Generalized Vertical Components of built-up areas from global Digital Elevation Models by multi-scale linear regression modelling

The estimation of the vertical components of built-up areas from free Digital Elevation Model (DEM) global data filtered by multi-scale convolutional, morphological and textural transforms are generalized at the spatial resolution of 250 meters using linear least-squares regression techniques. Six test cases were selected: Hong Kong, London, New York, San Francisco, Sao Paulo, and Toronto. Five global DEM and two DEM composites are evaluated in terms of 60 combinations of linear, morphological and textural filtering and different generalization techniques. Four generalized vertical components estimates of built-up areas are introduced: the Average Gross Building Height (AGBH), the Average Net Building Height (ANBH), the Standard Deviation of Gross Building Height (SGBH), and the Standard Deviation of Net Building Height (SNBH). The study shows that the best estimation of the net GVC of built-up areas given by the ANBH and SNBH, always contains a greater error than their corresponding gross GVC estimation given by the AGBH and SGBH, both in terms of mean and standard deviation. Among the sources evaluated in this study, the best DEM source for estimating the GVC of built-up areas with univariate linear regression techniques is a composite of the 1-arcsec Shuttle Radar Topography Mission (SRTM30) and the Advanced Land Observing Satellite (ALOS) World 3D–30 m (AW3D30) using the union operator (CMP_SRTM30-AW3D30_U). A multivariate linear model was developed using 16 satellite features extracted from the CMP_SRTM30-AW3D30_U enriched by other land cover sources, to estimate the gross GVC. A RMSE of 2.40 m and 3.25 m was obtained for the AGBH and the SGBH, respectively. A similar multivariate linear model was developed to estimate the net GVC. A RMSE of 6.63 m and 4.38 m was obtained for the ANBH and the SNBH, respectively. The main limiting factors on the use of the available global DEMs for estimating the GVC of built-up areas are two. First, the horizontal resolution of these sources (circa 30 and 90 meters) corresponds to a sampling size that is larger than the expected average horizontal size of built-up structures as detected from nadir-angle Earth Observation (EO) data, producing more reliable estimates for gross vertical components than for net vertical component of built-up areas. Second, post-production processing targeting Digital Terrain Model specifications may purposely filter out the information on the vertical component of built-up areas that are contained in the global DEMs. Under the limitations of the study presented here, these results show a potential for using global DEM sources in order to derive statistically generalized parameters describing the vertical characteristics of built-up areas, at the scale of 250x250 meters. However, estimates need to be evaluated in terms of the specific requirements of target applications such as spatial population modelling, urban morphology, climate studies and so on.