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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

This article presents the clearest description to date concerning how to compute the hypothetical classification errors that could explain deviations from uniform land changes in the context of Intensity Analysis. Intensity Analysis is an accounting framework that analyses a square contingency table to measure how the sizes of the changes compare to the sizes of the categories. Our case study analyses maps of a portion of southern Nigeria at 1987 and 2002 that show the categories: cultivation, forest, settlement, and water. The data reveal that the changes are not uniformly proportional to the sizes of the categories in terms of categorical gains, categorical losses, and transitions. The methods in this article show that hypothetical error in 9% of the 2002 map could explain all the deviations from uniform categorical gains, hypothetical error in 11% of the 1987 map could explain all the deviations from uniform categorical losses, and hypothetical error in 6% of the 1987 map could explain all deviations from uniform transitions. Larger hypothetical error indicates stronger evidence for a particular deviation from the relevant hypothesized uniform intensity. It is helpful to know the strength of evidence, even when the actual errors in the maps are unknown, which is frequently the case for historical time points. [ABSTRACT FROM PUBLISHER]

A common task is to measure the difference between two maps that show the same spatial extent for the same categorical variable, such as land-cover type. One popular technique is to express the overall difference as the sum of two components called quantity and allocation. This article shows how to take an additional step to express allocation difference as the sum of two components called exchange and shift. Exchange exists for a pair of pixels when one pixel is classified as category A in the first map and as category B in the second map, while simultaneously the paired pixel is classified as category B in the first map and as category A in the second map. If there are more than two categories, then it is possible to have a component called shift, which is allocation difference that is not exchange. Our article shows how to compute all three components of overall difference: quantity, exchange, and shift. We show also how to compute the three components for each category and to reveal the category pairs that account for the largest exchanges. Our article applies the principles to characterize both temporal changes and classification errors using land-cover maps from suburban Massachusetts, USA. [ABSTRACT FROM PUBLISHER]

The family of Kappa indices of agreement claim to compare a map's observed classification accuracy relative to the expected accuracy of baseline maps that can have two types of randomness: (1) random distribution of the quantity of each category and (2) random spatial allocation of the categories. Use of the Kappa indices has become part of the culture in remote sensing and other fields. This article examines five different Kappa indices, some of which were derived by the first author in 2000. We expose the indices' properties mathematically and illustrate their limitations graphically, with emphasis on Kappa's use of randomness as a baseline, and the often-ignored conversion from an observed sample matrix to the estimated population matrix. This article concludes that these Kappa indices are useless, misleading and/or flawed for the practical applications in remote sensing that we have seen. After more than a decade of working with these indices, we recommend that the profession abandon the use of Kappa indices for purposes of accuracy assessment and map comparison, and instead summarize the cross-tabulation matrix with two much simpler summary parameters: quantity disagreement and allocation disagreement. This article shows how to compute these two parameters using examples taken from peer-reviewed literature. [ABSTRACT FROM AUTHOR]

If a scientist overlays two perfectly accurate maps of land categories of the same place from two points in time, then the differences indicate land change. A land transition matrix summarizes the amount of land that changes from each category at the initial time to each category at the subsequent time. This article proposes methods to compute the land transition matrix in a manner that accounts for errors in the maps, where confusion matrices estimate those errors. If empirical confusion matrices are not available, sensitivity analysis can show the effect of possible errors. The proposed methods produce maps that show the probability of any land transition, given the maps and their confusion matrices. Additional techniques show how possible errors in the maps influence the total land change in terms of two components of quantity and allocation. This article illustrates the methods using data from 1971 to 1999 in Massachusetts, USA. [ABSTRACT FROM AUTHOR]

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 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 model's 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 BLM's assumption that deforestation within household lots occurs near roads. A large source of location disagreement is the BLM's 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. [ABSTRACT FROM AUTHOR]

A correction to the article "Object-Based Classification With Features Extracted by a Semi-Automatic Feature Extraction Algorithm--SEaTH," by Yan Gao and colleagues, published in previous issue.