Application of Transiograms to Markov Chain Simulation and Spatial Uncertainty Assessment of Land-Cover Classes

The recently proposed two-dimensional (2-D) Markov chain conditional simulation approach has the advantage of incorporating interclass dependences into simulation of categorical variables, which is crucial for spatial prediction and uncertainty assessment of multinomial land-cover classes. To work with sampled point data, the key step is to effectively model experimental transiograms, which are estimated from sampled point data and serve as parameter input to a Markov chain simulation. However, it is difficult to fit complex curve shapes of experimental transiograms using mathematical models. In this paper we suggest a linear interpolation method to efficiently interpolate experimental transiograms into continuous models so that the 2-D Markov chain model works with sampled point data. Case studies show that: (1) land-cover patterns are captured in simulated realizations conditioned on point data using transiograms; (2) spatial uncertainty of land-cover classes, particularly the uncertainty of class polygon boundaries, is clearly revealed in occurrence probability maps; and (3) complex features of transiograms are reproduced in simulated realizations. It is concluded that the method may provide a practical way of using complex transiograms in 2-D Markov chain simulations of multinomial classes.