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.

中文翻译：

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使用 Flow 矩阵测量土地变化的时间不稳定性

本文介绍了 Flow 矩阵，它表示两个时间点之间类别之间的转换大小。我们使用 Flow 矩阵来创建一个度量 R，它测量划分时间范围的时间间隔之间的年度变化的不稳定性。具体来说，R 是需要重新分配到不同时间间隔以在时间范围内实现均匀变化的变化比例。本文根据已发布的土地变化数据计算了 10 个长期生态研究 (LTER) 站点和七个案例研究的 R。在分析的 10 个 LTER 站点中，俄勒冈州的安德鲁斯站点的 R 值最高（变化的 37.1%），而波多黎各的 Luquillo 站点的 R 值最低（变化的 1.7%）。我们分析 R 的数学行为，