Search

Intensity Analysis is a mathematical framework to express differences within a set of categories that exist at multiple time points. The original version of Intensity Analysis communicated land cha...

Some popular metrics to evaluate land change simulation models are misleading. Therefore, land change scientists have called for the development of methods to evaluate various aspects of modelling applications. This article answers the call by giving novel methods to compare three types of land change: 1) reference change during the calibration time interval, 2) simulation change during the validation time interval, and 3) reference change during the validation time interval. We compare these changes by using Intensity Analysis’ three levels and the Figure of Merit’s four components: Misses, Hits, Wrong Hits and False Alarms. We illustrate the concepts by applying a Cellular Automata – Markov land change model to a case study in northeast Hungary. We used reference maps of five land categories to calibrate the model during 2000–2006, then to validate the simulation during 2006–2012. Intensity Analysis’ time interval level shows that the simulation change and the reference change decelerated from 2000–2006 to 2006–2012. Intensity Analysis’ category level shows that the simulation losses were less than what a pure Markov chain would have dictated. Intensity Analysis’ transition level shows that the model’s Markov algorithm simulated correctly that the gain of Forest targeted Agriculture and Wetland. The Figure of Merit’s components reveals more allocation error than quantity error. Our collection of metrics show that more error derived from the Cellular Automata algorithm than from the Markov algorithm. We recommend that scientists use Intensity Analysis and the Figure of Merit’s components to reveal various fundamental aspects of modelling applications.

This article uses the GlobeLand30 maps of land cover to characterize the difference between years 2000 and 2010 in Asia. Methods of Intensity Analysis and Difference Components dissect the transition matrix for nine categories: Barren, Grass, Cultivated, Forest, Shrub, Water, Artificial, Wetland and Ice. Results show that Barren, Grass, Cultivated, and Forest each account for more than 21% of Asia at both 2000 and 2010, while transitions among those four categories account for more than half of the temporal difference. Nearly ten percent of Asia shows overall temporal difference, which is the sum of three components: quantity, exchange and shift. Quantity accounts for less than a quarter of the temporal difference, while exchange accounts for three quarters of the temporal difference. The largest quantity components at the category level are a net gain of Barren and net losses of Grass and Shrub. Shrub demonstrates the most intensive loss and gain relative to a category’s size. The largest and most intensive transitions to Barren are from Grass and Shrub. The largest and most intensive transition to Artificial is from Cultivated. Error information is not available for GlobeLand30 concerning 2000 or temporal change, but a confusion matrix is available for the global extent at 2010. This article applies methods to interpret the difference between two time points when a confusion matrix is available for only the latter time point. If the 2010 global confusion matrix reflects errors in Asia, then such errors could help to explain some of the gross gain of Barren and the counter-intuitive loss of Artificial. If the GlobeLand30 data indicate true change, then gross change in Asia is 4.4 times larger than net change.

This article gives methods to analyze the difference between two datasets that describe a mutual set of categories. The methods can analyze classification error between mapped and reference categories, or change between two time points. Previous work showed how to compute difference size as the sum of three components: Quantity, Exchange and Shift. These components exist for difference by category and for difference overall. These components can be challenging to compare when the categories’ differences vary by size. To address this challenge, this article introduces equations to compute a component’s intensity, which is the size of the component divided by the size of the difference. Component intensities facilitate comparison of each category with other categories and with difference overall. The case study illustrates how to use component intensities to characterize temporal change using remotely sensed data. Results show how an intensive Exchange component can signal possible confusion of two categories with each other. The literature shows that authors could benefit from interpretation of component intensities. Readers can perform the calculations for free by using the diffeR package in R or the PontiusMatrix spreadsheet available at www.clarku.edu/∼rpontius .

Several factors influence the performance of land change simulation models. One potentially important factor is land category aggregation, which reduces the number of categories while having the potential to reduce also the size of apparent land change in the data. Our article compares how four methods to aggregate Corine Land Cover categories influence the size of land changes in various spatial extents and consequently influence the performance of 114 Cellular Automata-Markov simulation model runs. We calculated the reference change during the calibration interval, the reference change during the validation interval and the simulation change during the validation interval, along with five metrics of simulation performance, Figure of Merit and its four components: Misses, Hits, Wrong Hits and False Alarms. The Corine Standard Level 1 category aggregation reduced change more than any of the other aggregation methods. The model runs that used the Corine Standard Level 1 aggregation method tended to return lower sizes of changing areas and lower values of Misses, Hits, Wrong Hits and False Alarms, where Hits are correctly simulated changes. The behavior-based aggregation method maintained the most change while using fewer categories compared to the other aggregation methods. We recommend an aggregation method that maintains the size of the reference change during the calibration and validation intervals while reducing the number of categories, so the model uses the largest size of change while using fewer than the original number of categories.

We compare two popular methods to quantify temporal change among categories: 1) Intensity Analysis and 2) the land use dynamic degrees. We apply the methods to measure land change both outside and inside the coastal zone of Longhai, which is a typical county-level coastal city in Southeast China. The maps show eight categories at four time points: 1986, 1996, 2002, and 2010. Intensity Analysis shows graphically the size and the intensity of changes at three increasingly detailed hierarchical levels in a manner that facilitates interpretation. In contrast, the comprehensive land use dynamic degree (CLUDD) has no practical interpretation because the CLUDD is the sum of loss intensities of categories that have different sizes. The single land use dynamic degree is the annual net change as a percentage of the initial size of the category, which offers limited information because the single degree: 1) fails to reveal the sizes of the category’s loss and gain, 2) does not indicate how each category contributes to total change, 3) is sensitive to the category’s initial size, and 4) reveals neither the size of the category’s annual net change nor the size of the category’s initial size.

This article compares and assesses eight remotely sensed maps of Philippine forest cover in the year 2010. We examined eight Forest versus Non-Forest maps reclassified from eight land cover products: the Philippine Land Cover, the Climate Change Initiative (CCI) Land Cover, the Landsat Vegetation Continuous Fields (VCF), the MODIS VCF, the MODIS Land Cover Type product (MCD12Q1), the Global Tree Canopy Cover, the ALOS-PALSAR Forest/Non-Forest Map, and the GlobeLand30. The reference data consisted of 9852 randomly distributed sample points interpreted from Google Earth. We created methods to assess the maps and their combinations. Results show that the percentage of the Philippines covered by forest ranges among the maps from a low of 23% for the Philippine Land Cover to a high of 67% for GlobeLand30. Landsat VCF estimates 36% forest cover, which is closest to the 37% estimate based on the reference data. The eight maps plus the reference data agree unanimously on 30% of the sample points, of which 11% are attributable to forest and 19% to non-forest. The overall disagreement between the reference data and Philippine Land Cover is 21%, which is the least among the eight Forest versus Non-Forest maps. About half of the 9852 points have a nested structure such that the forest in a given dataset is a subset of the forest in the datasets that have more forest than the given dataset. The variation among the maps regarding forest quantity and allocation relates to the combined effects of the various definitions of forest and classification errors. Scientists and policy makers must consider these insights when producing future forest cover maps and when establishing benchmarks for forest cover monitoring.

The profession debates how to encode a categorical variable for input to machine learning algorithms, such as neural networks. A conventional approach is to convert a categorical variable into a collection of binary variables, which causes a burdensome number of correlated variables. TerrSet’s Land Change Modeler proposes encoding a categorical variable onto the continuous closed interval from 0 to 1 based on each category’s Population Evidence Likelihood (PEL) for input to the Multi-Layer Perceptron, which is a type of neural network. We designed examples to test the wisdom of these encodings. The results show that encoding a categorical variable based on each category’s Sample Empirical Probability (SEP) produces results similar to binary encoding and superior to PEL encoding. The Multi-Layer Perceptron’s sigmoidal smoothing function can cause PEL encoding to produce nonsensical results, while SEP encoding produces straightforward results. We reveal the encoding methods by illustrating how a dependent variable gains across an independent variable that has four categories. The results show that PEL can differ substantially from SEP in ways that have important implications for practical extrapolations. If users must encode a categorical variable for input to a neural network, then we recommend SEP encoding, because SEP efficiently produces outputs that make sense.

Remote sensing, or Earth Observation (EO), is increasingly used to understand Earth system dynamics and create continuous and categorical maps of biophysical properties and land cover, especially based on recent advances in machine learning (ML). ML models typically require large, spatially explicit training datasets to make accurate predictions. Training data (TD) are typically generated by digitizing polygons on high spatial-resolution imagery, by collecting in situ data, or by using pre-existing datasets. TD are often assumed to accurately represent the truth, but in practice almost always have error, stemming from (1) sample design, and (2) sample collection errors. The latter is particularly relevant for image-interpreted TD, an increasingly commonly used method due to its practicality and the increasing training sample size requirements of modern ML algorithms. TD errors can cause substantial errors in the maps created using ML algorithms, which may impact map use and interpretation. Despite these potential errors and their real-world consequences for map-based decisions, TD error is often not accounted for or reported in EO research. Here we review the current practices for collecting and handling TD. We identify the sources of TD error, and illustrate their impacts using several case studies representing different EO applications (infrastructure mapping, global surface flux estimates, and agricultural monitoring), and provide guidelines for minimizing and accounting for TD errors. To harmonize terminology, we distinguish TD from three other classes of data that should be used to create and assess ML models: training reference data, used to assess the quality of TD during data generation; validation data, used to iteratively improve models; and map reference data, used only for final accuracy assessment. We focus primarily on TD, but our advice is generally applicable to all four classes, and we ground our review in established best practices for map accuracy assessment literature. EO researchers should start by determining the tolerable levels of map error and appropriate error metrics. Next, TD error should be minimized during sample design by choosing a representative spatio-temporal collection strategy, by using spatially and temporally relevant imagery and ancillary data sources during TD creation, and by selecting a set of legend definitions supported by the data. Furthermore, TD error can be minimized during the collection of individual samples by using consensus-based collection strategies, by directly comparing interpreted training observations against expert-generated training reference data to derive TD error metrics, and by providing image interpreters with thorough application-specific training. We strongly advise that TD error is incorporated in model outputs, either directly in bias and variance estimates or, at a minimum, by documenting the sources and implications of error. TD should be fully documented and made available via an open TD repository, allowing others to replicate and assess its use. To guide researchers in this process, we propose three tiers of TD error accounting standards. Finally, we advise researchers to clearly communicate the magnitude and impacts of TD error on map outputs, with specific consideration given to the likely map audience.

This paper couples a Forward Feature Selection algorithm with Random Forest (FFS-RF) to create a transition index map, which then guides the spatial allocation for the extrapolation of urban growth using a Cellular Automata model. We used Landsat imagery to generate land cover maps at the years 1998, 2008, and 2018 for the Tehran-Karaj Region (TKR) in Iran. The FFS-RF considered the independent variables of slope, altitude, and distances from urban, crop, greenery, barren, and roads. The FFS-RF revealed temporal non-stationary of drivers from 1998–2008 to 2008–2018. The FFS-RF detected that altitude and distance from greenery were the most important drivers of urban growth during 1998–2008, then distances from crop and barren were the most important drivers during 2008–2018. We used the Total Operating Characteristic to evaluate the transition index maps. Validation during 2008–2018 showed that FFS-RF produced a transition index map that had predictive power no better than an allocation of urban growth near existing urban. Simulation to 2060 extrapolated that Tehran, Karaj, and their adjacent cities will interconnect spatially to form a gigantic city-region.

We apply a method to evaluate the strength of the evidence for deviations from uniform land change in a coastal area, in the context of Intensity Analysis. The errors in the CORINE maps at 1990 and 2006 can influence the apparent change, but the errors are unknown because error assessment of the 1990 map has never been released, while the error of the 2006 map has been checked for only some countries. The 1990 and the 2006 maps of a coastal watershed in Portugal served as the data to compute the intensities of changes among eight categories. We evaluate the sizes and types of errors that could explain deviations from uniform intensities. Errors in 2.0% of the 2006 map can explain all apparent deviations from uniform gains. Errors in 1.5% of the 1990 map can explain all apparent deviations from uniform losses. Errors in less than 0.7% of the 1990 map can explain all apparent deviations from uniform transitions to each gaining category. We analyse the strength of the evidence for deviations from uniform intensities in light of historical processes of change. Historical processes can explain some transitions that the data show, while the hypothesised errors in the data are the explanation for other transitions that are not consistent with known processes. Inconsistent transitions are an indication of the misclassification errors that could propagate to other land cover change applications, as in the assessment of hydrological processes.

Land change in Kigali, Rwanda, is examined using Intensity Analysis, which measures the temporal stationarity of changes among categories. Maps for 1981, 2002 and 2014 were produced that show the land categories Built, Vegetated and Other, which is composed mainly of croplands and bare surfaces. Land change accelerated from the first time interval (1981–2002) to the second time interval (2002–2014), as increased human and economic activities drove land transformation. During the first interval, Vegetated showed net loss whereas Built showed net gain, in spite of a small transition directly from Vegetated to Built. During the second interval, Vegetated showed net gain whereas Built showed nearly equal amounts of gross loss and gross gain. The gain of Built targeted Other during both time intervals. A substantial portion of overall change during both time intervals consisted of simultaneous transitions from Vegetated to Other in some locations and from Other to Vegetated in other locations.

Conventional methods to analyze a transition matrix do not offer in-depth signals concerning land changes. The land change community needs an effective approach to visualize both the size and intensity of land transitions while considering possible map errors. We propose a framework that integrates error analysis, intensity analysis, and difference components, and then uses the framework to analyze land change in Nanchang, the capital city of Jiangxi province, China. We used remotely sensed data for six categories at four time points: 1989, 2000, 2008, and 2016. We had a confusion matrix for only 2016, which estimated that the map of 2016 had a 12% error, while the temporal difference during 2008–2016 was 22% of the spatial extent. Our tools revealed suspected errors at other years by analyzing the patterns of temporal difference. For example, the largest component of temporal difference was exchange, which could indicate map errors. Our framework identified categories that gained during one time interval then lost during the subsequent time interval, which raised the suspicion of map error. This proposed framework facilitated visualization of the size and intensity of land transitions while illustrating possible map errors that the profession routinely ignores.

Comparison between two time points of the same categorical variable for the same study extent can reveal changes among categories over time, such as transitions among land categories. If many categories exist, then analysis can be difficult to interpret. Category aggregation is the procedure that combines two or more categories to create a single broader category. Aggregation can simplify interpretation, and can also influence the sizes and types of changes. Some classifications have an a priori hierarchy to facilitate aggregation, but an a priori aggregation might make researchers blind to important category dynamics. We created an algorithm to aggregate categories in a sequence of steps based on the categories’ behaviors in terms of gross losses and gross gains. The behavior-based algorithm aggregates net gaining categories with net gaining categories and aggregates net losing categories with net losing categories, but never aggregates a net gaining category with a net losing category. The behavior-based algorithm at each step in the sequence maintains net change and maximizes swap change. We present a case study where data from 2001 and 2006 for 64 land categories indicate change on 17% of the study extent. The behavior-based algorithm produces a set of 10 categories that maintains nearly the original amount of change. In contrast, an a priori aggregation produces 10 categories while reducing the change to 9%. We offer a free computer program to perform the behavior-based aggregation.

Time-series maps have become more detailed in terms of numbers of categories and time points. Our paper proposes methods for raster datasets where detailed analysis of all categorical transitions would be initially overwhelming. We create two measurements: Incidents and States. The former is the number of times a pixel’s category changes across time intervals; the latter is the number of categories that a pixel represents across time points. The combinations of Incidents and States summarize change trajectories. We also describe categorical transitions in terms of annual flow matrices, which quantify the additional information generated by intermediate time points within the temporal extent. Our approach summarizes change at the pixel and landscape levels in ways that communicate where and how categories transition over time. These methods are useful to detect hotspots of change and to consider whether the apparent changes are real or due to map error.

The aim of this study is to improve the understanding of land changes in the Jiulong River watershed, a coastal watershed of Southeast China. We developed a stratified classification methodology for land mapping, which combines linear stretching, an Iterative Self-Organizing Data Analysis (ISODATA) clustering algorithm, and spatial reclassification. The stratified classification for 2002 generated less overall error than an unstratified classification. The stratified classifications were then used to examine temporal differences at 1986, 1996, 2002, 2007 and 2010. Intensity Analysis was applied to analyze land changes at three levels: time interval, category, and transition. Results showed that land use transformation has been accelerating. Woodland's gains and losses were dormant while the gains and losses of Agriculture, Orchard, Built-up and Bare land were active during all time intervals. Water's losses were active and stationary. The transitions from Agriculture, Orchard, and Water to Built-up were systematically targeting and stationary, while the transition from Woodland to Built-up was systematically avoiding and stationary.

Intensity Analysis has become popular as a top-down hierarchical accounting framework to analyze differences among categories, such as changes in land categories over time. Some aspects of interpretation are straightforward, while other aspects require deeper thought. This article explains how to interpret Intensity Analysis with respect to four concepts. First, we illustrate how to analyze whether error could account for non-uniform changes. Second, we explore two types of the large dormant category phenomenon. Third, we show how results can be sensitive to the selection of the domain. Fourth, we explain how Intensity Analysis’ symmetric top-down hierarchy influences interpretation with respect to temporal processes, for which changes during a time interval influence the sizes of the categories at the final time, but not at the initial time. We illustrate these concepts by applying Intensity Analysis to changes during one time interval (2000–2004) in a part of Central Kalimantan for the land categories Forest, Bare and Grass.

The multiple uses of land-cover models have led to validation with choice metrics or an ad hoc choice of the validation metrics available. To address this, we have identified the major dimensions of land-cover maps that ought to be evaluated and devised a Similarity Validation (SimiVal) tool. SimiVal uses a linear regression to test a modelled projection against benchmark cases of, perfect, observed and systematic-bias, calculated by rescaling the metrics from a random case relative to the observed, perfect case. The most informative regression coefficients, p-value and slope, are plot on a ternary graph of 'similarity space' whose extremes are the three benchmark cases. SimiVal is tested on projections of two deliberately contrasting land-cover models to show the similarity between intra- and inter-model parameterisations. We find metrics of landscape structure are important in distinguishing between different projections of the same model. Predictive and exploratory models can benefit from the tool. SimiVal is a tool that provides a consistent validation of land-cover change maps.The method validates quantity allocation, distance allocation and spatial metrics.Extreme benchmark scores for metrics and boundless metrics are computed.A model projection is validated to the perfect, random and systematic-bias cases.Many model projections can be validated together in 'similarity space'.

Geospatial analysis and statistical analysis are coupled in this study to determine the dynamic linkage between landscape characteristics and water quality for the years 1996, 2002, and 2007 in a subtropical coastal watershed of Southeast China. The landscape characteristics include Percent of Built (%BL), Percent of Agriculture, Percent of Natural, Patch Density and Shannon's Diversity Index (SHDI), with water quality expressed in terms of COD(Mn) and NH(4)(+)-N. The %BL was consistently positively correlated with NH(4)(+)-N and COD(Mn) at time three points. SHDI is significantly positively correlated with COD(Mn) in 2002. The relationship between NH(4)(+)-N, COD(Mn) and landscape variables in the wet precipitation year 2007 is stronger, with R(2) = 0.892, than that in the dry precipitation years 1996 and 2002, which had R(2) values of 0.712 and 0.455, respectively. Two empirical regression models constructed in this study proved more suitable for predicting COD(Mn) than for predicting NH(4)(+)-N concentration in the unmonitored watersheds that do not have wastewater treatment plants. The calibrated regression equations have a better predictive ability over space within the wet precipitation year of 2007 than over time during the dry precipitation years from 1996 to 2002. Results show clearly that climatic variability influences the linkage of water quality-landscape characteristics and the fit of empirical regression models.

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.

It is important to know how the results from a land change model vary based on both the pixel resolution of the maps and the precision of the independent variables because subjective decisions or default values frequently determine these two factors. This paper presents an approach to measure the variation in model accuracy that is triggered by alteration of the pixel resolution and the precision of the independent variable, which are bins of distance to previously built area for our case study. We illustrate the principles with an application of the Geomod land change model contained in the Idrisi GIS, applied to simulate the gain of built land in central Massachusetts, USA. Results reveal four general principles: (1) change in pixel resolution using the majority-takes-all rule can influence quantity error, (2) change in bin width of an independent variable does not influence the quantity error, (3) resolution and bin width interact so that bin width does not have an effect on error when bin widths are smaller than the pixel resolution, and (4) researchers are wise to examine the implications of their subjective decisions by plotting clearly how the resolution and bin size influence the mathematical relationships that the model uses. We have found no universal, hard, and fast rules that dictate how to decide on an appropriate pixel resolution and bin width, but our method demonstrates how these decisions can be influential. These insights can offer scientists guidance in how to prepare data in an appropriate manner.

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 model's 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 model's 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.

This paper presents a method to compare maps that contain pixels that have partial membership to multiple categories, i.e., mixed or soft classified pixels. The method quantifies ranges for associations among categories based upon possible variations in sub-pixel spatial allocation. The paper derives the mathematical equations for constructing the range of associations based on three types of cross-tabulation matrices, the greatest matrix, the random matrix, and the least matrix. We demonstrate how the analysis can be combined with multiple resolution map comparison to specify the resolution at which clusters exist on a single map or between two maps. The method produces a range that reflects the amount of uncertainty in the categorical associations. We illustrate the procedure with both a simple example and data from the Plum Island Ecosystems study site in Massachusetts, USA.

This paper describes three important inter-related factors in multipleresolution categorical map comparison that can affect the measured association between two maps: resolution effect, matrix effect, and parameter effect. We demonstrate how cross-tabulation matrix construction affects the quantitative comparison of categorical maps by analyzing synthesized and empirical examples at fine and several coarser resolutions. We consider three soft classification rules and their corresponding matrices—multiplication, minimum, and composite. We measure association using popular coefficients of agreement at multiple resolutions. The results show that the composite matrix has useful interpretability because it assesses clearly the information of quantity and spatial allocation concerning map categories.

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.

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 BLM's 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 ne...

This paper presents quantitative methods that allow scientists to compare the patterns in two maps that show a shared real variable. Specifically, this paper shows how to budget various components of agreement and disagreement between maps. The components are based on the separation of a map’s information of quantity from its information of location. The technique also examines how variation in resolution influences the measurement of the components of information. The manner in which the measurements change as a function of spatial resolution can be more important and interesting than the results at any single particular resolution, because the results at a single particular resolution may indicate more about the format of the data than about the overall pattern in the landscape. An example illustrates the mathematical concepts, and an application compares mapped vegetation indices in Africa to illustrate the usefulness of the proposed approach vis-a-vis a conventional approach. The results are presented visually in the form of stacked bar graphs that show separable components of information. The entire analysis is performed twice, each time with a different mathematical measurement of deviation: (1) root mean square error, and (2) mean absolute error. This paper compares these two approaches and discusses their relative advantages and disadvantages. Hopefully, this approach of budgeting components of information at multiple resolutions will become adopted as standard practice in the measurement of patterns.

Our article illustrates how to compare the outputs from models that simulate transitions among categories through time. We illustrate the concepts by comparing two land change models: Land Change Modeler and Cellular Automata Markov. We show how the modeling options influence the quantity and allocation of simulated transitions, and how to compare output maps from pairs of model runs with respect to a reference map of transitions during the validation interval. We recommend that the first step is to assess the quantity of each transition and to determine the cause of the variation in quantity among model runs. The second step is to assess the allocation of transitions and to determine the cause of the variation in allocation among model runs. The separation of quantity and allocation of the transitions is a helpful approach to communicate how models work and to describe pattern validation. We compare three runs of models that simulate transitions among land categories.Pattern validation compares a reference map of transition to maps from pairs of runs.Quantity and allocation are helpful concepts to describe models and to compare maps.Quantity refers to the size of each transition from one category to another category.Allocation refers to the spatial distribution of the transitions.

This paper introduces a new statistical method that we recommend should become standard procedure to quantify the goodness-of-fit of calibration and validation for land-use change models. We present a multiple-resolution Relative Operating Characteristic (ROC) that measures the goodness-of-fit between a reference map, which is considered reality, and a simulated map, which is a model’s output. This proposed ROC is based on: (1) multiple-resolutions, (2) soft classification, (3) sampling without replacement, and 4) explicit separation of factors of quantity versus location of land-use change. We illustrate the method with a case study in India’s Western Ghats, a biodiversity hotspot, where we have maps of cumulative forest disturbance for 1920 and 1990. We use a predictive modeling approach similar to GEOMOD in which we calibrate the model with the map of 1920, then predict the map of 1990, at which point we subject the model to validation. We show that the fit of calibration tends to be much larger than the fit of validation. Thus if a modeler assess a model by goodness-of-fit of calibration only, then the modeler will likely be over confident in the model’s predictive ability.

This paper offers techniques of validation that land-use and -cover change (LUCC) modelers should find useful because the methods give information that is useful to improve LUCC models and to set the agenda for future LUCC research. Specifically, the validation technique: (a) budgets sources of agreement and disagreement between the prediction map and the reference map, (b) compares the predictive model to a Null model that predicts pure persistence, (c) compares the predictive model to a Random model that predicts change evenly across the landscape, and (d) evaluates the goodness-of-fit at multiple-resolutions to see how scale influences the assessment. This paper introduces a new criterion called the Null Resolution, which is the spatial resolution at which the predictive model is as accurate as the Null model. For illustration, these techniques are applied to assess an LUCC model called Geomod, which predicts land change in the 22 towns of the Ipswich River Watershed in northeastern Massachusetts, USA. For this application, the Null Resolution is approximately 1 km. At resolutions finer than 1 km, the Null model performs better than Geomod, which performs better than the Random model. At resolutions coarser than 1 km, both Geomod and the Random models perform better than the Null model, but Geomod and the Random models are nearly indistinguishable beyond the 1 km resolution. © 2004 Elsevier B.V. All rights reserved.

This article introduces the Flow matrix, which expresses the sizes of transitions among categories between two time points. We use the Flow matrix to create a metric R that measures the instability of annual change among time intervals that partition the time extent. Specifically, R is the proportion of change that would need to be reallocated to different time intervals to achieve uniform change during the time extent. This article computes R for 10 Long Term Ecological Research LTER sites and for seven case studies from published land change data. Of the 10 LTER sites analyzed, the Andrews site in Oregon had the highest R value 37.1% of change, while the Luquillo site in Puerto Rico had the lowest 1.7% of change. We analyze the mathematical behavior of R, especially with respect to how the partitioning of the time extent into intervals can influence R.

The Receiver Operating Characteristic (ROC) is widely used for assessing the performance of classification algorithms. In GIScience, ROC has been applied to assess models aimed at predicting events, such as land use/cover change (LUCC), species distribution and disease risk. However, GIS software packages offer few statistical tests and guidance tools for ROC analysis and interpretation. This paper presents a suite of GIS tools designed to facilitate ROC curve analysis for GIS users by applying proper statistical tests and analysis procedures. The tools are freely available as models and submodels of Dinamica EGO freeware. The tools give the ROC curve, the area under the curve (AUC), partial AUC, lower and upper AUCs, the confidence interval of AUC, the density of event in probability bins and tests to evaluate the difference between the AUCs of two models. We present first the procedures and statistical tests implemented in Dinamica EGO, then the application of the tools to assess LUCC and species distribution models. Finally, we interpret and discuss the ROC-related statistics resulting from various case studies.

International audience; During the last decades, there has been an increasing interest from the academic and policy communities to monitor and model changes of the earth surface. Modeling environmental dynamics helps to understand changes that are taking place currently and to anticipate future evolutions. Prospective simulation supports decision-making for environmental management and land planning. This special issue is dedicated to advances in land change modeling. Land Use / Land Cover Change, also called LUCC, is certainly a prominent interface between natural and social dynamics because anthropogenic LUCC has a profound impact on Earth. LUCC impacts a large amount of highly relevant topics such as resource exploitation, climate change, biodiversity loss, etc. Land change modeling can provide transparent, efficient and sustainable decision support to these current and rising environmental problems

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 1...

It is essential to measure whether maps of various scenarios of future land change are meaningfully different, because differences among such maps serve to inform land management. This paper compares the output maps of different scenarios of future land change in a manner that contrasts two different approaches to account for the uncertainty of the simulated projections. The simpler approach interprets the scenario storyline concerning the quantity of each land change transition as assumption, and then considers the range of possibilities concerning the value added by a simulation model that specifies the spatial allocation of land change. The more complex approach estimates the uncertainty of future land maps based on a validation measurement with historic data. The technique is illustrated by a case study that compares two scenarios of future land change in the Plum Island Ecosystems of northeastern Massachusetts, in the United States. Results show that if the model simulates only the spatial allocation of the land changes given the assumed quantity of each transition, then there is a clearly bounded range for the difference between the raw scenario maps; but if the uncertainties are estimated by validation, then the uncertainties can be so great that the output maps do not show meaningful differences. We discuss the implications of these results for a future research agenda of land change modeling. We conclude that a productive approach is to use the simpler method to distinguish clearly between variations in the scenario maps that are due to scenario assumptions versus variations due to the simulation model.

This paper applies methods of multiple resolution map comparison to quantify characteristics for 13 applications of 9 different popular peer-reviewed land change models. Each modeling application simulates change of land categories in raster maps from an initial time to a subsequent time. For each modeling application, the statistical methods compare: (1) a reference map of the initial time, (2) a reference map of the subsequent time, and (3) a prediction map of the subsequent time. The three possible two-map comparisons for each application characterize: (1) the dynamics of the landscape, (2) the behavior of the model, and (3) the accuracy of the prediction. The three-map comparison for each application specifies the amount of the prediction's accuracy that is attributable to land persistence versus land change. Results show that the amount of error is larger than the amount of correctly predicted change for 12 of the 13 applications at the resolution of the raw data. The applications are summarized and compared using two statistics: the null resolution and the figure of merit. According to the figure of merit, the more accurate applications are the ones where the amount of observed net change in the reference maps is larger. This paper facilitates communication among land change modelers, because it illustrates the range of results for a variety of models using scientifically rigorous, generally applicable, and intellectually accessible statistical techniques. © Springer-Verlag 2007.