Detecting urban and rural sprawl and its relationship with eco-physical
factors in Missouri
Bo Zhou, Hong S. He, Timothy A. Nigh, John H. Schulz
Abstract
The increase and dispersal of human population in recent decades has been the cause of urban
and rural sprawl. The increase activity of human development is closely associated with the
increase of impervious surface. A lot of the recent sprawl studies have used impervious surface
as an indicator. In the US, impervious surface mapping has rarely been attempted at state or
national level due to the lack of accurate, fast and cost-effective approach. This study assessed
the state wide impervious surface for three stages of the year 1980, 1990, and 2000. Accuracy
assessment is conducted on the 2000 impervious surface with the help of high resolution
airphotos obtained in 2004 with a total accuracy of 86%. A total of 129853.2 hectare of land is
converted to impervious surface during the time frame of this research. While sprawl is very
prominent on urban fringe during 1980s with 23674.5 hectare of land converted to impervious
surface comparing to 22918.2 hectare in 1990s, there is a temporal shift of sprawl happening
more in the rural landscapes in the 1990s with 48079.7 hectare of land converted to impervious
surface compared to 35180.8 hectare in 1980s. This research goes beyond the usual sprawl
research’s hot spots of metropolitan cities and regions to cover the less noticeable rural sprawl
where more damage is done to the ecosystem due to the low density of development that for the
same amount of land being converted to impervious surface larger areas will be affected.
Keywords: impervious surface; subpixel classification; sprawl; Missouri
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Introduction
In the domain of land use studies, sprawl may be defined as “low-density development on the
edge of cities and towns that is poorly planned, land consumptive, automobile dependent and
designed without regards to its surroundings” (Freilich, 2003). It is often referred to as
uncontrolled, scattered suburban development that increases traffic problems, depletes local
resources, and destroys open space (Peiser, 2001). For larger metropolitan areas, urban sprawl
tends to be relatively dense affecting a smaller area per housing unit; but the number of housing
unit also tends to be greater, thus increasing local environmental impacts. In contrast, for mid-to
small-size cities and towns, rural sprawl often occurs at lower densities and affects much larger
areas than urban sprawl (Radeloff et al., 2004). In both cases, the effects of sprawl ripple through
the economic, fiscal, social, government tax revenues, and quantity and quality of public services.
Moreover, sprawl has cumulative ecological and environmental effects at large scales (e.g.
ecoregion), effects which may often occur over long period of time (e.g. decades) before they are
recognized (Mckinney, 2002; Liu et al., 2003). Such large scale effects include land use change,
degradation of soil, air and water quality, increased pollution and reliance on fossil fuel,
fragmentation and loss of wildlife habitat, and ultimately the decline of the amenities and
heritage values that enhance the quality of life and bestow a sense of place on regions and
localities where people live (Knight et al., 1995; Theobald, 2001; Hansen et al., 2002). In light of
the negative effects of sprawl, understanding spatial and temporal trends of sprawl is essential to
establish scientifically sound conservation policies, as well as to raise the public awareness of the
negative effects of sprawl.
Situated in the heartland, Missouri reflects the full range of sprawl reality in the U.S. The
state has a mixture of large metropolitan centers, namely Kansas City and St. Louis, and
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numerous small to mid size cities and towns, and vast rural agricultural, forest, and prairie (Nigh
and Schroeder, 2002). Missouri has experienced shifting patterns of population growth over the
past decades. Other research has also pointed out the shifting trend of sprawl from suburban to
rural areas throughout United States (Fuguitt, 1985; Johnson and Fuguitt, 2000). During the
1980s Kansas City and St. Louis metro areas accounted for the largest share of growth in the
state (57.5%), followed by smaller metropolitan areas (23.6%) and rural areas (18.9%)
(Brookings Institute, 2002). In the 1990s the population growth in the state’s rural areas has a
share of (36.4%) versus smaller metropolitan area (23.3%) and metropolitan areas (40.2%)
(Brookings Institute, 2002). This increase of rural population growth has been fueled by small
metropolitan growth with four smaller metropolitan areas (Springfield, Joplin, Columbia, and St.
Joseph) emerged as the fastest growing regions expanding their size into the rural areas at a rate
of 18.3%. The dispersal of population in Missouri required the conversion of 435,400 acres of
fields, farmland, forests, and green space to “urban” use in the decade of 80s and 90s combined.
The growth is equivalent to 35% increase of the state’s urbanized area, given the population
growth of only 9.7% during the same period of time yielding an actual decrease in population
density which is a strong sign of unhealthy urban sprawl (Brookings Institution, 2002).
Besides the shifting pattern of population growth, more recent urban growth, sprawl, has
the tendency to consume open land faster and occur more often on distinctive or otherwise
significant ecological land types (Johnson and Beale, 2002; Schnaiberg et al., 2002, Barlett et al.,
2000; Heimlich and Anderson, 2001), thus, poses greater threat to the conservation of natural
resources and environment. These urban growths occurred both at the fringe of urban areas and
in forested rural amenity areas including southern Missouri (REF). In fact, this phenomenon is
not unique to the state of Missouri. Previous research have indicated this phenomenon to be
3
common in most of U.S. Midwest, and about one-third of the growth in the form of housing
growth occurred outside non-metropolitan areas in the Midwest from 1940 to 2000 (Radeloff et
al., 2005).
Sprawl is gaining increasing recognition from policy makers. Although this phenomenon
is much discussed though poorly defined, more often it is studied qualitatively than
quantitatively not even to mention spatially. Previous research used population density defined
by US Census Bureau to define urban and rural sprawl which can be misleading in cases where
good development can be classified as sprawl. For example, a sewage processing plant newly
built near urban fringe will be classified as sprawl due to extreme low population density. Others
used derived indicators to measure and define sprawl. Jaeger et al. (2009) used four new
measures: degree of urban dispersion, total sprawl, degree of urban permeation of the landscape,
and sprawl per capita to characterize urban sprawl. While degree of urban dispersion and degree
of urban permeation may give a good geometrical characterization of urban sprawl in a certain
city or town, it is not appropriate for statewide assessment due to the uneven scatter of cities and
towns throughout the landscape. Total sprawl and sprawl per capita, on the other hand, do show
some merit even used at state level. In this research, impervious surface, an indicator of
urbanization, is used to describe total sprawl in both urban and rural sprawl areas. The use of
impervious surface sprawl (ISS) instead of urbanized area sprawl is because the former is found
to be more closely tied to urban and rural sprawl than measuring urban and rural growth areas
(Powell et al., 2008). Sprawl per capita, in this research, is measured by per capita share of
impervious surface (PCIS) to describe the sprawl phenomenon instead of population density.
More efforts will be towards describing sprawl instead of defining sprawl.
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The primary goal of this project is to depict quantitatively and geographically the ISS
from 1980s to 1990s in Missouri. The ISS is analyzed in respect to eco-physical factors such as
elevation, slope, and land type associations (LTA) and human environmental factors such as road
networks and county boundaries to identify factors most prone to ISS.
Methods
Data
Landsat TM and ETM+ images are collected for 1980s, 1990s, and 2000s from the US
Geological Survey (USGS), a total of 15 scenes cover the whole state of Missouri for each time
frame. The image selection criteria are: a) all imageries must be taken close to the winter season
with leaf-off for maximum impervious exposure; b) image acquisition time (month and year)
needed to be within a close range to have minimum color difference; and c) low cloud coverage.
All of the images have a resolution of 30 m by 30 m upon acquisition.
One type of high spatial resolution image digital ortho quarter quad tiles (DOQQs) of
National Agriculture Imagery Program (NAIP) color photography are obtained from Missouri
Spatial Data Information Service (MSDIS) for accuracy assessment. With a nominal spatial
resolution of 2 m, the DOQQ image has three bands: red, green, and blue1. A total of 115 frames
of images with each covering a county are obtained. The selection of 2004 image is due to the
high image quality and low cloud cover (Timothy Nigh, personal communication).
All satellite image preprocessing followed standard procedures, including: (a) navigation
registration, (b) radiometric calibration (Jensen, 2004), (c) rectification and geo-referencing to
the UTM projection (NAD 83 datum, Zone 15 North). The images of each time step are not
1
Detailed information on the DOQQ image can be found at
<http://www.fsa.usda.gov/FSA/apfoapp?area=home&subject=prog&topic=nai>
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mosaiced together because the innate color differences caused by different acquisition time.
Great effort has been invested to obtain images of similar acquisition condition. But there are
only limited numbers of images that qualify the time restriction of this research. So each image is
processed individually to obtain the best results possible, and the processed images are mosaiced
later to obtain the statewide images.
Impervious surface mapping
Numerous research efforts have been diverted towards technical aspects of sprawl studies.
Traditionally, census data have been primarily relied upon in sprawl studies. Theobald (2001)
and Radeloff et al. (2005) both used housing density as an indicator for sprawl studies. But there
are few issues with census data, for instance: census block and block group boundaries change
over time which complicates sprawl studies (Hammer et al., 2004). And census blocks are often
too coarse plus their decadal interval is not timely for the needs of monitoring purpose (Harris
and Longley, 2000; Plane and Rogerson, 1994). Besides, housing development only reflect a
portion of the sprawl problem, the other part of the problem comes from the development of
amenities such as infrastructure development will not be reflected in the census data. A better
sprawl study needs to take into consideration all the developments that replace on natural
landscapes with build-ups. Moreover, the nonlinear variation of the aggregated population
density of urban areas as a function of total population due to different size of measurement unit
(i.e. block group) will make it difficult to identify the impact of urban sprawl in a uniform spatial
context (Sutton, 2002).
Remote sensing technology as a uniform spatial representation of landscape is then used
to overcome the limitations of census data in many researches with per-pixel classification (Chen,
et al., 2000; Epstein et al., 2002; Ji et al., 2001; Lo and Yang, 2002; Ward et al., 2000; Yeh and
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Li, 2001). While this approach might have great success in rural areas analyzing problems such
as agriculture and forestry, it is not so effective in urban areas due to their high heterogeneity and
the limited resolution of Landsat images, since virtually every pixel represents a mixtures of
different surface materials either concrete, asphalt, metal, vegetation or water (Clapham, 2003).
While as in rural areas, problem is caused by similar reason that a lot of the rural developments
are left un-detected due to their small size as compared to the satellite resolution and this
phenomenon is vividly described as: “We are blind where we need most to see” (Raup, 1982;
Theobald, 2001).
More recent studies, in order to overcome such limitations, have focus on deriving and
quantify impervious surface, a well-accepted indicator of development, at sub-pixel level using
ground-measured and also remotely sensed data with different techniques. Yang et al. (2003)
proposed a General Classification and Regression Tree (CART) approach that used Landsat data
derived Tasseled Cap transformed data along with ancillary data including elevation, slope, and a
soil index to produce rule-based models for prediction of continuous measure of impervious
surface. Other approaches include multiple regression (Ridd, 1995) in which a vegetationimpervious-soil (VIS) model is proposed to parameterize biophysical composition of urban
environment. In this model, urban land use and land cover could be modeled by the fractions of
each component. Later this concept is improved by Wu and Murray (2002) and Lu and Weng
(2006). In their research four endmembers from feature space of Minimum Noise Fraction
(MNF), a process to determine the inherent dimensionality of image data to segregate noise in
the data to reduce further computation, are used. The four endmembers include: high-albedo,
low-albedo, soil and vegetation. Both researches have indicated that the impervious surface can
be extracted by adding the high- and low-albedo fractions from MNF. While these two
7
components are useful at identifying impervious surface, they also bring along some unnecessary
information such as dry soils mixed with high-albedo fraction, water, building shadows,
vegetation shadows, and dark impervious surface materials. To correct for confusions, overestimated impervious surface is removed from those two fractions by expert rules developed
from sample plots using high spatial resolution aerial photos (Lu and Weng 2004). Thus far,
most research attempted is limited to metropolitan cities or county level. Procedures developed
for a metropolitan use are often not applicable to a large geographic area such as the state of
Missouri when each image is processed independently. The CART approach is tailored to largearea impervious surface extraction. But the lack of high resolution airphotos in the corresponding
time frame of satellite image acquisition is preventing the application of this approach in this
research.
In this research, Sub-pixel ClassifierTM (SPC) engineered by Applied Analysis Inc., an
add-on module to Leica Geosystes’ Erdas Imagine software is used due to its immediate
applicability. This approach involves a combination of multi-stage remote sensing image
processing, GIS-based ISS spatial quantification, and road network integration. SPC allows the
detection of materials of interest, impervious surface in this case, as a whole or fraction of a pixel
with 10 percent increments with anything below 20% treated as no impervious. The classified
pixel will have percentage values of 0%-20%, 20-30%, 30-40%, ~ 90-100%, a total of 9 classes,
representing the percent of impervious surface (PIS) inside each pixel.
The general process includes a preprocessing step that intended specifically for sub-pixel
classification, together with signature derivation, and material of interest classification. Signature
derivation is conducted semi-automatically. Areas-of-interest (AOI) are first derived to represent
pixels with a minimum of 90 percent or more of impervious surface which is assisted by Google
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MapTM due to the difficulty of interpreting PIS on Landsat images. Because of the diverse
reflectance characteristics of ISs, various levels of brightness of ISs are all represented by a
collection of AOIs. The AOIs are then used as inputs to the automatic signature derivation
function in SPC. The derived signatures are then combined to form a well-rounded signature that
represented different kind of ISs. The classification of SPC used the initial preprocessed image,
the corresponding environmental correction file, and derived signature. Due to previously
reported findings that SPC tend to under classify materials of interest (Civco, 2006). The
classification tolerance is set to be slightly higher than default and tailored to each unique
Landsat image. Previous assessment of PIS mapping has concluded that SPC only has a slight
disadvantage compare to other more complicated approaches, but it does provide the advantage
of being spatially explicit that PIS is reported at a per pixel level which is very useful for future
ISS modeling (Civco, 2006).
Extraction of PIS is a complicated process even with commercial software such as SPC.
Due to the highly mixed pixels of different land cover from Landsat images, the training process
will require many trial-and-error to obtain the purist impervious pixels in each of the 45 frames
of image. To control the quality of the imperviousness map, they are compared visually with
high resolution airphotos to ensure consistency. The major consistency issue is found to be bare
soil areas where SPC’s performance is not adequate. In order to tackle the problem, a buffer
generated from the Tiger 2000 roads from the U.S. Census Bureau is used as a mask to reduce
the commission error introduced by bare soil in rural areas. The justifications of using the road
buffer are that: (i) any type of development has to be close to the road network; and (ii) beyond a
certain distance from road network man-made structures rarely exists. The buffer distance is thus
set to be 90 m equal to three pixels on both sides of road network. The determination of buffer
9
distance is based on the visual interpretation of several road buffers versus airphotos to ensure
the buffer zone covers most of the development in most part of the state. A detailed comparison
between impervious surface and the actual airphoto of the same area in Columbia, MO is shown
(Fig. 1). Judging by the spatial pattern of imperviousness extracted from Landsat image versus
the actual aerial image, the performance of the SPC classifier is satisfactory. In particular, the
classifier is able to identify high imperviousness in downtown, high density residential, low
density residential as well as major road networks even the random rural developments outside
the city area are identified and shown on the map as little gray specks.
Figure 1. (a) Sub-pixel classifier (SPC) classified impervious surface for Columbia, MO. A. Downtown; B.
High density residential; C. Low density residential. (b) NAIP airphoto of the same region. SPC is
showing good performance at identifying impervious surface.
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A similar mapping procedure in the vicinity of the Kansas City metropolitan region is
also very satisfactory as compared against airphoto of the same location (Fig. 2). In particular,
the leap frog development as indicated by ‘A’ not only showed the high density imperviousness
in the middle but also low density residential immediately surrounding it giving a radial
development pattern. In the mean time, ‘B’ indicates the medium to low density housing
development on the fringe of Kansas City. While as ‘C’ indicates some rural sprawl going on
between the city boundary and the leap frog development. As usual the road network are
identified and mapped very clearly.
Figure 2. (a) SPC classified imperviousness for Kansas City, MO. A. Leap frog development; B. Medium
to low density residential; C. rural sprawl. (b) NAIP 2004 2m resolution image of the same region. SPC
is able to identify both urban and rural sprawl.
PIS mapping is conducted for all 15 scenes of 2000 covering the whole state of Missouri.
The same procedures are used for the mapping process of 1980 and 1990. The rationale behind
11
the mapping sequence is because accuracy assessment will only be performed on 2000 images
due to the availability of good quality high resolution airphotos. Once the accuracy on 2000
images is calculated, similar accuracy on 1980 and 1990 images could be assumed, because
consistent procedures are used on both 1980 and 1990 Landsat images. To present statewide PIS
results in one map is unrealistic because of the sheer size of the image is preventing it from
giving any information. Instead, zooms of certain hotspots of ISS will be highlighted in insets to
present more details. Unlike ISS in urban area, ISS in rural areas are hard to be seen due to the
less change and more dispersed nature. Thus, image results will not be displayed and statistical
results will be presented. To highlight rural sprawl, ISS for the whole state is separated into
urban and rural sprawl. The cut off between urban and rural is by using city boundaries of 1994
from MSDIS buffered with a distance where all cities have their contiguous impervious surface
covered. All three stages of impervious surface used the same urban rural mask to ensure
comparability.
Accuracy assessment
A common method of accuracy assessment is error matrix. Accuracy indicators such as overall
accuracy, producer’s accuracy, and user’s accuracy can be reported from error matrix (Congalton,
1991; Congalton & Green, 1999).
Previous researches on sampling design for large area include multi-level stratification
and random sampling (Stehman et al., 2003; Wulder et al. 2006). In this research, due to the
unique features of impervious surface, which (i) represents only a small portion of the whole
study area; and (ii) has uneven distribution. Traditional geographical stratification does not work
for our study. Thus, accuracy assessment based on population density distribution is used. The
whole state of Missouri is divided into five sub-regions: (i) high; (ii) medium high; (iii) medium;
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(iv) medium low; and (v) low population density sub-regions. One hundred random points are
generated in each sub-region and a total of 500 sampling point for the entire state were used.
This is consistent with the general guideline of 50 sample points per class (Goodchild et al.
1994). The rationale behind the population density stratification is the fact that impervious
surface usually coincides with human population (REF). The advantages of this design are: (i) no
bias towards impervious surface of different percentage; and (ii) more concentrated sampling
points close to impervious surface instead of rural areas.
Response design (Stehman 2001) is the protocol for determining the reference class
attributed to each sampling unit. It includes two parts: (i) evaluation procedure; and (ii) labeling
rules. For conventional classification the evaluation process is to identify the class at each
sampling point on reference map, image or data. Whereas labeling is to give each reference point
a class name to be compared with the classification result. In this research, only PIS is reported
in the classification. Labeling is by visually compare classified result with reference airphoto.
And an estimated PIS is given to all the sample points.
Ecophysical and human environmental factors
ISS for two decades are calculated by subtracting PIS of 1990 by that of 1980 and 2000 by that
of 1990 resulting two difference images that are deemed as ISS for two decades. The layers of
eco-physical factors of Missouri include: elevation, slope, and ecological units of LTA. And the
human and environmental factors include: road network, and county boundaries. The
summarization is done in such that each eco-physical layer is overlaid with the ISS of 1980-1990
and 1990-2000. Histograms will be generated from statistics by overlaying ISS with elevation,
slope, and road network. Maps will be generated by overlaying ISS with LTAs, county, and
watersheds boundaries to summarize ISS by different boundaries.
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Previous research has indicated that geophysical factors such as topography and slope are
strong explanatory variables for urban expansion (Batisani & Yarnal, 2009). We used 30 meter
resolution DEM data of Missouri to study the relationship between topography on ISS. The ISS
of two decades are summarized over the DEM file to extract the relationship between elevation
and ISS. The range of elevations most susceptible to ISS will then be identified for the past
decades. Similar procedures are done to the slope to obtain the ranges of slope that are most
vulnerable to ISS. The relationships of ISS and eco-physical factors can later be used as to model
future ISS.
Road networks have been used in urban sprawl policy studies (Behan, 2008) and urban
sprawl simulation models (Patnam, 2003). It is presumed to greatly influence the development
pattern. To understand the influence of Missouri’s road networks on ISS, we calculated a road
network density map and summarized the ISS for two decades to identify certain density of road
networks that are most susceptible to ISS.
ISS is not spatially homogeneous across the state of Missouri. In order to understand the
effects of ISS on particular ecological units Missouri ecological classification system (ECS) is
used. An ECS is a framework that maps units of land with similar physical and biological
characteristics at scales suitable for natural resource planning and management (Nigh and
Schroeder 2002). Due to the vast difference between the sizes of LTAs, the ISS will be weighted
by the area of each LTA. LTAs most vulnerable to sprawl will be identified for two decades.
Comparisons will be done to identify ecological units constantly under ISS pressure.
A major challenge of sprawl study is the fragmented political boundaries. Local
governments enact land use regulations to secure the desired lifestyle preferences in their own
local jurisdictions inside their political boundaries (Carruthers, 2003). In order to distinguish the
14
differences of ISS caused by political boundaries, we used county boundaries, appropriate for
statewide studies, from U.S. Census Bureau to analyze the pattern of ISS. Population growth,
another identified driver of sprawl development (Esch et al., 2009) will be compared with ISS in
two decades to identify counties influenced most by sprawl, i.e. counties with increased PCIS.
Such counties could then be identified for more detailed research to find out the factors that drive
this type of ISS that is not experienced in other places.
Results
Statewide statistics of urban and rural ISS
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In the decade of 1980s, a total of 58855.3 hectare of land is converted to impervious surface.
Among the conversions, more land is consumed in rural areas representing about 60% of the
total converted land with an urban/rural ratio of 67.3%. Most ISS for urban areas occur in a
fashion that 30-40% of impervious surface mixed with other land cover classes (likely vegetation,
bare soil, and water body). Most ISS for rural areas is characterized with 20-30% impervious
surface mixed with other land cover classes. Lower impervious surface density in rural areas
suggests that rural sprawl converts more open land to impervious surface at lower density (Table
1).
In the decade of 1990s, a total of 70997.9 hectare of land is converted to impervious
surface. Among the conversions, about 70% of land is being consumed in rural areas with an
urban/rural ratio of 47.7. The peak density of development in urban area is between 30-40% of
PIS. For rural area, the peak of development is the same with urban although the development
between 20-30% of PIS density range is also very high. The biggest difference between ISS of
the 1980s and 1990s is the shift of development focus from urban to rural areas and more land is
being consumed in the latter decade (Table 1).
High density developments are more likely in urban areas than in rural areas. This
phenomenon is confirmed by the continuous increase trend of urban/rural ratio from low to high
PIS in both 1980s and 1990s. The other very distinctive feature of ISS is the sudden increase in
development for 90-100% of PIS. The mapped result shows that the corresponding high density
developments for urban areas are shopping centers, plazas, and parking lots, whereas for rural
areas the high density developments are predominantly the new airport runways and warehouses.
The other part of the sudden increase of ISS for 90-100% of PIS can be explained by the fact that
almost no 100% pure impervious pixels existed due to both the large pixel size and heterogeneity
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of the landscape. Thus, the signature file used for classification does not have a PIS of 100%. In
the mean time, the chance of getting a signature file with the highest PIS of any image is very
low. So we end up with a situation where some pixels in the image have higher PIS than the
“100%” PIS signature file, thus classification overflow occurred, the corresponding category of
pixels with PIS larger than 100% are eventually grouped with 90-100% of PIS. So we end up
having more pixels in the 90-100% category than there actually are.
Table 1. Impervious surface sprawl (ISS) in hectare
PIS(%)
Urban sprawl(ha) Rural sprawl(ha)
Total(ha)
U/R(%)
1980-1990
0-10
0.5
238.8
239.3
0.2
10-20
0.5
169.7
170.2
0.3
20-30
3460.5
9971.8
13432.3
34.7
30-40
4340.8
9526.5
13867.3
45.6
40-50
4117.6
6587.1
10704.7
62.5
50-60
3283.5
3146.2
6429.7
104.4
60-70
2356.1
1513.1
3869.2
155.7
70-80
1534.1
769.3
2303.4
199.4
80-90
876.0
414.5
1290.5
211.3
90-100
3704.9
2843.8
6548.7
130.3
Total
23674.5
35180.8
58855.3
67.3
1990-2000
0-10
0.4
258.4
258.8
0.2
10-20
0.3
175.4
175.7
0.2
20-30
3674.8
13205.9
16880.7
27.8
30-40
4287.1
13420.5
17707.6
31.9
40-50
3744.2
9294.8
13039.0
40.3
50-60
2930.9
4558.5
7489.4
64.3
60-70
2022.9
2002.2
4025.1
101.0
70-80
1231.0
849.7
2080.7
144.9
80-90
686.2
403.5
1089.7
170.1
90-100
4340.4
3910.8
8251.2
111.0
Total
22918.2
48079.7
70997.9
47.7
U/R stands for urban sprawl versus rural sprawl ratio. The ISS is calculated by the number of pixels in
each PIS category multiplied by the corresponding PIS, in this case 10% to 100% with 10% increment,
added together and converted to hectare. The column total is the sum of all 10 categories of PIS. The row
total is the sum of urban and rural sprawl. U/R is calculated by urban and rural sprawl in each category of
PIS as well as the total value.
Accuracy assessment
17
The analysis of accuracy assessment will follow the traditional approach due to the nature of this
research explained in the response design part. The overall classification accuracy is 86% for 9
classes and the overall Kappa Statistics is 0.7982 (Table 2). A very noticeable trend in the
producer’s accuracy column is the positive correlation between the increase of accuracy and
percent of impervious surface which is in accordance with a lot of the previous research (Civco
et al. 2006; Lu and Weng, 2006; Yang et al. 2003). The uneven distribution of sampling points is
caused by two reasons: (i) population density distribution may not have a linear correlation with
PIS, for certain PIS categories such as 30 to 60%, medium density residential, more population
are present thus more sampling points in those categories; (ii) 100% pure impervious surface
training pixel is impossible to obtain, the same problem of overflow, explained earlier, occurred
in this case too.
Table 2. Summary statistics
Class
Reference
Classified
Name(%)
Totals
Totals
0-20
238
284
20-30
16
3
30-40
41
23
40-50
61
50
50-60
49
46
60-70
29
29
70-80
22
22
80-90
6
8
90-100
38
35
Totals
500
500
Number
Correct
232
3
22
47
44
28
19
6
29
430
Producers
Accuracy
97.48%
18.75%
53.66%
77.05%
89.80%
96.55%
86.36%
100.00%
76.32%
Users
Accuracy
81.69%
100.00%
95.65%
94.00%
95.65%
96.55%
86.36%
75.00%
82.86%
Spatial patterns of ISS
The extent of impervious surface is highly visible around metropolitan area and along the
highways with the most current result in 2000 shown (Fig. 3a). Impervious surface shows
diverse patterns across the state. They can be summarized as the following general patterns. First,
a uniform pattern in which more residential developments are in very similar density and spatial
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pattern. This pattern is represented by Springfield where we could see clearly the block pattern of
development inside as well as on the city fringe which are to a large degree caused by the block
pattern of road networks (Fig. 3b). Second, a radial pattern in which residential developments
trend away from urban centers in various directions with various speed and density and is less
organized than the first pattern. This pattern is represented by Jefferson City which has various
residential densities scattering around its vicinity (Fig. 3c). Third, a leap frog pattern in which
new developments jump away from current developments on the fringe of cities to start a new
development from a nearby location, in most cases both locations are usually connected by
highways. Such pattern is very common for large metropolitan cities. This pattern is represented
by Kansas City which has several leap frog developments such as Blues springs (A of Fig. 4).
Fourth, an infill pattern which new developments fill the empty space in between developments
or inside the empty space enclosed by highways. Such pattern is also common for large
metropolitan cities. This pattern is represented by St. Charles which is in the St. Louis metro area
where the triangle formed by three sections of highways is filled with developments in the last
two decades (Fig. 5a, 5b, and 5c). Fifth, a pattern where growths are along interstate highways
that is close to metropolitan cities. This pattern is represented by the developments along
highway (I-70) (C of Fig. 5). Sixth, rural sprawl pattern where developments are scattered in
open space outside cities and towns and usually occur at more random fashion than urban sprawl.
19
Figure 3. (a) SPC classified imperviousness for the state of Missouri of 2000, (b) Impervious surface of
Springfield, MO, and (c) Jefferson City, MO.
20
Besides general patterns of development, there are more details associated with the ISS
patterns that can only be shown by comparing impervious surface extent of different times. For
that purpose, two sets of progression maps for Kansas City vicinity and St. Charles vicinity are
used. The details are summarized by inspecting the two sets of maps. The leap frog development
of Blue Springs (A of Fig. 4) has more low density development than Kansas City itself (B of
Fig. 4). In between the above mentioned two cities, there are many low density developments
going on along the highway (I-470) as well as a small patch of leap frog development (C of Fig.
4) on the left side of highway (I-470). Moreover, rural developments are springing out in all of
the open space shown as gray specks. St. Charles is experiencing more dramatic development
during the same period. During the decade of 1980s, the development is mostly filling the gaps
of older development (A of fig. 5). Whereas the development in 1990s is so overwhelming that
the triangular zone (B of fig. 5) formed by the three highway sections is completely filled with
development albeit in relatively low density. The development in St Charles is a very typical
illustration of sprawl development. Most new developments are showing the infill pattern. The
reason for that pattern is home owners appreciate the convenience of being close to highways.
But in the mean time they don’t want to be too close to highways for both privacy and noise
issues which explains the fact that we rarely see residential development very close to highways.
Last but not least, most of the relatively higher density developments, presumably business,
restaurants etc., are along the highways. This is explained by the fact that business owners want
to be visible to the commuters on the highway to create volume for their businesses.
21
Figure 4. (a) SPC classified PIS for the state of Missouri of 1980; (b) 1990; and (c) 2000.
22
Figure 5. a) SPC classified PIS for the state of Missouri of 1980; b) 1990; and c) 2000.
23
ISS by topography and road network
Histograms of total ISS by elevation for 1980s and 1990s show a similar pattern (Fig. 6a),
suggesting that most ISS in the last two decades occurred in the same elevation range. To be
more specific, about 70% of ISS took place between the elevations of 200 m to 350 m. The result
also revealed that there is an increase of ISS in 1990s between the elevations of 50 m to 100 m
and between 350 m to 400 m (Fig. 6a), suggesting ISS in 1990s have moved to both higher and
lower elevations. This result is on contrary to the belief that more development have shifted to
higher elevations due to the exhaustion of flat low lands.
Histograms of total ISS by slope for 1980s and 1990s show that ISS in both decades
occur within 0-40 degrees of slope (Fig. 6b). Over 80% of the sprawl took place within less than
20 degrees of slope and about 50% at less than 10 degrees of slope. Not surprisingly, the ISS
pattern against slope is very similar for the past two decades, since for most part the two curves
overlapped. It is noticeable that ISS in the 1990s is slightly higher between 0-20 degrees of slope.
In essence, ISS during 1990s is on similar slope conditions with that of the 1980s, only more
land is being consumed.
Histograms total ISS by density of road show that ISS occurs within 0.2-3.5% range of
road density (Fig. 6c). Open land with less than 0.2% of road density is not suitable for sprawl
because of travel limitations, whereas land with over 3.5% road density has already been filled
with developments and has no space for further ISS. The road network density effect on ISS is
very similar for the last two decades with about 80% of the ISS between the density range of 0.5
to 1 percent (Fig. 6c). ISS in the 1990s is claiming more land than in the 1980s in the
aforementioned range.
24
Figure 6. ISS versus a) elevation, b) slope, and c) density of road networks for 1980-1990, and 1990-2000.
25
ISS by eco-regions
Results from analyzing ISS by land type association (LTA) show the shifting pattern from 1980s
to 1990s. In 1980s, sprawl only affected LTAs that are close to large metropolitan areas, namely
St. Louis and Kansas City. It is less noticeable in most of the LTAs in Till Plains (TP) and
Mississippi Basin (MB) ecological sections which are the state’s primary agricultural regions
(Fig. 7a). Also, LTAs at the core of Ozark Highlands (OZ) ecological section, the primary forest
region of the state, were not affected much in 1980s (Fig. 7a). In 1990s, noticeable increases in
ISS are shown by LTAs in TP and MB as well as OZ sections (Fig. 7b).
It is very obvious that in 1990s more land type associations are being affected by ISS
(Fig. 7). While most LTAs have experienced less than 1% ISS in both decades, there are few
LTAs stand out to show that they are under constant pressure. The LTAs are St. Charles Co.
Prairie, Chesterfield Loess Woodland, Manchester Oak Savanna, Lower Meramec Oak/Mixed
Hardwood/Forest Hills, Jackson Co. Prairie, and, Platte River Loess Prairie. Most of these LTAs
are very close to St. Louis and Kansas City metro regions. Despite the fact that ISS has started to
affect more eco-regions during the 1990s, the most dominant growth hotspots are still close to
metropolitan cities. The LTAs being affected most are predominantly nearby metros. In the mean
time, the most vulnerable ecological land type is identified to be prairie. Since clearing forests
for development is more difficult both economic wise and policy wise.
26
Figure 7. Impervious surface increase summarized by eco-regions.
ISS by county
The sprawl can be expressed in terms of the increase of per capita share of impervious surface
(PCIS). The PCIS for 1980, 1990, and 2000 are 0.133, 0.139, and 0.140 hectare of impervious
surface per person. Although PCIS increased more in the 1980s than the 1990s, there is more ISS
in the 1990s than the 1980s. The slight increase of PCIS for 1990s is due to the faster population
increase in the 1990s. For individual counties, most are experiencing increase in PCIS with
various rates (Fig. 8). There are a few counties experiencing slight decrease in PCIS with the
exception of Stoddard County with a dramatic decrease in PCIS during the decade of 1980s. The
cause of this reverse sprawl trend is because of the unusual increase of population in that county
from 9009 to 28895 in the 1980s although the amount of impervious surface actually increased
during the same period. The other distinctive feature of PCIS is for counties with metropolitan
27
cities, the PCIS is usually much lower than rural counties. The cause of this phenomenon is twofold: first, the population in rural counties is very small; second, the portion of impervious
surface intended for infrastructure such as road networks, airport runways is higher than those
intended for residential use. With less people sharing relatively more public facilities, the share
of PCIS for each person in rural counties is usually higher than counties with large cities.
The spatial pattern of ISS during the 1980s suggests that counties with the highest ISS all
have metropolitan or small metropolitan cities inside. The other counties with relatively high ISS
are adjacent to the metropolitan counties (Fig. 9a). The corresponding PCIS map shows the
counties with the biggest increase of PCIS are mostly rural which have very little or even no
increase in ISS. The cause of the increase in PCIS is due to loss of population. Among them,
Worth, Mercer, and Pike county have the highest loss of population thus highest increase in
PCIS. Whereas for the counties with a slight decrease in PCIS are usually metropolitan counties
or counties nearby which have some significant increase of ISS (Fig. 9b). In this case, the cause
of decrease in PCIS is due to the increase of population. Among them, Stoddard County has the
highest increase of population. The spatial pattern of ISS during the 1990s shows an expansion
pattern where more counties are being affected by significant ISS. Many rural counties
untouched by ISS in the 1980s are being encroached by ISS during the 1990s (Fig. 9c). The
corresponding PCIS map shows less rural counties have PCIS increased compared to 1980s.
Considering more rural counties have ISS increased, the phenomenon can only be explained by
the fact that for the rural counties used to lose population during the 1980s have their population
stabilized or even increased (Fig. 9d). However, Pemiscot County which has the highest increase
in PCIS is still caused by loss of population. The other very distinctive pattern is a collection of
adjacent counties have significant decrease in PCIS as highlighted by thicker outlines (Fig. 9d).
28
These counties share the Lake of the Ozarks which is a hotspot that attracts huge numbers of
retirement population in the 1990s.
The spatial pattern of ISS for the two decades is very intuitive. In the case of PCIS maps,
the interpretation is not so straightforward. For example, for counties with a decrease in PCIS,
there are predominantly two situations. First, rural counties with little increase of ISS but slightly
more population increase. Second, counties close to big cities and retirement hotspots such as
Lake of the Ozarks that experience very significant ISS and even more significant population
growth. These counties may have a decrease in PCIS. It is probably mostly due to the buildingup process not in time to catch up with the sudden influx of population. If current standard of
living is to be pursued, more development is bound to occur. So these counties with decrease in
PCIS may have the greatest potential for sprawl.
29
Figure 8. Impervious surface per capita summarized by county.
30
Figure 9. Percent change of impervious surface per capita by county.
31
Discussion
assessment . Our approach for mapping impervious surface uses buffered mask generated from
Tiger 2000 roads from the U.S. Census Bureau for the whole state of Missouri. This reduces
confusions from bare soil or similar materials which resemble impervious surface mostly in
rural areas in Landsat images. This approach may greatly increase both producer’s and user’s
accuracy of impervious surface mapping in urban areas. It only increases user’s accuracy of
impervious surface in rural areas due to the exclusion of possible impervious pixels outside the
proposed road buffer. However, by increasing the buffer distance will increase producer’s
accuracy but reduces user’s accuracy since more confusion with soil is introduced. Thus, an
additional mask of soil will be necessary to dramatically increase the classification accuracy.
Similar approaches have been applied in large scale research (Esch et al. 2009). Others have used
multi-date imagery to minimize the confusion by bare soil (Yang et al. 2003). However, multidate images are not always readily available especially for such a large scale study as state of
Missouri. Results from accuracy assessment suggest that the approach we employed is suitable
for statewide sprawl mapping.
In order for this approach to be widely applied as an instrument for statewide and even
nationwide monitoring system the quality of images used as well as preprocessing is crucial. We
found the quality of signature file representing pure impervious surface have a strong influence
on the classification result. Due to the nature of that pixels are classified at subpixel level, a
universal signature file for the whole state is proved to be impossible because of the vast
differences between images and the infinite material combination inside each pixel that is not
solvable by image preprocessing. Previous impervious surface mapping research are mostly
focused in metropolitan cities with only one frame of image involved, thus, such problem was
32
not an issue earlier (Lu and Weng, 2006; Wu and Murray, 2003). Even with one frame of image,
the result is not always stable (Clapham, 2003). On the other hand, generating suitable signature
file tailored to each individual image will produce better result. But it will require a substantial
amount of user interaction which hinders the operational efficiency and larger scale
implementation. The efficiency issue with this approach is also faced by all large scale
applications which are yet to be improved in future research.
We have provided the statewide impervious surface extent for 1980, 1990 and 2000 as
well as preliminary analysis results based on eco-physical and human environmental factors. For
the decade of the 1980s and 1990s, respectively, a total of 58855.3 hectare of land (0.41% of the
whole state) and 70997.9 hectare of land (0.48% of the whole state) are being converted to
impervious surface for development use. Similar results have been reported by previous research
(Brookings Institution, 2002). Only the amount of land being converted to impervious surface
identified by this research is less than the amount claimed by Brookings Institution. The
difference between the two is caused by different assessment approach. Essentially, the former
used impervious surface as indicator which measures accurately the amount of land being
converted to developed use, the latter used plot data which includes not only impervious surface
but other land covers that are inside the development plot. Thus, the second approach tends to
overestimate compared to the first approach. The first approach is more scientifically sound
because it gives not only the spatial extent of sprawl but also the pattern and density of sprawl.
Since the negative effect of sprawl is caused not only by the total area of development but also
the dissecting effect of low density development as well as the pollution caused by human
activity. And such negative effect can only be measured or estimated by the detailed information
provided by impervious surface; impact assessment could also be made based on texture and
33
density information provided by PIS mapping results, whereas for plot data such inference is not
applicable.
Although there is an obvious shift of the ISS from urban areas to rural areas, the
topographical influence on ISS is not obvious for the two decades at the state level. But Kansas
City does show more urban growth during the 1990s than St. Louis partly due to the flat land in
its vicinity that promotes urban expansion (Ji et al., 2006). The mapping result of the whole state
can be aggregated into more detailed administrative and ecological units to facilitate further
analysis by both policy makers and scientific research. The PIS map derived from the three
stages could be used in more focused research on the trend of urban and rural development as
well as some local impact assessment on the ecological regions affected most by ISS in future
research. More importantly, future impervious mapping result could be integrated with the
results obtained in this research to derive more useful information all because of the consistent
nature of impervious surface mapping that it will not be affected by definition like other
indicators such as population density. Moreover, the indicator of PCIS can be explored more at
individual city level to hopefully discover some unique relationship between impervious surface
and population that is never discovered by population density, earlier research has already
indicated similar measure with PCIS is more appropriate than population density when it comes
to sprawl studies (Jaeger, et al. 2009). The rationale is for a certain amount of impervious surface,
the holding capacity of population will be limited. The upper limit of such holding capacity is
decided by land-cover, residential areas in this case, and the PIS of the residential area which
also has a limited range of value as indicated by this research. Thus, the possible range of PCIS
should be very limited compared to population density. The phenomenon will be more obvious
at larger scale since more undeveloped land that contains few or no population will be included
34
in the calculation of population density. A good example is the range of population density for
the 50 states range from 1.1 to 9378 person per sq. mile (2000 U.S. Census). Previous research
has estimated population successfully by taking advantage of the special relationship between
impervious surface and population (Lu et al. 2006). The other significance of introducing PCIS
to the mix is sprawl pressure can be measured more directly. For example, the counties that
cover the Lake of the Ozark region have decrease in PCIS, considering the large influx of
retirement population in a short period of time the development pace was not able to catch up. So
the decrease of PCIS may appear to a good phenomenon at the moment of the study. There is
actually great pressure in this region to build more houses and PCIS will eventually bounce back
to its original level. Future research could take advantage of the deciding factors of impervious
surface and population as well as influencing factors such as topography and ecology, etc. to
model ISS.
The ultimate purpose of this research is to provide scientific information that will be
useful to guide future developments to reduce the impact of sprawl on the natural landscape.
With the information derived from this research as well as possibly information derived from
future predictions. We should be able to monitor urban and rural sprawl accurately. Provided
with more detailed impact assessment as well as good future projections, a better decision
making for future development is possible.
35
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