Robert Gilmore Pontius

Comparison of the structure and accuracy of two land change models

Clark University, Department of International Development, Community andEnvironment, Graduate School of Geography, 950 Main StreetWorcester MA 01610-1477, USA; Tel: 508-793-7761; Fax: 508-793-8881; Email: rpontius@clarku.eduThis paper compares two land change models in terms of appropriateness forvarious applications and predictive power. Cellular Automata Markov(CA_Markov) and Geomod are the two models, which have similar options toallow for specification of the predicted quantity and location of land categories.The most important structural difference is that CA_Markov has the ability topredict any transition among any number of categories, while Geomod predictsonly a one-way transition from one category to one alternative category.To assess the predictive power, each model is run several times to predict landchange in central Massachusetts, USA. The models are calibrated withinformation from 1971 to 1985, and then the models predict the change from1985 to 1999. The method to measure the predictive power: 1) separates thecalibration process from the validation process, 2) assesses the accuracy atmultiple resolutions, and 3) compares the predictive model vis-a`-vis a null modelthat predicts pure persistence. Among 24 model runs, the predictive models aremore accurate than the null model at resolutions coarser than two kilometres, butnot at resolutions finer than one kilometre. The choice of the options account formore variation in accuracy of runs than the choice of the model per se. The mostaccurate model runs are those that did not use spatial contiguity explicitly. Forthis particular study area, the added complexity of CA_Markov is of no benefit.Keywords: Cellular Automata; Geomod; Land change; Markov; Model; Predict;Resolution; Scale; Validate

A generalized cross‐tabulation matrix to compare soft‐classified maps at multiple resolutions

This paper addresses two grand challenges in the development of methods for Geographic Information Science (GIS). First, this paper presents techniques to compute a cross‐tabulation matrix for soft‐classified pixels. Second, it shows how to compute the cross‐tabulation matrix at multiple scales. The traditional approach to construct the cross‐tabulation matrix uses a Boolean operator to analyse pixels that are hard‐classified. For soft‐classified pixels, the contemporary approach uses a Multiplication operator; the fuzzy approach uses a Minimum operator; whereas this paper proposes a multiple‐resolution approach that uses a Composite operator. There are difficulties with the traditional, contemporary, and fuzzy methods of computing the cross‐tabulation matrix. The proposed multiple‐resolution method resolves those difficulties. Furthermore, the proposed method facilitates multiple‐resolution analysis, so it can examine how results change as a function of scale. The paper derives the equations to compute cross‐tabulation matrices at multiple resolutions and connects those equations to ontological foundations of GIS.

Modelling Land-Use and Land-Cover Change

The decade since the initiation of the Land-Use/Cover Change (LUCC) project in 1995 (see Chap. 1) has witnessed considerable advances in the field of modeling of land-use/cover change. The science plan of the project indicated that the major task would be the development of a new generation of land-use/cover change models capable of simulating the major socioeconomic and biophysical driving forces of land-use and land-cover change. In addition, these models were supposed to be able to handle interactions at several spatial and temporal scales. Recent publications indicate that the LUCC science community has successfully met this challenge and a wide range of advanced models, aiming at different scales and research questions, is now available (Briassoulis 2000; Agarwal et al. 2001; Veldkamp and Lambin 2001; Parker et al. 2003; Nagendra et al. 2004; Veldkamp and Verburg 2004; Verburg et al. 2004b; Verburg and Veldkamp 2005). One of the most important observations that can be made examining the range of available land-use/ cover change models is the wide variety of approaches and concepts underlying the models. This chapter intends to describe the variety of modeling approaches, discuss the strengths and weaknesses of current approaches and indicate the remaining challenges for the land-use science community. Not being able to discuss all individual models and approaches, we will focus on broad distinctions between approaches and discuss how modelers have dealt with a number of important aspects of the functioning of the landuse system. A land-use system is understood here as a type of land use with interrelated determining factors with strong functional relations with each other (see Fig. 1.2). These factors include a wide range of land-use influencing factors than can be biophysical, economic, social, cultural, political, or institutional. The discussion of modeling approaches in this chapter is illustrated with examples of models and results from selected research projects.

Identifying Systematic Land-Cover Transitions Using Remote Sensing and GIS: The Fate of Forests inside and outside Protected Areas of Southwestern Ghana

We use remote sensing and GIS to map changes in land cover and to identify systematic land-cover transitions in Southwestern Ghana. Landsat Thematic Mapper satellite imagery of 1990 and 2000 is used to create two land-cover classifications, and the two maps are then compared to produce transition matrices both for protected and for unprotected areas. These matrices are analyzed according to their various components to identify systematic landscape transitions based on deviations between the transitions observed and the transitions expected owing to random processes of change. The results show that closed forest regions inside the protected area transition systematically to bare ground or bush fire, but closed forest outside the protected area transitions systematically to open cultivated woodland. These results are consistent with the hypothesis that logging is the main cause of the loss of closed forest inside the protected areas whereas farming is the main cause of the loss of closed forest outside the protected areas. The research highlights the need for the implementation of this methodological approach to landscape change. Identification of strong signals of forest transformation is particularly important in the light of efforts by policy makers to curb deforestation in Ghana.

Research on Coupled Human and Natural Systems (CHANS): Approach, Challenges, and Strategies

William J. McConnell, James D. A. Millington, Nicholas J. Reo, Marina Alberti, Heidi Asbjornsen, Lawrence A. Baker, Nicholas Brozov, Laurie E. Drinkwater, Scott A. Drzyzga, Jose, Fragoso, Daniel S. Holland, Claire A. Jantz, Timothy Kohler, Herbert D. G. Maschner, Michael Monticino, Guillermo Podesta, Robert Gilmore Pontius, Jr., Charles L. Redman, David Sailor, Gerald Urquhart, and Jianguo Liu. (2011). Research on Coupled Human and Natural Systems (CHANS): Approach, Challenges, and Strategies. Bulletin of the Ecological Society of America April: 218-228.

Uncertainty in extrapolations of predictive land-change models

This paper gives a technique to extrapolate the anticipated accuracy of a prediction of land-use and land-cover change (LUCC) to any point in the future. The method calibrates a LUCC model with information from the past in order to simulate a map of the present, so that it can compute an objective measure of validation with empirical data. Then it uses that observed measurement of predictive accuracy to anticipate how accurately the model will predict a future landscape. The technique assumes that the accuracy of the model will decay to randomness as the model predicts farther into the future and estimates how fast the decay in accuracy will occur based on prior model performance. Results are presented graphically in terms of percentage of pixels classified correctly so that nonexperts can interpret the accuracy visually. The percentage correct is budgeted by three components: agreement due to chance, agreement due to the predicted quantity of each land category, and agreement due to the predicted location of each land category. The percentage error is budgeted by two components: disagreement due to the predicted location of each land category and disagreement due to the predicted quantity of each land category. Therefore, model users can see the sources of the accuracy and error of the model. The entire analysis is computable for multiple resolutions, so users can see how the results are sensitive to changes in scale. We illustrate the method with an application of the land-use change model Geomod to Central Massachusetts, where the predictive accuracy of the model decays to 90% over fourteen years and to near complete randomness over 200 years.

Accuracy Assessment for a Simulation Model of Amazonian Deforestation

Abstract This article describes a quantitative assessment of the output from the Behavioral Landscape Model (BLM), which has been developed to simulate the spatial pattern of deforestation (i.e. forest fragmentation) in the Amazon basin in a manner consistent with human behavior. The assessment consists of eighteen runs for a section of the Transamazon Highway in the lower basin, where the BLMs simulated deforestation map for each run is compared to a reference map of 1999. The BLM simulates the transition from forest to non-forest in a spatially explicit manner in 20-m × 20-m pixels. The pixels are nested within a hierarchical stratification structure of household lots within larger development rectangles that emanate from the Transamazon Highway. Each of the eighteen runs derives from a unique combination of three model parameters. We have derived novel methods of assessment to consider (1) the nested stratification structure, (2) multiple resolutions, (3) a simpler model that predicts deforestation near the highway, (4) a null model that predicts forest persistence, and (5) a uniform model that has accuracy equal to the expected accuracy of a random spatial allocation. Results show that the models specification of the overall quantity of non-forest is the most important factor that constrains and correlates with accuracy. A large source of location agreement is the BLMs assumption that deforestation within household lots occurs near roads. A large source of location disagreement is the BLMs less than perfect ability to simulate the proportion of deforestation by household lot. This article discusses implications of these results in the context of land change science and dynamic simulation modeling. Eugenio Arima and Marcellus Caldas were affiliated with Michigan State University during the time the work reported in this article was done.

Comparison of Three Maps at Multiple Resolutions: A Case Study of Land Change Simulation in Cho Don District, Vietnam

Geographic modelers frequently compare maps of observed land transitions to maps of simulated land transitions to relate the patterns in reference maps to the output from a simulation model. Pixel-by-pixel analysis of raster maps at a single resolution is useful for this task at a single scale, but scientists often need to consider additional scales. This article presents methods to satisfy this need by proposing a multiple-resolution method to compare land categories in three maps: a reference map of time 1, a reference map of time 2, and a simulation map of time 2. The method generates a three-dimensional table that gives the percentage of the study area for each combination of categories at the maps’ native resolution and at several nested sets of coarser squares. The method differentiates allocation disagreement within coarse squares, allocation disagreement among coarse squares, quantity disagreement, and agreement. We illustrate the method with output from a run of the SAMBA agent-based model from 1990 to 2001 using 32-m resolution pixels for Cho Don District, Vietnam. Results show that half of the overall disagreement is attributable to allocation disagreement within squares that are 506 m × 506 m, which is about the average size of a village. Much of the remaining disagreement is misallocation of forest and shrub between the northern and southern parts of the district, which is caused by differences between the data and the simulation concerning transitions from the crop and shrub categories.

Can Error Explain Map Differences Over Time

This paper presents methods to test whether map error can explain the observed differences between two points in time among categories of land cover in maps. Such differences may be due to two reasons: error in the maps and change on the ground. Our methods use matrix algebra: (1) to determine whether error can explain specific types of observed categorical transitions between two maps, (2) to represent visually the differences between the maps that error cannot explain, and (3) to examine how the results are sensitive to possible variation in map error. The methods complement conventional accuracy assessment because they rely on standard confusion matrices that use either a random or a stratified sampling design. We illustrate the methods with maps from 1971 and 1999, which show seven land-cover categories for central Massachusetts. The methods detect four transitions from agriculture, range, forest, and barren in 1971 to built in 1999, which a 15 percent error cannot explain. Sensitivity analysis reveals that if the accuracy of the maps were less than 77 percent, then error could explain virtually all of the observed differences between the maps. The paper discusses the assumptions behind the methods and articulates priorities for future research.

Assessing a predictive model of land change using uncertain data

This paper presents a method to assess models that predict changes among land categories between two points in time. Cross-tabulation matrices show comparisons among three maps: 1) the reference calibration map of an initial time, 2) the reference validation map of a subsequent time, and 3) the models predicted map of the same subsequent time. The proposed method analyzes these three maps to evaluate the ability of the model to predict land change vis-a-vis a null model, while accounting for the error in the reference maps. We illustrate this method with a prediction of land change from 1971 to 1999 in Central Massachusetts, USA. Results reveal that the land change model predicts a larger quantity of transition from forest to built than the reference maps indicate, and the model allocates the transition erroneously in space, thus causing substantial error where the model predicts built in 1999 but the reference map shows forest. If the accuracy of each category in the 1971 reference map is greater than 81 percent, then the predicted change is larger than the error in the 1971 reference map. If the accuracy of each category in the 1999 reference map is greater than 82 percent, then the models prediction disagreement with respect to truth is larger than the error in the 1999 reference map. Partial information concerning the accuracy of the reference maps indicates that the maps are likely to be more accurate than the 82 percent threshold. The method is designed to analyze predictions for the common situation when the levels of accuracy in the reference maps are not known precisely.