## 1 Introduction
VB was eliminated using canopy heights from the 30\({}^{\prime\prime}\) Global Tree Height Map [6], canopy densities from the 250 m mesh size MODIS Vegetation Continuous Field (VCF) product [8], and climate and vegetation type classification maps and the ICESat ground elevation dataset. VB was defined as a function of canopy density multiplied by canopy height. The percentage of canopy heights to be removed was tested with linear, polynomial, \"power\", and exponentiation functions. The parameters for each function were fit based on ICESat point differences to SRTM4. The best result was reported for the \"power 1\" function (\(f_{\text{VCF}}=a\text{VCF}^{\text{b}}\)). Additionally, they investigated the static correction approach: removal of 50% of the canopy heights as in [9], without taking into account canopy densities. Both vegetation bias removal methods provide improvement in SRTM4. However, the method that considers canopy heights and their scaling by canopy density provided better results: for global estimation, the original mean/Root Mean Square (RMS) error of 11.2/14.1 m was reduced to 2.9/7.6 m for the static method and 1.2/6.1 m for the \"power 1\" method. [PERSON] et al., 2015 [10] reduced 3\({}^{\prime\prime}\) SRTM DEM for vegetation bias for the Sierra Nevada in the USA. Canopy density estimated from aerial imagery, canopy heights from LiDAR and ICESat observations, and slope data were used to compute a vegetation correction model. SRTM was corrected for VB by a regression model dependent on Tree Height (TH), Canopy Cover (CC), and Slope (S) as \(\text{VB}=0.367\text{TH}+9.43\text{CC}+2.4\tan\text{S}-1.039\). Validation using LiDAR DEM showed that the mean/standard deviation between the original and corrected SRTM DEM improved from 12.0/10.9 m to \(-0.8/8.9\) m. Another method for the reduction of vegetation and slope bias was presented by [PERSON] et al., 2021 [11] for a test site in North Carolina. A multiple regression technique was applied to reduce vegetation bias from 1\({}^{\prime\prime}\) SRTMGL1 using its vertical differences to ICESat-2 reference heights, terrain Slopes (S), and canopy cover (V) provided by Landsat VCF, as \(dz=0.7989\text{V}^{2}+8.6350\text{S}^{2}+9.6792(\text{VS})-14.78\text{V}+2.410 \text{S}+0.6116\). The mean/RMSE of the uncorrected and corrected height differences with respect to ICESat-2 points showed improvement from 3.7/5.5 m to 0.0/3.2 m, while validation with a LiDAR DTM showed improvement from 3.2/5.0 m to 0.4/2.6 m.  
Some earlier studies of VB in DEMs did not consider canopy density, but only canopy heights. [PERSON] et al., 2013 [9] removed vegetation bias from SRTM4 and showed improve ments in the hydrodynamic model accuracy for the Amazon floodplain. The study searched for the optimal value for the percentage of canopy heights (taken from the 30\({}^{\prime\prime}\) Global Tree Height Map [6]) to be reduced from SRTM. The ten options studied examples from 10 to 100% (10% increment) and showed that the optimum value is between 50 and 60%. [PERSON] et al., 2007 [12] conducted fieldwork in the Amazon region and mapped vegetation heights in different habitats for a limited area. They detected edges of deforested areas using Landsat 7 imagery and performed ground and vegetation height surveys across this boundary. The estimated canopy penetration depth for the C-band Shuttle Radar Topography Mission (SRTM) signal was 50%. [PERSON] and [PERSON] 2006 [13] studied the penetration of C-band SRTM pulses into vegetation canopies using ICESat observations in several regions (Australia, Amazon, Africa, United States, and Asia) and the canopy density from Landsat VCF product [8]. Several relevant conclusions were drawn. First, on average, the C-band radar phase centre penetrates slightly less than halfway into the canopy for all the tree cover classes, meaning that SRTM elevations are located approximately 40% of the distance from the canopy top to the ground.