Abstract
Takada’s group developed a method for estimating the yearly transition matrix by calculating the mth power roots of a transition matrix with an interval of m years. However, the probability of obtaining a yearly transition matrix with real and positive elements is unknown. In this study, empirical verification based on transition matrices from previous land-use studies and Monte-Carlo simulations were conducted to estimate the probability of obtaining an appropriate yearly transition probability matrix. In 62 transition probability matrices of previous land-use studies, 54 (87%) could provide a positive or small-negative solution. For randomly generated matrices with differing sizes or power roots, the probability of obtaining a positive or small-negative solution is low. However, the probability is relatively large for matrices with large diagonal elements, exceeding 90% in most cases. These results indicate that Takada et al.’s method is a powerful tool for analyzing land-use dynamics.
Highlights
Land-use and land-cover change with natural processes and human activities, which further depends on ecological, economic, political institutional, and social constraints [1]
Empirical verification based on transition matrices from previous land-use studies and Monte-Carlo simulations were conducted to estimate the probability of obtaining an appropriate yearly transition probability matrix with TAM
This study has revealed that (1) the possibility of obtaining yearly transition probability matrices with real field data set is high, (2) the theoretical possibility of obtaining yearly transition probability matrices is low, as shown in Monte-Carlo simulation with random matrices, and (3) the difference between real and theoretical results may be explained by high possibility of obtaining yearly transition probability matrices in Biased Monte-Carlo simulation, suggesting that the possibility of obtaining yearly transition probability matrices is high when the diagonal elements of the transition probability matrix were relatively larger than non-diagonal elements
Summary
Land-use and land-cover change with natural processes and human activities, which further depends on ecological, economic, political institutional, and social constraints [1]. Studying land-use/cover change (LUCC) may contribute to better understanding of the interaction between environmental and human-driven processes and finding key processes within the local human–environment system [2]. The probability-based transition matrix approach has been used to analyze, compare, and predict LUCC over specific periods with a stationary Markov model [7,8,9,10]. In this approach, two maps of a single site for two points in time are classified into the same set of land-use/cover categories and the transition probabilities between the categories are estimated by comparing these two maps [11].
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