5 The WSF3Dv1 analysis framework introduced by Esch et al. (2022) consists of three automated processing modules: a first workflow defines the building fraction (BF) within each 90 m grid cell based on TDX-DEM, TDX-AMP, and S2. The second module analyzes height differences occurring along building edges in the TDX-DEM elevation data to derive the average building height (BH) at 90 m gridding. A last processing workflow combines the previously derived BF and BH information to calculate the building volume (BV).<sup>1</sup> To determine the building fraction BF, the temporal maximum of the Normalized Difference Vegetation Index (NDVI ~~m~~ ax) is calculated for all WSF2019 pixels from a time series of _∼_ 2.27 million S2 granules with _<_ 60% cloud cover (level 2A, bottom of the atmosphere reflectance) acquired in 2018-2019 (Marconcini et al., 2020). Using NDVI ~~m~~ ax and building footprint data from OpenStreetMap (OSM, 2017), an ensemble of support vector regression models is trained separately for all K ̈oppen-Geiger climate zones to estimate the BF for each WSF2019 settlement pixel.<sup>2</sup> The resulting information on BF (%) can be employed to define the total building area BA (m<sup>2</sup> ) of each cell by applying BF as a multiplication factor to the cell’s 12*12 m ground area.

The generation of the building height (BH) product is based on analyzing local height differences at vertical edges (VE) in the 12 m resolution TDX-DEM within the settlement area of WSF2019. In the TDX-DEM, VEs appear as distinct punctual or linear height variations along the outlines of quasi vertical structures such as buildings, walls, trees, or hedgerows. A given pixel in TDX-DEM is considered as a VE candidate if the ratio between the height of the target pixel (above sea level) and the median height (ditto) in its immediate neighborhood (within a 5 x 5 moving window) is _>_ 1.0 (Esch et al., 2022). Since the natural slope of the local terrain also leads to height differences, the slope-induced height differences are factored out by normalizing the measured local edge height VE with the local slope of the terrain. The terrain slope is measured by first removing all local maxima and vertical edges (TDX-DEM pixels where VE _>_ 0.0) before filling the resulting local gaps in the TDX-DEM elevation data with a four-direction conic search distance weighting (Esch et al., 2022). This generates an edge-smoothed version of the TDXDEM that only shows height differences due to the local terrain, whereas previously included height structures in the original TDX-DEM that arose from local vertical objects are now leveled in. By subtracting the edge-smoothed version of TDX-DEM from the original TDX-DEM, the effect of slope-induced height differences is minimized so that the resulting VE layer only shows

> 1Note that all analyses are exclusively carried out for areas assigned as settlement by the World Settlement Footprint 2019 (WSF2019) human settlements mask (Marconcini et al., 2021).

> 2 Empirical tests with a WSF settlement mask and WSF-IMP layer generated on the basis of 30 m Landsat data collected in 2012 (meaning the exact time of the TDXDEM data acquisition) clearly indicated the superiority of the WSF mask and WSF-IMP information derived from the 10 m S2 data (not yet available in 2012), although the imagery was collected in 2019. Indeed, the WSF2019 settlement mask, although including additional settlement areas that arose between 2012 and 2019, still shows a higher accuracy compared to the settlement mask derived from the coarse 30 m Landsat imagery. Moreover, the imperviousness estimation at 10 m based on NDVI ~~m~~ ax from 2019 S2 data led to a more precise masking of urban green spaces compared to the results obtained from Landsat.