform intensity in the extent. Figure 5 shows that segments parallel to the uniform line appear approximately half way from left to right in the TOC space. All segments to the left of the correct quantity are steeper than the uniform line. For the threshold at 1 km on the presence patches curve, Figure 5a illustrates how the TOC curve shows the sizes of hits, false alarms, correct rejections, and misses. This is the case for each point on the TOC curve. The size of hits is the distance from the vertical axis to the left bound of the parallelogram. The size of false alarms is the distance from the left bound of the parallelogram to the point on the TOC curve. The size of correct rejections is the distance from the point on the TOC curve to the right bound of the parallelogram. The size of misses is the distance from the right bound of the parallelogram to the maximum value of the horizontal axis. Figure 5: TOC curves showing the fit during the validation interval for (**a**) full TOC parallelogram and (**b**) zoom into the origin. The red annotation of 0 m and 30 in (**b**) refers to the thresholds on the red curve for change pixels. The green annotation of 30 in (**b**) refers to the threshold on the green curve for presence pixels. Figure 5b zooms into the origin of the TOC parallelogram to compare the thresholds for the red change pixels curve to the green presence pixels curve. The change pixels curve has a threshold at zero meters, which indicates the pixels where crop lost during 2000-2010. This threshold at zero is the only reason why the change pixels curve is above the presence pixels curve near the origin. Both curves have a threshold at 30 m, which captures pixels neighboring the change or presence pixels. The segments immediately to the right of 0 m for the change pixels are flatter than the corresponding segments for the presence pixels, which causes the curves to cross near the threshold of the correct quantity.