Transiograms for Characterizing Spatial Variability of Soil Classes

Abstract

The characterization of complex autocorrelations and interclass relationships among soil classes call for effective spatial measures. This study developed a transition probability-based spatial measure-the transiogram-for characterizing spatial heterogeneity of discrete soil variables. The study delineated the theoretical foundations and fundamental properties, and explored the major features of transiograms as estimated using different methods and data types, as well as challenges in modeling experimental transiograms. The specific objectives were to: (i) provide a suitable spatial measure for characterizing soil classes; (ii) introduce related knowledge for understanding spatial variability of soil types described by transiograms; and (iii) suggest methods for estimating and modeling transiograms from sparse sample data. Case studies show that (i) cross-transiograms are normally asymmetric and unidirectionally irreversible, which make them more capable of heterogeneity characterization, (ii) idealized transiograms are smooth curves, of which most are exponential and some have a peak in the low-lag section close to the origin, (iii) real-data transiograms are complex and usually have multiple ranges and irregular periodicities, which may be regarded as non-Markovian properties of the data that cannot be captured by idealized transiograms, and (iv) experimental transiograms can be approximately fitted using typical mathematical models, but sophisticated models are needed to effectively fit complex features. Transiograms may provide a powerful tool for measuring and analyzing the spatial heterogeneity of soil classes.