Forecasting enrollment in differential assessment ... - Semantic Scholar

Environment and Planning B: Planning and Design 2011, volume 38, pages 829 ^ 849

doi:10.1068/b37010

Forecasting enrollment in differential assessment programs using cellular automata Jeffrey A Onsted

Earth and Environment/Global Sociocultural Studies, Florida International University, ECS 332, 11200 SW 8th Street, Miami, FL 33199, USA; e-mail: [email protected]

Keith C Clarke

Department of Geography, UC Santa Barbara, EH 1720, 1832 Ellison Hall, Santa Barbara, CA 93106-4060, USA; e-mail: [email protected] Received 5 November 2010; in revised form 22 January 2011

Abstract. Urban growth models have been used for decades to forecast urban development in metropolitan areas. Since the 1990s cellular automata, with simple computational rules and an explicitly spatial architecture, have been heavily utilized in this endeavor. One such cellularautomata-based model, SLEUTH, has been successfully applied around the world to better understand and forecast not only urban growth but also other forms of land-use and land-cover change, but like other models must be fed important information about which particular lands in the modeled area are available for development. Some of these lands are in categories for the purpose of excluding urban growth that are difficult to quantify since their function is dictated by policy. One such category includes voluntary differential assessment programs, whereby farmers agree not to develop their lands in exchange for significant tax breaks. Since they are voluntary, today's excluded lands may be available for development at some point in the future. Mapping the shifting mosaic of parcels that are enrolled in such programs allows this information to be used in modeling and forecasting. In this study, we added information about California's Williamson Act into SLEUTH's excluded layer for Tulare County. Assumptions about the voluntary differential assessments were used to create a sophisticated excluded layer that was fed into SLEUTH's urban growth forecasting routine. The results demonstrate not only a successful execution of this method but also yielded high goodness-of-fit metrics for both the calibration of enrollment termination as well as the urban growth modeling itself.

1 Introduction The fact that much urban growth takes place on prime farmland is a critical doubleedged problem facing urban planning and land conservation in the next century. Effective planning to measure and forecast the expansion of urban lands into their surrounding agricultural hinterlands very much depends on computer simulation, informed by geographic information systems (GIS). Taking advantage of new data and tools, urban, land-use, and land-cover modeling has become increasingly sophisticated. Though modeling has not always been met with universal acclaim, even its detractors must admit that many of the strongest criticisms from past work (Lee, 1973; Mercer and Powell, 1972; Pickles, 1999; Tuan, 1971) have been solved with advances in technology or at least attenuated by development of theory both in the field of urban geography as well as in modeling itself (Batty, 1997; Benenson and Torrens, 2005; Harris, 1985; Tayman, 1996; Wegener, 1994). A common critique of simulation models is their poor link to policy. Consequently, ways of integrating policy into models in more meaningful ways, beyond simple scenario modeling, seem highly desirable if the process of farmland loss is to be managed for a sustainable future. This research tested a novel methodology for forecasting agriculturally preserved landscapes under threat from urban expansion. Using cellular automata, the method allows the modeler to derive a calibrated probabilistic future distribution of land available for development that can be extremely useful for conservation and planning.

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J A Onsted, K C Clarke

70

140

280 km

Figure 1. Tulare County, California (geographic coordinate system: GCS-North American-1983; source: ESRI, Inc.). WA enrollment beginsö either through legacy or choice of the current landowner. Tax breaks begin

Landowner decides to leave WA

Nonrenewal initiated. Tax rate slowly ramps up to nonexempt values. WA constraints still in place

Land is automatically renewed each year, along with tax breaks

Cancellation initiated. Large fee is paid and land is instantly freed from WA constraints

Nonrenewal completed after nine years. Tax breaks gone and WA constraints no longer in place

Figure 2. Williamson Act (WA) enrollment flowchart.

Public acquisition ö usually for purpose of a park or other natural public amenity

Local government decides to remove land from WA

Eminent domain ö often for nonnatural uses of land (eg roads, schools)

Forecasting enrollment in differential assessment programs

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If the available land is adjusted for the consequences of policy changes during modeling, then more-informed forecasting, and so better planning, seems possible. This approach is demonstrated in the context of voluntary differential assessment programs öin particular California's Williamson Act (WA) (California State Legislature, 1965)öand their impacts on urban growth and land-use change in Tulare County, California (figure 1). In the application we explore what differences result from the implementation of different policy strategies, from making the act perpetual rather than voluntary all the way to eliminating the WA altogether. The operational modeling question becomes: which lands currently off-limits to development, due to enrollment (see figure 2) in the native differential assessment program of that area, will be available for urban development in the future? The approach we advocate here offers a novel method for creating an excluded layer that solves this problem methodically and results in not only a probabilistic excluded layer for use in an urban growth model but also permits the modeling of a future regulatory landscape, hereafter referred to as a Gov-Scape (Veldkamp, 2009). This ability, by itself, will be of interest to planners and other government officials. 2 Material and methods 2.1 Program, study area, and data

Most of California's farmland is enrolled in a state-wide differential assessment program known popularly as the WA. In 2002, 59% of California's 11.3 million ha of total farmland were enrolled in the program (California Department of Conservation, 2003). The WA, whereby farmers agree not to develop their land and to keep it productive in return for lower property taxes, and the even more restrictive Farmland Security Zone program, not only offers financial incentives to farmers but, with the Open Space Subvention Act (1) (California State Legislature, 1972), partially compensates local governments for their lost tax revenue. To enroll, farmers in participating counties must join for a rolling ten-year period. They are automatically reenrolled every year until they choose to (a) nonrenew or (b) cancel. To nonrenew, farmers declare this and they are slowly ramped up to full property taxation over a nine-year phase-out period. To cancel, farmers must pay a large cancellation fee to exit the program. Some lands are also terminated by eminent domain or public acquisition, often for the creation of a public park or other open space. (Figure 2 is a flowchart that describes the enrollment process.) Tulare County, California, located in the state's agricultural Central Valley, was the study area used for this research. This county was chosen for several reasons. First, most of its private land is devoted to agriculture (90% in 2002) and most of this land (85% in 2002) was enrolled in the WA. Second, Tulare County collects comprehensive data reflecting current enrollment. Third, the Central Valley, including Tulare County, has become a new locus of population growth in California, drawing would-be homeowners priced out of the coastal market as well as newcomers from out-of-state (Teitz et al, 2005). This has put its farmland in great jeopardy, making it an excellent area to witness agricultural land-use change. At approximately 1 249 000 ha, the county is also rather large. The most productive and valuable farmland is in the west of the county, with ranching lands in the hills found in the center longitudinal strip, and National Forest land in the steep and forested eastern third of the county. Located in the flat and agricultural west of the county, two major and expanding cities are Visalia, the

(1) State budget cuts in California have resulted in subvention allocation dropping from $28 million to $1000, a reduction of 99.996%, effectively erasing the program.

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largest and the county seat, and nearby Tulare City. The study of Tulare County, therefore, covers a considerable range of different land uses and regulatory regimes. 2.2 Overview of the SLEUTH model

SLEUTH is a cellular automata model whose acronym signifies its necessary inputs, all of them grayscale raster map layers in graphics interchange format (GIF): slope (given as slope percentage cell), land use (for two time periods if the land-use-change module is engaged), excluded areas (one layer), urban extent (four historical layers), transportation (at least two historical layers), and hillshade (a noninteractive layer for display purposes only). SLEUTH uses five growth coefficients for model calibration and prediction: dispersion, breed, spread, slope, and road gravity. Each of these values, calibrated between 0 and 100, influence one or more of the four steps of growth: spontaneous, new spreading center, edge, and road-influenced growth (Clarke 2008a; 2008b). The coefficients of urban growth are derived through a `brute force' method of calibration, which requires several rounds of calibration using increasingly narrow ranges of values for each growth coefficient. For each combination of coefficients, a number of Monte Carlo (MC) iterations are designated by the user to reduce uncertainty caused by the stochastic nature of the simulation, with the maps of urban growth averaged. These map outputs are then compared with actual data maps and metrics of accuracy are then applied for the user to examine (see table A3 in the methodological appendix). For land-use change, a difference matrix is produced for each pixel corresponding to the two historical land use layers. These matrices, along with the degree of similarity of slope percentages, are used to enforce spatial autocorrelation and simulate the land use change. The degree of urban growth drives the corollary amount of landuse change, with past land-use transitions and slope determining the type of land-use change (Clarke, 2008a; 2008b). The model is open source, coded in the C programming language, and is supported by both websites (http://www.ncgia.ucsb.edu/projects/gig/ index.htm) and discussion fora (Clarke et al, 2007). 2.3 SLEUTH's excluded layer

Though SLEUTH is not a panacea, in the last thirteen years, the model (Clarke et al, 1997) has been applied in numerous metropolitan areas around the world on almost every continent (Clarke, 2007). By (a) allowing the user to choose the metrics (table A3) for goodness of fit, (b) using MC simulation and averaging the results, and (c) using a brute force method of calibration, SLEUTH provides a highly defensible approximation of the land-use dynamics for a given area. It also provides great flexibility for the user by allowing many different land-use classes to be defined and modeled within the program as well as having the ability to include probabilities of land being excluded from urban spread. Earlier incarnations of SLEUTH allowed only a binary classification of excluded areas: totally excluded from development or totally open for development. More recent versions, however, permit resistance probabilities ranging from 0% to 100% where 0% represents no resistance to development and 100% or higher represents complete resistance to development. This allows for a nuanced excluded layer since many areas of a modeled environment are known to offer resistance to development, yet could still feasibly become developed. Natural examples include wetlands or flood-prone areas, steep slopes (which in SLEUTH are addressed separately from excluded areas), fire-hazard areas, landslide-prone areas, areas near eroding sea cliffs, or sites in other harsh or environmentally unfriendly conditions. Regulatory examples include areas not currently zoned for development or other parcels under nonpermanent protection or temporary exclusion from development.


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Differential assessment programs are a common example of such measures and exist throughout the United States. Though studied for decades by agricultural economists and policy analysts (Blewitt and Lane, 1988; Brand, 1995; Daniels and Bowers, 1997; Dean, 1975; Dresslar, 1979; Lynch and Carpenter, 2003; Parks and Quimio, 1996; Sokolow, 1990), they present a conundrum for urban modelers. First, these lands, which in some states comprise a very high percentage of agricultural land, are at present off-limits to development. However, since these programs are often voluntary, the landowner can choose to opt out of them, opening up their lands for urbanization. The two most obvious approaches to this problem, and the ones most widely employed, are to: (1) ignore these lands and assume they enjoy no protection whatsoever; or (2) assign them full exclusion. However, a third possibility is to assign them a userdefined resistance to development (Teitz et al, 2005), which, though often subjective, comes closer to expressing the reality of their tenuously protected nature. Though arbitrarily assigning this resistance, of course, involves no rigor or scientific analysis, we have designed a method that utilizes SLEUTH to derive these values, pixel by pixel, for the modeler. To accomplish this, a few modifications to a typical SLEUTH approach are in order. 2.4 Our alternative use of SLEUTH

The specific algorithms used to prosecute the growth and land-use change within SLEUTH's architecture have remained untouched. However, as we will demonstrate, the landscape upon which this growth and change is drawn has been replaced. This redirection of the model's purpose, besides requiring some specific attention during the scenario file creation (described in table A1), necessitates some substitutions for the input layers (see figures 3 and 4). Also, most importantly, we have utilized one of SLEUTH's output images as a new input layer for a different simulation and this use, we believe, has not been explored before. SLEUTH's execution is controlled by modifying a simple text file termed the `scenario file.' Some of the urban growth simulation modeling layers prescribed on the roman Initial conditions

Generate growth cycles

Conclude simulation

input typical images are replaced with: Slope Land cover a set of coefficient values

seed

No substitution WA Gov-Scape [6 classes, figures 10(a) and 10(b)]

Excluded Urban

Transportation Hillshade

Lands in the WA/not in the WA (figure 5) Former WA and urban (figure 6) No subsitution Excluded layer used in SAWA scenario (figure 7)

Figure 3. SLEUTH input layer substitutions for simulating Williamson Act (WA) termination and enrollment (revised from National Center for Geographic Information and Analysis website: http://www.ncgia.ucsb.edu/projects/gig/About/bkStrSimulation.htm).

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Generate simulations

Conclude simulations

Input images

S1 MC1

Slope

WA Gov-Scape S2 MC2 Lands in the WA/ not in the WA (figure 5)

Output named cumcolor urban should be found in OUTPUT DIR=. . /Output/ wa/. This image must then be copied to the INPUT DIR=. . /Input/ urb/ Once there it should be renamed .excluded. This probabilistic image is now ready to be used for urban growth simulation

Former WA and urban (figure 6)

Transportation Excluded layer used in SAWA scenario (figure 7)

Sn MCn where MCn 4 100 and where MCn 1 number of possible probability classes (PPC). PPC number of probability colors permitted in scenario file, Section XII (colortable settings), Part 3 (probability colortable for urban growth). Scenario file must be written with guidance from table A1.

Figure 4. From former Williamson Act (WA) simulation to creation of probabilistic excluded layer for urban growth simulation (revised from National Center for Geographic Information and Analysis website: http://www.ncgia.ucsb.edu/projects/gig/About/bkStrPrediction.htm).

numeral-labeled sections of this scenario fileöas documented on the SLEUTH website (http://www.ncgia.ucsb.edu/projects/gig/About/dtInput.htm)öcan remain, while others must be substituted. It is also important to understand the loose coupling necessary to fully exploit the advantages of this approach. First, as depicted in figure 3, the following input layers must be substituted with analogous WA layers: land use with WA Gov-Scape (Veldkamp, 2009); excluded from urban growth with excluded from WA termination; urban with the combined former WA (FWA) lands and urban; and hillshade with the excluded layer from the strict adherence to the WA (SAWA) scenario. This layer and the scenarios will be explained later. Slope and transportation layers need not be substituted. Certain aspects of the scenario file, as delineated in the methodological appendix (table A1), must also be specifically addressed in order to apply this method effectively. 2.5 WA termination simulation

By simultaneously examining the growth of development and the spread of FWA parcels on the assembled GIS maps, the spread of FWA parcels appeared to respond to the same stimuli that would encourage urban growth. In particular, proximity to urban areas and transportation corridors appeared to have strong correspondence with the decision to leave the WA. Therefore, it was decided to use SLEUTH's built-in calibration (table A3) to quantify what was being observed. Though it is debatable exactly what constitutes a reasonable degree of fit for SLEUTH (Clarke et al, 1997;


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Herold et al, 2003; 2005; Jantz and Goetz, 2005; Wu et al, 2009), scores comparable with other published urban growth applications (Mahiny and Gholamalifard, 2007; Silva and Clarke, 2002; Teitz et al, 2005) of SLEUTH were considered a reasonable barometer to justify the forecasting of FWA lands. SLEUTH's land-use-change module was also utilized to experiment with WA enrollment growth. The different land-use classes express two different dimensions: type of farmland (prime farmland, nonprime farmland, FWA/urban, or òther' land (2) öusually protected areas) as well as WA status (WA or nonWA land). This gives a total of six different land-use classes: Prime WA, NonPrime WA, Prime nonWA, Nonprime nonWA, FWA/urban, and òther' land. As the results will show, FWA growth was high but so also was the addition of new WA lands. A very different excluded layer was used for modeling FWA growth. Only existing WA lands are available for termination, leaving all other lands (including existing urban lands) as excluded from possible FWA growth. This acts as a `complementary excluded layer' since most lands off-limits for FWA growth are the very lands available for urban growth and vice versa. All of those WA lands unavailable for development in the urban growth simulation are, in this case, the only lands available for FWA growth. The metrics selected and their scores are discussed in section 3. The transportation and slope layers were the same for both the FWA growth modeling and the urban growth modeling. Since SLEUTH offers a suite of goodness-of-fit metrics (table A3), each researcher must determine which metrics to weight and evaluate before proceeding to the next round of calibration. In this research, a metric called the optimal SLEUTH metric (OSM, see table A3) (Dietzel, 2004) that uses a product of seven of the built-in metrics, was chosen. The resulting scores of this metric for each round are shown in table A2. 2.6 Urban growth simulation using FWA results

The application of SLEUTH's urban growth and land-use-change simulation modules in Tulare County is not, in itself, a novel use. However, the use of a probabilistic excluded layer based on a complementary run to forecast WA behavior, to our knowledge, is new. For contrast, three different WA-based scenarios were created using three different excluded layers for Tulare County's projected urban growth and land use change. These three scenarios were named: (1) SAWA, which freezes 2002 enrollment and allows no additional enrollment or termination; (2) abolition of the WA (AWA), which removes all WA protections, leaving all agricultural land available for development; and (3) business as usual (BAU), which relies on the use of the FWA growth modeling. For urban growth calibration purposes, the excluded layer that included the 2002 WA lands was used, along with other appropriately disqualified lands, such as parks and National Forests. Just as in the FWA growth modeling, the OSM was chosen for calibration evaluation between rounds (tables A2 and A3). Of SLEUTH's six input layersöslope, land use, excluded, urban, transportation, and hillshade öonly five are actually interactive because hillshade is essentially an inert layer. The hillshade layer is included to form a user-controlled background for the urban growth forecasts. This is helpful because it is descriptive of those places that (2) Òther

land' is defined by the California Department of Conservation as: ``Land not included in any other mapping category. Common examples include low density rural developments; brush, timber, wetland, and riparian areas not suitable for livestock grazing; confined livestock, poultry or aquaculture facilities; strip mines, borrow pits; and water bodies smaller than forty acres. Vacant and nonagricultural land surrounded on all sides by urban development and greater than 40 acres is mapped as Other Land.''

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are too steep for development. Since SLEUTH also uses MC simulation, any number of iterations can take place, with the number of successful urbanizations normally overlaying the pixels in the hillshade layer. Usually, the output of this simulation would be different colored cells reflecting the number of times they were selected for development. Though the colors used for input into SLEUTH must always be in the form of grayscale GIF format digital images, the outputs from urban growth runs are allowed to be any number of colors. By removing the hillshade layer and replacing it with the excluded layer used in the SAWA scenario from the urban growth modeling, the stage is set for the creation of the BAU urban growth excluded layer. We note that SLEUTH's naming conventions demand this layer still be called hillshade, even though it is representing something else in this case. The resulting overwritten image is then the new excluded layer to be used for the BAU scenario in urban-growth modeling. 3 Results 3.1 WA-forecasting results

The described methodology resulted in three different urban growth and land use change scenarios as well as one FWA growth and WA change scenario. Figure 5 displays the excluded layer for the FWA growth forecasting, with model runs out to the year 2030. Since only those parcels that were enrolled in the WA in 2002 can actually terminate their contracts, all nonWA lands are excluded from FWA growth. In these images, cells with grayscale values of 100 or greater are excluded and those with a value of 0 (black), representing 2002 WA lands, offer no resistance to FWA growth. Figure 6 illustrates the 2002 ùrban' input image for the FWA growth. The word ùrban' is used to emphasize the necessity of obeying the naming conventions required to run SLEUTH, even though, in actuality, the gray in this image represents both urban and FWA land in the year 2002. The value 0, appearing black, indicates nonurban land. The SAWA urban growth excluded layer is shown in figure 7. The black (0 in the grayscale) are those lands not currently in the WA (in 2002). The two other shades of gray both prohibit development in this scenario but are presented as different colors in order to differentiate WA lands from National Forest lands and parklands.

Figure 5. Excluded layer used for former Williamson Act (WA) growth. Gray pixels are nonWA lands and are excluded; black are lands in the WA; white are water.


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Figure 6. Urban/former Williamson Act (WA) layer for former WA (FWA) growth. Gray pixels are urban and FWA lands; black are lands that are neither urban nor FWA lands.

Figure 7. Excluded layer used for strict adherence to the Williamson Act (WA) (SAWA) scenario. Dark gray pixels are public lands; light gray are WA lands (both are excluded); black are lands already developed or available for development; white are water.

The AWA scenario uses the excluded layers shown in figure 8. This scenario simply ignores the WA by assigning such cells an operational grayscale value of 0 (black), leaving only parks and other perpetually protected lands as off-limits to development. The final scenario, BAU, uses the excluded layer predicated upon the FWA growth runs, and is shown in figure 9. Figure 10(a) depicts the Visalia Metropolitan area's WA status in 2003 while figure 10(b) shows one MC simulation. A total of one hundred MC simulations were run and the probabilities were output in grayscale on top of the urban excluded layer corresponding to SAWA (ie, all lands in the WA as well as all public and parklands are shown as off-limits). This is displayed in figure 9. As seen in figures 10(a) and 10(b),

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Figure 8. Excluded layer used for abolition of the Williamson Act (AWA) scenario. Gray pixels are public lands and other protected areas off-limits to development; black are those lands open to development; white are water.

Figure 9. Excluded layer for business-as-usual scenario. This was created from the 100 Monte Carlo iterations of the former Williamson Act (WA) growth simulation that overwrote the strict adherence to the WA excluded layer (figure 6). White pixels are areas completely off-limits; solid gray are WA lands; fuzzy gray are land with probability between 0 and 100 of being open to development. The darker the gray the greater the availability of the land. The very light gray in the east of the county is National Forest land and is totally off limits to development.

many lands under WA contract in 2002, but near urban areas, terminated in nearly all of the 100 MC simulations in figure 8. There is a distance-decay effect, therefore, moving away from the roads and urban areas, seen as fuzziness between the black and the more solid outlying gray areas. Figure 10(b) presents only one possible future for the WA, based on a single MC iteration. Though there are significant land areas added to the WA program, shown by lighter shades of gray turning to darker shades of gray (but not black), thousands of


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(b) Former WA and urban

Nonprime WA

Nonprime nonWA

Prime WA

Prime nonWA

Other land

Figure 10. Visalia Metropolitan Area Williamson Act (WA) status in (a) 2003; (b) in 2030 after one Monte Carlo simulation.

hectares were also terminated, as evidenced by the growth of black pixels. This increase is primarily found close to urban and FWA areas as well as along roads. There was also a dynamic interplay of nonprime farmland both leaving and entering the WA in this forecast but FWA and urban land more than triples between 2002 and 2030. There is no certain method for disaggregating the forecast FWA land from urban growth in the FWA forecast. However, by assuming that the amount of urban land at the start of the modeling cycle can be subtracted from the FWA and forecast urban growth gathered from the BAU scenario, the amount of FWA land alone can be deduced as growing from approximately 1.8% of Tulare County's land to nearly 10%, more than a five-fold increase. This approach is inexact as these two modeling processes were run separately, but it is a convenient way of differentiating between the conflated FWA and urban land. It is also important to note that over the twenty-eightyear time-period the simulated amount of farmland that is neither in the WA nor was ever in the WA is continually shrinking. Over half of the unprotected nonprime farmland in 2002 joined the WA while over half of the unprotected prime farmland joined as well (see figures 11 and 12). Overwhelmingly, it is prime farmland, as opposed to nonprime, that is expected to terminate enrollment. Although 1.1% of all of Tulare County's land in 2030 is newly contracted prime WA farmland, the amount leaving the WA far exceeds this value. The total amount of protected prime farmland drops by nearly a third. That is only the net loss, however, since 1.1% of new lands were added during this process. The gross loss equals 7.5% of all Tulare County's land. Only one fourth of the total lands leaving the WA are nonprime, with a very small fraction being òther' land (see figures 11 and 12).

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NonWa nonprime 4.5% FWA and Urban 4.0%

NonWA prime 2.0%

WA nonprime 17.9% Other land 52.3%

WA prime 18.9%

Water 0.1%

Farmland security zones 0.2%

Figure 11. Tulare's Williamson Act (WA) status in 2002. FWA former WA. FWA and Urban 14.4%

NonWa nonprime 2.0% NonWA prime 0.9%

Other land 52.2%

WA nonprime 17.8%

Water 0.1%

Farmland security zones 0.1%

WA prime 12.4%

Figure 12. Tulare's Williamson Act (WA) status in 2030. FWA former WA. 3.2 Urban growth forecasting results

As useful as modeling WA change may be, it still does not necessarily describe physical changes on the ground. However, it does create a Gov-Scape that can affect land cover, which will now be discussed. The final MC run for the years 2003 and 2030 for each of these scenarios and geographic areas are displayed in figures 13(a) ^ (d). Tulare County quite clearly has increased growth by 2030, particularly in the BAU and AWA scenarios, while SAWA, not surprisingly, shows the least amount of difference from 2002 (see figure 14). Development along major roads is another striking


(a)

(b)

(c)

(d) Urban

Nonprime farmland

Prime farmland

Other land

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Figure 13. Tulare (a) in 2003; (b) the business-as-usual scenario in 2030; (c) the strict adherence to the Williamson Act (WA) scenario in 2030; (d) the abolition of the WA scenario in 2030.

feature of these output images. Together, the moderately high road-gravity coefficient (57), the breed coefficient (96), and the dispersion value (99) have a multiplicative effect on development along the roads. The high dispersion coefficient also explains the large number of clusters to be found during the spontaneous growth phase (see methodological appendix, table A2). This becomes less apparent with greater WA retention since dispersed development is not possible with all of those lands excluded.

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SAWA

30 000

BAU AWA

25 000 20 000 15 000 10 000 5 000 0

Prime farmland 2 643

Nonprime farmland 4 223

Other land

BAU

10 383

13 777

4 613

AWA

16 380

25 085

3 500

SAWA

512

Figure 14. Urbanized hectares in Tulare County by type and by scenario in 2030. SAWA strict adherence to the Williamson Act; BAU business as usual; AWA abolition of the Williamson Act.

An examination of figure 14 allows a comparison of the three different scenarios for Tulare County. Across scenarios, forecast urbanization ranges from 2.8% urbanized land for the SAWA scenario to 5.8% for the AWA scenario. BAU is closer to AWA in agricultural conversion, with 4.5% urbanized land, than it is under the SAWA conditions. In BAU, nonprime farmland is slightly more favored as it comprises 47% of the lost land area, with prime farmland making up 37%, and òther' land equaling 15%. In each scenario, nonprime farmland is the land-use class that loses the greatest amount of land to urbanization. However, the percentage lost is different for each scenario. In the SAWA scenario the breakdown for prime, nonprime, and other land is 36%, 57%, and 7%, respectively. For BAU these figures are 36%, 48%, and 16%, respectively. For the AWA scenario the results are 36%, 56%, and 8%, respectively. Though in actual hectares nonprime farmland faces the greatest conversion, the highest percentage of land lost within each land category in each scenario is consistently prime farmland. It would also appear that the proportion of available prime farmland, given the different excluded layers as well as slope conditions, remains approximately equal across the different scenarios. There is greater variability, on the other hand, between nonprime farmland and òther' land across the scenarios. The SAWA scenario does not allow for much of its conversion because many hectares of the òther' land that are not public are actually enrolled in the WA and relatively distant from urban areas. The low rate of urbanization, therefore, both in absolute hectares and percentages should not be surprising. Also, SLEUTH's self-modification parameters cause urban growth to follow a sigmoidal curve. Consequently, as available land disappears growth also abates, gradually approaching full build-out. Concerning the conversion of òther' land, the difference between BAU and AWA was unexpected since BAU actually has more òther' land converted than AWA. However, this may be due to a reduction in the amount of farmland available for development in the BAU scenario, causing more pressure to be brought upon òther' land. The results demonstrate that the effect of the WA on urban growth, whether it is completely removed or softened over time by gradual contract termination, is significant.


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4 Discussion and conclusion 4.1 Contribution of novel method

Since it was determined that the same geographical phenomena that apply pressure on lands to develop also apply pressure on lands to leave the WA, an urban growth model such as SLEUTH is well suited to forecast the future landscape of farmers' choices with respect to the WA. The attempt has also yielded several improvements to the model. First, with the addition of the complementary modeling cycle, SLEUTH is endowed with greater spatial complexity. Although SLEUTH currently has the capacity to have `weighted resistance' to development this still must be programmed in by the user and is difficult to arbitrarily quantify from general policy knowledge (Dietzel and Clarke, 2004). Our approach reduces this capriciousness by employing SLEUTH to build this layer. Second, the addition of human decision making to SLEUTH is the greatest improvement offered in this research. During the FWA growth modeling, cells reflect the individual decisions of landowners to leave the WA, which need no approval from government agencies. These agents simulate human decision making by acting in their own interests to leave the WA, often in the hopes of converting their land for immediate profit. This lays the groundwork for not only forecasting future differential assessment landscapes but also a method for using these outputs to construct probabilistic excluded layers for use in traditional urban growth models. Though the results may vary depending on specific regulatory conditions, we believe that the approach offered in this research and the difference between scenarios has relevance for not only any county in California that is party to the WA, but also any area in the nation employing differential assessment programs. There could also be changes made to the WA excluded layer in order to secure forecasts that correspond to different policy options. For instance, if only certain WA parcels (such as those of a certain area threshold) were allowed to terminate their contracts then a different excluded layer could be used for WA-termination forecasting. Though this was not explored in this study, it is an area ripe for future research. Several important lessons were learned, and new questions provoked, throughout the course of this research that warrant further investigation. First, there is a parcelto-pixel problem embedded within parcel-based cellular automata land-use-change modeling. Unlike urbanization, which can and does occur one building at a time, WA parcels, which can be quite large, are either in or out of the WA and these occurrences can happen instantly. Once released from the confines of the WA, however, the large parcel may cover many cells, some of which may urbanize quickly, while others may not. Though the model is calibrated with data that reflect these changes, future forecasts of a WA landscape are less blocky and more refined than a true future cadastral landscape would be [see figures 10(a) and 10(b) for comparison]. Therefore, future attempts may benefit from coarser resolution for the FWA forecasting than for the actual urban growth modeling. Second, there is a temporal dissonance that exists in the administration of the WA that can more justifiably be ignored in urban growth modeling. This issue relates to the WA's nonrenewal condition of termination requiring a nine-year phase-out period. Also, since there are other methods of removal that are more or less instantaneous (eg, cancellation, eminent domain, public acquisition) it is challenging to conflate these two temporally different methods of WA termination in the same modeling environment (see figure 1). Perhaps experimenting with modeling nonrenewal separately from the instant forms of removal could result in greater accuracy since many remote WA parcels are purchased for the purposes of park creation or other

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nonurban amenities, and therefore serve to confound the rationale for using SLEUTH's geographical phenomena (eg, urban proximity, roads) as criteria for WA removal. It should also be noted that since every state's differential assessment programs vary to one degree or another, this specific problem is not necessarily an affliction with which applications in other states must contend. On the other hand, it is likely that the unique regulatory conditions of each state's differential assessment programs may prove challenging for different reasons. 4.2 Future research

The employment of cellular automata to forecast a regulatory landscape that controls which lands may or may not be developed is, to our knowledge, novel. This could, however, be only the beginning of a new line of inquiry and use for cellular automata models. Simulating urban growth alone is asymmetrical since, in every metropolitan area there is competition over land between environmentalists and developers, in a race to develop or protect before the other side secures the fate of the land. By scientifically identifying, if at all possible, those factors relevant for the forecasting of newly protected land we may widen the scope of modeling priorities. In the case of the WA, this forecasting was made more tractable due to the great similarity between factors influencing both WA removal and urban growth. Nevertheless, a new cellular automata approach that addresses this competition between protection and development would allow for a more refined look at the future. A modeling environment that allows these two phenomena to influence each other at each time step would be better still, whether they be coupled models or housed in the same program. Much has been written concerning the schism between those who design geospatial tools and their target users, in this case planners and policy makers. Planning support systems have emerged to bridge this gap (Batty, 2003; Couclelis, 1991; Harris and Batty, 1993; and many others). We hope that the methodology described in this paper can act as a pillar within that bridge. Acknowledgements. This research includes collaboration with the Florida Coastal Everglades Longterm Ecological Research program under National Science Foundation Grant No. DEB-9910514. References Batty M, 1997, ``Cellular automata and urban form: a primer'' Journal of the American Planning Association 63 264 ^ 274 Batty M, 2003, ``Planning support systems: technologies that are driving planning'', in Planning Support Systems in Practice Eds S Geertman, J Stillwell (Springer, Berlin) pp v ^ viii Benenson I, Torrens P, 2005 Geosimulation (John Wiley, Chichester, Sussex) Blewett R A, Lane J I, 1988, ``Development rights and the differential assessment of agricultural land: fractional valuation of farmland is ineffective for preserving open space and subsidizes speculation'' American Journal of Economics and Sociology 47 195 ^ 205 Brand P S, 1995, ``Putting agricultural values into dollars and cents'' California Coast and Ocean 11(3) 14 ^ 16 California Department of Conservation, 2003 The California Land Conservation Act: Status Report 2002 (California Resources Agency, Sacramento, CA) California State Legislature, 1965 California Land Conservation Act Government Code Section 51220; http://www.leginfo.ca.gov/cgi-bin/displayecode?section=gov&group=5100152000&File=51200-51207 California State Legislature, 1972 California Open Space Subvention Act Government Code Section 16140 ^ 16154; http://www.consrv.ca.gov/dlrp/lca/ossa/Pages/index.aspx Clarke K C, 2008a, `À decade of cellular urban modeling with SLEUTH: unresolved issues and problems'', in Planning Support Systems for Cities and Regions Ed. R K Brail (Lincoln Institute of Land Policy, Cambridge, MA) pp 47 ^ 60


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Clarke K C, 2008b, ``Mapping and modelling land use change: an application of the SLEUTH model'', in Landscape Analysis and Visualisation: Spatial Models for Natural Resource Management and Planning Eds C Pettit, W Cartwright, I Bishop, K Lowell, D Pullar, D Duncan (Springer, Berlin) pp 353 ^ 366 Clarke K C, Hoppen S, Gaydos L, 1997, `À self-modifying cellular automaton model of historical urbanization in the San Francisco Bay area'' Environment and Planning B: Planning and Design 24 247 ^ 261 Clarke K C, Gazulis N, Dietzel C K, Goldstein N C, 2007, `À decade of SLEUTHing: lessons learned from applications of a cellular automaton land use change model'', in Classics from IJGIS. Twenty Years of the International Journal of Geographical Information Systems and Science Ed. P Fisher (Taylor and Francis, Boca Raton, FL) pp 413 ^ 425 Couclelis H, 1991, ``Geographically informed planning: requirements for planning-relevant GIS'' Papers in Regional Science 70 9 ^ 19 Daniels T, Bowers D, 1997 Holding our Ground: Protecting Americas Forms and Farmland (Island Press, Washington, DC) Dean J B, 1975, `À panacea that wasn't'' Cry California Summer 18 ^ 23 Dietzel C K, 2004, ``Spatio-temporal difference in model outputs and parameter space as determined by calibration extent'' in Geodynamic Eds P Atkinson, G Foody, S Darby, F Wu (CRC Press, Boca Raton, FL) pp 251 ^ 271 Dietzel C, Clarke K C, 2004, ``Determination of optimal calibration metrics through the use of self-organizing maps? '', paper presented at ``The future of land use'', 30 October meeting, available from Institute for Environmental Studies, Amsterdam Dresslar J, 1979, `Àgricultural land preservation in California: a time for a new view'' Ecology Law Quarterly 8 303 Harris B, 1985, `Ùrban simulation models in regional science'' Journal of Regional Science 25 545 ^ 567 Harris B, Batty M, 1993, ``Locational models, geographical information and planning support systems'' Journal of Planning Education and Research 12 184 ^ 198 Herold M, Goldstein N C, Clarke K C, 2003, ``The spatio-temporal form of urban growth: measurement, analysis and modeling? '' Remote Sensing of Environment 86 286 ^ 302 Herold M, Couclelis H, Clarke K C, 2005, ``The role of spatial metrics in the analysis and modeling of urban land use change'' Computers, Environment and Urban System 29 369 ^ 399 Jantz C A, Goetz S J, 2005, `Ànalysis of scale dependencies in an urban land use change model? '' International Journal of Geographical Information Science 19 217 ^ 241 Lee D B Jr, 1973, ``Requiem for large-scale models'' Journal of the American Institute of Planners 39 163 ^ 178 Lynch L, Carpenter J E, 2003, `Ìs there evidence of a critical mass in the mid-Atlantic agricultural sector between 1949 and 1997? '' Agricultural and Resource Economic Review 32 116 ^ 128 Mahiny A S, Gholamalifard M, 2007, ``Dynamic spatial modeling of urban growth through cellular automata in a GIS environment'' International Journal of Environmental Research 1 272 ^ 279 Mercer D C, Powell J M, 1972 Phenomenology and Related Non-positivistic Viewpoints in the Social Sciences Monash Publications in Geography, Clayton, VIC Parks P J, Quimio W R H, 1996, ``Preserving agricultural land with farmland assessment: New Jersey as a case study'' Agricultural and Resource Economics Review 25 22 ^ 27 Pickles J, 1999, `Àrguments, debates, and dialogues: the GIS ^ social theory debate and the concern for alternatives'', in Geographical Information Systems: Principles, Techniques, Applications, and Management 2nd edition, Eds P A Longley, M F Goodchild, D J MacGuire, D W Rhind (John Wiley, New York) pp 49 ^ 60 Silva E A, Clarke K C, 2002, ``Calibration of the SLEUTH urban growth model for Lisbon and Porto, Portugal'' Computers, Environment and Urban Systems 26 525 ^ 552 Sokolow A D, 1990 The Williamson Act: 25 Years of Land Conservation The Resources Agency of California, Sacramento, CA Tayman J, 1996, ``The accuracy of small-area population forecasts based on a spatial interaction land-use modeling system'' Journal of the American Planning Association 62 85 ^ 98 Teitz M, Dietzel C, Fulton B, 2005 Urban Development Futures in the San Joaquin Valley (Public Policy Institute of California, San Francisco, CA) Tuan, Y F, 1971, ``Geography, phenomenology, and the study of human nature'' The Canadian Geographer 15 181 ^ 192 Veldkamp A, 2009, `Ìnvestigating land dynamics: future research perspectives'' Journal of Land Use Science 4(1/2) 5 ^ 14

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Wegener M, 1994, `Òperational urban models: state of the art'' Journal of the American Institute of Planners 60 17 ^ 30 Wu X, Hu Y, He H, Bu R, Onsted J, Xi F, 2009, `Ùsing multiple methods to evaluate the performance of SLEUTH in the Shenyang metropolitan area'' Environmental Modeling and Assessment 14 221 ^ 230

Appendix SLEUTH methodological appendix (3) To fully realize this method, first MC iterations should ideally be maximized to 100 in section VIII (see table A1) in order to allow the greatest number of probability classes, according to the equation: MCn 4 100 and MCn 1 possible probability classes (PPC). MCn number of Monte Carlo iterations. Actual probability classes (APC) 4 PPC (as long as this is obeyed the APC is at the discretion of the user). Second, for section X (input images) (see table A1) we obeyed the naming conventions of SLEUTH while utilizing the ùser info' suffix of the file, as in .urban..[].gif. It is here that we differentiated between analogous WA GIFs and typically employed urban growth simulation GIFs. We created different scenario files for FWA simulation and urban growth simulation and stored the two sets of analogous input images in separate folders to avoid confusion. The most important substitution is the replacement of the hillshade image with the excluded layer from the SAWA scenario for urban growth simulation. In our particular situation, this excluded layer had to be used as the background because it contained all 2002 enrolled WA lands that could be shaded probabilistically from gray to black through the simulation. Finally, and most importantly, under section XII, part 3 (see table A1) of the scenario file, entitled `Probability color table for urban growth', we established eleven different grayscale classes according to the number of times a pixel is selected for WA enrollment termination (or FWA growth). For example, a pixel that is selected 27 times for enrollment termination would fall between a lower limit of 20 and an upper limit of 30 in our scenario filed, yielding a grayscale of 75 out of 255. The greater the number of times a pixel is selected, the lower the resulting grayscale value will be for the overwritten image. It is important to note that though we only chose eleven classes, 101 are possible. After the 100 MC iterations have been completed, the cumulative growth of, in this case, FWA pixels, can be found in the output images file, named, according to the convention, cumcolor urban . We copied this file to the input images of our urban growth simulation, and named it .excluded.. Our name of choice was BAU, signifying business as usual. This corresponds with the BAU scenario discussed in the main text.

(3) For

abbreviations not defined in the text of the appendix please see the main paper.


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Table A1. Significant portions of scenario file of which to be aware a. Section, part of code as written in Demo200 predict scenario file offered as part of downloading SLEUTH model Section VII. Monte Carlo iterations: MONTE CARLO ITERATIONS 10

Our code for same section, part of FWA forecasting scenario file Section VII. Monte Carlo iterations: MONTE CARLO ITERATIONS 100

Section X. Input images: # Urban data GIFS URBAN DATA demo200.urban.1930.gif URBAN DATA demo200.urban.1950.gif URBAN DATA demo200.urban.1970.gif URBAN DATA demo200.urban.1990.gif

Section X. Input images: # FWA GIFS URBAN DATA tulare:urban:1974:fwa:gif URBAN DATA tulare:urban:1986:fwa:gif URBAN DATA tulare:urban:1996:fwa:gif URBAN DATA tulare:urban:2002:fwa:gif

# Road data GIFS ROAD DATA demo200:roads:1930:gif ROAD DATA demo200:roads:1950:gif ROAD DATA demo200:roads:1970:gif ROAD DATA demo200:roads:1990:gif

# Road data GIFS ROAD DATA tulare:roads:1970:gif ROAD DATA tulare:roads:1987:gif ROAD DATA tulare:roads:1990:gif ROAD DATA tulare:roads:2002:gif

# Landuse data GIFs LANDUSE DATA demo200:landuse:1930:gif LANDUSE DATA demo200:landuse:1990:gif

# Landuse data GIFs LAND DATA tulare:landuse:1974:wa:gif LAND DATA tulare:landuse:2002:wa:gif

# Excluded data GIFs EXCLUDED DATA demo200:excluded:gif

# Excluded data GIFs EXCLUDED DATA tulare:excluded:wa:gif

# Slope data GIF SLOPE DATA demo:200:slope:gif

# Slope data GIF SLOPE DATA tulare:slope:gif

# Background data GIF BACKGROUND DATA demo200:hillshade:water:gif

#The Excluded layer from the SAWA urban growth # simulation scenario, upon which is overwritten the # number of times each pixel leaves the WA. BACKGROUND DATA tulare:excluded:sawa:gif

Section XII. Part 3. PROBABILITY COLORTABLE FOR URBAN GROWTH

Section XII. Part 3. PROBABILITY COLORTABLE FOR FWA growth. Grayscale output is absolutely essential. Though only 11 classes were used, 101 are possible # low, upper, hex, (optional name) PROBABILITY COLOR 0, 10, 0X5F5F5F, # 95 grayscale PROBABILITY COLOR 10, 20, 0X555555, # 85 grayscale PROBABILITY COLOR 20, 30, 0X4B4B4B, # 75 grayscale PROBABILITY COLOR 30, 40, 0X414141, # 65 grayscale PROBABILITY COLOR 40, 50, 0X373737, # 55 grayscale PROBABILITY COLOR 50, 60, 0X2D2D2D, # 45 grayscale PROBABILITY COLOR 60, 70, 0X232323, # 35 grayscale PROBABILITY COLOR 70, 80, 0X191919, # 25 grayscale PROBABILITY COLOR 80, 90, 0X0F0F0F, # 15 grayscale PROBABILITY COLOR 90, 99, 0X050505, # 5 grayscale PROBABILITY COLOR 100, 100, 0X000000, # 0 grayscale

# PROBABILITY PROBABILITY PROBABILITY PROBABILITY PROBABILITY PROBABILITY PROBABILITY PROBABILITY PROBABILITY PROBABILITY PROBABILITY a Note

low, upper, hex, (optional name) COLOR 0, 1, , # transparent COLOR 1, 10, 0X00ff33, # green COLOR 10, 20, 0X00cc33, # COLOR 20; 30, 0X009933, # COLOR 30, 40, 0X006666, # blue COLOR 40, 50, 0X003366, # COLOR 50, 60, 0X000066, # COLOR 60, 70, 0XFF6A6A, # lt orange COLOR 70, 80, 0Xff7F00, # dark range COLOR 80, 90, 0Xff3E96, # violetred COLOR 90, 100, 0Xff0033, # dark red

that most comments found after # symbol in actual code have been removed for table brevity.

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Table A2. Routines and results SLEUTH calibration of Tulare County: fa,b, c, d, e, f, gg (total number of Monte Carlo iterations, number of combinatorial simulations, diffusion, breed, spread, slope resistance, road gravity). WA Runs growth parameters

range

step

Urban runs integrating 2002 WA into excluded layer growth parameters

range

step

Course a4 b 3125 c 1 ± 100 25 d 1 ± 100 25 e 1 ± 100 25 f 1 ± 100 25 g 1 ± 100 25 Resulting metrics: Lee-Sallee 0:44139, OSM 0:616536

a3 b 3125 c 1 ± 100 25 d 1 ± 100 25 e 1 ± 100 25 f 1 ± 100 25 g 1 ± 100 25 Resulting metrics: Lee Sallee 0:67246, OSM 0:86165

Fine a7 b 7776 c 1 ± 50 10 d 1 ± 50 10 e 75 ± 100 5 f 25 ± 75 10 g 1 ± 50 10 Resulting metrics: Lee-Sallee 0:3491, OSM 0:619798


Final a8 b 7776 c 1 ± 25 5 d 1 ± 25 5 e 85 ± 100 3 f 50 ± 75 5 g 1 ± 25 5 Resulting metrics: Lee-Sallee 0:33685, OSM 0:637348


Final growth parameters

final value

growth parameters

final value

Highest values in final calibration c 1 d 25 e 97 f 65 g 1

c d e f g

85 82 1 46 52

Self-modified parameter value c 1 d 33 e 100 f 43 g 3

c d e f g

99 96 1 1 57


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Table A3. SLEUTH's built-in metrics. These can be used to evaluate the goodness-of-fit between simulated urban growth and actual urban growth for each round of calibration (as excerpted from Teitz et al, 2005). Note: italicized text indicates additional metric added by author. Metric name

Description

Product Compare

All other scores multiplied together Modeled population for final year/actual population for final year, or IF Pmodeled > Pactual f1 ÿ (modeled population for final year/actual population for final year)g Least squares regression score for modeled urbanization compared to actual urbanization for the control years Least squares regression score for modeled urban edge count compared to actual urban edge count for the control years Least squares regression score for modeled urban clustering compared to known urban clustering fro the control years Least squares regression score for modeled average urban cluster size compared to known average urban cluster size for the control years A shape index, a measurement of spatial fit between the model's growth and the known urban extent for the control years Least squares regression of average slope for modeled urbanized cells compared to average slope of known urban cells for the control years Least squares regression of percentage of available pixels urbanized compared to the urbanized pixels for the control years Least squares regression of average x values for modeled urbanized cells compared to average x values of known urban cells for the control years Least squares regression of average y values for modeled urbanized cells compared to average y values of known urban cells for the control years Least squares regression of average radius of the circle which encloses the urban pixels Product of Compare, Pop, Edges, Clusters, Slope, X-mean, Y-mean (Dietzel, 2004)

Pop Edges Clusters Cluster size Lee-Sallee Slope % urban X-mean Y-mean Rad OSM

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