A Regression-Based Procedure for Markov Transition Probability Estimation in Land Change Modeling

Abstract

Land change models commonly model the expected quantity of change as a Markov chain. Markov transition probabilities can be estimated by tabulating the relative frequency of change for all transitions between two dates. To estimate the appropriate transition probability matrix for any future date requires the determination of an annualized matrix through eigendecomposition followed by matrix powering. However, the technique yields multiple solutions, commonly with imaginary parts and negative transitions, and possibly with no non-negative real stochastic matrix solution. In addition, the computational burden of the procedure makes it infeasible for practical use with large problems. This paper describes a Regression-Based Markov (RBM) approximation technique based on quadratic regression of individual transitions that is shown to always yield stochastic matrices, with very low error characteristics. Using land cover data for the 48 conterminous US states, median errors in probability for the five states with the highest rates of transition were found to be less than 0.00001 and the maximum error of 0.006 was of the same order of magnitude experienced by the commonly used compromise of forcing small negative transitions estimated by eigendecomposition to 0. Additionally, the technique can solve land change modeling problems of any size with extremely high computational efficiency.

Improving the predictive performance of CLUE-S by extending demand to land transitions: the trans-CLUE-S model

“…For a land type in its row, the Markov matrix can then be used to project the demanded transitions in map 2 from map 1, by multiplying the row’s entries by the total number of cells covered by the land type in map 1. If the map 1–map 2 time interval is not of the same duration as the map 0–map 1 interval, there exist techniques for projecting the transition matrix of the map 0–map 1 interval to the duration of the map 1–map 2 interval (Eastman and He, 2020; Takada et al, 2010).…”

Application of land-use change model for supporting land-use planning in An Bien district, Kien Giang province, Vietnam

“…Regarding land-use and land cover models, there are many studies applied land-use change models such as CLUES, SLEUTH, DINAMICA EGO, IMAGE and Cellular Automata [5] [6], ANN [7] in many countries including the mountainous areas of Vietnam. They have been used to describe urban growth and land-use changes over time.…”

A Land-Use Change Model to Support Land-Use Planning in the Mekong Delta (MEKOLUC)

“…With respect to modeling land-use changes, although existing models are widely used in urban planning, the landscape of many countries, including the mountainous areas of Vietnam, requires the development of a specific model for large-scale land-use management for the complex hydrological features of these landscapes. Many studies applying GIS [14][15][16] and Markov chains [17] to land-use forecasting have been widely used to describe land-use changes over time. However, the Markov model does not consider the driving factors behind the changes; it only considers the area changes over the years in order to build a transition probability matrix.…”