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Abstract
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 interval(s) 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.
Acknowledgements
The United States’ National Science Foundation (NSF) supported this work via the following programs: Long Term Ecological Research via grants OCE-0423565 & OCE-1058747 for Plum Island Ecosystems and OCE-0620959 for Georgia Coastal Ecosystems, Coupled Natural Human Systems via grant BCS-0709685, Research Experiences for Undergraduates via grant SES-0849985, and Urban Long Term Research Areas via grant BCS-0948984. The NSF supplied additional funding through a supplement grant entitled “Maps and Locals (MALS)” via grant DEB-0620579. The work has also benefited from the NICHD funded University of Colorado Population Center (grant R21 HD51146) for research, administrative, and computing support. Any opinions, findings, conclusions, or recommendation expressed in this paper are those of the authors and do not necessarily reflect those of the funders. Anonymous reviewers supplied constructive feedback that helped to improve this paper.