## 1 Introduction  
A Digital Elevations Model (DEM), a digital representation of topography on a geo-referenced mesh grid, in practice, can be represented by a Digital Surface Model (DSM), a surface that includes both vegetation and man-made objects, or a bare-earth surface that excludes them and is referred to as a Digital Terrain Model (DTM). Since 2000, various 3\({}^{\prime\prime}\) (\(\approx\)90 m) mesh size global DEMs have been released to the public, and in the last few years, several 1\({}^{\prime\prime}\) (\(\approx\)30 m) mesh size DSMs became available. Many applications require bare-earth DTMs, especially now, during an unprecedented period of climate-change-related disasters [1]. Bare-earth models are an essential tool for hazard assessment, monitoring, and mitigation of natural disasters such as floods, landslides, and erosion. Furthermore, hydrology, including coastal change due to sea-level rise and freshwater resources' estimation, geology and volcanology, geodesy and geoinformation systems, as well as many other Earth sciences and engineering applications, require high-resolution DTMs ([2, 3, 4]). Our goal is to take advantage of the three \(\approx\)1\({}^{\prime\prime}\) global publicly available models that rely on data from various space-borne remote sensors and find the best analytical approach for DEM Vegetation Bias (VB) correction that could be applied to the total area of study independently of the vegetation type or land use in order to produce a regional 1\({}^{\prime\prime}\) \"Bare-Earth\" DTM for Costa Rica. Several methods of VB removal in the computation of 3\({}^{\prime\prime}\) DTMs have been published, and recently, the first results for VB correction with regression method for a 1\({}^{\prime\prime}\) DSM have become available. [PERSON] et al., 2022 [5] applied machine learning to eliminate VB and buildings to produce a 1\({}^{\prime\prime}\) DTM from the Copernicus DEM, a very recent DSM based on TanDEM-X data. VB correction was performed using random forest regression modelling using reference data from LiDAR DTMs from 12 countries and predictor data for forest height from the Global Forest Canopy Height 2019 (GFCH2019) model. Cells with tree cover fraction from the Copernicus Global Land Service land cover on a 100 m mesh grid greater than 10% and canopy heights greater than 3 m were considered forested for the vegetation correction algorithm. Buildings were then removed separately, and further steps were taken to correct noisy and \"over-corrected\" areas. The global Multi-Error-Removed Improved-Terrain (MERIT) DEM by [PERSON] et al., 2017 [4] is a global 3\({}^{\prime\prime}\) DTM. Not only VB was eliminated from the base SRTM3/AW3D30 (above 60\({}^{\circ}\)N) DSMs, but in addition, three other major error components were corrected for: stripe noise, absolute bias, and speckle noise. It was highlighted that the magnitude of each height error component can be as large as 10 m. Space-borne laser altimetry data from Ice, Cloud,and land Elevation Satellite (ICESat) were used as a reference ground elevation dataset. For the estimation of VB, first, a canopy height model was computed for a 3\({}^{\prime\prime}\) grid matching SRTM3 from a 30\({}^{\prime\prime}\) Global Tree Height Map [6] and a 3\({}^{\prime\prime}\) canopy density model from the Global Forest Change 2000-2019 Model [7]. Then, VB was estimated in two different ways: for cells with ICESat observations, it was a difference between DSM and ICESat ground elevation; for other cells, VB was estimated from regionalised look-up maps. These were prepared for quadrangles using available ICESat observations and provided the VB value for a given canopy height and canopy density for the cell. VB was assumed to be 0 m when the tree density was below 10% or the canopy height below 2 m. The Bare-Earth SRTM Terrain DEM (BEST DEM) was computed by [PERSON] et al., 2016 [2] from the SRTM4 DEM.