Estimating the Land Transition Matrix Based on Erroneous Maps

This article presents methods to estimate a land cover transition matrix based on maps from two points in time. The land cover transition matrix indicates the amount of land that transitions from each category at time 1 to each category at time 2. Observed differences between the two land cover maps can be due to change on the ground or error in the maps. If the maps were perfectly correct, then the observed differences would indicate true land transition on the ground. This paper considers the situation when the maps are not correct, and a confusion matrix indicates the structure of the errors in each map. For situations where formal confusion matrices are not available, we perform sensitivity analysis to show how the suspected error in the maps influences the estimates of the land cover transitions. We illustrate the technique using land cover data from 1971 and 1999 in the Plum Island Ecosystems of Northeastern Massachusetts, which is a Long Term Ecological Research site of the National Science Foundation. If the maps were perfectly correct, then the transition from forest to residential would account for 6% of the study area. Our method shows that if each category were to have a user’s accuracy of 85 percent, then this transition would account for 7% of the study area, and could range from 4% to 8% depending on the assumptions concerning the distribution of errors in the maps. The method also produces maps that show the probability of any particular land cover transition, given the observed data and the confusion matrix.