Time-Lag Transiograms and Their Implications for Landscape Change Characterization

Markov chain transition probability matrices (TPMs) have traditionally been used to characterize land use and land cover (LULC) changes and species succession. However, previous studies relied solely on TPMs or transition area matrices to describe overall class area/proportion changes, overlooking important time correlation features. This study introduces the concept of idealized time-lag transiograms and demonstrates how they can be computed from temporal TPMs, using illustrative examples. The primary objective is to explore the potential value and utility of idealized time-lag transiograms in revealing additional characteristics of landscape change. Specifically, we focus on computing idealized time-lag transiograms with a fixed starting point and highlighting their fundamental features, such as sills, practical correlation ranges, and curve shapes, along with peak positions and peak height ratios of peaked cross-transiograms. These features are identified and discussed in terms of their potential implications for characterizing LULC changes. While idealized time-lag transiograms with a fixed starting point may not precisely predict future LULC changes due to the assumptions of the Markov property and time homogeneity (i.e., stationarity), they provide new insights into future LULC dynamics, revealing aspects that traditional Markov chain analysis has overlooked.