PROBABILISTIC LAND COVER TRANSITION MODELING USING DELTATRONS

Our research on the impact of human induced change upon the natural landscape has produced a cellular automaton "deltatron" model of land cover transition. The deltatron model is tightly coupled to and driven by the Clarke Urban Growth Model, a cellular automaton model that simulates urban spread based on initial spatial conditions derived by digital map data and rules governing the behavior of a cellular automaton. The land use change model uses the number of new urban pixels at each time step in the simulation as the driver for further land use change. The deltatrons act as independent agents of change that rely upon historically measured land cover transition probabilities, local topography and the previous time period's changes as a control for enforcing new change within a neighborhood. Using modeled urban growth as a driver, land cover change, classified at Anderson Level 1, has been simulated for the EPA's Mid-Atlantic Integrated Assessment (MAIA) study area at a resolution of 1km. The result is a simulated land use forecast for the area that uses Monte Carlo simulation to estimate both the most likely future land covers class, and the associated uncertainty of the prediction. We introduce the deltatron model in detail, using the MAIA application as a specific data set. We propose that the simplistic spatial assumptions of the deltatron nevertheless are quite powerful in emulating the effect of land use dynamics. COMPLEX SYSTEM MODELING WITH CELLULAR AUTOMATA Evolving from previous work, a model of land cover change has been developed and applied to a regional dataset. The cellular automaton (CA) Clarke Urban Growth Model (UGM) simulated the affect of topography, adjacency and transportation networks on the patterns of urbanization though time (Clarke, Gaydos and Hoppen, 1996). This model was calibrated using historical data for a region compiled in a geographic information system (GIS) (Clarke, Hoppen and Gaydos, 1996). These results were then used to forecast the development of the regional urban system into the future (Clarke and Gaydos, 1997). The land cover change Deltatron model, introduced here, is tightly coupled with the UGM, and also utilizes historical, digital data maps to calibrate model performance. The models together are referred to as SLEUTH by reference to the models’ input data requirements: Slope, Land cover, Exclusion, Urban, Transportation, Hillshade. Using only the clues given by known data input, SLEUTH seeks to predict the emerging form in a dynamic landscape by modeling the processes of change. The evolution of land cover patterns is a process governed by a large number of forces both natural to the environment and imposed by human disruption. The state of the system at any given time is the result of the interplay of its many components. Trying to identify the intricate relationship of these many drivers may quickly lead to frustration since the problem is underdetermined. Nevertheless, an emerging body of theory suggests the multitude of interactions that take place on a large scale, at the individual level, forms the basis of system-wide aggregate behavior. A first application of complexity theory was offered from the discipline of computer science. Von Neuman (1966) presented the idea that a type of computing machine could not only reproduce itself, but could generate a machine of greater complexity than the original. This concept was expressed in the form of a CA. Perhaps one of the most well known examples of a CA is the Gam of Life developed by Conway (Gardener, 1972). The game is executed upon a regular tessellation of cells, in this case a grid of uniform, square pixels. The cells may exist in one of two states: alive or dead. Configuring the grid so some of the pixels are alive, while others are dead, establishes an initial set of conditions. A simple set of behavior rules determines if a cell changes states: less than three or greater than four live neighbors indicates an area unsuitable for life due to overcrowding. Three to four live neighbors indicate a good opportunity for growth, and new life. Searching each cell’s four or eight cell neighbors, these behavior rules are applied across the game space simultaneously. In this decision process, each cell acts within the system as an independent agent. Its condition is dictated not through outside determinants, but rather, as a result of the spatial and temporal changes dependant upon the current state of a cell and the state of its neighbors. Depending on the configuration of the initial conditions, complex spatial patterns emerge though repeatedly applying the behavior rules to the grid. In recent years CA has been applied in many and various fields, and has now been applied to modeling urban form (White and Engelen, 1992; Papini and Rabino, 1997; Batty and Xie, 1994; Clarke, Hoppen, and Gaydos, 1996). We have extended the scope of our earlier research from modeling urban development to include how this expansion in turn affects subsequent land transitions. As Clarke pointed out (1997), these land transitions may be characterized in several ways. The first is indicated by a state change . A transition occurs when an area changes from one defined land class to another. A parcel’s conversion from forest to agriculture is an example. We assume that urbanization drives this change, and within the model, urban land is an invariant class. Once a pixel is urbanized it will remain so for the duration of that model run. Urban is therefore considered an “absorbing class.” Secondly, the local context of transitions must be considered. Transitions are affected by neighborhood dynamics. If many of an area’s neighboring parcels are experiencing a conversion to agriculture, a transition in that area, especially to agriculture, is more likely than in an area that is not experiencing land cover change. Lastly, a transition can take place at a discrete location . This can be defined as a point, an area, or in our case a pixel. Although the neighborhood and driving forces do affect the likelihood of change, each transition is made on the spatial level of the individual. FIGURE 1: THREE CHARACTERISTICS OF LAND TRANSITIONS Physical patterns of land cover change may be shown three ways. The first is the tendency of one land class to expand into another where the two meet. This is the most common type, and may be seen as the expression of a land type “growing” into its neighbors as topography and neighborhood resistance allows. The second is a less predictable occurrence of a new land cover type being introduced into an otherwise homogenous area. Both of these trends, though they begin at a discrete point and time, may trigger similar transition events in their neighborhood. This third occurrence, a perpetuation of change, enables transition forces to be propagated across a landscape. The deltatron model seeks to build upon and exploit these concepts of how and where land cover dynamics take place. LAND TRANSITION MODELING Probability of change Creating a two-dimensional matrix T (table 1) of identical land cover maps at different time periods (figure 2) initializes a framework for land transition (Clarke, 1997). This matrix is normalized by the numbers of years between land cover data, and so represents an annual, or single step, probability of class transition. The transition matrix enforces the shift of regional land patterns over time. This design is obviously rudimentary and offers no opportunity to test statistical robustness. Use of three or more land cover maps, and a model of transitional probability change would allow a greater understanding of change dynamics and allow an estimation of variance. FIGURE 2: LAND COVER MAPS AT DIFFERENT TIME PERIODS FOR FICTIONAL REGION “DEMO_CITY” Urban Agric Range Forest Water Wetland Barren Urban 100.0[ 924] 0.0[ 0] 0.0[ 0] 0.0[ 0] 0.0[ 0] 0.0[ 0] 0.0 [ 0] Agric 0.6[1793] 99.3[2777] 0.0[ 17] 0.0[ 48] 0.0[ 0] 0.0[ 0] 0.0 [ 0] Range 0.1[ 405] 0.3[1193] 99.5[4230] 0.1[ 229] 0.0[ 0] 0.0[ 0] 0.0 [ 0] Forest 0.1[1319] 0.3[4513] 0.1[1529] 99.5[17754] 0.0[ 1] 0.0[ 3] 0.0 [ 1] Water 0.0[ 1] 0.0[ 0] 0.0[ 0] 0.0[ 0] 100.0[2580] 0.0[ 0] 0.0 [ 0] Wetland 0.2[ 61] 0.4[ 159] 0.0[ 0] 0.0[ 0] 0.0[ 0] 99.4[405] 0.0 [ 0] Barren 0.0[ 0] 0.0[ 0] 0.0[ 0] 0.0[ 0] 0.0[ 0] 0.0[ 0] 100.0[ 58] TABLE 1: TRANSITION MATRIX T FOR DEMO_CITY Influence of Topography In regions of even moderate topography, the average slope associated with each class may differentiate land cover types. Urbanization will often occupy the flattest land available, coastal plains and flat valley bottoms for instance, until these areas are all occupied. Steeply sloped forestlands are unlikely candidates for agriculture. However, rolling foothills might easily be cleared for orchards or grazing. The practical consideration of how topography affects land cover patterns is implemented in the model by giving preference to those classes whose slope is most similar to that of the pixel being looked at.