## 3 Results
### Vegetation Bias  
Four VB models (VB1-VB4) for the correction of NASAADEM were evaluated in order to determine which approach provides the best bare-earth DTM. For the models VB3 and VB4, the scaling coefficient \(a\) was estimated to be 0.585 for both NASAADEM_VB3 and NASAADEM_VB4 based on a comparison with the LVIS2005 dataset. The LVIS1998 and LVIS2019 datasets were not used and saved for validation of the VB models only. The choice of \(a\) was based on the statistics of the differences, mean, MED, STD, MAD, and the percentages of points with absolute differences of 5, 10, 15 and 20 m. The LVIS survey from 2005 was chosen for its spatial distribution, a large number of points (\(>\)9 million), and its closeness to the year 2000. By stepwise increments of \(a\) between 0.1 and 0.9, the coefficient was determined to be between the values of 0.57 and 0.6. Therefore, \(a=0.585\) was adopted and used in all analyses. The shapes of the histograms of differences between LVIS datasets and NASAADEM corrected for VB are particularly useful in the evaluation of the success of each VB model. Figure 11 presents the statistics from Table 3 for differences between LVIS2019, LVIS2005, and LVIS1998 bare-earth ZG elevations and the elevations from the original NASAADEM and corrected NASAADEM_VB1 to NASAADEM_VB4. A 50 m threshold was used for the visual interpretation of the histograms and for calculating the STD* values, which are, otherwise, strongly influenced by large outliers. It can be concluded that NASAADEM_VB1 and NASAADEM_VB2 in Figure 11b,c overestimate vegetation bias as the distribution acquires a bulge on the right-hand side of the histogram, while in the original NASAADEM in (a), it is on the left-hand side. NASAADEM_VB3 and NASAADEM_VB4 provide histograms that are similar to the probability density function of a normal distribution, with a prominent peak near the zero value, which we interpreted as the difference in bare-earth cells. The difference between the solution NASAADEM_VB3 or NASAADEM_VB4 using the proposed validation methods is not significant. Most of the statistics are better for VB3 for the three LVIS surveys, but slightly worse as compared to the levelling dataset, as can be observed at the end of Table 3. Overall, VB3 provides better results. However, the choice between VB3 and VB4 can be considered more conceptual and depends on whether CHM2000 is assumed to depend on canopy density directly. The VB3 model was chosen for the computation of CRDTM2020, and we made the assumption that canopy height and canopy density are independent. Figure 10: Histograms and statistics of differences in canopy heights between two canopy models and LVIS data (ZT-ZG)): (**a**) CHM2000 versus LVIS2005. (**b**) GFCH2019 versus LVIS2005. (**c**) CHM2000 versus LVIS1998. (**d**) GFCH2019 versus LVIS1998. The statistics is provided in terms of the mean difference, Standard Deviation (STD), and minimum (min) and maximum (max) differences. Figure 11: Results of the correction of NASADEM for Vegetation Bias (VB), as compared to LVIS data from 2019 (red), 2005 (blue), and 1998 (orange). (**a**) Distribution and statistics for the original NASADEM. (**b–e**) Distribution and statistics for NASADEM corrected by VB Models 1–4, respectively. The statistics is provided in terms of the Median Difference (MED) and Median Absolute Difference (MAD).