Unveiling patterns in human dominated landscapes through mapping the mass of US built structures

Built structures increasingly dominate the Earth’s landscapes; their surging mass is currently overtaking global biomass. We here assess built structures in the conterminous US by quantifying the mass of 14 stock-building materials in eight building types and nine types of mobility infrastructures. Our high-resolution maps reveal that built structures have become 2.6 times heavier than all plant biomass across the country and that most inhabited areas are mass-dominated by buildings or infrastructure. We analyze determinants of the material intensity and show that densely built settlements have substantially lower per-capita material stocks, while highest intensities are found in sparsely populated regions due to ubiquitous infrastructures. Out-migration aggravates already high intensities in rural areas as people leave while built structures remain – highlighting that quantifying the distribution of built-up mass at high resolution is an essential contribution to understanding the biophysical basis of societies, and to inform strategies to design more resource-efficient settlements and a sustainable circular economy.

We derived Spectral Temporal Metrics (STM) [19][20][21] from the preprocessed data to retain temporal information while reducing data volume considerably.STMs are statistical aggregations of all available high-quality observations within a specified time period (one year in this case), and as such provide rich information on spectral-temporal variability and data distribution 7 .Due to their spatial completeness and fairly high robustness against different observation densities, they are suitable features for machine learning applications, and have proven to be effective for a large variety of land cover mapping or quantitative variable estimation e.g., 22,23 .For the optical time series, only clear-sky, non-cloud, non-cloud shadow, nonsnow observations were considered, which were further passed through an outlier detection routine.For the radar time series, each observation was considered.The STMs were generated separately for each band of the SAR (two bands) and optical time series (10 bands), as well as for several spectral indices.To capture the spatial characteristics originating from shadows cast off from nearby buildings as well as settlement structure, texture metrics are an established means to capture spatial context in image processing 24 .We computed texture metrics on top of the STMs with a circular structuring element with a 50 m radiusdenoted as spatial STM (SSTM) 1 .A list of employed STMs and SSTMs is given Supplementary Table 1 and Supplementary Table 2 for building height and building type mapping, respectively.

Supplementary Methods 2. Conversion to mass factors per volume
In the literature, material stocks in buildings are usually reported as either absolute mass per building unit, or as materials per square meter of useful floor area.Because this study derives the above-ground building volumes as three-dimensional LOD1 blocks (see also volume definition in 25 ) from Earth Observation data, a re-estimation and transformation of published information was required to match the definition depicted in Supplementary Figure 5.
The following equations summarize our conversion approach; each given equation is individually applied to each building type with building type-specific values.In-depth details can be found in 26 .When building volumes were not reported in studies, they were calculated based on available data by dividing the gross floor area gfa [m²] by the number of floors nf to obtain the gross footprint gf [m²]: If only the usable floor area ua [m²] was reported, a factor for the assumed share of the useable area in the gross floor area sua [%] provided by 26 was used: Subsequently, the above ground building height agbh [m] was calculated by multiplying the number of floors nf by the floor height fh [m].If floor heights were not listed, values provided by 26 or in similar U.S.
case studies were used.
The above-ground building volume (excluding the roof) agbv [m³] was then calculated by multiplying the gross footprint [m²] by the above-ground building height [m]: To account for the usually unreported roof volume of some building types such as low-rise single-and multi-family houses, the gross footprint was multiplied by the roof volume factor provided by 27 .The sum of the above ground volume (excluding the roof) and the roof volume corresponds with the building volume that is mapped via Earth Observation data.The material quantities reported in case studies were then divided by the above ground volume, producing the final mass factors.Supplementary Table 9 shows the developed mass factors per building type and climate zone in four broad material categories.These four material categories were further differentiated into 15 specific materials, which we published as supplementary data to this article 28  uncertainty of the complete stock, and that of buildings and mobility infrastructures, were computed using 10,000 random combinations of low, average, and high material factors, eventually computing the standard deviation of the 10,000 sums.This resulted in an estimated uncertainty of 5.8 Gt, 4.7 Gt, and 3.5 Gt for the total, building, and mobility infrastructure stock, respectively.

Supplementary Methods 4. Relationship between building and mobility infrastructure density
To analyze the relationship between buildings and mobility infrastructure stocks per area on the county level, a linear Ordinary Least Squares (OLS) regression model was employed using R 4.2.0 and the stats package 29 .Both variables were log-transformed to shift their frequency distributions towards normality.A highly significant relationship (p < 2e-16, n = 3,108) was found with R² = 0.88.Note however, that the high significance is substantially affected by the large sample size.

Supplementary Methods 5. Multivariate regression
To link material consumption of buildings and mobility infrastructure to possibly explanatory variables on the county-level (Supplementary Table 17), multivariate regression analyses were carried out using R 4.2.0 and the stats and spdep packages 29,30 .
Both target variables (i.e., material intensity of buildings, and material intensity of mobility infrasructures in t cap -1 ) were log-transformed to shift their frequency distributions towards normality.Population density and per-capita GDP were log-transformed, too.All dependent and independent variables were z-score normalized scaled to allow a comparison of the final regression coefficients of the models.
A Moran test indicated strong spatial autocorrelation effects (p=0.001) in the two target variables.
The statistical analysis was accomplished in two steps.First, for both target variables, a variable selection was performed using stepwise multivariate regression using the Bayesian Information Criterion (BIC) as selection criterion.To control the spatial autocorrelation problem in this stage, a random subsample of 500 observations from our original dataset (n = 3108) were drawn to reduce the likelihood that results were influenced by spatially clustered points.In a second step, the identified relevant predictor variables were used to fit for each target variable a spatial autoregressive model to the complete dataset using the spdep::sacsarlm R-function, to account for the full spatial dependency in the dependent variables (Bivant   et al., 2013).This model has the form The model outcomes (Supplementary Table 18, Supplementary Table 19) suggest that all of the included predictors have significant statistical associations with material intensity, which is also triggered by the large sample size (>3000 observations).Therefore, it is also mandatory to consider the effect sizes.The outcome of the Moran test applied to the model residuals indicates that both models have effectively accounted for the spatial structure in the data.
As the SAR model could not produce reliable Pseudo-R² values (note that the mobility infrastructure model generated an R² of 1.00), we further used the lrtest function from the lmtest library for carrying out a likelihood ratio test between the full SARCAR-model and a nested model without explanatory variables.A significant test result supports the assumption that the estimations of the full model provides a significantly better fit to the data and that they are not primarily based on the spatial autocorrelation structure.

Supplementary Notes 1. Definition: urban / rural
We analyze stocks, and the relative dominance of stock categories with regards to the percentage of the urban and rural population in the US counties.We follow the urban and rural classification of the US census "For the 2010 Census, an urban area will comprise a densely settled core of census tracts and/or census blocks that meet minimum population density requirements, along with adjacent territory containing nonresidential urban land uses as well as territory with low population density included to link outlying densely settled territory with the densely settled core.To qualify as an urban area, the territory identified according to criteria must encompass at least 2,500 people, at least 1,500 of which reside outside institutional group quarters.The Census Bureau identifies two types of urban areas: • Urbanized Areas (UAs) of 50,000 or more people; • Urban Clusters (UCs) of at least 2,500 and less than 50,000 people.
Rural encompasses all population, housing, and territory not included within an urban area." Under the above link, the US census 2010 provides a dataset that contains the percentage of urban and rural population per county, i.e., the population living in urban or rural areas according to the definition above.
The percentage of urban and rural population sums to 100%.Microsoft reports a precision of 99.3% and a recall of 93.5%.An independent validation of version 1.0 of this dataset was performed by 31 ; visual checks confirmed that raised issues are still apparent in version 1.1.

Supplementary
According to Heris et al. 31 , the accuracy for large building is indeed very high, but the dataset has a strong omission of small accessory buildings (< 150 m²): precision drops to 80% with decreasing area; recall drops significantly below 150 m², in some cases below 40%.This might be related to uncertainty in generating training data by manually digitizing very high-resolution data 32 or might even be implemented on purpose to avoid false positive detections of other infrastructure types that might be confused with small buildings, e.g., transportation containers or trucks.Please note that the dataset description of Microsoft is rather short.
Another issue of this dataset is that connected buildings with similar height are consolidated into superblocks 31 .This does not affect our measure of building area, but our prediction of building type is partially affected by this as footprint centroid density was used as one of the predictive variables.False positives have been identified in lakes, rivers, and snow-covered areas 31 , as well as in desert areas (https://github.com/microsoft/USBuildingFootprints/issues/57).We largely eliminated these false positives with a building height threshold of 2 m.False negative blocks were identified in some geographic areas, presumably due to a lack of aerial imagery 31 .These false negatives will however persist in our maps and will most likely be represented by parking and yard area, as most buildings still appear in the National Land Cover Database's imperviousness layer (see section Remaining impervious areas).As most unresolved issues and quality measures indicate underdetection, we rather expect that the uncertainty in the building footprint dataset results in an underestimation of building stocks.

Supplementary Discussion 2. Quality of building height prediction
The reference data were manually quality screened and homogenized.We validated the model using 1) a 70-30 data split for evaluating overall model performance (Supplementary Figure 3), and 2) a per-dataset cross-validation (Supplementary Table 3).
Most reference samples are taken from buildings shorter than 10-15 m, for which we obtained very accurate predictions close to the one-to-one line.Ground reference sample (height = 0) were also predicted with high accuracy, although some overprediction is apparent (bottom row in Supplementary Figure 3a), which however is uncritical for our final map: ground samples were incorporated into the modelling process to adapt the machine learner to non-building surfaces.All height predictions shorter than 2 m were set to 0 m in a postprocessing step, which eliminated false positive building detections to a large degree.Saturation, i.e., underprediction, is however apparent for buildings taller than ca.35 m (cf.Supplementary Figure 3b).
This effect was also described by 1 for Germany, which the authors attributed to 1) physical limitations inherent in the employed satellite data, and 2) insufficient number of training points as high-rise buildings in Germany are rather rare.In the CONUS, high-rise buildings and skyscrapers are more commonplace, however.Our validation confirms that saturation takes effect when predicting tall buildings, which partially corroborates those physical limitations are inherent in the employed data.However, in our case, saturation takes place above ca.35 m as compared to ca. 20 m in 1 .The better performance of the present model could be driven by both a more frequent occurrence of tall building samples and by their higher density that results in a more distinct representation in the SSTMs.
Nevertheless, saturation is still a dominant factor that precludes predicting high-rise buildings, or even skyscrapers, for which we would substantially underestimate material stocks.Thus, we additionally compiled data from the tall building database maintained by the Council on Tall Buildings and Urban Habitat (https://www.ctbuh.org,accessed on 03.11.2020), which contains the architectural height and coordinates of buildings taller than circa 65m.There is no information on the completeness of this database, but visual investigation suggests that the completeness increased rapidly towards the tallest buildings.As the Microsoft building footprints are subject to superblock issues, and upon visual inspection OSM completeness was found to be high for these prominent structures, we matched the coordinates of the tall building database with building geometries from OSM.We burned the database's height attribute into the EO-based building layer to better accommodate for tall buildings.For buildings not included in the tall buildings database, and larger than ca.35 m, the EO-based underestimation of building height accordingly adds an underestimation component to our final material stocks estimation.

Supplementary Discussion 3. Quality of building type prediction
The accuracy assessment of building types is presented in Supplementary Table 7. Two major data characteristics should be discussed regarding building type mapping.First, as actual building functions and uses are nearly impossible to detect from satellite imagery, building types were mapped based on textural context indicating their potential construction type.Thus, in selected cases, e.g., a closed production site now being used for residential purposes, the validation procedure has limitations.The sampling of RES and RCMU housing was sometimes challenging in transition zones between city centers and adjacent suburban areas, especially where both types were present in the local vicinity.In general, however, the distinction of these broad building type categories worked reasonably well as RES, CI, and MLB buildings have very distinct structural characteristics in many parts of the country.Second, the building footprint data provided an underestimation of the number of buildings in areas where many attached buildings with similar height and roof structure were merged into superblocks in the Microsoft building footprint dataset, for example in residential row development.Here, the small number of building centroids rather suggested industrial and commercial building structures instead of residential use.

Supplementary Discussion 4. Geographic origin of material factors for buildings
Preferably, studies for the United States were used to derive material factors (Supplementary For the other building types, it was assumed that construction practices and standards do not differ to an extent that would justify the use of a differentiated mass factor.

Supplementary Discussion 5. Remaining impervious areas
To safeguard our assumption that these remaining impervious surfaces are parking-related spaces or surfaces that have a similar material composition, we drew a random sample across the CONUS and manually labeled 1,000 sample points using visual interpretation of Google Earth imagery.Nearly 70% of the samples (type I in Supplementary Table 16) were indeed related to parking, yards, or similar surfaces.
Five percent of the samples were impervious surfaces that were not covered by any of the other layers (type II in Supplementary Table 16), which suggests that our class catalogue is not complete and we are missing specific mass-per-area factors for these surfaces.However, given the low share of these surfaces, we believe this uncertainty to be reasonably small with regards to the entire material stocks budget.Some samples were labeled as buildings (type III), which is presumably related to the underdetection tendency of the building footprint dataset, especially for smaller buildings.A portion of samples was found to be other mobility infrastructures (type IV), which suggests some uncertainty in the buffer procedure to convert OSM line features to polygons, e.g., when a street is wider than the design manual specificationwhich are defined as minimal width requirements.About 6% of the samples were natural surfaces like trees, soils, or rocks (type V), which represents an overestimation component towards our material stocks estimation.
Nevertheless, the largest share by far are parking and yard areas.Thus, we subsumed the remaining impervious area and the OSM-extracted parking spaces into the "parking and yards" class.

Supplementary Table 1. Predictive variables building height
Earth Observation variables from Sentinel-1 * and Sentinel-2 used for modelling building height; the method for selecting these features is documented in the supplemental material of 1 .Aggregation percentages represent percentiles.0% Gradient * As some data gaps were apparent in the Sentinel-1 dataset, we additionally trained a fallback model that only considered independent variables originating from Sentinel-2.Tests in 1 have shown that a model with optical data only can achieve performances comparable to a model trained with both optical and radar data.The fallback model was only applied to the few areas with limited Sentinel-1 coverage and results were checked for consistency, especially at the edge of the cutline.No validation data was available within this region.

Supplementary Table 2. Predictive variables building types
Earth Observation variables used for modelling building type with Random Forest classification following 26,46   , here supplemented by a building centroid density variable to better distinguish between small-scale buildings against large commercial, industrial and office buildings that spectrally resemble, but are less densely packed.S5) were translated into relevant building types from a material-specific point of view.Buildings lower than 2 m were labeled as no building, which reduced overdetection in the building footprint data and accounted for temporal misalignments between our employed EO data and the Bing imagery used by Microsoft.Buildings taller than 75 m were labeled as skyscrapers, and buildings between 30 and 75 m were labeled as "high-rise residential/commercial mixed use".The residential buildings were further split into low-and mid-rise buildings using a 10 m threshold, i.e., approximately three stories.Following the procedure in 26 , we further reduced the building area of the lowrise residential buildings by 10% and added this share to the lightweight buildings category to represent attached garages and other accessory buildings that cannot be reliably separated using EO data.

Supplementary Table 5. Intermediate building types
Building type classes for Earth Observation-based mapping.

Supplementary Table 6. Building type training sites
Training sites for building type prediction.The sites were equally distributed within the nine U.S. Geographic Regions identified by the National Centers for Environmental Information 47 , accounting for possibly different building structures across the country.Both urban agglomerations and rural settlements as well as a broad variety of bioclimatic conditions were represented within and across the sampling sites.We collected a maximum of 30 samples per class and site.6).We additionally classified motorways and motorway links on bridges, as well as all other roads on bridges if the bridge attribute of a feature was set.We also differentiated bridges and tunnels, excluding the roads in and on them.Since local roads and rural roads vary in the number of lanes, an average number of 1.5 lanes was assumed for both, based on design manuals, and selective screening of Google Earth images.To account for the diversity in road design standards across the CONUS, the averages of officially reported road widths [72][73][74] and various county-level road design manuals were used for the individual road classes.
When transforming buffered polygons to image-based area, it was made sure that the sum of all road raster layers did not exceed a completely filled pixel.In case this did happen, roads were prioritized from top to bottom; Tunnels and bridges were not subject to this condition.

Road type OSM class OSM class definition Buffer width (m) Motorway motorway
A restricted access major divided highway, normally with 2 or more running lanes plus emergency hard shoulder.Equivalent to the Freeway, Autobahn, etc. 13.6 motorway_link The link roads (sliproads/ramps) leading to/from a motorway from/to a motorway or lower class highway.Normally with the same motorway restrictions.

Primary trunk
The most important roads in a country's system that aren't motorways.
(Need not necessarily be a divided highway.)

trunk_link
The link roads (sliproads/ramps) leading to/from a trunk road from/to a trunk road or lower class highway.

Secondary primary
The next most important roads in a country's system (often link larger towns).

primary_link
The link roads (sliproads/ramps) leading to/from a primary road from/to a primary road or lower class highway.

Tertiary secondary
The next most important roads in a country's system.(Often link towns.)5.3 secondary_link The link roads (sliproads/ramps) leading to/from a secondary road from/to a secondary road or lower class highway.

Local tertiary
The next most important roads in a country's system (often link smaller towns and villages).

tertiary_link
The link roads (sliproads/ramps) leading to/from a tertiary road from/to a tertiary road or lower class highway.

unclassified
The least important through roads in a country's systemi.e., minor roads of a lower classification than tertiary, but which serve a purpose other than access to properties (often link villages and hamlets).

residential
Roads which serve as an access to housing, without function of connecting settlements.Often lined with housing.

living_street
For living streets, which are residential streets where pedestrians have legal priority over cars, speeds are kept very low and where children are allowed to play on the street.

service
For access roads to, or within an industrial estate, camp site, business park, car park, alleys, etc.

footway
For designated footpaths; i.e., mainly/exclusively for pedestrians.This includes walking tracks and gravel paths.13.Railway types and buffer widths Definitions and re-classification of railways as given in OpenStreetMap to railway types as used in this study based on functional characteristics.We additionally separated bridges and tunnels, excluding the rails in and on them if the bridge attribute of a feature was set.Subways were further split into underground tracks, aboveground tracks, and elevated tracks.Buffer widths span half of the entire railway width.Width estimates were adopted from 26 with the underlying assumption that US-American and Austrian/German track widths are comparable, knowing that all three countries use international gauge.When transforming buffered polygons to image-based area, it was made sure that the sum of all raster layers did not exceed a completely filled pixel.In case this did happen, roads were prioritized from top to bottom; Tunnels and bridges were not subject to this condition.

OSM class OSM class definition Buffer width (m) Railway rail
Full sized passenger or freight trains in the standard gauge for the country or state.
6.0 light_rail A higher-standard tram system, normally in its own right-of-way.
Often it connects towns and thus reaches a considerable length (tens of kilometers).

Subway subway
A city passenger rail service running mostly grade separated.Often a significant portion of the line or its system/network is underground.

Tram tram
One or two carriage rail vehicles, usually sharing motor road, sometimes called "street running".

3.5
Other narrow_gauge Narrow-gauge passenger or freight trains.Narrow-gauge railways can have mainline railway service like the Rhaetian Railway in Switzerland or can be a small light industrial railway.

preserved
A railway running historic trains, usually a tourist attraction.

disused
A section of railway which is no longer used but where the track and infrastructure remains in place.

funicular
Cable driven inclined railways on a steep slope, with a pair of cars connected by one cable.

monorail
A railway with only a single rail.A monorail can run above the rail like in Las Vegas and Disneyland or can suspend below the rail like the Wuppertal Schwebebahn (Germany).

miniature
Miniature railways are narrower than narrow gauge and carry passengers, frequently at an exact scale of "standard-sized" rail (for example "1/4 scale").They can often be found in parks.

Supplementary Table 14. Mass factors for railways
Mass factors and widths for railway types.Totals may not add up due to rounding.For metals, we further distinguish between iron or steel, copper and aluminum.We published the full mass factor dataset as supplemental data to this article in 28 .

Further specifications
Material factor (kg m -2 ) Width (m) References 1 width for OSM-key "rail"; 2 width for OSM-key "light_rail"; 3 Unit: kg m -2 tube Supplementary Table 15.Mass factors for airport and parking infrastructure Mass factors and widths for airport-and parking-related mobility infrastructure.Totals may not add up due to rounding.We published the mass factor dataset as supplemental data to this article in 28 .

Metals
, i.e. (i) metals: iron and steel, copper, aluminum, and other metals; (ii) non-metallic minerals: concrete, bricks, glass, aggregate, and other minerals; (iii) biomass-based materials: timber and other biomass-based materials such as boards; (iv) petrochemical-based materials: bitumen and other petrochemical-based materials; and (v) other materials: insulation materials and all other materials.
: y = dependent variable X = matrix of independent variables β = vector of coefficients for the independent variables u = (autocorrelated) error term W = spatial weights matrix, which defines the neighborhood structure based on regions with contiguous boundaries λ = spatial autoregressive parameter for the error term ε = residual term A sacsarlm model can capture complex spatial relationships by combining a Spatial Error Model (SEM)that assumes a moving average process of the spatially lagged error term and a Spatial Autoregressive Model (SAR) that can handle a spatial autoregressive process by including lagged effects of the dependent variable.In the equation ρ captures the spatial autocorrelation in the dependent variable (y), and λ captures the spatial autocorrelation in the error term (u).
2010 Census Urban and Rural Classification and Urban Area Criteria https://www.census.gov/programs-

Table 9 )
. About 58% of 71 building mass factors used were sourced from building studies for the United States.For those building types where data was scarce, studies from economically comparable countries (mainly Canada and Australia) were used, where similar building standards and climate zones were assumed (ca. 33% of all mass factors).Mass factors for buildings in other countries make up the remaining 10% of all building mass factors.For the classes of high-rise buildings (RCMU-HR, RCMU-SKY), studies from East Asia and Europe were used as well, as such structures were assumed to be sufficiently homogeneous across the globe.Furthermore, the mass-per-volume factors for mobile homes and other light-weight structures are based on material quantities of post-disaster pre-manufactured housing in Turkey33as this case study was evaluated to be most analogous to mobile homes or structures, colloquially known as trailer parks.Different construction standards across climate zones are particularly relevant for residential buildings across the CONUS.Mass factors for this building type were therefore developed for each climate zone (Supplementary Table8).A total of 21 mass factors from U.S. case studies and 13 mass factors from case studies outside the United States were aligned to five climate zones based on the location of each case study.

Table 3 . Building height cross-validation and data sources
Cross-validation of building height prediction.OLS: ordinary least squares regression; RTO: regression through origin; RMSE = root mean squared error; MAE: mean absolute error.

Table 4 .
Building typesDefinitions of building types as used in this study.
* Intermediate building types (Table

Table 7 . Quality of building type prediction
Confusion matrix of the building type classification.See Supplementary Table5for the class definition.n = number of samples, OA = Overall Accuracy

Table 9 .
Mass factors for buildingsMass factors per building type and main material category in [kg/m³].Totals may not add up due to rounding.In total, mass factors for 15 material sub-categories were developed and used in this study.We published the full mass-per-volume factor dataset as supplemental data to this article 28 .

Table 10 .
Road types and buffer widthsDefinitions and re-classification of roads as given in OpenStreetMap to road types as used in this study based on shared characteristics such as pavement thickness, surface, and road width.Buffer widths span half the entire road width, including shoulders and median strip, if present (see Supplementary Figure

Table 16 .
Composition of remaining imperviousness areasInvestigation of the composition of the remaining impervious area class.
1as referred to in Supplementary Discussion 5