## 2 Materials and Methods
### Methods
#### 2.3.3 NASADEM Correction for Vegetation Bias  
To remove stochastic VB from NASADEM using a model of canopy heights on the matching mesh grid, the first approach would be, naturally, to subtract the canopy model from the DSM. To determine the success of VB correction, the reduced DTM was compared to the ground heights ZG of the LVIS datasets and the levelling dataset. However, it will be shown that this straightforward approach overestimates VB. Therefore, to develop an analytical VB removal model for NASADEM, let us consider the measurement principle of SRTM and discuss what is represented in the GFCH2019 and Canopy Density 2000 Model. Figure 8 visualises the concepts of the measurements of SRTM and LVIS. Figure 7: Steps in preparation of the model of Canopy Height Model for 2000 (CHM2000) for two example areas in (**I**) the agricultural zone in Alajuela and (**II**) the natural area in Portuguese. (**a**) GFCH2019 Model. (**b**) Canopy density for the year 2000 from the Global Forest Change Model. (**c**) Cells identified as canopy clearing (in red) and growth (in cyan) plotted above the canopy height map presented in (**a**). (**d**) The 1 km mesh size FCHM. (**e**) Computed CHM2000. SRTM data represents not the tops of vegetation and man-made structures, but the scattering phase centre height. It is dependent on the target, namely vegetation structure and moisture, soil roughness and moisture, as well as sensor characteristics, such as polarisation (horizontal/vertical) and incidence angle (30\({}^{\circ}\)-60\({}^{\circ}\)), which are variable within each SRTM swath [39], as well as other parameters. In other words, for vegetated areas, all SRTM-based DEMs are not exactly DSM nor DTM, but models that represent the elevations of some point in between these two surfaces depending on the vegetation, which is, in turn, a function of canopy density and canopy height. The canopy height model GFCH2019 is the first model that provides such valuable information on global vegetation height at high resolution. The model is based on the 30 m resolution Landsat optical imagery and multi-temporal metrics and calibrated by GEDI laser ranging data. Each 900 m\({}^{2}\) cell might include a number of trees and bushes, as well as grassland, cropland, rock, water bodies, and artificial structures. The heights in GFCH2019 represent the mean height of vegetation within the cell or possibly the mean height including the bare-earth, and not only vegetation. The implication of the two views is whether to consider canopy heights, a function of canopy density, or not, which is relevant for VB modelling when canopy heights are multiplied by canopy densities in two  
Figure 8: Schematic 2D representation of Shuttle Radar Topography Mission (SRTM) and LVIS measurements for a cross-section of three cells with \(\approx\)50%, 100%, and 67% vegetation cover, as viewed from above. The SRTM C-band signal is emitted from the main antenna at a 5.3 GHz frequency and a varying look angle. Indicative ”sight” black lines reach the surface at a 45\({}^{\circ}\) angle; arrows indicate the points of contact with the ground/vegetation. The part of the signal returned to the Shuttle (red arrows) is collected by two antennas, the second placed on a 60 m-long mast. The signal phase difference allowed the determination of the mean scattering phase centre heights. On the right, the vertical axis indicates canopy heights above the ground; the axis is shared with the LVIS return waveform schematic. The LVIS laser altimeter measurement principle is based on the emission of 1064 nm wavelength pulses at up to a 500 Hz repetition rate [29]. The figure shows the cone of an \(\approx\)25 m diameter reaching the surface at its maximum 7\({}^{\circ}\) look angle.