## 4 Discussion
### Statistical Results  
The analysis of the test results revealed the general statistical reliability of the proposed methodology. Although the sample size was not extensive, it was deemed somehow representative enough to demonstrate the method's effectiveness in real-world applications.  
From the results presented in Table 2, a preliminary observation is that there should be no systematic bias between the two datasets (heights calculated from the drone 3D model and the proposed methodology). This outcome was not guaranteed, despite referencing the same CORSN, due to potential decimetric systematic discrepancies observed in similar past experiments [41]. The discrepancies in mean errors, with maximum values of a few centimeters, confirm the proper planimetric and altimetric alignment of the two datasets.  
Further analysis of Table 2 shows that, overall, the results are highly satisfactory, with standard deviations (SDs) between 10 and 20 cm. Considering the 30 cm resolution of the satellite images, these results exceed our expectations in certain respects. A key factor contributing to these outcomes was the precise absolute and relative planimetric and altimetric alignment of the two datasets (satellite orthophoto and UAV point cloud).  
In Test 1a, it was observed that the accuracy of height measurements at points with higher identification difficulty (\"0\" class) was slightly better than at points with greater collimation certainty (\"1\" class). However, the difference (in terms of SD) is less than 3 mm, suggesting that the difficulty of identification of shadow points has little to no significant impact on the results.  
In Test 1b, which involves the height calculated from the tree canopy apex to the corresponding point on the shadow for the same set of trees, the results appeared slightly less accurate than those of Test 1a. This is because, in Test 1b, the height is not calculated from a clearly identifiable point on the canopy but rather from the point that generates the longest shadow. Additionally, we are assuming that the point generating the longest shadow is located at the outermost edge of the canopy, which is true for most olive trees given their canopy structure, but this may not always be the case. However, the differences between the results of Test 1a and Test 1b amount to only a few millimeters, rendering them relatively insignificant given the satellite image resolution. Moreover, Test 1b might be more suitable for applications where a rapid and approximate estimation of tree heights is required.  
Tests 2 and 3 produced even more accurate results, approximately twice as accurate as the previous tests. However, it should be noted that the dataset for these tests was smaller and therefore not directly comparable to the previous ones, but only relatively comparable among themselves. The similarity of errors obtained in Test 2 (flat terrain) and Test 3 (sloped terrain) can be attributed to the inclusion of a term in the height calculation formula (Equation (1)) that properly accounts for both the slope and aspect of the terrain. Test 3 was specifically designed to assess the impact of these factors, and the results suggest that this adjustment, considering the image resolution, effectively modeled potential distortions in sloped areas.  
The \(t\)-test indicated that the difference between the tree heights obtained from Equation (1) and those from UAV surveys (Test 1a, 1b, 2, and 3) was not statistically significant at the 5% significance level. Detailed \(t\)-test outcomes are provided in Appendix B (Tables A1-A4).  
Concerning the olive cultivars surveyed, there is a convergence with what was described in the section \"Study area and surveying methods\" about the normal size of the different cultivars. In fact, the average heights obtained in Test 1b were as follows: \"Frantoio\": 3.04 m, \"Leccino\": 3.20 m, \"Maurino\": 2.57 m, and \"Moraiolo\": 2.63 m, basically confirming what was reported above.