1. Introduction

A suite of complex factors, including policy, population change, culture, economics, and environmental characteristics, drive land use change. Land use change is one of the most critical dynamic elements of ecosystems (e.g. Baker 1989, Richards 1992, Houghton 1994, Riebsame et al., 1994, Bockstael et al., 1995). Human-induced changes to the land often result in changes to patterns and processes in ecosystems such as alterations to the hydrogeochemistry (Flintrop et al. 1996), vegetation cover (e.g., Ojima et al., 1991), species diversity (Costanza et al., 1993) and changes to the economies of a community. It is for these reasons that issues surrounding land use are central to the concerns of local and regional resource managers and community land use planners.

Information about current land use patterns, the causes of land use change and the subsequent effects of these changes can be effectively communicated to resource managers, community planners and policy analysts using geographic information systems, predictive models and decision support systems (Cheng et al. 1996, Watson and Wadsworth 1996). The advancements in many geographic information system applications such as ARC/INFO (ESRI 1996), and the increased accessibility of spatial databases, makes developing simulation models within geographic information systems more feasible than even a few years ago.

This paper presents an overview of the modeling framework, systems approach, spatial class hierarchies, and a summary of the ARC/INFO commands used to construct our Land Transformation Model. A pilot Land Transformation Model has been developed that integrates a variety of land use change driving variables, such as population growth, agricultural sustainability, transportation, and farmland preservation policies for Michigan’s Saginaw Bay Watershed. The pilot LTM utilizes a set of spatial interaction rules, which are organized into an object class hierarchy. The model is coded within a geographic information system with graphical user interfaces that allow users to change model parameters. Output of the LTM includes a time series of projected land uses in the watershed at user specified time steps.

The objectives of the Land Transformation Project are to:

1. develop a spatial-temporal model that characterizes land use change in large regions;
2. create a model that is transferable in scope to other regions undergoing land transformation;
3. incorporate policy, socioeconomics and environmental factors driving land use change;
4. develop a pilot LTM that demonstrates proof of concept and that can be used to generate spatial and temporal aspects that can be generalized for the development of new model components;
5. apply a systems approach to model development; and,
6. use the model to test ‘what-if’ policy scenarios.

The Land Transformation Model (Pijanowski et al., 1995; 1996; in review) describes the influence of land use change on ecosystem integrity and economic sustainability of large regions. Conceptually, the Land Transformation Model contains six interacting modules (Figure 1): 1) Policy Framework; 2) Driving Variables; 3) Land Transformation; 4) Intensity of Use; 5) Processes and Distributions; and 6) Assessment Endpoints. All modules and submodules within the conceptual diagram are recognized not to be mutually exclusive; we use this diagram to illustrate main points and provide a foundation for the description of more detailed model components. The pilot LTM that is described below contains two of the six LTM modules, driving variables and land transformation. The spatial extent of the LTM can be any definable region; however, because future model developments will be focused on coupling land use change and hydrogeologic and geochemical processes, we give precedence to watersheds as the spatial extent in LTM applications.

The Policy Framework module of the LTM organizes the goals for the watershed’s stakeholders who include resource managers, private and corporate landowners, and local land use planners. Stakeholder goals may include: control of pollutant inputs, ecological restoration, habitat preservation, improving biodiversity and biological integrity, and facilitating economic growth. Within this framework, many stakeholder goals are under certain types of constraints (e.g., economic, environmental), are made with certain expectations of outcomes and with specific spatial and temporal scales in mind. For example, a township land use planner is likely to be making decisions within his/her own township. Likewise, a state or federal government resource manager might be concerned about areas that encompass several counties.

The Land Transformation Model (LTM) contains three general categories (Figure 1) of Driving Variables: Management Authority, Socioeconomics and Environmental. Management Authority includes the institutional components and policies of land use. Land ownership is an important component in this module of the model since state and federally-owned lands (e.g., state and federal forests, parks and preserves) need to be excluded from development. Socioeconomic driving variables include population change, economics of land ownership, transportation, agricultural economics and locations of employment. Environmental driving variables of land transformation are: (1) abiotic, such as the distribution of soil types and elevation; and, (2) biotic, such as the locations of endangered and threatened species, or the attractiveness of certain types of vegetation patterns in the landscape for development. Driving variables may contain intercorrelated subcomponents; hence the model can be hierarchical. For example, the farming socioeconomic system in the Saginaw Bay Watershed application of the pilot model is composed of farm-size dependent economics, farmer demographics and environmental influences on farm productivity.

Land Transformation is characterized by change in land use and land cover. Land use describes the anthropogenic uses of land as its affects ecological processes and land value (Veldkamp and Fresco 1996). Land uses that we consider at the most general level are: urban, agriculture/pasture, forest, wetlands, open water, barren and non-forested vegetation. Land cover characterizes the plant cover of associated land use and is thus not mutually exclusive of land use. Land cover types that are considered include: types of agriculture (row crops versus non-row crops), deciduous and coniferous forests, and non-forested vegetation.

Within each land use, we consider Intensity Of Use such as land management practices, resource use and human activities. Intensity of use can be measured as chemical inputs to the land to increase its productivity (e.g., herbicides), chemical inputs as it results from human activities (e.g., salting of roads), and natural resource use (e.g, subsurface water for irrigation, per unit area energy consumption and forest harvesting). Socioeconomics, policy and environmental factors will also drive the intensity of use as well.

Changes in land use and cover, and intensity of use, alter Processes (e.g., hydrogeologic and geochemical) and Distributions of plants and animals in ecosystems. Processes that we are interested in characterizing include groundwater and surface water flows, chemical and sediment transport across land and through rivers and streams, geochemical interactions and fluxes such as nutrients (nitrogen and phosphorus). Land use and land cover will affect the types and numbers of animals inhabiting areas.

Assessment endpoints are indicators of ecological integrity and economic sustainability. These assessment endpoints are used to quantify the nature of changes in landscapes. It is important that assessment endpoints be: 1) relatively easy to quantify, 2) unambiguous, 3) correlated with changes to land use; and, 4) reflect qualitative aspects of landscapes. These assessment endpoints provide input to the decision making process by watershed stakeholders.

Figure 1. Conceptual Elements of the Land Transformation Model

Land use and features (roads, rivers, etc.) in the watershed are characterized in the pilot LTM model as a grid of cells. Each cell is assigned an integer value based on land use (e.g., urban, agriculture, wetlands, forest) or land feature. Driving variable calculations produce land use conversion probabilities for each cell. The GIS is used to perform these driving variable calculations, integrate all driving variable conversion probabilities and produce future land use maps for the entire watershed. GIS calculations in grids commence at the upper left corner of the grid and end at the lower right corner of the grid. In the Saginaw Bay Watershed application of the pilot LTM, up to 5.2 x 10⁷ cells are contained in each grid.

Figure 2 illustrates conceptually how land use transitions are determined in the Land Transformation Model. This hypothetical landscape contains three agricultural parcels: a small parcel near a highway, a large parcel some distance away from the highway and another small parcel a relatively large distance away from the highway. The drivers to land use change operate on these parcels differently depending upon the spatial relationships of the parcel and the drivers. For example, parcel #1 is under pressure for development due to its: proximity to a highway; proximity to urban infrastructure such as city water and sewers; proximity to high density employment centers found in the urban areas; and, due to its size, the farm is not likely to be profitable. Furthermore, its landowner may also be older and because few younger people are not entering agriculture, it is at a high risk of being converted out of agriculture and into an urban use. The second farm, as indicated by parcel # 2, is held in agriculture by the nature of its ownership (i.e., corporate). Parcel #3 in this figure has a higher probability of converting to urban land use because of the demographics of the owner, and the size of the parcel.

 

Figure 2. Relative Land Transition Probabilities

 

In the LTM, we use the GIS to make spatial calculations between drivers of land use change and cells being considered for land transition. The values resulting from these calculations are converted to relative land transition probabilities. Relative land transition probabilities that are used range from 1 (lowest probability of undergoing transformation to urban land use) to 10 (greatest chance of being converted to urban land use). Creating these relative probabilities from absolute GIS calculations requires: 1) spatial scaling or assigning relative transition probabilities based on absolute values; and, 2) making adjustments to state transition patterns. The types of spatial scaling and state transitions considered in the LTM are described below as part of the presentation of spatial class hierarchies.

In addition to calculating relative land transition values based on: 1) spatial interactions of drivers; and, 2) cells within a parcel, relative weights for each driving variable are assigned and these are then used to calculate urban transition values for each cell in an area. All land transition probabilities and weights for each driving variable are then integrated with the GIS for each location. Values are then placed into equal area percentile classes. Cells with the greatest percentile value are assumed to transition first to urban. The number of cells for each future transition is based on the per unit area requirements for urban given population growth projections for an area (township, county or entire region). The number of cells that meet the demands for each successive projection (e.g., decades) are then transitioned to urban. A more detailed description of the model calculation process can be found in Pijanowski et al. (in review).

5. Spatial Class Hierarchies

Figure 3 illustrates the LTM Spatial Object Class Hierarchy. There are six principal spatial classes in the LTM: interactions, resolution, spatial scaling, state transitions, landscape features and the number of subdrivers. Each of the principal spatial classes in turn are composed of several subclasses, which may be further divided into more refined spatial objects. The terminal positions of the space object classes become rules from which software modules are developed within the geographic information system.

5.1. Spatial Interactions

Spatial interactions used in the LTM are: neighborhood, distance, patch size, and site specific characteristics. Neighborhood spatial interactions are based on the premise that trends and patterns in neighboring locations influence a cell’s land use transition probability. Neighborhood interactions can also vary in size, from those that only occur among proximal locations to large neighborhoods that encompass large areas (counties, subwatersheds or the entire watershed). We also recognize that the shape of neighborhood’s may differ, from square, circular to irregular (e.g., watershed catchment).

Distance functions are the second type of spatial interactions used to characterize driving variables of land use change. We use the geographic information system to calculate the distance of locations in the watershed from landscape features (e.g., roads, rivers, employment centers) and convert these ‘raw’ values into relative probabilities of land transformation (conversion rules are described under state transitions below).

Patch Size is based on the principle that the size of a parcel of land held by an owner has an influence on whether a land use conversion is eminent. For example, farm size in the United States impacts profitability such that small farms cannot compete with larger farms who can invest in advanced farm machinery, etc. Thus, small farms are at greater risk of failure and hence being converted to a non-agricultural use than larger farms.

Finally, site specific characteristics are also important to land use conversion. Certain characteristics (e.g. soil type or elevation) make each site suitable or unsuitable for a particular land use. Policy may also influence site specific characteristics of land transformation by either ‘locking’ land in a specific land use or ‘promoting’ its conversion.

5.2. Resolution

Examples of the resolution spatial object class in the LTM include those for cell size. Four different resolution classes are used in the LTM: parcel (30 x 30m), plat (100 x 100m), block (300m x 300m), and local (1km x 1km). These rules were developed to characterize certain processes such as land ownership changes which occur at relatively high resolutions (e.g., 30 x 30m) and hydrologic dynamics that occur at more coarse resolutions (e.g. 1 km x 1km resolution). Selection of resolution is also determined by the resolutions of databases available to study a process or pattern (e.g., land use is 30x30m as it might be developed from Landsat TM). We integrate multiple grids in the GIS using either the minof or maxof option in the setcell function in ARC/INFO GRID.

5.3. Spatial Scaling


Creating these relative probabilities from absolute GIS calculations requires: 1) spatial scaling or assigning relative transition probabilities based on absolute values; and, 2) making adjustments to state transition patterns.

Spatial scaling to convert all ‘raw’ GIS calculations (e.g., distances) to relative probabilities is accomplished using the slice function in ARC/INFO GRID. Two options of this function are employed: equal area or equal class sizes. The former option of the slice function produces driving variable grids with equal numbers of cells with values between 1 and 10. The latter option provides driving variable grids with equal size classes between the largest and smallest values in the entire grid

Relative transition probabilities can be assigned based on absolute values rather than using spatial scaling routines as described in the previous paragraph. For example, in the Saginaw Bay Watershed application of the pilot LTM, relative transition probability values of 10 were assigned to all cells 30 m on either side of state and county roads within 100 m of highway intersections; all cells 30 m around county and state intersections were assigned values of 7; and all cells on either side of state and county roads were assigned values of 5.

5.4. State Transitions

Two different state transition adjustments made in the LTM. First, the direction of the relationships between the spatial scaling routine result and land transition probability may be positive or negative. For example, land closer to road intersections have the greatest probability of conversion to urban. The GIS is used to calculate the Euclidean distance of cells from the nearest road intersection and these values are then spatially scaled to create grids with relative probability values where the largest values are assigned 10s and the smallest values a 1. However, land closet to a driver such as a road have the greatest probability of conversion to urban; thus, there is a negative relationship between the result of the spatial scaling and the degree of urbanization. We ‘invert’ these transition values using the following simple expression:

outgrid = 11 – ingrid

where outgrid is the inverted driving variable grid and the ingrid is the input grid that contains values from 1-10.

The relationship between a spatial calculation and the influence of this result on urbanization can also be linear or nonlinear (Figure 3). In the case of nonlinear relationships, prior to spatial scaling, all values are adjusted by transforming values using the exp() function in ARC/INFO GRID. The equal size class option of slice is only used for spatial scaling of these state transitions.

5.5 Landscape Features

The fifth type of spatial class objects in the LTM are landscape features. In many instances, the presence of absence of a feature in the landscape is important in the calculation of a land transition probability. For example, the relative density of farms in a local area are derived by producing a map of the presence (coded as 1) or the absence thereof (coded as 0) of agriculture in all locations in the watershed. Features are also cells that are considered for transition and those that are drivers of land use change.

5.6 Number of Subdrivers

Single or multiple layers are required to develop a driving variable. Multiple layer examples include those subdrivers that influence farm failure such as farm size, farmer age, amount of available surrounding arable land, soils, climate, and farm infrastructure (e.g., drains).

Figure 3. Spatial Objective Class hierarchy


6.0. GIS Framework and Syntax

6.1. GIS Integration Schematic

Figure 4 illustrates how the GIS is used to produce land use projection maps. The first step is to create driving variable grids that contain values representing relative transition urban probabilities. This process may first require producing grids that contain information about the absence (cell value = 0) or presence (cell value = 1) of a feature (e.g., road) or land use type (e.g., agriculture); several grids may be integrated to produce the necessary input layer (Figure 4; Step 1A). Spatial calculations (e.g., neighborhoods, Euclidean distances) are performed (Figure 4; Step 1B) on the input grids so that resultant ‘raw’ values (e.g., distance a cell is from a driver cell) are stored in each cell in the grid (Figure 4; Step 1C). These ‘raw’ values are then scaled (Figure 4; Step 1D) so that there are an equal number of values between 10 (greatest probability on urbanization) and 1 (least probability for urbanization). This process produces driving variable grids (1E) that are then multiplied by a driving variable weight (1F). All driving variable grids are then summed (i.e., all cells for each location are added together) and this sum is stored in a final integrated driving variable grid (Figure 4; Step 2).

Cells within the grid that are identified as non-buildable due to policy (e.g., development rights have been restricted) or ownership (e.g., land is state or federally owned) are created (Figure 4; Step 3A) so that non-buildable cells are assigned value of ‘0’ and potentially buildable areas assigned values of ‘1’. All of these grids are integrated by multiplying them together so that a single ‘building exclusion’ grid is produced Figure 4; Step 3B).

An urban pressure grid is produced as part of Step 4 in the GIS integration process; this is created by multiplying the ‘building exclusion grid’ with the integrated driving variable grid. A nonurban grid (nonurban cell = 1; urban = 0) is used to multiply with the urban pressure grid. This step results in an ‘area to be transformed grid’ (Figure 4; Step 5A) that contains integrated driving variable values for all nonurban areas. Values in the nonurban areas are then scaled (Figure 4; Step 5B) into percentile classes so that each percentile is represented by an equal number of cells (i.e., each value between 1 and 100 contains equal areas) in the grid labeled as 5C. The number of cells transformed to urban is determined by calculating a ‘critical threshold value’ (Step 5D). Estimating the appropriate critical threshold value can be accomplished as follows. First, the amount of future urban land is determined using population growth projections and per capita urban land requirements:

U (t) = * A (t). (1)

where U is the amount of new urban land required in the time interval t, P is the number of new people in any given area in a given time interval and A is the per capita requirements for urban land. The critical threshold value is then simply a proportion of the current nonurban land use to the amount of new urban land use required in the future:

C (t) = 100 -{[U(t) / N] *100.0 } (2)

where N is the amount of current non-urban land use that can be developed in the future, expressed as a percent. Note that N is also a function of non-buildable area. Future land use grids are produced that ‘step’ through the critical threshold values (Step 6).

Figure 4. GIS Integration Schematic


6.2. ARC/INFO Commands


The cell-based spatial modeling software module found in ARC/INFO GRID (ESRI 1997) is used to model land use change. The GRID functions used most often in the LTM are:

setcell: this sets the cell size prior to any calculation;

focalsum: this calculates the sum of all values of any given area surrounding each cell and stores that value in that cell. This function allows the user to set the size and the shape of the neighborhood.

eucdistance: this calculates the distance between two cells in the landscape and stores that value in each cell;

zonalarea: this calculates the area of contiguous cells which have the same assigned value;

test: this performs a Boolean operation on input data and stores a 1 if the given expression is true and 0 if it is false; and,

slice: this changes all input values to an integer ranking based on the amount of area assigned to each ranking or the size of the category of values.

 

6.3. Model Interface

Figure 5 shows a sample user interface of the Land Transformation Model. This interface was developed using the Formedit GUI development tool in ARC/INFO in the OpenWindows UNIX environment. The interfaces allow users to set values for driving variable calculations (e.g., cell size, neighborhood extent) as well as provide access to visualization and output analysis tools.

 

Figure 5. Sample Graphical User Interface of the pilot LTM


7.0 Model Application

7.1 Site Description

The Saginaw Bay Watershed (SBW) is one of the largest watersheds in the Great Lakes (Figure 6) area covering approximately 15,000 km² (15% of the total area of the state of Michigan). The SBW is composed of 10 smaller watersheds which are further divided into 69 subwatersheds. The principal river in the watershed is the Saginaw, which is only 47 km long; however, it drains 28 rivers and streams and nearly 73% of the watershed (MUCC 1993). There are three major tributaries of the Saginaw River: the Cass River to the east, the Flint River to the south, and the Titabawassee River to the west. The major cities within the watershed include Flint, Saginaw, Bay City, Midland, and Mt. Pleasant. There are 22 counties, 42 cities, 50 villages, and 277 townships in the watershed. Each municipality (e.g. township or cities) is given the authority to govern their own land use. Over 1.1 million people live in this watershed.

Figure 6. Saginaw Bay Watershed



Agriculture is by far the most common land use in the SBW (46%), followed by forested areas (27%), and open vegetation (non-forested vegetation) (11%). In the SBW, fewer than 8% of the cropland is under conservation tillage compared to the statewide average of 40%. The lack of conservation tillage practices has created a situation of massive soil erosion due to wind and water. Urban use makes up only 6.6% of the entire area. Within urban areas, residential areas comprise 67% of the urban area. The other major urban uses are commercial (9%), transportation (8%), and industrial (4%). Topography does not vary considerably in the watershed. Areas near the mouth of the Saginaw Bay differ by less than 3 meters from 10 miles inland. As a result, flow of the major streams in the Saginaw is relatively slow; in some cases, the Saginaw River has been known to flow in the reverse direction during strong northeasterly winds.

7.2. Pilot LTM Driving Variables


We have used the LTM conceptual diagram (Figure 2) to develop a pilot GIS-based simulation model that forecasts land use in the Saginaw Bay Watershed using policy, socioeconomic and environmental driving variables. This model represents two of the six LTM modules. This pilot model’s driving variables are: land ownership; the state’s farmland preservation act and its affect on farm to urban conversion; the state’s wetland protection act; the effect of the state’s property tax assessment method on farm failure; the Suburban Control Act; local and regional population change; economics of land ownership; transportation effects on urbanization; local and farm level agricultural economics; location and density of employment opportunities and social factors that affect farm failure; the presence or absence of buildable soils; the affects of drainage system on agricultural performance; and, the relative attractiveness of several landscape features for urban development. Figure 7 illustrates some of the driving variable calculations results. A more detailed description of the driving variable calculation formulation can be found in Pijanowski et al. (in review).

Figure 7. Sample pilot LTM Driving Variables


8.0 Results and Discussion

8.1 Summary of Results


The pilot LTM was executed without assigned weights to the 13 driving variables listed above (Figure 8). The critical threshold values for each 10 year time step was determined from State of Michigan population projections for the next 50 years. In addition, the base land use map that was used was developed by synthesizing land use polygons from 350 townships in the watershed from the Michigan Resource Information System (MiRIS). Land use from this database is current only to 1980. Thus, the first projection created a land use map for 1990. In the near future, the pilot LTM will be calibrated by conducted an historical forecast in order to attempt to predict current land use conditions. A current land use map for the entire watershed is planned to be completed by August of 1997.

Figure 8. Zoom of LTM Execution Results in Genessee County



9.0 Acknowledgements

We gratefully acknowledge funding from the Consortium for International Earth Science Information Network (CIESIN), University Center, Michigan, through Cooperative Agreement (CX821505) between the U.S. Environmental Protection Agency and CIESIN. William Cooper and Tom Edens, two co-PIs on the project, provided substantial input on the development of the model. We would also like to thank Bob Worrest, Mike Thomas, and Bob Bourdeau of CIESIN; Charles Bauer and James Bredin of the Michigan Department of Natural Resources for helpful comments during the model development phase. Dennis Tenwolde reviewed earlier versions of the manuscript. Amos Ziegler, Katie Jones, Tom Sampson, Gary Icopini, John Abbott and Mark Rousseau helped to prepare a variety of the spatial databases used in this project.

10.0 Refernces

Clarke, K.C., Gaydos, L., Hoppen, S., .1996a. A Self-Modifying Cellular Automaton Model of Historical Urbanization in the San Francisco Bay Area, Environment and Planning B.

Clarke, K.C., Hoppen, S., Gaydos, L., .1996b. Methods and Techniques for Rigorous Calibration of a Cellular Automaton Model of Urban Growth, Third International Conference/Workshop on Integrating GIS and Environmental Modeling, Santa Fe, New Mexico, January 21-25, 1996. Santa Barbara: National Center for Geographic Information and Analysis. WWW and CD.

Costanza, R. 1989. Model goodness of fit: a multiple resolution procedure. Ecological Modeling 47: 199-215.

Costanza, R. and T. Maxwell. 1994. Resolution and predictability an approach to the scaling problem. Landscape Ecology 9(1):47-57.

Costanza, R. F. Sklar, M. White. 1990. Modeling coastal landscape dynamics. Bioscience 40 (2): 91-107.

Costanza, R., and F. Skalr. 1985. Articulation, accuracy and effectiveness of mathematical models: a review of freshwater wetland applications.

Environmental Systems Research Institute. 1996. Cell-based modeling with GRID. Environmental System Research Institute, Atlanta, Georgia.

Flintrop, C., B. Hohlmann, T. Jasper, C. Korte, O. Podlaha, S. Scheele, and J. Veizer. 1996. Anatomy of pollution: streams of North Rhine-Wesphalia, Germany. Am. J. of Science 296: 58-98.

Kolak, J.J., D.T. Long, J.M. Matty, G.J. Larson, and D.F. Sibley (1996) Groundwater, stream, lake dynamics: Saginaw Bay Watershed. International Association for Great Lakes Research Annual Meeting 1996.

Michigan Department of Natural Resources. 1994. Saginaw Bay Watershed Prioritization Process. MDNR. 65 pp.

Michigan United Conservation Clubs. 1993. Saginaw Bay Watershed Land Use and Zoning Study. 308 pp.

Pijanowski, B. C., T. Machemer, S. Gage, D. Long, W. Cooper and T. Edens. 1995. A land transformation model: integration of policy, socioeconomics and ecological succession to examine pollution patterns in watershed. Report to the Environmental Protection Agency, Research Triangle Park, North Carolina. 72 pp.

Pijanowski, B. C., T. Machemer, S. Gage, D. Long, W. Cooper and T. Edens. 1996. The use of a geographic information system to model land use change in the Saginaw Bay Watershed. Proceedings of the Third International Conference on GIS and Environmental Modeling, Sante Fe, New Mexico, January 21-26, 1996. GIS World Publishers on CD-ROM.

Pijanowski, B.C. 1997. Issues of space and time scales in changing landscapes: systems approach and the use of geographic information systems. In Lecture Series in Landscape Ecology. Larry Harris, ed.

Pijanowski, B. C., T. Machemer, S. Gage, and D. Long. In press. A land transformation model: conceptual and analytical framework and its application to Michigan’s’ Saginaw Bay Watershed. To Ecological Modeling.

Sklar, F. And R. Costanza. 1991. The development of dynamic spatial models for landscape ecology: a review and prognosis.