to Map Urbanization in

Baltimore/Washington*

Lee De Cola

U.S. Geological Survey

521 National Center

Reston VA 20192

ldecola@usgs.gov

*A revised version of a paper that originally appeared in the Technical Papers of the 1997 Convention of ACSM/ASPRS, Vol. 5 Auto-Carto 13, pp. 56-65.

During the past year researchers at the U.S. Geological Survey
have been using historical maps and digital data for a
2^{°} × 2^{°}
(168-km × 220-km)
area of the Baltimore/Washington region to produce a dynamic
database that shows growth of the transportation system and built-up
area for 30-meter grid cells for several years between 1792 and
1992. This paper presents results from the development of a *Mathematica*
package that spatially generalizes and temporally interpolates
these data to produce a smoothly varying urban intensity surface
that shows important features of the 200-year urban process. The
boxcount fractal dimension of a power-2 grid pyramid was used
to determine the most appropriate level of spatial generalization.
Temporal interpolation was then used to predict urban intensity
for 4320-m cells for 10-year periods from 1800 to 1990. These
estimations were spatially interpolated to produce a 1080-m grid
field that is animated as a surface and as an isopleth (contour)
map (see USGS 1997 for the Internet address of the animation).
This technique can be used to experiment with future growth scenarios
for the region, to map other kinds of land cover change, and even
to visualize quite different spatial processes, such as habitat
fragmentation due to climate change.

In 1994 a team of U.S. Geological Survey (USGS) and academic researchers
produced an animation of the growth of the San Francisco/Sacramento
region using a temporal database extracted from historical maps,
USGS topographic maps, digital data, and Landsat imagery (Gaydos
and Acevedo 1995). Publicly televised videotapes of this work
received sufficient attention to support a larger team that had
planned to work on the development the Boston/Washington megalopolis
(Gottmann 1990)^{ }(The current research involves staff
from USGS, National Air and Space Administration, the Smithsonian
Institution, and University of Maryland Baltimore County.) Resource
and time constraints, however, limited efforts to the southern
part of the region shown in figure 1 (Crawford-Tilley et al 1996,
Clark et al. 1996). The animation of urbanization in this region
is based on a 512^{2}-cell grid data structure that represents
whether or not a given 270-meter cell is built-up in each of 8
base years (figure 2). This raster was interpolated for intervening
years, but still represents a binary condition for each of the
grid cells. Throughout this work there was interest in how we
might analyze the intensity of development, perhaps by sacrificing
spatial resolution for temporal and measurement resolution (table
1). Because the urban phenomenon (cartographic feature) is self-organized,
complex, and probably also critical (Bak 1996), it is reasonable
to suppose that scaling properties would assist in this transformation
(Quattrochi and Goodchild 1997).

Consider therefore a location in space *x* at a given time
*t* and spatial resolution level *l* for which a measurement
*f* is made; call this measurement *f _{l}(x_{t)}*.
For example, in the present case we are interested in whether
or not a given grid cell of a certain size is built-up (covered
by buildings, has a dense road network, etc.). In this simplest
case we have a binary function

Consider the 0-level image of figure 2, which contains 41,183
built-up cells, as reported in the last row of table 3, which
presents the box counts for each level and each of the raw data
years The table shows at the next highest level *l* = 1 that
14,892 cells are necessary to cover these cells. This number is
45% larger than the (41,183 / 4 =) 10,296 level-1 cells that would
be necessary if all the level-0 cells were spatially compact.
The excess number is due to spatial complexity of the urban phenomenon,
which has fractal dimension *D* < 2, where *D* =
2 would be the dimension of say a perfect disk (for a comprehensive
discussion of the fractal nature of cities see Batty 1995).

The 0-level row of the table 3 illustrates that for at least 200
years there has been some urbanization in the region (A fit of
a linear model to the 0-level data yields ln[*f*_{0}(*x _{t}*)]
= 40 + 0.026

The box counts in table 3 can be used to compute the fractal dimension
of the built-up area for each year. For example, figure 3 shows
the regression line estimating log_{2}[*f _{l}*(

The box counts for each level and each
year are used to compute the 8 values of *D _{t}*,
the fractal dimensions for each of the data years, shown in figure
4. There is a continuing debate in urban studies about how regions
develop. One school argues that so-called "primate"
metropolitan regions continue to grow from a point to a centralized
but spreading metropolitan pole. But another school envisions
a dispersed metropolis that may eventually completely disperse,
returning to a collection of isolated points (Alonso 1980, De
Cola 1985). Figure 3 certainly shows the early stages of this
process; we can only speculate about whether

Each of the fractal dimensions *D _{t}* for the data
years is a linear estimate of the behavior of the box counts over
the scale levels. Yet the fit is not perfect, as figure 3 shows
for 1953; there is a similar pattern of parabolic residuals among
all the years. In general the middle scale levels

Let *l* = 4 and consider the central-cell *x* = (col,
row) = (16, 16) for each of the *t* = 1,…,8 data years.
The values of *fsum*_{4}(*x _{t}*) for
this cell are shown in figure 6 and (as did

**gain in feature resolution**(from [0,1] data to [0, 256] values), and a**gain in temporal resolution**(from 8 irregularly spaced measurements to 20 decadal interpolations), by sacrificing**a loss in spatial resolution**(from 270-m to 4321-m cells).

The unique temporal interpolation functions for each of the (32^{2}
=) 1024 level-4 cells can be arrayed into a *Mathematica*
table that provides a grid of predictions for any year in the
study period. A sample for 1990 is shown in figure 7, taken from
the animation (USGS 1997). The data have been spatially linearly
interpolated to level 1 (540 meters) to provide a smooth surface
for visualization (for a alternative approaches to the interpolation
problem see Tobler 1979 and Bracken and Martin 1989). The image,
which is one frame of a 20-period animation, illustrates the polycentric
nature of the Baltimore/Washington urban process. The animation
shows reveals a self-organizing system that has been growing along
the Northeast U.S. transportation corridor. During the past 200
years urban leadership has shifted between the two centers at
least three times, and since World War II there has arisen a polycentric
post-industrial system whose fractal dimension has been growing
logistically and may be leveling off.

Another way to visualize the growth process is isopleths or contours, which emphasize the geographic location of urbanization. figure 8 shows not only the 2 urban centers in 1992, but such other features as the edge cities of Frederick, Annapolis, and La Plata, MD as well as Potomac Mills, VA. The picture also highlights the linear nature of the whole system, oriented along Interstate 95, which continues from Boston to Miami.

Naturally we are interested in the future of the region, and the
analysis suggests approaches. (A logistic curve fitted to the
0-level data in table 2 yields *f _{0}*(

The analysis of the last 3 data years (1972, 1982, 1992) was based
on Landsat imagery, and the growth both of the fractal dimension
*D _{t}* (figure 4) as well as of one of the generalized
cells

The research presented here is part of a 118-year history of the use of USGS core skills in the physical, and-more recently-human and biological sciences to understand human-induced land transformations. These efforts exhibit not only institutional expertise but also rich historical databases that can be used to understand spatial processes, to forecast change, and help to shape future policy. The dimensions highlighted in table 1 suggest new directions for this research. First, the analysis can profit from a broader spatial view, expanding to Megalopolitan and even world urbanization. Second temporal extrapolation and deeper "data mining" will help planners envision the future of the region-as well as its distant past. Third, more features (shoreline, land cover, climate) need to be studied and animated. A central theoretical and policy problem highlighted by this work therefore is the development of rigorous, informative, and visually effective transformations of data along and among spatial, temporal, and phenomenological scales.

Acevedo, William, Timothy Foresman, and Janis Buchanan 1996 Origins and philosophy of building a temporal database to examine human transformation processes, ASPRS/ACSM Technical Papers I:148-161.

Alonso, William 1980 Five bell shapes in development

, Papers and proceedings of the Regional Science Association, 45:5-16.Bak, Per 1996

How nature works, NY: Cambridge University Press.Batty, Michael 1994

Fractal cities, NY: Wiley.Bracken, I and D. Martin 1989 The generation of spatial population distributions from census centroid data,

Environment and Planning A, 21:537-543.Clark, Susan C., John Starr, William Acevedo, and Carol Solomon 1996 Development of the temporal transportation database for the analysis of urban development in the Baltimore-Washington region, ASPRS/ACSM Technical Papers, 3:77-88.

Crawford-Tilley, Janet S., William Acevedo, Timothy Foresman, and Walter Prince 1996 Developing a temporal database of urban development for the Baltimore/Washington region, ASPRS/ACSM Technical Papers, 3:101-110.

De Cola, Lee 1985 Lognormal estimates of macro-regional city size distributions, 1950-1970

Environment and Planning A17:1637-1652.De Cola, Lee 1997 Multiresolution covariation among Landsat and AVHRR vegetation indices, in Quattrochi and Goodchild 1997.

Falconer, K.J. 1990

Fractal geometry: mathematical foundations and applications, New York: Wiley.Gaydos, Leonard J and William Acevedo 1995 Using animated cartography to illustrate global change, International Cartographic Association, Barcelona.

Gottmann, Jean 1990

Since Megalopolis: the urban writings of Jean GottmannBaltimore: Johns Hopkins University Press.Haggett, Peter, Andrew Cliff and Allan Frey 1977

Locational analysis in human geographyLondon: Edward Arnold.Quattrochi, Dale and Michael Goodchild 1997

Scale in remote sensing and GISBoca Raton FL: CRC Press.Tobler, Waldo R. 1979 Smooth pyncnophylactic interpolation for geographical regions

Journal of the American Statistical Association74(367):519-530.Whyte, William H. 1968

The last landscape, Ch. 8, NY: Doubleday.