## 2 Materials and Methods
### Methods
#### 2.3.2 Model of Canopy for Year 2000  
For the correction of the VB of NASADEM, which is based on SRTM data collected in 2000, a canopy model for the year 2000 is required. However, at the moment, no such model is available, but [17] mentioned that they might process historical Landsat imagery, enabling forest structure analysis from the 1980s to the present. If GFCH2019 is used for canopy heights, errors due to differences in vegetation cover between 2000 and 2019 could be substantial. In this study, we did not specify land use types and did not distinguish forests and other types of vegetation and, therefore, avoided the terms \"deforestation\" and \"reforestation\"; we instead use the terms \"clearing\" and \"growth\". Moreover, different guidelines define the term deforestation differently. For example, managed forestry with cycles of forest clearing and reforestation is usually not considered deforestation. To calculate a Canopy Height Model for 2000 (CHM2000) for the area of study, the canopy heights from GFCH2019 and FCHM2005 and canopy densities from the Global Forest Change 2000-2019 Model were employed. First, all the cells identified as water in GFCH2019 were set to have a 0% density in the canopy density model. Then, three cases were considered:  
* Clearing: Cells with zero canopy height in 2019 and densities above 50% in 2000. CHM2000 for these cells was computed as canopy height interpolated with the nearest neighbour method from FCHM2005 and multiplied by the canopy density value. The choice of the threshold for density was made using different test areas and comparisons to Landsat images. If no threshold was set or FCHM2005 was taken without scaling by density, the resulting model tended to add rather high vegetation to agricultural areas given that FCHM2005 is a low-resolution model that overestimates canopy heights. Furthermore, for this reason, the expected accuracy of CHM2000 for the clearing case is lower than for others. It was observed that the areas of volcano craters and their surroundings that are not covered by any vegetation had positive canopy densities in 2000. These areas were manually enclosed in polygons and excluded from clearing cases. * Growth: In this case, canopy heights in 2019 were above 5 m, but the density was zero in 2000. The value for canopy height in CHM2000 was then set to zero. The reason for the 5 m threshold is that GFCH2019 defines canopy height for vegetation above 3 m, while the canopy density model uses a 5 m value. In this way, all cells with heights below 5 m are the same in CHM2000 and GFCH2019. * No change: In all other cases, CHM2000 was equal to GFCH2019 assuming no natural change in canopy height. In [PERSON] et al., 2010 [38], the estimation of tree height change specifically in a tropical forest of Costa Rica was provided. They quantified changes in forest canopy height and other related parameters using data from LVIS 1998 and LVIS2005. Pairwise comparisons of nearly coincident LiDAR footprints between these years showed that secondary forests had a net gain of 2.08 m in height, while old-growth forests had diminished, with a height net loss of \(-0.33\) m. Therefore, in similar forest types in Costa Rica, a 19-year linear prediction would give growth in secondary forests of 6.5 m and height loss in primary forests of \(-0.9\) m. As our study did not distinguish either land use nor forest types, as well as such a linear trend is not reasonable for long-term prediction, no such estimation was applied. Nevertheless, we are aware that using canopy heights determined for 2019 for the correction of a DEM that corresponds to the year 2000 could result in errors of several metres magnitude just due to the natural canopy height change. Two examples of the process of CHM2000 calculation are shown in Figure 7(I,II). The first example is for an agricultural area, with many cells identified as clearing and growth. The second is for a forested area surrounding Portuguese National Park that has boat-only access and many clearing cells.