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ENVIRONMENTAL STUDIES
Two centuries of settlement and urban development
in the United States
Stefan Leyk1,2,3*, Johannes H. Uhl1,2, Dylan S. Connor4, Anna E. Braswell3,5, Nathan Mietkiewicz3,5,
Jennifer K. Balch1,3,5, Myron Gutmann2,6
Over the past 200 years, the population of the United States grew more than 40-fold. The resulting development
of the built environment has had a profound impact on the regional economic, demographic, and environmental
structure of North America. Unfortunately, constraints on data availability limit opportunities to study long-term
development patterns and how population growth relates to land-use change. Using hundreds of millions of
property records, we undertake the finest-resolution analysis to date, in space and time, of urbanization patterns
from 1810 to 2015. Temporally consistent metrics reveal distinct long-term urban development patterns characteriz-
ing processes such as settlement expansion and densification at fine granularity. Furthermore, we demonstrate
that these settlement measures are robust proxies for population throughout the record and thus potential sur-
rogates for estimating population changes at fine scales. These new insights and data vastly expand opportuni-
ties to study land use, population change, and urbanization over the past two centuries.
INTRODUCTION
The population of the United States grew from an estimated 5.3 million
in 1800 to 309 million people in 2010 (1). On the basis of the defi-
nitions from the Census Bureau, the share of the U.S. population living
in urban areas grew from 6 to 81% over this period. Urbanization oc-
curred through population growth and the transformation of physical
landscapes and ecological systems into developed land. Thus, researchers
typically measure these changes through either population- or land-
based methods [e.g., (2–6)]. While these two perspectives paint differ-
ent but complementary pictures of urbanization, they are also sensitive
to the scale of measurement. Thus, because of the absence of consistent
and detailed, historical information on local land use and local popula-
tion change, our knowledge of the historical development of the United
States is far from complete. Advancing such knowledge would greatly
improve our understanding of the broad impacts of urbanization and
allow for refined projections of demographics and the built environment.
The absence of detailed historical population data before the
mid-20th century severely constrains any population-based assess-
ment of urban processes. Although the U.S. Census records are made
publicly available after a period of 72 years, spatially registering and
encoding these data are resource-intensive. While researchers have
begun to transcribe and extract these data for fine-scale analysis
[e.g., (7–9)], publicly available historical population data are acces-
sible only at coarse spatial resolution [e.g., county boundaries; (10)].
This coarse resolution in combination with boundary changes over
time (fig. S1) poses a major barrier to studying historical urbaniza-
tion in the United States using census data [e.g., (11,12)].
Studying urbanization from a land perspective typically includes
land use or land cover data, or, more recently, settlement layers that
provide consistent spatial data on the timing, location, and nature
of land use. Although many historical maps contain detailed infor-
mation on land use over long time periods, their extraction at fine
resolution is prohibitively costly because of the volume, complexity,
and low quality of such graphical documents (13). Most prior efforts
to characterize historical fine-grained settlement or land cover
changes rely on remote sensing imagery, which are constrained to
the post-1970 era of satellite technology [e.g., (14–17)]. Such historical
satellite-derived data are usually coarsely classified, provide limited
information on the specific characteristics of built-up land, and are
often less accurate for rural areas (18,19).
In this study, we present a new means of understanding the
speed, spread, and nature of urbanization in the United States from
1810 to 2015. We use gridded settlement layers from the Historical
Settlement Data Compilation for the United States [HISDAC-US;
(20)], which is derived from property records compiled in the Zillow
Transaction and Assessment Dataset (ZTRAX). HISDAC-US de-
scribes the built environment of most of the conterminous United
States back to 1810 at fine temporal (5 years) and spatial (250 m)
granularity using different settlement measures. These measures in-
clude the number of built-up property records, which can refer to
individual properties or units within built-up properties (BUILD)
in a grid cell in a given year and the built-up intensity (BUI), or the
sum of gross indoor area of all built-up properties. We also extracted
for each grid cell the first built-up year (FBUY), which is the earliest
construction year on record. For larger analytical units, such as counties,
we derived the built-up area (BUA), or the number of grid cells over-
lapping with one or more built-up properties in a given year.
The principal goal of this analysis is to foreground the value of
these novel data in providing insight into long-term settlement and
urban development. Building on Leyk and Uhl (20) and other on-
going efforts (9), we leverage the HISDAC-US data to undertake an
unprecedented multiscale analysis of the history of U.S. urban de-
velopment and settlement. These new data can be leveraged to explore
and characterize fundamental processes of urban growth through
measurement of changes in the built environment, potentially pro-
viding insights into the fundamental drivers of development pat-
terns. We anticipate that these measures and insights will provide
vast new opportunities to study and understand the history of U.S.
urbanization from a land-based perspective.
1Department of Geography, University of Colorado Boulder, 260 UCB, Boulder,
CO 80309, USA. 2Institute of Behavioral Science, University of Colorado Boulder,
483 UCB, Boulder, CO 80309, USA. 3Earth Lab, University of Colorado Boulder, 4001
Discovery Drive Suite S348, 611 UCB, Boulder, CO 80309, USA. 4School of Geo-
graphical Sciences and Urban Planning, Arizona State University, Tempe, AZ 85281,
USA. 5Cooperative Institute for Research in Environmental Sciences, University of
Colorado Boulder, 216 UCB, Boulder, CO 80309, USA. 6Department of History, Uni-
versity of Colorado Boulder, 234 UCB, Boulder, CO 80309, USA.
*Corresponding author. Email: stefan.leyk@colorado.edu
Copyright © 2020
The Authors, some
rights reserved;
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American Association
for the Advancement
of Science. No claim to
original U.S. Government
Works. Distributed
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NonCommercial
License 4.0 (CC BY-NC).
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In addition to new land-based assessments of urban change and
development, these novel data also unlock new opportunities to
model the spatial distribution of population in the past. Our moti-
vation in this regard is rooted in recent research. First, while recent
work shows relationships between historical population counts and
built-up property attributes, this analysis is confined to the national
scale and lacks the spatial detail necessary for understanding varia-
tion and change (21). Second, data on developed or built-up land
are often used as the main ancillary variable in population modeling
using dasymetric refinement approaches. This refinement method
is a form of areal interpolation that makes use of relationships be-
tween the target variable (population) and the ancillary variables used
for subunit estimation [e.g., (22–25)]. Third, parcel data combined
with population and road network data were used in recent efforts
to study long-term urbanization processes within U.S. cities (26),
but such data have not been available for the entire nation to date.
Last, researchers applied similar principles of land availability and
suitability to disaggregated historical census summary statistics and
created fine-resolution population distributions (27). However, these
approaches lack robust testing and validation for the years before
2000. Given this body of research, we argue that data products such
as the HISDAC-US provide unique opportunities to model not only
changes in the built environment but also, potentially, fine-grained
historical population estimates. Progress in this area could unlock new
possibilities for the spatiotemporal analysis of urbanization in the United
States, combining both land- and population-based perspectives.
While our main findings confirm well-known broad diffusion
patterns of urbanization, HISDAC-US settlement layers enable us
to identify detailed building trajectories as well as expansion and
densification patterns at various spatial scales. The fine granularity
of the data is depicted by maps of the FBUY (Fig.1) and the number
of built-up property records (BUILD; Fig.2, BtoF) from 1810 to
2010. Finer-scale data break down broader national and regional
development trends and describe, for example, local processes of
expanding urban and suburban areas or infilling in built-up places
during different time periods. We also demonstrate relationships
between settlement measures and population growth. We estimate
that, on average, each additional built-up property at the county-
level is associated with around 2 to 2.25 additional people with
some regional variation. This finding is notable as there are, at pres-
ent, no reliable estimates of long-term, fine-resolution population
growth for the United States. Thus, we argue and demonstrate that
the novel HISDAC-US data provide an unprecedented opportunity
to study and understand long-term urbanization and settlement
processes at fine spatial and temporal granularity from the begin-
ning of the 19th century to today.
RESULTS
Taking a land perspective on urbanization: Where, when,
and how much land was built-up?
Using the fine temporal and spatial granularity as well as different
built characteristics, we elucidate new spatiotemporal settlement
patterns. With these patterns, we draw a detailed picture of the evo-
lution of built-up land use in the conterminous United States from
1810 to 2015.
Mapping the earliest recorded built-up properties (FBUY) within
boundaries of varying spatial scale, we find that urban development
trends are strongly dependent on the size of the spatial unit used (broad
national to local; Fig.1). By using the contemporary county bound-
aries of the 2010 decennial census as consistent mapping units, we
observe two primary, well-known national trends (Fig.1,AandB).
First, we find trends of urban development diffusing westward from
Northeastern and coastal Southern states into the interior of the
United States, including the eastern parts of Texas, Kansas, and
Arkansas. These trends unfold later in the Appalachian Mountains
and parts of Florida, likely because of the rough topography and lim-
ited habitability of these areas. Second, while buildings in counties in
the central and western states of the United States tend to be newer
than their Eastern counterparts, there are isolated counties across the
western seaboard and interior regions (e.g., Denver and Wichita
Falls; Fig.1, Dand E) that experienced particularly early waves of
Fig. 1. Maps of the FBUY at different levels of granularity. The maps depict national-, regional-, and local-scale processes of human development: (A) county-level
FBUY within contemporary (Census 2010) boundaries used as constant units of analysis over time (counties where no built-up year is available are shown in gray); more
detailed distributions of FBUY for the states of Colorado, Kansas, and Ohio within (B) county boundaries, (C) 2500-m grid cells, and (D) 250-m grid cells, respectively. (E) A
detailed depiction of the 250-m resolution data for the cities of Denver, CO; Wichita Falls, KS; and Columbus, OH.
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development relative to the rest of their respective states. In many
instances, these nodes of early development predate the demarcation
of these regions as U.S. states.
By assigning FBUY values to smaller spatial units such as indi-
vidual grid cells of specific size (e.g., 2,500-m resolution, Fig.1C; or
250-m resolution, Figs.1D and 2A), we are able to assess local settle-
ment trends within consistent spatial units that break down the
county-level patterns. For example, early settlement and growth
along Colorado’s Front Range emanates from a number of isolated
centers, with Denver being the largest (Fig.1,Dand E, left). Also,
earliest records of development in more rural settings of the state
(in mountainous areas or in the plains) appear spatially related to
streams and topographic conditions that facilitated development,
livelihood, access to water, and transportation. In contrast, new de-
velopment in Kansas spreads as a broader national pattern of west-
ward expansion, rather than as sprawl from discrete larger urban
hubs (Fig. 1, D and E, middle). In Ohio, urban centers begin to
overlap over time as they expand into one another (Fig.1,DandE,
right). These patterns illustrate the opportunities provided by such
multiresolution data for detecting local-to-regional scale settlement
and land development trends over long time periods.
We used the built year of each property in combination with build-
ing attributes to compute time series of various settlement variables at
different resolutions to more holistically measure local and regional
development trends. As discussed above, these settlement measures
include the total number of built-up properties (BUILD), the BUI of
land derived from the sum of indoor floor area of existing built-up
properties, and the number of grid cells built-up within a chosen unit
or BUA (see Materials and Methods for details). We extracted these
variables within consistent spatial units across time periods to gener-
ate long-term trajectories (e.g., fig. S2 at the state-level) and multitem-
poral spatial distributions (e.g., fig. S3 at the county-level) to characterize
variation in settlement patterns over time. We illustrate county-level
estimates of BUILD and its change every 5 years between 1810 and
2015 and spatial clusters for each point in time (movie S1). However,
the full details of local settlement processes can only be uncovered at
the finest granularity.
Taking Rockingham County, NH and the areas surrounding
New Hampshire and Massachusetts as an example region, we trace
spatial distributions of BUILD at the finest spatial resolution of
250m over five points in time (1810, 1860, 1910, 1960, and 2010;
Fig.2,BtoF). This analysis allows us to track the number of built-
up property records at the grid cell-level and better understand local
urban growth processes. In this particular case, the cities of Manchester,
NH; Newburyport, MA; Amesbury, MA; and Portsmouth, NH grew
as separate small urban hubs until 1860. Fewer built-up properties
Fig. 2. HISDAC-US settlement layers derived from the ZTRAX data at fine granularity for different points in time. The layers are shown at 250-m spatial resolution
for different points in time, 1810–2010, for Rockingham County, NH and surroundings, including: (A) FBUY layer in which raster cells are assigned the earliest built year
recorded, and a time series of the number of built-up property records (BUILD) located within a raster cell in (B) 1810, (C) 1860, (D) 1910, (E) 1960, and (F) 2010. County
boundaries of the 2010 census are shown in black.
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were established in rural parts of the area along roads during the
early and mid-1800s. By 1910, Manchester grew substantially, in area
and density, while the port cities developed at slower rates. This
trend continued, and by 1960, low-density settlement in rural areas
had expanded along roads to increasingly connect higher-density
urban hubs. Furthermore, during this time period, development
increased rapidly along the coastline. Last, by 2010, the area had expe-
rienced intensified sprawl in its southern and coastal regions, a con-
tinued expansion of urban hubs, and increasing densification in the
South, which grew into a larger urban and suburban conglomerate.
Such subcounty, temporal settlement patterns have the potential to
yield vast new insight into the geographical unfolding and intensity
of local urban development processes.
Land-based measures of change characterize types of urban
development at varying scales
Fine-scale settlement layers provide unique opportunities to distinguish
between land-based processes of urbanization such as expansion and den-
sification. Expansion refers to the amount (or proportion) of new devel-
oped area over time, and densification is the ratio of the change in BUI
to the change in BUA over time (see details in Materials and Methods).
Coarser-scale, county-level maps of expansion and densification
reveal notable regional variation (see fig. S4 and movie S1 for a
complete sequence of those maps and their spatial cluster maps).
These results complement the observed regional settlement pat-
terns but provide more details about the underlying processes of
urban growth, often a function of time, infrastructure, and access to
technology. Maps of peak timing of densification and expansion
(fig. S5) reveal that both processes are temporally associated and
vary regionally. For example, along the coastlines of the Southeast
and the Southwest of the United States, the vast majority of counties
have expansion peaks earlier than densification, indicative of land
expansion maxima followed by maximum infilling in already built-up
areas. We found the opposite process in the noncoastal Northeast,
the Midwest, and parts of the Mountain West. In these areas, devel-
opment and peak densification occurred over the early to mid-
1900s, and expansion—often in the form of sprawl—subsequently
unfolded and peaked during the second half of the 20th century.
We assessed city-level measures of expansion and densification
for San Francisco, CA; Atlanta, GA; and Boston, MA (Fig.3A). With
the exception of the time period from 1920 to 1950, which was a period
of rapid rise and decline in terms of expansion and densification, in
Boston, both measures trended gradually upward over time but took
opposite trends after 2000 (expansion declining and densification rising).
Atlanta and San Francisco exhibit more notable variation. In the
sprawling city of Atlanta, densification has remained modest (with
some recent increases), but expansion has markedly increased since
the mid-20th century. Over the past decade, Atlanta had decreasing
expansion and increasing densification. For San Francisco, in contrast,
we find the opposite pattern: Expansion remained relatively low
over time, but densification continued to rise sharply. These trends are
consistent with the widely held view of Atlanta as a sprawling metropol-
itan region and the greater compactness of San Francisco.
From these trajectories, we can track the development of a city at
fine temporal resolution over 200 years and visualize accompanying
spatial change patterns at the grid cell-level. By assessing the change
in BUA (∆BUA; i.e., locations that were developed during a given
time period) and the change in BUI (∆BUI; i.e., interior area added
per grid cell during a given time period) in detailed maps (Fig.3,
BandC, respectively), we gain insight into the development mech-
anisms generating differences across cities. The spatial patterns sug-
gest that San Francisco (Fig.3B, left) developed under topographic
constraints allowing limited new development and creating notable
changes in density over the past 100 years. Atlanta (Figs.3B, middle),
in contrast, had a massive increase in developed area since the 1960s
and developed into one of the most sprawling cities in the United
States with low building density. Last, the spatial patterns for Boston
(Fig.3B, right) are illustrative of a city with an early-developing and
high-density urban core. Continued new development and increases
in density were more balanced in Boston over the past century than
in the other two cities. Thus, these novel data products provide vast
Fig. 3. Settlement trends and multitemporal distributions for San Francisco,
Atlanta, and Boston. (A) Time series of densification and expansion, calculated
over 15-year time increments computed within metropolitan statistical area bound-
aries of 2010. (B) New built-up grid cells (indicated by black grid cells) during the
given time periods. (C) Change in BUI (i.e., the sum of building indoor area per grid
cell) during the given time periods, with warmer colors indicating greater change.
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new opportunities for measuring and testing proximate patterns
and determinants of urban spatial development (e.g., topographical
influences on land use). To further illustrate the dynamism of these
data products, we developed fine-grained distributions of BUI with
a temporal resolution of 5 years for these three cities, as well as Los
Angeles, CA; Dallas–Fort Worth, TX; and Philadelphia, PA between
1810 and 2015 (movie S2).
Dissecting and measuring forms of growth at fine scale
in urban and rural areas
Across the conterminous United States, we find that land-based ex-
pansion and densification show converging and diverging trends
over recent decades, particularly in more developed counties. We
created trends of densification (Fig.4A) and absolute expansion
(Fig.4B) for counties in two strata, which we refer to as rural and
urban, over time. The rural stratum is composed of counties that have
less than the 66th percentile of BUI across all counties (using the 2010
census boundaries), calculated individually for each year. The urban
stratum is defined by counties with BUI values greater than the 66th
percentile. This stratification allows us to assess how settlement in
relatively more and less developed places changed over time.
The two strata have different trajectories for both measures with
significantly higher values in the urban stratum. For urban counties,
both measures have an increasing trend up to the 1930s (Fig.4,A
andB). After 1940, expansion increases markedly until the early 2000s
but decreases notably during the past decade (Fig.4B). Densification
has varying trends since 1930: It levels off for a short time, increases
between 1940 and 1960, then decreases until the 1980s, and si nce t hen,
increases sharply until 2010 (Fig.4A). The rural stratum shows
continuous increases in both measures, steepest for densification
between 1910 and 1960 and for expansion between the 1940s and
1980s, somewhat temporally offset to densification. Both measures
remained relatively constant between 1980 and 2010. Counties in the
urban stratum have significant variability indicating wide ranges of
expansion and densification values, likely found in different regions.
In general, we find compelling differences in comparing the two
Fig. 4. Settlement trends describing different types of growth in rural and urban strata. Boxplots of semi-decadal distributions of (A) densification and (B) absolute
expansion in rural and urban counties. (C) Graphic display of relative locations of newly and previously built-up grid cells to calculate midrange expansion, internal, and
peripheral growth within the Greater Washington, DC area including Arlington, Bethesda, and Georgetown. (D) Trends of building indoor area (BIA) in urban and rural
strata (counties), each broken down into whether the increase happened in newly built-up cells (midrange expansion), in previously built-up cells at the edge of larger
BUAs (peripheral growth), or in previously built-up cells in inner parts of BUAs (internal growth). (E) Proportion of internal, peripheral, and internal-peripheral combined
growth (i.e., growth in previously built-up cells) in relation to overall change for the two strata (rural and urban).
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strata that appear to characterize the rural-urban divide in the de-
velopment of the conterminous United States.
To better understand the observed growth patterns, we spatially
decomposed the trends of built-up interior area (BIA), which is the
BUI aggregated across the whole United States, within both rural and
urban counties into different types of growth. The different growth
categories include midrange expansion (i.e., the appearance of newly
built-up cells), peripheral growth (i.e., in previously built-up cells at
the edge of larger BUAs), and internal growth (i.e., in previously
built-up cells in inner parts of BUAs; Fig.4C). The resulting trends
illustrate the magnitudes of BIA across and within strata (Fig.4D). By
2010, BIA in the urban stratum is roughly 10 times greater than in
the rural counties. Within the urban stratum, the dominant type of
growth has been peripheral growth followed by midrange expansion.
These two types of growth are very similar in the rural stratum. Inter-
nal growth has the lowest values of BIA, but its proportion has been
notably higher in the urban stratum in the past.
To examine the relationships and changes between different types
of growth across each stratum, we computed ratios of changes of BIA
in previously built-up cells (i.e., peripheral and internal growth) to all
changes in BIA (in previously and newly built-up cells; Fig.4E). For
urban counties, we see a steep increase of the proportion of previously
built-up land to overall growth until a peak in the early 1930s, when
approximately 85% of new growth happened as either peripheral or
internal growth. This percentage declined to approximately 62% in
2010, likely as a result of increased expansion (newly built-up land,
often in the form of sprawl). Peripheral growth, which is higher than
that of internal growth, has a peak around 1900 at 55% and since
declined to 42%. In contrast, internal growth increased steeply until
it reached a peak in the early 1930s at 40% and declined until 2000 to
25%. During the past decade, internal growth shows a slight uptick,
which corresponds to increasing densification, seen in urban coun-
ties. In rural counties, the proportion of internal and peripheral growth
combined increases steeply to approximately 60% in the 1950s and
since then shows varying trends between 55 and 65%. As internal
growth never exceeded 20%, most of these trends are driven by pe-
ripheral growth.
The main trends in rural and urban counties converge over time,
indicating that by 2010, the proportion of growth in previously
built-up cells to growth in newly built-up cells is very similar in both
strata (between 60 and 62%). This convergence also indicates that
during the past seven decades, the proportion of growth due to ex-
pansion has been increasing in urban counties and slightly decreasing
in rural counties. We expect to find significant regional variability
in these patterns if evaluated for different geographic units (e.g., states
or counties), describing deviating trajectories for different criteria
used for defining urban and rural strata.
Supporting a population perspective of urban development:
Settlement as a reliable predictor of historical
and contemporary population
We conclude our results by using a panel analysis approach to illus-
trate that built characteristics can meaningfully capture human set-
tlement and urbanization patterns (28). This method serves as a test
for whether the settlement layers can support population modeling
for the study of urban development. In this analysis, we predicted
population counts from the decennial censuses of 1860, 1910, 1960,
and 2010 by the number of built-up property records (BUILD) ob-
served in the HISDAC-US data; we tested all land-use types together
and residential land use only. We relied on BUILD because it has
the highest overall correlation with population counts over time in
comparison to other settlement measures (Fig.5). Through this anal-
ysis, we attempted to accomplish two objectives. First, we examined
how much of the temporal variation in population can be explained
using BUILD. Second, we estimated the number of people associated
with each additional built-up property in a county.
On the basis of the R2 values for a pooled ordinary least squares
(OLS) regression model of all counties from 1860 (Table1), BUILD
based on all land-use types explains almost 93% of the variation in
population across counties over time (column 1; R2 = 0.926). This
result holds even when we restrict the sample to counties with con-
sistent boundaries through time (<10% change in area measures; col-
umn 2; R2 = 0.898; see Materials and Methods for details). As these
models include no other control variables, we conclude that BUILD
appears to be highly effective in characterizing county-level changes
in population over time. We suspect that much of the variation across
these models is a function of changes in household size and the distri-
bution of dwelling units by size over time and space. The estimates
from the standard OLS models suggest that, on average, one unit in-
crease in BUILD is associated with an increase of around 2.6 to
2.7 people. There are, however, many difficult-to-observe reasons for
why counties with more or less built-up properties differ in popula-
tion (e.g., many coastal cities have both economic opportunity and
high- density building stock due to land constraints).
We also ensure the robustness of our results to omitted variables
by presenting more conservative estimates when regressing changes
in population on changes in BUILD (columns 3 to 5 of Table 1). We
ran a least squares dummy variable (LSDV) model with county-level
fixed effects (column 3) in which the model variation comes from
population changes within counties over time [within estimator; (29)],
revealing a consistent and significant relationship of around 2.2 people
for each additional built-up property within a county. We ran a gener-
alized least squares (GLS) estimator (column 4) and controlled for
potential decadal trends in population and BUILD (column 5), pro-
ducing generally consistent estimates. Thus, our analyses suggest that,
on average, an additional built-up property in each county is roughly
associated with a 2.2- to 2.25-person increase in the total population.
Although the quality of HISDAC-US data is considerably poorer be-
fore 1860, our analyses using earlier starting points yield very similar
results (table S1). Results were very similar for BUILD based on all
land-use types ( = 2.246, R2 = 0.873), as well as residential land-use
types only ( = 2.246, R2 = 0.875). We examined the effect of regional
variation by running the same GLS estimator shown in column 5 of
Table 1 for the four regions Northeast, South, Midwest, and West
(table S2). Coefficients vary between 2.029 and 2.537, indicating low
levels of regional variation in the statistical relationship at the county-
level. While these results are robust and provide strong indication
of predictive power of BUILD for population at the county-level, the
observed effects of spatial and temporal variability have to be fur-
ther investigated, particularly at finer spatial scales.
DISCUSSION
Fine-scale spatial and temporal data improve our
understanding of long-term settlement patterns
Settlement patterns can only be fully understood from a multiscale
perspective (30) that characterizes local, regional, and national patterns
of urban development and land-use change. Through our unique
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Fig. 5. Correlation measures between county-level population counts and settlement variables. The different plots show correlations over the time period from
1810 to 2010 between population and (A) the number of built-up property records (BUILD), (B) BUI, and (C) BUA. avg. corr., average correlation. In (D), correlation
measures between county-level population change and absolute expansion (Abs. expansion) are shown for the same time period. Population counts are enumerated
within historical county boundaries, while settlement measures (all land use classes) are calculated within contemporary county boundaries. Correlation measures are
shown for various levels of temporal county boundary stability (e.g., the blue lines represent only counties whose area did not change more than 10% over time) to
demonstrate the importance of compatible spatial units in spatiotemporal analysis. Average correlation coefficients are shown over all years in parentheses.
Table 1. Panel analysis results using different points in time, 1860–2010. SEs are given in parentheses. Statistical significance is provided (*P < 0.05,
**P < 0.01, and ***P < 0.001). The different models tested are OLS, least squares dummy variables (LSDVs), and generalized least squares (GLS). LSDV and GLS are
“within” estimators. BUILD is based on all land-use types; results for residential land-use types only are very similar.
OLS OLS LSDV GLS GLS
(1) (2) (3) (4) (5)
Total population Total population Total population Total population Total population
Number of built-up
property records
(BUILD)
2.680*** 2.668*** 2.190*** 2.190*** 2.246***
SE (0.007) (0.012) (0.058) (0.013) (0.014)
Constant 10503.8*** 13767.2*** 22513.3*** 22513.3*** 16123.0***
SE (550.069) (815.994) (1068.970) (701.136) (1274.106)
N10996 5900 5900 5900 5900
R20.926 0.898 0.946 0.864 0.873
Adjusted R20.926 0.898 0.929 0.819 0.831
County sample All Consistent Consistent Consistent Consistent
Fixed effects – – County County County, decade
Clustered SE No No Yes Yes Yes
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data products with unprecedented temporal coverage and fine spa-
tial and temporal resolution, we are able to provide new multiscale
depictions of historical settlement. From these depictions, we iden-
tify time periods of slow or fast growth and characterize different
urban processes that are only discoverable at very fine scales. Our
results document and analytically evaluate regional and local pat-
terns depicting rural-urban transformations, urban expansion and
peripheral growth, as well as densification and infilling processes.
We envision that our new measures on when structures were
built (FBUY), the number of built-up property records (BUILD), the
BUI, and the BUA at a given point in time as well as derived process
measures such as expansion or densification will enable new oppor-
tunities to answer scientifically and theoretically grounded questions
in urban research. For example, in ongoing projects, we have started
to deploy these data to better understand the changes in the built
environment that unfolded in U.S. cities related to residential segre-
gation, postwar suburbanization, and the more recent resurgence of
central city areas (9). Thus, we see enormous potential in these data
for examining landscape evolution, fragmentation, and the role of
technology, economic, and social forces in shifting the contours of
urban development.
Methodologically, the use of gridded settlement time series allows
researchers to conduct their analyses consistently with studies that
apply remote sensing images [e.g., (31,32)] and extract urban or
developed land within any spatial unit. However, the HISDAC-US
data are less limited temporally than remote sensing products that
cover time periods of no more than three to four decades. Further-
more, the HISDAC-US layers are more accurate (20), richer in attri-
bution related to the built environment, and cover a time period of
more than 150 years for most of the conterminous United States. By
tackling critical process questions in urbanization, we use the new
HISDAC-US data-derived measures of development to connect data-
scientific analysis of large spatiotemporal data and substantive in-
quiry in urban geography, demography, and land use science.
Detailed built environment attributes enable holistic
examination of settlement and urban development
Temporal trajectories of different settlement measures within spatial
units of interest, such as counties, cities, or tracts, provide a detailed
picture of the complexity of long-term development in the United
States. This knowledge of development fuels our understanding of
when, where, and how quickly humans have urbanized the country.
Evaluating the interrelationship between different settlement measures
is essential to understanding how the nature of urban development
has differed across time and space. We demonstrate that settlement is
difficult to describe in either univariate or linear terms, and different
development attributes follow timelines that vary across urban strata
and regions, which are likely dictated by existing infrastructure, tech-
nology, and the developability of land (such as in coastal ecosystems).
Complementing other findings [e.g., (33)], we also demonstrate that
processes such as densification and expansion are interrelated tem-
porally. However, we found that the synchrony between the peaks of
those processes varies greatly across regions and cities, pointing to
different forms of historical settlement and urban development.
These types of development vary markedly between coastal and in-
terior areas, northern and southern regions, and with topographic
constraints and environmental conditions. With these insights, re-
searchers can draw an unprecedented picture of the nature and tim-
ing of rural, suburban, and urban development in the United States
at varying scales. The advances in our understanding of settlement
processes have the potential to inform ongoing discussions about
the spread and compactness of urban areas (2,34,35).
Following the paradigm of “people are where people build,”
this study demonstrates an effective way to estimate
historical population at fine spatiotemporal granularity
There is a common understanding in the fields of rural studies, urban
geography, and demography that the built environment is related to
population and other demographic attributes (21,27). These insights
provide the basis for a population-based perspective on urban devel-
opment assessments. Our panel analysis results demonstrate that
historical settlement layers in HISDAC-US (20) are associated with
population at relatively fine spatial granularity (i.e., counties). Such
results are important in two distinct but related ways.
First, the predictive power of the population models indicates
that the settlement-population relationship is highly robust. These
models enable us to build county-level population data over more
than 150 years at fine temporal resolution. These data help over-
come the dependence on traditional decadal census surveys [e.g.,
(36)] and may support the creation of future population assessments
to improve population projections. Such model outcomes can be
used to create time series of consistent population estimates (e.g.,
within contemporary county boundaries from the 2010 census) to
perform unprecedented temporal analysis. Using these analytical in-
novations, demographers and urban modelers can study demographic
processes related to rural-urban transitions over long time periods at
meaningful spatial scales and inform population projections.
Second, the robust settlement-population linkages indicate the
potential for reproducing such population models within different
spatial units including census units of finer spatial granularity (e.g.,
census tract boundaries of 2010) or alternative geographic units. For
example, researchers might need to estimate population and its changes
within certain land cover classes or zones of high vulnerability to
natural or industrial hazards. The fine resolution of the settlement
layers makes it possible to model population at fine scales using at-
tributes such as the number of built-up property records or BUI
allocated to such alternative analytical units. Such advances will
greatly benefit research on coupled socio-environmental systems
and improve our understanding of existing interrelationships and
processes. However, variance in the relationship between population
and built environment attributes across time and space requires further
investigation. While our comparison of county-level relationships
by region produces quite consistent results, we have yet to investigate
the stationarity of these relationships at finer spatial scales. We suspect
that land-use type will play a particularly crucial role in inferring
small-area population quantities from built-environment data.
Novel and extensive spatial information necessitates serious
investigation into uncertainty and potential data limitations
While the use of such novel data layers opens unprecedented research
opportunities, it is important to instruct and educate the data user on
existing uncertainties. In Leyk and Uhl (20), some of these temporal,
positional, and thematic uncertainties are reported, assessed, and mea-
sured in detail. For our analysis, the settlement layers were systemat-
ically corrected on the basis of focal raster operations and adjusted
using census data (see Materials and Methods). However, while these
adjustments reduce some of the inherent bias and result in population
models with high predictive power, the reported missingness in the
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original ZTRAX data will still potentially cause underestimation of
settlement and has to be considered for critical use of the data products
in subsequent analyses. We expect these issues to further improve as
Zillow continues to update their database, but certain data gaps will
always remain. Furthermore, it is important to note that temporal
information, such as the FBUY, does not necessarily indicate the year
of the first settlement but represents the earliest built years on
record in the ZTRAX database of currently existing buildings. Thus,
we may not know about earlier built units that have been demolished
and rebuilt (or not rebuilt) or still exist but miss built-year records
(Fig.1B). This uncertainty varies across regions and can be addressed
by sensitivity analysis and detailed case studies where high-quality
data are available.
Future opportunities
Future steps to leverage these new opportunities will explore the cre-
ation of settlement estimates at finer spatial and temporal resolution
as well as the inclusion of demographic variables and ancillary data
for alternative geographies to fully use the potential of these data layers
for improved fine-scale urban and population modeling. Of particular
interest is the estimation of alternative demographic and housing-
related attributes to create a more insightful picture of the human-
built environment and its population. These fundamental components
will enable the research community to advance research and theory
on urban studies, land use science, natural hazards, landscape ecology,
and other interdisciplinary pursuits (9,37,38). Using the attribute
richness of the settlement data, researchers can explore questions of
great societal importance at spatial and temporal scales relevant to
the operational scale of urban and human-environmental processes
including local rural-urban transitions, changes in ecological ser-
vices, and trends in land fragmentation.
MATERIALS AND METHODS
Settlement and census data
We use the ZTRAX to derive data products that can be used for the
extraction of settlement measures at different points in time. ZTRAX
is a geocoded housing and property-level database based on existing
cadastral data sources that contains more than 374 million data re-
cords for approximately 200 million parcels in over 3100 counties
in the United States (https://zillow.com/ztrax). Zillow Group is an
online real estate database company that was founded in 2006. We
extracted attributes such as the land-use class, the construction year
of the structure on a parcel, and geolocation information (e.g., an
approximate location for an address point) to create time series of
raster layers. The workflow for creating the spatiotemporal database
model, an SQLite database with spatial query extension, and the data
products used in this study are described in full detail in Leyk and
Uhl (20). The data layers are collected in the HISDAC-US, which is
organized as a collection of datasets at the Harvard Dataverse repos-
itory (https://dataverse.harvard.edu/dataverse/hisdacus). First, we
produced a series of semi-decadal raster layers representing the BUI,
the sum of gross indoor area of all built-up properties in a grid cell
(250m by 250 m) in a given year between 1810 and 2010. Second,
for the same time period, we also produced a series of semi-decadal
raster layers representing the number of built-up property records
(BUILD) in a cell in a given year. Third, we built a composite raster
layer that indicates for each raster cell the first year a built unit was
established (FBUY). Last, we derived the BUA as the number of grid
cells in a spatial unit of interest (e.g., counties) with at least one built
unit in a given year. The spatial resolution of all raster layers is 250 m,
and the temporal resolution available in HISDAC-US is 5 years.
HISDAC-US also contains uncertainty layers at the pixel and
county levels (20) that the data user is urged to use for the assessment
of positional, temporal, and thematic uncertainty. First, there are pro-
portions of records without a construction year in some counties. Also,
in some instances, the year refers to the most recently built unit, and
it remains unknown whether there has been a structure before; in other
cases, there are several built years given, indicating the very first year
and the most recent one, for example. Second, the land-use class attri-
butes vary across counties and states but have been generalized and
consolidated to some degree, making them more comparable across
the nation. Third, the latitude/longitude records are missing for a por-
tion of the records prohibiting fine-scale localization of the records
but indicate the county. The geolocation records represent approxi-
mations for the corresponding address, and thus, there is inherent
positional uncertainty that needs to be addressed.
Census data and boundary files at the county-level were collected
from the National Historical Geographical Information System
[NHGIS; (10)]. We used the contemporary county boundaries (2010
census) to extract ZTRAX measures at different points in time. To
build our population models at the county-level, we used nominal popu-
lation statistics (persons count) in 1810, 1860, 1910, 1960, and 2010
and the corresponding time-specific county boundaries from the
NHGIS websi te (fig. S1) as well as the number of housing units in 2010
for our correction procedure, as described below.
Data correction and geoprocessing
We extracted the settlement measures (BUILD, BUI, and BUA) from
the raster time series within contemporary county boundaries (2010
census) using zonal statistics geoprocessing functions to create settle-
ment measures for different points in time within consistent spatial
units. To mitigate some of the data quality issues, particularly the
missingness of built-year records as described above, we applied a
spatiotemporal correction procedure to improve county-level settle-
ment measures at different points in time as follows. We carried out
this procedure for all variables using built-up properties of all land-
use types together and for the BUILD variable based on residential
land-use type only to test both corrected data versions in the popula-
tion model.
We assumed that records in the database without a built year
exist at present if they indicate the presence of a built-up property
(i.e., in 2015, which is the most recent year in the currently available
ZTRAX database) and the likelihood of the actual built year is the
same across all years.
For each county, we computed the proportion of missing built-
year records (TMiss) in 2015
TMiss = SumBYMiss / (SumBuilt2015 + SumBYMiss) (1)
where SumBYMiss is the sum of missing built-year records and
SumBuilt2015 is the sum of built-up properties in 2015 with built-
year records. Depending on the magnitude of TMiss (i.e., TMiss <
50%, TMiss > 50%, TMiss = 100%; these thresholds can vary as needed),
we corrected the contemporary and earlier county-level settlement
measures. Of the 3108 counties in 2010, 1636 counties had less than
25% TMiss; 2201 counties had less than 50% TMiss. The spatial and
statistical distributions of county-level TMiss are shown in fig. S6.
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First, for counties with TMiss < 50% (or another user-defined
threshold), relative changes in BUILD, BUI, and BUA were consid-
ered reliable. Thus, assuming that records without built-year infor-
mation existed in 2015, a corrected BUILD2015,corr per county was
calculated as
BUILD 2015,corr = BUILD 2015,uncorr + SumBYMiss (2)
A correction factor was calculated as
c BUILD = BUILD 2015,corr / BUILD 2015,uncorr (3)
Then, each value of the county-level BUILD time series was mul-
tiplied with cBUILD, resulting in a corrected BUILD time series while
preserving relative changes between years as observed in the uncor-
rected data.
To correct BUI, for each county, the average BUI per built-up prop-
erty in 2015 was calculated as
BUI AVG = BUI 2015,uncorr / BUILD 2015,uncorr (4)
and then multiplied with the corrected BUILD value in 2015 result-
ing in the adjusted county-level BUI in 2015
BUI 2015,corr = BUILD 2015,corr × BUI AVG (5)
In analogy to Eq. 3, a correction factor cBUI was calculated and then
applied to the whole BUI time series for each county. The BUA time
series layers (with value 1 for grid cells with one or more records
that had a built year and value 0 for all other cells) were corrected
slightly differently. For each county in 2015, we created another binary
layer, BUA0, with value 1 for those grid cells that contained at least one
record without a built year and value 0 for all other cells. We then
calculated the area of the spatial union of BUA2015 and BUA0, which
results in the corrected 2015 BUA
BUA 2015,corr = BUA 2015,uncorr ∨ BUA 0 (6)
Earlier BUA layers were then corrected using a correction factor
cBUA, calculated in analogy to cBUILD and cBUI. Second, for counties
where TMiss > 50%, changes in BUILD, BUI, and BUA were not
considered reliable. As before, BUILD in 2015 was corrected by
SumBYMiss. We then derived relative change estimates in BUILD
between different points in time based on the five nearest counties
where TMiss < 50%. These average regional gradients of BUILD
were used to retrospectively extrapolate BUILD to earlier points in
time. To correct BUI in these unreliable counties, we interpolated
the average BUI values per built-up property found in the five nearest
counties where TMiss < 50%, multiplied them with the corrected
BUILD values, and extrapolated the resulting BUI values to earlier
data layers in the time series while preserving the average relative
changes in the five reliable neighboring counties. Similar to the re-
liable counties above, the BUA in 2015 was corrected by the spatial
union of BUA in 2015 and BUA0. These corrected values were then
extrapolated retrospectively while preserving the relative change be-
tween years derived from BUA gradients within neighboring counties
where TMiss < 50%.
Once the above correction steps were finalized, BUILD, BUI,
and BUA values were estimated for those counties where there was
no information at all. Using the corrected time series resulting from
the steps above, BUILD, BUI, and BUA for each year were inter-
polated using the corresponding values from the nearest five counties
where TMiss < 50%.
Last, we further adjusted the corrected and extrapolated settle-
ment measures BUILD and BUI using the number of housing units
published by the U.S. Census in 2010 as follows. First, for each county
in 2010, we used the difference between census housing unit counts
and BUILD to adjust BUILD in 2010. Then, we adjusted BUILD for
the whole time series while preserving the relative changes between
years. Using these adjusted values of BUILD in each year, we adjusted
the BUI time series proportionally. The BUA time series could not
be corrected using census data, because there is no reference infor-
mation on the spatial distribution of census housing unit counts
within counties and thus no BUA-compatible measure.
Expansion and densification calculation
We used the extracted settlement measures to derive variables that
indicate more implicitly the process of change. We calculated rela-
tive and absolute expansion as the proportion and absolute value of
new developed area, respectively
Expansion rel = ( BUA t1 − BUA t0 ) / BUA t0
)
(7)
Expansion abs = ( BUA t1 − BUA t0 ) (8)
where BUAt0 and BUAt1 are the BUA estimates for the beginning
and ending year, respectively. This measure was used to evaluate the
amount of change in developed area over a given number of years,
reflecting how much development has been added, absolutely and
proportionally to the initial condition, respectively.We also calculated
densification, which is the change in BUI over the change in BUA
Densification = ( BUI t1 − BUI t0 ) / ( BUA t1 − BUA t0 ) (9)
where BUIt1 and BUIt0 are the built-up intensities for the beginning
and ending year of the considered time period, respectively. This
measure quantifies the increase in BUI in proportion to newly de-
veloped areas over a given number of years.
Statistical analysis
We created the maps of the local indicators of spatial association
[LISA; (39)] to identify statistically significant spatial clusters in the
county-level distribution of the target variable (e.g., change in BUILD;
999 permutations; P < 0.05). A hot spot is a statistically significant
high-high (HH) cluster, i.e., a high value that is surrounded by other
places with high values to constitute a statistically significant group
of counties of higher values. Accordingly, a cold spot [low-low (LL)
cluster] indicates a low value surrounded by other low values. Counties
labeled with HL and LH represent statistically significant outliers
from the spatial distribution.
Panel analysis allows us to control for individual-unit heteroge-
neity and thus variables that may explain differences across counties
(e.g., cultural or architectural differences) unmeasured or variables
that change over time but not across counties (time-invariant char-
acteristics such as policies, technological advancement, or regulations).
This way, panel analysis makes it possible to detect and measure effects
that cannot be observed in either the modeling of cross-sectional
data or purely descriptive time series analysis (28). To examine the
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relationship between the number of built-up property records (resi-
dential and all land use, corrected) as predictor, and population
(person counts) as the outcome variable within an entity (county),
we used two-way fixed-effects panel models to account for such
forms of heterogeneity. Thus, we include county and time period
fixed effects to help account for this bias, and assess the net effect of
the predictors on the outcome variable by allowing the model inter-
cept to vary across the spatial units as well as over time. The equa-
tion for the (time and entity) fixed-effects regression model is
Y it = β 0 + β 1 X 1,it + … + β k X k,it + γ 2 E 2 +
… + γ n E n + δ 2 T 2 + … + δ t T t + u it (10)
where Yit is the dependent variable with i = entity and t = time, Xk,it
are the independent variables with coefficients k, uit is the error
term, En is the county n [n – 1 entities included as binary (dummies)
in the model] with the coefficient n for the binary regressors (enti-
ties), and Tt is the binary variable (dummy) for time (there are t – 1
time periods) with coefficient t for the binary time regressors.
We compared OLS-based balanced panels with LSDV- and GLS
fixed-effects models to better understand the impact of fixed effects
on the estimators’ predictive power. We included all counties in the
balanced panel that remained sufficiently compatible over time, i.e.,
counties whose areas do not change more than 10% compared to
the contemporary county boundaries over the entire time period.
All settlement variables were tested but because of multicollinearity
issues, only individual ones could be used at a time. Data extraction,
analysis, and statistical modeling have been carried out in Python
and STATA; geoprocessing steps have been done using Feature
Manipulation Engine (FME) and the ArcGIS 10.6 Arcpy Python
package as well as NumPy, Pandas, and Matplotlib.
SUPPLEMENTARY MATERIALS
Supplementary material for this article is available at http://advances.sciencemag.org/cgi/
content/full/6/23/eaba2937/DC1
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Acknowledgments: The content is solely the responsibility of the authors and does not
necessarily represent the official views of the NIH. We acknowledge access to the Zillow
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Transaction and Assessment Dataset (ZTRAX) through a data use agreement between the
University of Colorado Boulder and Zillow Group Inc. More information on accessing the data
can be found at http://zillow.com/ztrax. The results and opinions are those of the author(s)
and do not reflect the position of Zillow Group. Support by Zillow Group Inc. is acknowledged.
We thank three reviewers for their constructive comments. Funding: Funding for this work
was provided through the Humans, Disasters, and the Built Environment program of the
National Science Foundation, Award Number 1924670 to the University of Colorado Boulder,
the Institute of Behavioral Science, Earth Lab, the Cooperative Institute for Research in
Environmental Sciences, the Grand Challenge Initiative and the Innovative Seed Grant
program at the University of Colorado Boulder as well as the Eunice Kennedy Shriver National
Institute of Child Health & Human Development of the National Institutes of Health under
Award Numbers R21 HD098717 01A1 and P2CHD066613. Publication of this article was
co-funded by the University of Colorado Boulder Libraries Open Access Fund. Author
contributions: S.L., J.H.U., D.S.C., and A.E.B. conceptualized and designed the study and
planned the analysis. S.L. and J.H.U. designed the gridded data products and developed the
dissemination strategies. J.H.U. processed the data and created the figures and movies. J.H.U.,
D.S.C., and S.L. performed the statistical analysis. S.L. wrote the paper and secured the data.
J.H.U., D.S.C., A.E.B., J.K.B., M.G., and N.M. revised the paper and provided the substantive
inputs on design and result interpretation. S.L., M.G., and J.K.B. secured funding. All authors
have contributed significantly to this research and have seen and approved the final version.
Competing interests: The authors declare that they have no competing interests. Data and
materials availability: All data needed to evaluate the conclusions in the paper are present in
the paper and/or the Supplementary Materials. The data layers are collected in the HISDAC-US,
which is organized as a collection of datasets at the Harvard Dataverse repository (https://
dataverse.harvard.edu/dataverse/hisdacus). Additional data related to this paper may be
requested from the authors.
Submitted 20 November 2019
Accepted 10 April 2020
Published 3 June 2020
10.1126/sciadv.aba2937
Citation: S. Leyk, J. H. Uhl, D. S. Connor, A. E. Braswell, N. Mietkiewicz, J. K. Balch, M. Gutmann, Two
centuries of settlement and urban development in the United States. Sci. Adv. 6, eaba2937 (2020).
on June 3, 2020http://advances.sciencemag.org/Downloaded from
Two centuries of settlement and urban development in the United States
Stefan Leyk, Johannes H. Uhl, Dylan S. Connor, Anna E. Braswell, Nathan Mietkiewicz, Jennifer K. Balch and Myron Gutmann
DOI: 10.1126/sciadv.aba2937
(23), eaba2937.6Sci Adv
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