Table 1 Urban spatial metrics used in this study: The variables, calculated per MSA and year, used to describe the evolution of urban areas in this study, categorized into two categories (i.e., size and form). Variables in each category are sorted by their factor loadings from principal component analysis, conducted across all MSAs and points in time, indicating how much data variance these variables explain (sorted per category, descending from top to bottom), see Supplementary TableĀ 1.

From: A century of decoupling size and structure of urban spaces in the United States

Variable

Characteristic of built-up areas

Description

Size

Built-up area (BUAREA)

Horizontal extension

Total built-up area

Number of built-up properties (NUMBUPROP)

Quantity of built-up elements

Number of built-up properties

Net built-up intensity (NETBUI)

Built-up volume

Total indoor area of buildings within an MSA

Built-up density (BUDENS)

Built-up density

Total indoor area of buildings per built-up area)

Average housing unit size (AVGHUSIZE)

Built-up element size

Average size of housing units, measured in indoor area

Form

Scatteredness (SCAT)

Dispersion

Scatteredness: number of isolated built-up grid cells

Number of built-up patches (NUMPATCH)

Dispersion

Number of contiguous areas (patches) of built-up land

Largest patch area proportion (MAXPATCHPROP)

Contiguity / dominance

Largest built-up patch area proportion of total built up area

Clusteredness (CLUST)

Compactness / dispersion

Deviation of built-up cells from a random spatial distribution

Mean circularity (CIRC)

Compactness

Circularity of the ten largest built-up patches