## 4 Discussion
### Vegetation Bias
A study of the penetration of the SRTM C-band signal in [30] in the Sierra Nevada, USA, showed that the signal was able to penetrate into 40% of red fir canopies, 47% of the Sierra mixed conifer, and 50% of the Ponderosa pine and montane hardwood-conifer forests. Additionally, they discussed the impact of canopy density (defined as a percentage of an area covered by the crowns of trees) on C-band signal backscattering and came to the conclusion that, for canopies with higher densities, backscattering mainly originates from the crown part. In contrast, for low cover densities, it comes mainly from the ground. Another study in the Sierra Nevada by [10] reduced SRTM for VB by a regression model dependent on Tree Height (TH), Canopy Cover (CC), and Slope (S) as \(\text{VB}=0.367\text{TH}+9.43\text{CC}+2.4\tan\text{S}-1.039\). Without consideration of slope (S = 0), these results agree with the VB3 model for high canopies above 20 m and high canopy densities, near 100%. For example, for 100% CC and TH of 40 m, the VB would be 23.1 m or \(0.58\text{TH}=0.58\text{TH}\cdot\text{CC}\), as in VB3. However, the regression model overestimates VB for low vegetation below 10 m, e.g., for TH of 5 m and 100% CC, the VB would be 10.2 m (2.0 TH-CC), twice the canopy height. Studies in regions with vegetation types closer to those found in Costa Rica report similar findings. For the Amazon floodplain, ref. [9] reported that the best results in terms of hydrodynamic model accuracy were obtained by subtracting between 50 and 60% of the vegetation height from the SRTM DEM, which corresponds to a 50 and 40% canopy penetration, respectively. Ref. [12] conducted fieldwork in the Amazon region and estimated canopy penetration depth for the C-band SRTM signal to be 50% of the vegetation height. Results for study areas in Australia, the Amazon, Africa, the United States, and Asia by [13] showed that, on average, SRTM elevations are located approximately 40% of the distance from the canopy top to the ground, meaning that 60% (\(a=0.6\)) of the canopy height shall be subtracted to remove VB. In addition, they suggested that with increasing canopy densities, SRTM heights become increasingly displaced upward into the canopy as more radar energy is reflected from canopy components and less from the ground. This is in agreement with [30] and our physical explanation of why the VB3 model outperforms the VB4 model. Additionally, we compared and discussed the differences and similarities of the proposed VB correction to the strategies used for the global DTMs MERIT DEM and BEST DEM. Below, the figures related to VB estimation in [2,4] are provided together with an equivalent figure for the VB3 model. [PERSON] et al., 2016 [2] investigated several functions to remove a fraction of vegetation (VRF) depending on canopy density, as can be observed in Figure 16a. They concluded that the function \"power 1\" provides the best results. In the figure, for a canopy density of 0%, the polynomial, exponential, and linear functions provide VRF values slightly above 20%, meaning that some vegetation is removed for cells that are identified as non-vegetated. The VRF for the \"power 1\" function is smaller than for other functions, but not equal to zero. For high densities, say above 90%, the polynomial and exponential functions remove over 100% of the vegetation provided by the canopy model. The fact that \"power 1\" removes a fraction of about 83% could be the reason why it performs better than the linear function with 87% removal. Another observation is that for a density of 50%, about 60% of the canopy height is removed by \"power 1\" and linear functions. In Figure 16b, the equivalent of the VRF is presented for the VB3 model. The scaling factor \(a\) times the canopy density represents the VRF, and both Figure 16a,b are plotted with the same axes. For 0%, 100%, and 50% canopy densities, the VB3 model estimates VB to be 0%, 58.5%, and 29.3% of canopy height, respectively. The MERIT DEM had good performance in the study area in Costa Rica.