## 2 Materials and Methods
### Data
#### 2.2.3 Levelling Dataset  
A classical geodetic gravity survey dataset containing orthometric heights of the points obtained by levelling was provided by the National Geographic Institute of Costa Rica. The dataset is valuable for validating DEMs as most of the points were measured on the bare-earth or very close to it. Most points follow major roads and railway lines, which are in general cleared of tall vegetation. However, it should be considered that some roads in Costa Rica have large trees growing next to them, and most of the railway lines were not functioning in the year 2000 and may have been overgrown with vegetation. Furthermore, the area of each cell of the evaluated DEMs is either \(\approx\)900 m\({}^{2}\), for 1\({}^{\prime\prime}\) models, or 8.100 m\({}^{2}\), for 3\({}^{\prime\prime}\) models, allowing the presence of a variety of vegetation and artificial structures in one cell.  
Elevations were collected during classical levelling surveys in 1940-1980 and refer to a zero reference surface established by one particular tide gauge in Puntarenas, Costa Rica. The locations and elevations of the dataset stations are shown in Figure 3. We computed gravity anomalies using the provided values of the gravity accelerations and orthometric heights and transformed the geodetic locations from the Octepeque datum to the CR05 (WGS84) datum. Then, to eliminate outliers, gravity anomalies were compared to global high-resolution gravity models EGM2008 and GGMplus. This approach permitted the elimination of outliers without direct comparison to any DEM and resulted in a dataset with 2233 points. This dataset is probably the most reliable source of bare-earth elevations in Costa Rica, though the accuracy of the elevations is unknown. Errors in horizontal locations of the points located in the areas with complex terrain and steep slopes can lead to considerable errors in elevations and significant discrepancies with respect to DEMs.  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Parameter** & **Description** & **Units** \\ \hline SHOTNUMBER & LVIS shot number for the unique identification of laser shots & N/A \\ GLON & Longitude of the lowest detected mode within the waveform & \({}^{\circ}\) \\ GLAT & Latitude of the lowest detected mode within the waveform & \({}^{\circ}\) \\ ZG & Mean elevation of the lowest detected mode within the waveform & m \\ ZH \({}^{\star}\) & Mean elevation of the highest detected mode within the waveform & m \\ ZT & Elevation of the highest detected signal & m \\ RHS5 \({}^{\star}\) & Height (relative to ZG) at which 85\% of the waveform energy occurs & m \\ RH90 \({}^{\star}\) & Height (relative to ZG) at which 90\% of the waveform energy occurs & m \\ RH95 \({}^{\star}\) & Height (relative to ZG) at which 95\% of the waveform energy occurs & m \\ RH100 & Height (relative to ZG) at which 100\% of the waveform energy occurs & m \\ \hline \hline \end{tabular} \({}^{\star}\)These parameters are only available in the LVIS2019 data files.  
\end{table}
Table 2: List of parameters from the Laser Vegetation Imaging Sensor (LVIS) Classic L1B Geolocated Waveforms and LVIS Classic L2 Geolocated Surface Elevation and Canopy Height Product used in the study.  
Figure 2: Locations and elevations of the points of the highest detected returns in three Laser Vegetation Imaging Sensor (LVIS) surveys over Costa Rica. From left to right: 1998 survey (2 tracks with 2,786,714 points), 2005 survey (5 tracks with 9,280,657 points), and 2019 survey (14 tracks with 5,195,224 points).