Cellular Automata and Urban Growth; A Case Study in the Western Shore Region of the Chesapeake Bay

Transcription

1 Cellular Automata and Urban Growth; A Case Study in the Western Shore Region of the Chesapeake Bay A THESIS PRESENTED TO THE DEPARTMENT OF GEOLOGY AND GEOGRAPHY IN CANDIDACY FOR THE DEGREE OF MASTER OF SCIENCE By Christopher S. Park

2 Northwest Missouri State University November 2011 Cellular Automata and Urban Growth Cellular Automata and Urban Growth; A Case Study in the Western Shore Region of the Chesapeake Bay Christopher S. Park Northwest Missouri State University THESIS APPROVED Thesis Advisor Date Dean of the Graduate School Date II

3 Cellular Automata and Urban Growth; A Case Study in the Western Shore Region of the Chesapeake Bay Christopher S. Park Northwest Missouri State University Abstract The Chesapeake Bay is one of our nation s natural treasures. In recent decades, the bay has been under siege by overfishing, extremely high nitrogen and phosphorous levels from stream runoff and encroachment by development of the vital wetlands that act like a sponge to regulate the water level and chemistry in the bay and its tributaries. Growth in the Chesapeake Bay region is unlikely to stop in the future with the large metropolitan presence in the area and key economic and government centers that feed suburban sprawl. This thesis seeks to better understand urban growth in this region by utilizing a computerized growth model known as the SLEUTH urban growth model. The model uses existing historical growth data to predict growth into the future. The results of this model, when visualized by census tract, provide a picture of slower but sustained growth by type in the western shore region of the bay. In addition, I combined the model output with census tract areas from the 2007 census, which in turn helps to visualize where the focus should be for emphasizing smart growth policies in the future. III

4 Table of Contents Abstract... III List of Tables... VI List of Figures... VII Acknowledgments... 1 Chapter 1: Introduction : The Chesapeake Bay Watershed (CBW) : Environmental Problems Associated with Urbananization in the CBW 4 1.3: Use of GIS for Tracking Pollution and Urban Growth in the CBW.5 1.4: Study Area 6 1.5: Urban Growth and Cellular Automata : Research Goals..11 Chapter 2: Literature Review : Cellular Automata : SLEUTH Cellular Automata and The Urban Growth Model Chapter 3: Methods : SLEUTH Model : Data : Applying Course Calibration Methods Using Data for LWS GIS..42 Chapter 4: Results : Calibration : Predictions : Prediction : Prediction : Prediction Chapter 5: Discussion : Growth Scenarios and the Region IV

5 5.3: Future Research Chapter 6: Conclusion References V

6 List of Tables Table 1: Data types and sources used in SLEUTH 38 Table 2: SLEUTH metric coefficents 40 Table 3: R2 values for the critical measures of fit 46 Table 4 R2 values for the critical measures of fit continued 47 Table 5: Calibration results summary 48 Table 6: Prediction coefficients and boom/bust coefficients 52 VI

7 List of Figures Figure 1: Overview of the study area 7 Figure 2: 1984 CBWLD of the western shore of the Chesapeake Bay 28 Figure 3: 2006 CBWLD of the western shore of the Chesapeake Bay 29 Figure 4: Urban extent data derived from CBWLCD 31 Figure 5: Excluded areas used in SLEUTH calibration and prediction 34 Figure 6: Road layers and slope 37 Figure 7: Example of a geoprocessing Workflow Using ESRI s Model Builder 45 Figure 8: Model simulated population growth 50 Figure 9: Population growth estimates from census data 50 Figure 10: Prediction 1: Growth Coefficients 53 Figure 11: Prediction 1 Growth Scenario 55 Figure 12: Prediction 2 Growth Coefficients 56 Figure 13: Prediction 2 Growth Scenario 57 Figure 14: Prediction 3 Growth Coefficients 58 Figure 15: Prediction 3 Growth Scenario 59 VII

8 Acknowledgments The following thesis relies heavily on the work that has been done throughout the last thirty years by many people at multiple institutions developing the SLEUTH urban growth model and research using cellular automata in urban growth. I would like to thank several key individuals that are responsible for writing, maintaining and advising on using SLEUTH for urban growth modeling: Keith Clarke and the Department of Geography at UC Santa Barbara, David Donato at the USGS Eastern Geological Science Center EGSC, Claire Jantz, Scott Goetz and Peter Claggette. I would also like to thank my family for being patient with me throughout this process, and co workers and professors at NWMSU who proof read, and provided guidance. 1

9 Chapter 1 Introduction The Chesapeake Bay is one of this nation s natural treasures. It is an estuary, or body of water where fresh and salt water mix; it is the largest estuary in the United States and the third largest in the world (Chesapeake Bay Program, 2010). It is fed by a 168,000 square kilometer watershed and thousands of streams and rivers that converge and flow into the bay from three primary rivers, the Susquehanna, the Potomac, and the James River (Jantz, et al., 2004). The watershed, or areas in the region that drain into the bay, touches six states (Maryland, Virginia, Delaware, Pennsylvania, New York and West Virginia) and Washington, D.C. (Chesapeake Bay Program, 2010). The Chesapeake Bay has provided an economy for fisherman, crabbers and the maritime industry since the 1700s. The Bay supports more than 3,600 species of fish and animals and 2,700 plant species. It is also a major resting ground for migratory birds, with more than one million waterfowl spending the winter there each year (Roberts, et al., 2009). In the last century, the bay has suffered the consequences of a growing Mid Atlantic population, increased industry, and overfishing. The most recent urban growth study (at the time of this writing) that has been completed for the Bay area was conducted in 2004 (Jantz, et al., 2004). Since that time, the Chesapeake Bay area has seen continued growth followed by a severe recession which almost certainly had an impact on both the rate of growth in the area and the revenue available for planning and Bay restoration. This thesis will examine the effects 2

10 of urban growth on an area of the Chesapeake Bay over the last decade. The examination of a small and focused area of the Bay has been chosen for two primary reasons: 1) The models will not be as computer intensive as many of the smaller scale regional modeling efforts have been; and 2) The scale can be larger and more detailed. 1.1 The Chesapeake Bay Watershed (CBW) The bay was created more than 35 million years ago when either a comet or large meteor struck the lower region of the Delmarva Peninsula (what is now the eastern shore of Maryland). The crater, which was 55 miles wide and possibly as deep as the Grand Canyon, was eroded into a series of tributaries by multiple glacier advances, and assumed its current form about 3000 years ago (McKendry, 2009). Population growth in the bay watershed region has put a strain on the ecological balance of the bay. In 1950, the population of the watershed was approximately 8.1 million people. Today the region s population is estimated at 16.7 million people (McKendry, 2009). The major population areas in the bay watershed are the cities of Washington DC, Baltimore, Philadelphia, Wilmington and Richmond, with many smaller suburban areas between these centers of gravity for economic activity which contributes to population growth. 3

11 1.2 Environmental Problems Associated with Urbanization in the CBW In the last century, the bay has suffered the consequences of a growing Mid Atlantic population, increased industry, and overfishing. The environmental problems that pose the highest threat to bay health are excess nitrogen and phosphorous from stream runoff that dump into the bay every year. According to the most recent bay assessment in 2008, 291 million pounds of nitrogen (Chesapeake Bay Program, 2010) and 13.8 million pounds of phosphorous washed into the bay (Chesapeake Bay Program, 2010). The main driver for this type of non point source pollution is development, particularly suburban sprawl. In the early 1980s, several organizations were constituted to start planning restoration strategies for the Bay. It was clear that disparate state agencies and organizations could not tackle many of the large issues that plagued the watershed across state and county lines. The Chesapeake Bay Program was formed in 1983 and is a partnership across all of the states that make up the watershed. It is the organization responsible for coordinating the overall strategy for restoring the bay (Chesapeake Bay Program, 2010). 4

12 1.3 Use of GIS for Tracking Pollution and Urban Growth in the CBW GIS is a vital tool in assessing and mapping both the progress that has been achieved, as well as quantifying the damage that is being done. GIS allows scientists to develop advanced methodologies that, along with remote sensing, give people a much better perspective of the scope and degree of pollution in the bay and aid in developing smart growth strategies for land use and development. Several federal, state, local and private organizations are using GIS and remote sensing to look at the way development upsets complex systems that interact with the chemistry of the bay such as the nitrogen/phosphorous cycles within the watershed. The ability to study and model many of these mechanisms at on a regional level even a decade ago was impossible due to a lack of computing power and the expense and availability of multispectral imagery (Roberts, et al., 2009). Good policy decisions in regards to urban growth strategies such as more parks, smart growth, land grants and easements in the CBW have shown to reduce these types of pollution into the bay (Cheapeake Bay Program, 2010). Urban growth research has experienced a renaissance of sorts over the past two decades. Historically, urban modeling often consisted of defining the extent of existing urban areas and characterizing growth over time through a city s economic, social and defined political boundary changes (Goldstein, et al., 2004). With the advent of modern computing, urban growth has developed growth prediction models that measure change and have the ability to develop multiple scenarios for growth. With these advances in urban growth research, it has become more influential in policy making and planning for future growth (Goldstein, et al., 2004). 5

13 1.4 Study Area The specific area that I chose for my research is the lower western shore (LWS) of Maryland. The LWS is as varied a geographic region as exists in the watershed. Bounded by Baltimore City in the north, the state capital, Annapolis, to the east, and Washington DC to the west, there are multiple urban centers of gravity pushing into this region. Geographically, the region drains approximately 270 miles of land and includes most of two Maryland counties, Anne Arundel, home of Annapolis, the state Capitol of Maryland and Calvert County to the south (LWS overview, 2003). Anne Arundel County has dense urban areas from Annapolis north towards Baltimore on State Route 2. Calvert County is much less populated with primarily farmland and coastal wetlands (Lower Western Shore Tributaries Team, 2003) Figure 1 below illustrates the geography of the region and highlights the study area within the two counties. 6

14 Figure 1: Overview of the Study Area 7

15 1.5 Urban Growth and Cellular Automata Urban growth is by no means unique to the Chesapeake Bay. By 1995, twenty one cities world wide had total populations over six million (Clarke & Gaydos, 1998) and more than half of the world s population lived in settlements of five thousand people or more (Clarke & Gaydos, 1998). The challenges that are associated with urban sprawl, the growth of cities, and development will not be overcome anytime soon. Tools that utilize GIS and remote sensing to produce urban growth models to better understand how areas are developing are critical in the balance of development with managing pollution, nature and our food supply. Modeling land use with GIS has evolved over time with raster based or cellular modeling becoming the primary mechanism for analysis, particularly with the advent of land classification using remotely sensed data (Longley, et al., 2005). The theory behind the cellular models used in land classification and urban growth are based on continuous data sets. Continuous data is data that is represented as a surface and, therefore, does not have definitive or discrete edges (Longley, et al., 2005). This trait makes continuous data very effective at displaying naturally occurring surfaces such as images of the earth, elevation data, land type, and other continuous phenomena. In images of the earth, for example, each pixel or cell has a reflectance value that represents the light captured by the imager (Campbell, 1996). Collectively to the eye it appears to be an image of the surface of the earth, but to the software it is a grid of numerical values where each value is unique but, at the same time, spatially related to the next. Similarly, the cellular automata model needs a gridded space where each cell 8

16 is related to the next. The theory of sameness by proximity is based on Waldo Tobler s first law of geography all places are similar, but nearby places are more similar than distant places (Longley, et al.,, 2005). Cellular Automata (CA) uses Tobler s first law and random probability to determine how a particular cell may change over time, given a set of rules (Longley, et al., 2005). In a CA over time (model repetitions), the cells may change from undeveloped to developed and the likelihood that an adjacent cell will change increases as the cells around it change. Therefore, if cell B changes its state based on an event that occurs at cell A, then cell C might change its state based on cell B. These cell states can be looked at as a function of growth or retreat (Batty, 1997) One of the strengths of this type of model for urban analysis is that through multiple time points, or iterations, the results can vary from stability, stochastic instability or chaos with a few minor changes to the rules (Clarke & Gaydos, 1998). Two key elements of any raster based model are the spatial and temporal resolution (Longley, et al., 2005). Spatial resolution is defined as the shortest distance over which change is recorded that is evident in the dataset (Longley, et al., 2005). Temporal resolution is the shortest time period in which change is recorded that is evident in the dataset (Longley, et al., 2005). For this model both spatial and temporal resolution are limiting factors in determining the accuracy of the results. One of the reasons that I chose this area is because of the varied landscape, but also because of the history of population changes in this region. The lower western 9

17 shore (LWS) has experienced dramatic changes over the past 100 years both in population and economics (Lutz, 2009). At the turn of the 20 th century, the LWS served as the vacation region for the booming cities that were at the heart of the industrial revolution. With automobiles not yet available to everyone, and no bridges across the bay in Maryland to get to the eastern shore of the Chesapeake and the Atlantic Ocean, resorts and casinos sprung up from Annapolis southward through Calvert County (Lutz, 2009). Throughout the last fifty years, many of these resorts and casinos have disappeared, leaving behind only small communities south of Annapolis where people have chosen to live to be close to the water. These people have developed the communities that have become commuting towns to Washington DC, Annapolis and Baltimore where the majority of the jobs exist. Today, much of the LWS has remained largely unchanged south of Annapolis, but from Annapolis north to the greater Baltimore City area, there has been a high degree of suburban sprawl (McKendry, 2009). Annapolis is the largest city on the LWS. The population has increased slowly, but consistently over the last decade and was approximately 37, 000 in 2009 (City of Annapolis, 2009). One major change that had a profound impact on this region occurred in 1951, which was the opening of the Bay Bridge, a span that crosses a relatively narrow (4.3 miles) area of the bay from Annapolis to Kent Island, and eventually, to the Eastern Shore(Lutz, 2009). With this bridge, city dwellers in Virginia, Maryland, Pennsylvania and Delaware now had faster access to the eastern shore and the Atlantic Ocean. This shifted development along the LWS from resorts and beach houses to year round commuters seemingly overnight (Lutz, 2009). 10

18 1.6 Research Goal The specific aims for this thesis are to: 1) Determine where and at what rate urban growth has changed in the western shore of the Chesapeake Bay over the last 10 years; and 2) Compare the predicted growth to existing studies, and develop scenarios for growth based on the history and geography of the region. To accomplish this I will apply the theories of cellular automata tested with the Clarke Urban Growth Model (UGM) (Clark & Gaydos, 1998) that were conducted seven years ago for the entire Chesapeake Bay Watershed (CBW). The hypothesis is that the SLEUTH urban growth model will accurately model and predict urban growth on the western Chesapeake Bay region according to past research and historical data. A combination of vector data and raster datasets will be used for the basis of the urban growth models. The methodology for calculating urban growth will be based on Clarke s Urban Growth Model utilizing the SLEUTH program to provide data output. This data will be integrated with census data using GIS software which is considered loose coupling with the UGM. The results will be displayed as a series of maps and tables. The goal will be to use the smaller area to improve the resolution of the model using more recent datasets and smaller parameters for growth. 11

19 Chapter 2 Literature Review 2.1 Cellular Automata The research on cellular automata can be traced back as far as 1970 in John H. Conway s Game of Life as referenced in a book by Clarke C. Abt called Serious Games (Abt, 1970). Michael Batty (1997) defines cellular automata (CA) as a raster analysis that is based on the value of a single cell in relation to its surrounding cells. The cells change their values or states, according to an initial set of rules that are applied repetatively (Batty, 1997). Clarke et al., (1995) applied CA to the spread of wildfire. Applying CA as a means to simulate urban growth is attractive due to the ability of cells to change states based on their neighbors. This adjacency influence is similar to types of neighborhood behaviors in cities (Batty, 1997). The use of CA for modeling urban growth has previously been explored at several institutions and by many urban growth researchers (Batty, 1997; Clarke & Hoppen, 1997; Wu, 1999; Silva & Clarke, 2002; Wu, 2002; Herold, et al., 2003; Yang & Lo, 2003; Jantz, et al., 2004; Straatman, et al., 2004; Herold, et al., 2005; Dietzel & Clarke, 2006; Kocabas & Dragicevic, 2006; Han et al., 2009; Crooks, 2010) 12

20 2.2 SLEUTH Cellular Automata and The Urban Growth Model There has been extensive research in coupling GIS with urban growth models, cellular automata, and raster based spatial analysis, several of which have used the Chesapeake Bay as case studies. Keith Clarke and Leonard Gaydos (1998), while at the University of California Santa Barbara, pioneered loose coupling of cellular automata and GIS, developing a CA model for urban growth using five parameters and several defining datasets for urban growth called SLEUTH (Clarke & Hoppen, 1997). The SLEUTH model is named after the datasets that are captured to simulate growth patterns: slope, landuse exclusion, urban extent, transportation, and hillshade (SLEUTH) (Clarke & Hoppen, 1997). These data elements are defined further by Clarke and Gaydos (1998) as a digital elevation model from which the slope layer is defined, a layer showing seeds or urban areas that would act as a catalyst for initial growth, as well as many historical layers that would provide seed information to the model, transportation layers for as many timepoints as possible and a layer of exclusion areas such as land easments, public parks, and established green areas. The SLEUTH urban growth model is defined as a CA based model with uniform growth rules that are applied cell by cell in a gridded representation of the data. Each iteration accounts for a single timespan (Clarke & Gaydos, 1998). The growth rules and the initial conditions at a given timepoint should be tailored to the specific location due to the differences in each area of study (Clarke & Gaydos, 1998). 13

21 Calibration is a critical phase of the modeling process and has been explored indepth in multiple papers (Silva & Clarke, 2002; Wu, 2002; Straatman, et al., 2004; Dietzal & Clarke, 2006; Dietzal & Clarke, 2007;. Calibration in the SLEUTH CA is defined be Dietzal and Clarke (2004) as the process of training the model for temporal and spatial growth. Silva and Clarke (2002) discuss calibration in detail for the geographic area of the cities of Lisbon and Porto, in Portugal. Their paper contrasts the calibration for two different cities. Silva and Clarke (2002) concluded that extended calibration was critical in developing good measures and getting reliable results, as well as local knowledge of the area of study is important for the calibration process. Straatman, et al. (2004) discusses callibration automation using a SLEUTH CA model that was described by White and Engelen (1997). Calibration is dependant on the coefficients that are applied to the model, and there is no clear methodology for developing values for the coefficients that are inputed (Straatman et al., 2004). Straatman et al., (2004), in an attempt at automating the calibration process, points out that Clarke and Gaydos (1998) calibrated the model with historical geographic data consisting of primarily maps. However, in this case, he considered SLEUTH too restrictive because it lacked any social or economic factors and did not apply it to his research. While making several suggestions for potential methodologies to develop coefficients, Straatman concludes that there are many difficulties in automating the CA calibration process, primarily because it is an iterative decision model, therefore the results are highly dependand on where you begin (Straatman, et al., 2004). Herold, et al. (2003) applied the SLEUTH growth model in Santa Barbara. Again in this study, they stated that the model must be calibrated for 14

22 the study area due to unique physical characteristeristics. In Dietzal & Clarke s (2007) article on calibration, they discuss the calibration process as it relates to the resolution of the datasets and concluded that resolution is a key factor in the calibration process. Resolution will be discussed further in the research and in the methods section of my case study. Most of the literature reviewed that used the SLEUTH growth model employed a multi resolution approach (Clarke & Gaydos, 1998; Jantz, et al., 2003; Dietzal & Clarke, 2004; Goetz, et al., 2004; Jantz, et al., 2010). There are two resolution concerns addressed in the literature. Clarke and Gaydos (1998) proposed running the SLEUTH data sets exported at multiple resolutions. The primary reason for this approach was processing time. The data would be exported at four resolutions generally from a course scale in pixels (50 columns X 100 rows) to the highest resolution of the datasets (Clarke & Gaydos, 1998). The coarse scale would be run first to assess the parameter settings before expending the time that the higher resolution datasets would require (Clarke & Gaydos, 1998). The second resolution concern discussed, is the spatial size and scale of the data sets. This ranges from the San Fransisco Bay area (Clarke & Gaydos, 1998) to the entire Chesapeake Bay Watershed (Varlyguin, et al., 2001). Clarke and Gaydos (1998) conclude that the calibration processing time and the results depend heavily on the size of the area, as well as the amount of historical data that are input into the model. 15

23 The parameters of the SLEUTH model and many of the statistical measures discussed in the literature have remained fairly consistent in a number of different geographic regions. This is one reason that the SLEUTH model has shown some flexibility to the regional differences in the datasets (Dietzal & Clarke, 2007). In Dietzal and Clarke s (2007) paper, they list the five SLEUTH model parameters as: diffusion the dispersiveness of the outward distribution, the breed coefficient the likelihood that the newly independent detached settlement will begin to grow on its own, the spread coefficient controls the amount of contagion diffusion that radiates from existing settlements, the slope resistance factor the degree of slope to which expansion becomes impossible and the road gravity factor an attraction by new settlements to develop near and along the road (Dietzal & Clarke, 2007). These parameters were consistently used in all of the literature I reviewed. Because SLEUTH is a predictive model, Clarke and Gaydos (1998) proposed several measures to determine the validity of the predicted growth, i.e. the best set of values for the growth parameters based on historical growth statistics in the region. One of the most common spatial measures of growth used for the SLEUTH urban growth model is the Lee Sallee metric (Dietzal & Clarke, 2007). This is the degree to which the historical input data matches the simulation data. This metric has its roots in work published by David Lee and Thomas Sallee (1974) determining measurement statistics for farm shapes and markets. The Lee Sallee metric compares the intersections and unions of simulated data to the historical data and outputs a ratio. The closer the ratio is to one is an indicator of zero growth (Jantz, et al., 2004). The population statistic, which is a least squares regression score for 16

24 the number of predicted urban pixels and the actual number of urban pixels in the final year, and the Lee Salle metric were used as ancillary fit statistics for their model (Jantz et al., 2004). Herold et al., (2003) introduced the concept of contagion maps to the statistical results of the model. Contagion maps are probability maps generated based on similar patches of cells and adjacency. This statistic provides a good indicator of the probable nature of growth based on the nature of the clusters of urban areas (Herold et al., 2003). Notably, from 2003 the research matured and there were less publications on the spatial models themselves, and several papers published applying models to predict urban growth in the CBW (Han, et al,. 2009; Roberts, et al., 2009; Jantz, et al., 2010). Also noted in the literature over the last decade was the increase in capability for urban growth modeling and GIS due to the improved speed of processors, the availability of better, more complex data and software and the increase in need for planning tools (Dietzal & Clarke, 2006). One of the datsets that factors prominantly in the literature is the Land Use Land Classification (LULC) datsets (Clarke & Gaydos, 1998). The LULC data that I used in my research was generated by the Mid Atlantic Regional Earth Science Center (RESAC) and is based off of LANDSAT 7 Thematic Mapper satellite imagery (Straatman, et al., 2004). Satellite imagery plays a prominent role in the literature as a key data source for mapping urban development (Herold, et al., 2003; Hoffhine, et al, 2003; Jansen & Di Gregorio, 2003; Gamba, et al., 2005; Griffiths, et al., 2010). Hoffine et al. (2003) argues that by using satellite imagery for urban modeling you fulfill the 17

25 criteria for accurate results: medium to high resolution data granularity, cover a large area, add historical depth and consistency over time. There have been increasingly complex methodolgies and revisions to the SLEUTH growth model as well as other models developed using cellular automata and other methods (Yang & Lo, 2003; Goldstein, et al., 2004; Gamba, et al., 2005; Kocabas & Dragicevic, 2006; Han, et al., 2009; Griffiths, et al., 2010). One such approach in a paper published by Griffiths et al. (2010), is heavily dependant on LANDSAT Thematic Mapper (TM) imagery with little additional data input. The model uses more of a qualitative approach to understanding growth patterns by interpreting changes to a neighborhood of pixels, rather than quantifying change at each pixel. The advantage to this model is that it needs only remotely sensed data and it reveals patterns of urban growth and relationships that exists in growth across neighborhoods (Griffiths et al., 2010). The literature suggests that imagery is a more accurate source for determining the extent of existing urban growth then maps or urban datasets derived from historical maps (Gamba, et al., 2005; Griffiths, et al., 2010). However, this type of urban growth model was built more to look at past growth patterns and does not posess the type of predictive capabilities that SLEUTH provides (Hoffhine, et al., 2003). An additional urban growth model that was applied to Strousburg, France used remote sensing as well, and applied a pixel based approach to determining potential values for urban growth. The study leveraged imagery as a means for more accurate base data; however this study also included GIS data layers for additional resolution (Weber, 2003). One significant 18

26 point about this study is that her results were a gradient of potential for growth rather than predicting where actual growth will occur (Weber, 2003). Ti Yan Shen, et al. (2007) described a similar theory to SLEUTH with additional data layers and a more integrated GIS based process called the spacio temporal dynamics model based on Forretter s urban dynamics model. Shen mapped the urban growth in greater Beijing (Shen, et al., 2007). Shen compares and contrasts Forretter s model to CA and points out that both have disadvantages. Forretter s model is based on a fixed urban border, which eliminates the possibility of expansion, a key variable in many urban environments. CA allows for expansion based on growth factors, but he considers it too simplistic to account for complex economic and social drivers (Shen, et al., 2007). Because of the large amount of data inputted into this model, Shen needed much more computer resources than what is needed for SLEUTH. Shen used the Spatial Modeling Environment developed at the University of Maryland, and has been used by researchers at the University of Vermont. The Spatial Modeling Environment is an icon based modeling environment that links users to high performance computing resources to build complex spatial models with little or no programming skills (University of Vermont, 2010). Shen concluded that while this model is very useful for urban planning, the model is extremely complex and requires a large knowledge base in everything from the economics of the region to the social policies that are in effect (Shen, et al. 2007). Another type of Urban Growth model that can be both more complex, but also more flexible are Agent Based Models (ABM). The ABM has many of the same characteristics of cellular automata, but can be applied to more than just cell based datasets as is the 19

27 case in a paper by A.T. Crooks (2010). Crooks (2010) developed a loosely coupled ABM using vector data to model and predict segregation in cities. The central argument revolves around the concept of loosely coupled versus a more integrated GIS model for urban growth, or a combination of the two (Allen & Lu, 2003). While providing more flexibility and complexity to modeling growth, an ABM requires a higher granularity and, as a result, is computionaly expensive for a large study area such as the western shore of the Chesapeake. One of the latest urban growth modeling projects was developed by a team of faculty, students, and staff at the University of Illinois Urbana Champlain (UIUC). Named the Land Use Evolution and Impact Assessment Model or LEAM, this group has incorporated the Clarke Urban Growth Model with modern programming techniques, ABM, computing power and the internet to provide users with scenario based models that take into account in depth demographic, economic, government and environmental statistics in a region to generate an accurate growth prediction (LEAM website, 2011). The benefits to this model are mainly in the resources provided with the data. They leverage several areas of expertise to develop a more complex scenario of data layers for modeling than many of the other models that have been presented in the literature (LEAM website, 2011). The drawback to this model is that it is a system/service that must be granted through UIUC and could take weeks or months to assemble the necessary datasets required, as well as create the web based portals for end users. 20

28 Two notable publications dealing with urban growth and applying the SLEUTH urban growth model to the entire CBW were conducted by Jantz and Goetz (2005). There have been several research projects that used areas in the CBW as the study area and applied SLUETH (Clarke & Gaydos, 1998; Jantz, et al., 2004; Jantz & Goetz, 2005; Roberts, et al., 2009; Jantz, et al., 2010). The most recent research is a 30 meter regional landcover monitoring system for the CBW, with an updated SLEUTH model program code to address issues in the original version such as the performance of the model, as well as the ability to incorporate economic, cultural and policy information (Jantz, et al., 2010). Throughout much of the literature there is considerable debate about the best methods for modeling urban growth. Yeh and Li (2006) discussed the inherent errors in cellular automata models such as problems with discrete entities in space and time, neighborhood definitions and stochastic variables. The established research on urban modeling and the SLEUTH urban growth model is critical in applying it to my research. SLEUTH is a complex program that demands a strong understanding of urban growth concepts as well as applying the lessons learned by past applications. The literature reviewed in this section documents the capabilities of the model, the applications, the data requirements, the statistical interpretations and the limitations of it in modeling urban growth. 21

29 Chapter 3 Methods 3.1 SLEUTH Model The SLEUTH CA is written in the C programming language. This program works similar to a traditional CA model with some subtle differences (Clarke & Gaydos, 1998). The model uses principles of cellular automata, to apply changes to pixel values based on existing neighbors, and applied rules of change, or in this case, growth. It is a basic loop program that applies growth rules throughout a standard grid of pixel values (cells) that represents the area of study. The model computes change on a cell by cell basis (Clarke & Gaydos, 1998). SLEUTH does not interact with GIS software or datasets specific to GIS (Clarke & Gaydos, 1998). In this sense it is considered loosely coupled with GIS because the datasets that it requires are developed using GIS, however, the input data for the model is required in graphics interchange format (GIF) with no spatial information associated with it. The code works in nested loops. The outer loop captures overall statistics for each year. The inner loop applies the coefficients of diffusions, spontaneous or spread, organic growth, or breed, and road based spreading (Dietzel & Clarke, 2006). These rules are coefficients set manually in the model. The values are derived by the user based on setting coefficients during the calibration phase of the model to the study area. In the simplest terms, the model moves through the dataset and evaluates each pixel based on the seed year and the growth coefficients. The model repeats this for each consecutive year until it reaches a seed year, then it captures statistics comparing the seed year s growth to the growth from the previous 22

30 seed year and compares that growth to the model runs. Using the results of these comparisons, the user adjusts the growth rates to improve the accuracy between seed years. The variable parameters are categorized as four overall types of growth. The first parameter is diffusion, or spontaneous growth of urban cells randomly selected by the model. For a cell to be a candidate for urbanization due to disffusion, it must not be in an area of exclusion. The coefficient value for diffusion is defined as the probability at a given time that any available cell in the grid space will turn into an urban area (Project Gigalopolis Website, 2011). The next parameter is breed, growing from urban clusters that are developed via spontaneous growth (Jantz, et al., 2004). The breed coefficient value is the probability of a cell to convert to urban area given the availability of two adjacent cells near the newly created urban cells via diffusion (Project Gigalopolis Website, 2011). The third coefficient is spreading, or growing from the edges of established seed urban areas. The coefficient value of spreading is defined as the probability of a cell to grow adjacent to any established urban cell including urban cells created by dispersion at year + 1, provided the cell is not excluded from urbanization. The last coefficient is road influenced growth, or growing urban areas along the transportation networks. The coefficient value of road influenced growth is a road gravity value that defines a radius around either an existing urbanized cell or a cell urbanized as a result of dispersion year +1. The road gravity coefficient seeks a road pixel within that radius and follows it a number of steps determined by the dispersion coefficient. Then the selected cell, if it is not excluded, will be urbanized and 23

31 categorized as random growth and the coefficients breed and spreading will apply (Project Gigalopolis Website, 2011). For each coefficient in the model, there is a start value, a step value, and a stop value. This is applied randomly for all possible combinations at each seed year between start, step and stop. The initial values that I used in my model were based on the test scenario downloaded at the Project Gigalopolis Website (2011), which applied a start value of zero, a step of 20 and a stop value of 100. The model has three modes of operation, a test mode, a calibration mode and a predict mode. The test mode allows the user to run the code on source data and compare the results to results provided by the developers (Project Gigalopolis Website, 2011). This confirms that the model is functioning properly. The calibrate mode runs the model using the historical datasets to determine the best parameter values for the specific data being modeled. The predict mode extends the model into the future, using the calibrated parameter values and predicts urban growth. The calibration mode is the most time consuming and computer intensive part of running SLEUTH. During calibration, the model tries hundreds of permutations of the control parameters from the first year to the final year of the datasets and calculates 13 measures of goodness of fit. This type of calibration is termed brute force calibration by the creators of SLEUTH (Silva & Clarke, 2002). This information is used to develop the most accurate growth parameters for your study area to apply in predict mode. The model requires a set of strict parameters for input data. All GIF files must be have the same number of columns and rows, be in black and white and have a specific 24

32 naming convention (Clarke & Hoppen, 1997). This is important for calibration in SLEUTH because it assigns a designated type value to each pixel which has to be consistent across each timepoint or GIF file (Clarke & Gaydos, 1998). It is recommended in the literature that you calibrate the SLEUTH data model for your data at three resolutions (Clarke & Gaydos 1998). This will save CPU run time during the calibration process. The lowest resolution would be a quarter of the highest resolution (Silva & Clarke, 2002). For my dataset I used 540 rows by 926 columns (my highest resolution multiplied by 0.25). Next is the fine calibration, which uses data at half of the resolution of the actual data, in this case it was 1081 by The final calibration is using the actual resolution of the data. This calibration will be the most time intensive and should only need to be run once; therefore the coarse and fine runs should provide the optimal coefficients for the final calibration. The results of the final calibration run in the model provide the most accurate parameters for the variables in SLEUTH, as applied to my region. In order to run a model prediction, the scenario file must be adjusted with the timeframe of prediction. The parameters that were developed from the calibration phase must then be added to the prediction best fit values section of the scenario file. The best fit values are what the calibration phase developed as the highest probability of the most accurate growth values for the region (Dietzel & Clarke, 2007). However, to adjust growth to simulate unknown variables that may not be accurately modeled in the calibration; multiple runs can be conducted with changes in the prediction values. A good historical example of an event that caused unforeseen changes in growth was the construction of the Bay 25

33 Bridge, which was a relatively small change to the overall road network in the immediate region, but had a profound effect on the growth of the region. Road gravity prediction values can be adjusted to try to model that change. The model output for the prediction phase is a series of GIF image files showing overall growth and yearly growth, as well as GIF files showing the growth types colorized by the four variables of growth for each year in the prediction. To display the results in ArcGIS, I had to georectify the GIF files by registering them to the original outputs. In order to quantify the growth spatially in the region and display it in a map graphic, I decided to use the 2010 Census tracts for the region. To do this I developed three models in ESRI s model builder, automating several of the geo processes required to create a choropleth map of census districts colorized by percent growth by parameter type in each census tract. To account for periods of growth that are not linear, the model has what is termed boom or bust coefficients (Project Gigalopolis Website, 2011). To simulate an era of rapid urban growth, growth has to be greater than a critical number set in the scenario file. If growth reaches this number, diffusion, spread, and breed are all multiplied by a constant greater than zero. Similarly, if the growth rate is less than a critical value, then diffusion, spread and breed are all multiplied by a constant less than zero (Project Gigalopolis Website, 2011). 26

34 3.2 Data There are several required datasets that must be loaded into SLEUTH for analysis in simulating urban growth (Silva & Clarke,, 2002). There has to be at least four time points for urban extent. The data used for urban extent as well as land cover in my model is derived from the Chesapeake Bay Watershed Land Cover Data Series (CBLCD). Development of the CBLCD was funded by the US Geological Survey (USGS), and collected using LANDSAT 7 Thematic Mapper (TM) imagery, available at the USGS ftp site. This data is processed and rasterized to display land classification based on Anderson s Land Classification System II (Phillips, 2007). Anderson s Land Classification System II was developed at the USGS in 1976 in order to facilitate the use of remotely sensed data in a GIS (Anderson, et al., 1976). The total schema consists of nine classifications, which break down into thirty six additional classes in the level II schema (Anderson, et al., 1976). Figure 2 illustrates the Land Use/Land Cover map for 1984 derived from the Chesapeake Bay Watershed Landcover Data Series for the study area. Figure 3: 2006 CBWLD of the western shore of the Chesapeake Bay also illustrates the Land Use/Land Cover map for 2006 derived from the CBWLD Series for the study area. The CBWLD was reclassified to accommodate SLEUTH land cover classification schema (USGS, 2011). 27

35 Maps were created using vector datasets and converted to raster format for input into SLEUTH urban growth model. Region Western Shore of the Chesapeake Bay. Coordinate system: US State Plane FIPS 19 (FEET) Figure 2: 1984 CBWLD of the western shore of the Chesapeake Bay 28

36 Maps were created using vector datasets and converted to raster format for input into SLEUTH urban growth model. Region Western Shore of the Chesapeake Bay. Coordinate system: US State Plane FIPS 19 (FEET) Figure 3: 2006 CBWLD of the western shore of the Chesapeake Bay 29

37 The USGS developed the CBLCD using the level II schema at thirty meter resolution and captured sixteen land cover classes. They developed GIS datasets for four timepoints: 1984, 1992, 2001 and This data is available online at USGS and can be viewed in ArcGIS with a colormap symbology. To use this data for urban extent, I reclassified the dataset, combining low intensity, medium intensity and high intensity urban records into one classification, then exported it to produce a monochrome GIF file for SLEUTH. Figure 4: Urban extent data derived from CBWLCD is the urban extent derived from the CBWLCD for four specific timepoints. Urban pixels were extracted for each year and converted to a binary GIF file for input into SLEUTH. 30

38 Maps were created using vector datasets and converted to raster format for input into SLEUTH urban growth model. Data is in binary format: white = 1, black =0. Region Western Shore of the Chesapeake Bay. Data Projection: US State Plane FIPS 19 (FEET) Scale: 1:389,771 Figure 4: Urban extent data derived from CBWLCD 31

39 SLEUTH requires an exclusion layer which consists of areas where the probability of development is zero (Silva & Clarke, 2002). This layer does not have to be from multiple timepoints as it is not a used for comparison, only for guiding the model to grow in areas where growth has the highest probability of occurring. However, variations on this layer can be inputted into different scenarios, causing increases or decreases in growth. This layer consists of permanent water bodies, rivers, city, county, state and federal parkland and land trust easements. For this dataset I used a hydrology dataset downloaded from the Chesapeake Bay Foundation website. This data is derived from a digital line graph (DLG) at a scale of 1:100,000. I combined this with several layers as land based exclusion layers. The first is a county easements layer that I downloaded from the Maryland Department of Natural Resources website. The easements layer was created in 2005 by the Maryland Agricultural Land Preservation Foundation (MALPF), a part of the Maryland Department of Agriculture (MALPF Districts shapefile metadata). MALPF has bought land sold by landowners that designated areas of their land for agriculture since This land is then owned by MALPF and kept free from development indefinitely as open space. This dataset was derived at a scale of 1:24000 (MALPF districts shapefile metadata). The next land polygon layer that I added as an exclusion layer is a Maryland DNR county owned properties shapefile, which was also downloaded from the Maryland DNR website. This layer primarily consists of county parks, open spaces and county owned maintenance facilities (county owned properties shapefile metadata). The year associated with this dataset is The final dataset that I used for the exclusion layer in SLEUTH is a federal lands layer that I 32

40 downloaded from the Maryland DNR website. This dataset contains polygons depicting federally owned lands in Anne Arundel and Calvert counties current as of 2010 (federal owned land shapefile). The derived scale of this dataset is unknown. However, a comparison of spatial registration to the orthorectified aerial photographs of the county showed good spatial correlation. I combined all of these datasets into one exclusion feature layer in ArcGIS. Then I converted the feature layer to a raster layer and reclassified the data into excluded and non excluded pixels. Figure 5 shows the combined results of the data from all of the sources. The left graphic shows lands excluded, including DNR lands, land easements and water. The right graphic shows the excluded areas without land easements. This data was used in prediction 2. 33

41 Maps were created using vector datasets and converted to raster format for input into SLEUTH urban growth model. Data is in binary format: white = 1, black =0. Region Western Shore of the Chesapeake Bay. Data Projection: US State Plane FIPS 19 (FEET) Scale: 1:389,771 Figure 5: Excluded areas used in SLEUTH calibration and prediction The SLEUTH model requires at least two transportation layers for analysis of spreading growth (Silva & Clarke, 2002). For this data type, I used a combination of sources to derive three road layers from multiple time periods. The first roads layer (roads_1949.shp) is derived from a scanned roadmap (1:7,000) created by The Maryland 34

42 State Roads Commission (Maryland State Roads Commission, 1948) and downloaded from the Maryland State Sheet Maps and State Map Series, Johns Hopkins Sheridan Library Digital Collection. Using ArcGIS, I georectified the map to an existing counties shapefile. I digitized the roads in four classes according to the map legend: major roads, secondary roads, unimproved and gravel. I converted the road features to a raster dataset, then exported them as a GIF file. The next roads layer is derived from TIGER Census data released in I used the feature class code (FCC) in the data to determine the road hierarchy, converted the feature data set to raster, and then reclassified the data into the same four classes as the roads layer from The third dataset for roads is also TIGER Census data from Similar to the 2006 dataset, the 2000 data was rasterized based on FCC code, then reclassified into four classes to match the other two datasets (see Figure 6). A percent slope layer is also required for the model. Slope is not a significant limiting factor in growth, but the amount of slope controls how quickly or slowly growth is going to occur. Slope also controls where growth will occur because people will only build where there is higher slope because they have to (Jantz & Goetz, 2005). This does not have to be from multiple time points due to the assumption that elevation will not change significantly in the given timeframe (Clarke & Hoppen, 1997). Slope allows SLEUTH to determine areas that will be excluded or significantly inhibited from growth. I downloaded the Maryland National Elevation Dataset from the United States Department of Agriculture (USDA) Geospatial Data Gateway website (datagateway.nrcs.usda.gov). The National Elevations Dataset comes in native raster 35

43 format in three different resolutions. For the areas of this study, one and three meter resolution datasets were available. SLEUTH requires percent slope; therefore I derived slope values as a percentage from the NED and exported them as a GIF file (Clarke & Gaydos, 1998). The final layer required for the model, primarily a visualization layer for the model output, is a hill shade layer derived from the NED layer. Figure 6 illustrates the slope for the study region by percent. Table 1 summarizes all of the data sources used for the SLEUTH model, the approximate scale, and source. 36

44 Figure 6: Road layers and slope 37

45 Table 1: Data types and sources used in SLEUTH Data Layer Source Resolution Description Year/s Exclusion layer Hydrology Maryland Hydrology data digital line graph (DLG) (Maryland DNR website, 2011) 1:100,000 DLG data imported into ArcMap. Polygon shapefile, consists of permanent water bodies, and rivers. NA County Easements Maryland Agricultural Land Preservation Foundation (MALPF) (MALPF website, 2011) 1:24,000 Polygon shapefile, Agricultural and owned by MALPF and designated as open space 1977 present County Owned Lands Maryland DNR County owned Properties (Maryland DNR website, 2011) Unknown Polygon shapefile, County facilities, parks, and open space 2006 Federally Owned Lands DNR reported federally owned lands. (Maryland DNR website, 2011) Unknown Polygon shapefile, Federally owned facilities, parks, and open space 2010 Urban Extent/Land Use Chesapeak e Bay Watershed Land Cover Data Series (CBLCD) (USGS Website, 2011) Raster datasets derived from LANDSAT 7 Thematic Mapper (TM) imagery. 16 land classifications based on Anderson s Land Classification System II 1984, 1992, 2001, 2006 Transportation Roads 1949 Scanned Maryland State Roads Commission (Maryland State Roads 1:7,000 Scanned roadmap, digitized roads layer into 4 classes: major roads, secondary, unimproved and gravel

46 TIGER Census Line files Commission, 1948) (US Census website, 2011) 1:24,000 Census DLG files converted to Line shapefiles. Categorized by FCC code into four classes: major, secondary, unimproved and gravel Slope/Hill Shade 2000, 2006 National Elevation Dataset US Department of Agriculture Geospatial Data Gateway Website. (US Department of Agriculture, 2011) 1, 3 meter DEM raster data for elevation data for the region. Derived percent slope and hill shade in ArcGIS using spatial analyst NA 3.3 Applying Course Calibration Methods Using Data for LWS I applied the methodologies for calibration of the model suggested in the research done by Silva and Clarke (2002) as well as the work done by Dietzal and Clarke (2006). The course calibration consisted of all of the datasets at one quarter their native resolution. I exported the datasets out of ArcGIS at a set cell size X = 540, Y=926. This produced GIF files that were the same extent which the model requires for proper registration of the cells between the GIF files (Clarke & Hoppen, 1997). To run the coarse calibration, I started with the suggested coefficient values from the Project Gigalopolis website. The first run took approximately nine hours and thirty one minutes. The calibration command in SLEUTH outputs several data files including GIF files of the simulated growth based on the given coefficient ranges. Two text files that are critical in assessment of the study area and developing coefficient values for the fine calibration 39

47 run, are the avg.log file and the control _stats.log files. The avg.log file provides average scores per year for thirteen variables that are measured by the model (Project Gigalopolis website). The control_stats.log file is an output of the least squares regression score ( 2 ) for each of the variables. The 2 is defined as the best estimate of the relationship between dependant and independent variables, or in this case, the actual data at the time points provided and the data being created by the model coefficients (McGrew, 2000). Table 2 lists the output data produced by SLEUTH during calibration that enables the best fit coefficients for growth in the study region. Variables in BOLD are part of the optimal SLEUTH metric (OSM) developed by Dietzal and Clarke (2007). Table 2: SLEUTH metric coefficients RUN: a run consists of a single set of coefficient values and is executed MONTE_CARLO_ITERATIONS number of times from start to stop year PRODUCT: all other scores multiplied together COMPARE: modeled population for final year / actual population for final year, or IF P modeled > P actual { 1 (modeled population for final year / actual population for final year)}. POP: least squares regression score for modeled urbanization compared to actual urbanization for the control years EDGES: least squares regression score for modeled urban edge count compared to actual urban edge count for the control years CLUSTERS: least squares regression score for modeled urban clustering compared to known urban clustering for the control years CLUSTER_SIZE: least squares regression score for modeled average urban cluster size compared to known average urban cluster size for the control years LEESALEE: a shape index, a measurement of spatial fit between the model's growth and the known urban extent for the control years SLOPE: least squares regression of average slope for modeled urbanized cells compared to average slope of known urban cells for the control years 40

48 %URBAN: least squares regression of percent of available pixels urbanized compared to the urbanized pixels for the control years XMEAN: least squares regression of average x_values for modeled urbanized cells compared to average x_values of known urban cells for the control years YMEAN: least squares regression of average y_values for modeled urbanized cells compared to average y_values of known urban cells for the control years RAD: least squares regression of average radius of the circle which encloses the urban pixels FMATCH: a proportion of goodness of fit across landuse classes. { #_modeled_lu correct / ( #_modeled_lu correct + #_modeled_lu wrong)} DIFF: run initializing dispersion_coefficient value BRD: run initializing breed_coefficient value SPRD: run initializing spread_coefficient value SLP: run initializing slope_coefficient value RG: run initializing road_gravity_coefficient value The second or fine calibration ran at twice the resolution of the coarse calibration: 1080 X This resolution provided more clarity in the road networks as well as the improved resolution of the image derived landclass data. The final calibration used data at its approximate native resolution. At this point the model run times actually decreased due to the narrow constraints on growth parameters, causing less runs; however the memory required to handle the datasets increased to 88 megabytes of swappable memory (memory that is free from use by any other programs or the operating system). I was unable to use GIF files of the layers at their true native resolution because of the memory constraints on my computer. At the full resolution, the swappable memory required to run the model was 270 megabytes. To overcome this constraint I used a resolution of 2018X2196. This is almost the full resolution of the rows, but only slightly better resolution for the raster columns than the data in the fine 41

49 calibration phase. Based on the resolution of the datasets themselves as well as the r2 values that were outputted, that the resolution was sufficient to calibrate and predict urban growth, however this highlighted some of the limitations of the model which I will address further in the discussion section. For the prediction phase, I ran three prediction scenarios all forecast to The first prediction used the coefficients derived through calibration, simulating continued growth at the current levels and with the current easements and land areas excluded. The second prediction used a less constrained exclusion layer with only DNR lands and water bodies excluded; this is similar to Jantz et al., (2004). 3.4 GIS I used ESRI s ArcGIS 10.0 to export the datasets into the required format. ArcGIS can only export data to a GIF file format if the raster is converted to unsigned 8 bit format. The data export function in the selection menu of the datasets allows the user to set the bit format, the image rows and columns. This was ideal for exporting the data in the SLEUTH required format. The approximate spatial resolution of the data is 30 meters. The data was exported at its approximate native resolution at a standard pixel size: 2160 rows by 4261 columns. Using GIS to reintegrate the data from the model to improve visualization of the results was critical in this project. To do this I used census data as a means of displaying the 42

50 aggregate growth based on the coefficient average values outputted for each run in the three predictions. Based on the literature, I believe this is a novel approach to combining census data and the model s output. In order to accomplish this, it was necessary to geo rectify the growth output GIFs in the model, convert raster data to vector data, parse out the growth types, then select them spatially by census tract. After summing the total area of each growth coefficient in its respective census tract, I then divided the summed area by the total area and multiplied by 100, giving the percent of growth in each area per census tract. After determining the proper workflow for this geo process, I was able to develop three models in ESRI s Model Builder program that automated it for multiple iterations. The first geoprocessing workflow in ESRI s Model Builder is a model that converts a raster output from SLEUTH into a vector dataset, and then parses the data out by growth type, converting the output to several shapefiles by growth type. The model also adds a field called census to the datasets and calculates the area in feet of each growth polygon. Figure 7 is an example of an analytic model that iterates through each record in the census tracts table. It then does a spatial query to select all growth polygons in each area then calculates the census tract name and populates the census field in the selected records. The third model I created is a geoprocessing workflow that creates a summary of the total area by census tract name then joins the summary table to the census tract shapefile. It then creates a copy of the shapefile with the joined summary records. Finally it creates a new field called perc_area, which it calculates using the formula: census_area/total_area *100. This 43

51 gives each census tract a percentage of area with new growth for each of the four growth coefficient. 44

52 Figure 7: Example of a geoprocessing Workflow Using ESRI s Model Builder 45

53 Chapter 4Results 4.1 Calibration The results of the final calibration were acceptable for comparison to the historical growth layers that were used in the model. For example an R2 value for the compare statistic of 95% means that the model was about 95% correct when compared at the historical timepoints. A value of 1 is an exact match. Table 3 and 3A list the R2 values for all of the measures of fit for the model calibration at the highest resolution from Table 3: R2 values for the critical measures of fit Run Product Compare Pop Edges Cluster Cluster Size 46

54 Table 4: R2 values for the critical measures of fit (continued) Run LeeSalee Slope %Urban Xmean Ymean Rad Fmatch The output from the calibration produced 100 records of values for each iteration of the model. I sorted the data to choose the highest regression values for each metric. I chose parameters that were used during these specific runs as the values for the predictions. Then, for each numbered run, I chose the associated growth coefficients for the next phase of calibration. Table 4 is the summary of the calibration coefficients chosen based on the coefficient log data returned by SLEUTH for each data resolution. The selected variables are part of the optimal SLEUTH metric (OSM) recommended by Dietzel and Clarke (2007). The variables are the results of sorting all of the variables in the control_stats.log file and selecting the top ten runs in order to apply those coefficients to the next data calibration. Table 5: Calibration results summary 47

55 Growth Parameter Dispersion Breed Spread Slope Road growth Coarse calibration Range Step Monte Carlo Iterations = 5 Total Number of Simulations = 3124 Compare Statistic = Population Statistic = Edges = Clusters = Slope = Xmean = Ymean = Fine Calibration Range Step Monte Carlo Iterations = 7 Total Number of Simulations = 3124 Compare Statistic = Population Statistic = Edges = Clusters = Slope = Xmean = Ymean = Final Calibration Range Step Monte Carlo Iterations = 10 Total Number of Simulations = 100 Compare Statistic = Population Statistic = Edges =

56 Clusters = Slope = Xmean = Ymean = 0.1 Final Calibration Results: Prediction Coefficient: Figures 8 and 9 are a comparison of the growth plotted for the control years to the US Census Bureau published data for growth during that period. The shape of the line is very similar. The actual population values do not match because the census used actual population, where the model estimates population based on number of urban pixels. Using this as a measure of the growth rate, however, proves that the model calibration has developed a realistic linear growth pattern based on the data provided. These results are also consistent with Jantz, et al., (2004) which discusses higher growth in the 80s and 90s with growth slowing in the 2000s. The growth coefficients that were selected based on the selection criteria showed high values for breed and road growth. This was expected based on the key factors of historical growth in the region; existing towns and the expanding road network. 49

57 Model Simulated Population Growth from Population Growth Figure 8: Model simulated population growth Population Growth Estimates Census Data ,000,000 5,000,000 4,000,000 3,000,000 2,000,000 1,000, Population Growth Estimates Census Data Figure 9: Population growth estimates from census data 50

58 4.2 Predictions Jantz et al., (2004) describes three scenarios for growth which are controlled by the level of protection in the excluded layer: (1) a current trends scenario, which is the current excluded layer, combined with the calibration coefficients of the model, (2) an unconstrained growth scenario, which allows for far less exclusion applied to the growth coefficients, and (3) an ecologically sustainable scenario which allows for more exclusion, simulating stringent land use policies and higher protections on undeveloped land. The model showed increased growth and provided some measure of how effective the current land easement policies work to control growth on the western shore. The third prediction changes the growth coefficients to create a boom period and show increased growth at a high level in an attempt to simulate a booming economy and a sudden change that promotes growth. Table 6 illustrates the prediction coefficients used for the scenarios. 51

59 Table 6: Prediction coefficients and boom/bust coefficients Scen 1 Scen 2 Scen 3 Prediction Diffusion Best Fit Prediction Breed Best Fit Prediction Spread Best Fit Prediction Slope Best Fit Prediction Road Best Fit Boom/Bust coefficients Critical Low Coefficient Critical High Coefficient Boom Multiplyer Coefficient Bust Multiplier Coefficient Prediction 1 Prediction one is based on continued growth at the current levels. This scenario used the coefficient values based on the calibration of the model, and variables for self modification based on best practices from the Project Gigalopolis Website (2011). This layer also utilized the full exclusion layer including the county easements data. Based on the model predictions, growth will continue to trend lower. This is due to the level of 52

60 growth in the model at year 2006, which met the bust threshold, therefore, causing a negative multiplier on the growth coefficients. In this scenario, growth continues to slow through This is appropriate due to the lack of new major roads that have been built on the western shore in the past decade. The model also attempts to simulate the lack of new spaces for growth particularly in the northern region of Anne Arundel County. However it may underestimate growth in more rural areas due to the dispersed nature of urban pixels (Silva & Clarke, 2002). Figure 10 shows a bar graph of growth coefficients used in model runs from The graph shows a decrease in growth coefficients and an increase in slope resistance Prediction 1: Growth Coefficients Diffusion Spread Breed Slope Road Gravity Figure 10: Prediction 1: Growth Coefficients Figure 11 is a map graphic showing the absolute growth , symbolized by US Census tracts. The four primary growth coefficients are displayed separately. This 53

61 prediction used the current land use constraints, the coefficients developed in the calibration and the best practices for growth variables in the model. 54

62 Maps were created using vector datasets and converted to raster format for input into SLEUTH urban growth model. Data is in binary format: white = 1, black =0. Region Western Shore of the Chesapeake Bay. Data Projection: US State Plane FIPS 19 (FEET) Scale: 1:389,771 Figure 11: Prediction 1 Growth Scenario 55