Table 1.
Characteristics of the study areas: The mean height of buildings is calculated as surface-weighted average of the buildings heights digitized at 1 m resolution.
Fig 1.
General logic schema of the study.
Fig 2.
250 m A sample of the input reference data for the city of Toronto and the derived GVC of built-up areas.
a) Very high resolution satellite data, b) the 1 m reference grid on building footprints and their heights (data source: City of Toronto Open Data Portal https://open.toronto.ca/), and the 250 m grids GVCs c) AGBH, d) ANBH, e) SGBH, and f) SNBH (image sources: Esri, DigitalGlobe, GeoEye, i-cubed, USDA FSA, USGS, AEX, Getmapping, Aerogrid, IGN, IGP).
Fig 3.
Height profiles calculated for a transect crossing the city centre of Toronto from five different DEMs.
a) Detail from the 1 m reference grid on building footprints (data source: City of Toronto Open Data Portal https://open.toronto.ca/), b) DEM height profiles at their native spatial resolution (image sources: Esri, DigitalGlobe, GeoEye, i-cubed, USDA FSA, USGS, AEX, Getmapping, Aerogrid, IGN, IGP).
Table 2.
The list of features derived from spatial filtering of the input DEM data.
Fig 4.
Illustration of the ancillary features characterizing built-up areas for the city of Toronto.
a) Built-up densities, b) high green surfaces (veg3bu), c) medium green surfaces (veg2bu) and d) low green surfaces (veg1bu).
Fig 5.
Minimal RMSE in the prediction of the GVCGVC of built-up areas, across 60 different input GSFs extracted from global DEM data, by DEM source and test area.
The test area name “All” on the left of the chart reports about the RMSE obtained by estimating the regression parameters using the total number of valid samples (59566) considered in the study.
Fig 6.
Example of AGBH as estimated by univariate regression using the MEAN_m2d1 DSF extracted from alternative DEMs in the two test cases of London (a,c,e) and New York (b,d,f). From top to bottom: SRTM30 (a,b), AW3D30 (c,d), and CMP_SRTM30-AW3D30_U (e,f). Red arrow and red circles signal different anomalies in data that are mitigated by the DEM composite. AGBH values are mapped from 0 (black-blue) to 25m and more (yellow).
Table 3.
The five best performing GSF extracted from the CMP_SRTM30-AW3D30_U composite and their errors expressed as RMSE by type of GVC (gross vs. net) of built-up areas.
Table 4.
Intercept and slope coefficient of the univariate linear regression for estimation of the GVCs from the best two GSFs.
Fig 7.
Correlogram between GSF.
Table 5.
Intercept and coefficients of the MLR models used for estimating the GVCs considered in the study.
Fig 8.
Estimated coefficients of the individual predictors and the associated uncertainties for each of the four models estimating the GVC of built-up areas.
Fig 9.
The proportion of the R2 contributed by each individual predictor in the four models associated with the four GVCs of built-up areas.
Table 6.
Summary results of the stepwise regression for comparing different models using a sequential replacement of GSF.
Fig 10.
Example of predicted (left) vs. observed (right) GVCs values at 250 m resolution using the MLR on the 16 GSFs selected in the study, as resulting in the test area of Toronto (33 X 44 km). From top to bottom row: AGBH, SGBH ANBH, and SNBH. GVC values are mapped in the colour range from 0 (black-blue) to 25m and more (yellow).
Fig 11.
Example of predicted (left) v. observed (right) values of AGBH by using the model proposed in the study. From top to bottom, data extracted from the test case of Hong Kong, London, and New York.
Fig 12.
Example of predicted (left) v. observed (right) values of AGBH by using the model proposed in the study. From top to bottom, data extracted from the test case of San Francisco, Sao Paolo, and Toronto.