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.