Transiograms for Characterizing Spatial Variability of Soil Classes

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.

[1]  Thomas A. Jones,et al.  Teacher's Aide: Modeling Hole-Effect Variograms of Lithology-Indicator Variables , 2001 .

[2]  E. Truog,et al.  A Soil Survey of Iowa County Wisconsin , 1911 .

[3]  A-Xing Zhu,et al.  A markov chain-based probability vector approach for modeling spatial uncertainties of soil classes , 2005 .

[4]  Robert F. Blakely,et al.  Generation of a Synthetic Vertical Profile of a Fluvial Sandstone Body , 1967 .

[5]  D. P. Franzmeier,et al.  Spatial Variability and Measurement Scale of Infiltration Rate on an Agricultural Landscape , 2004 .

[6]  Robert W. Ritzi,et al.  Behavior of indicator variograms and transition probabilities in relation to the variance in lengths of hydrofacies , 2000 .

[7]  Bernd Huwe,et al.  PAH mobility in contaminated industrial soils : a Markov chain approach to the spatial variability of soil properties and PAH levels , 2001 .

[8]  Yuanchun Shi,et al.  Markov-chain simulation of soil textural profiles , 1999 .

[9]  J. Chilès,et al.  Geostatistics: Modeling Spatial Uncertainty , 1999 .

[10]  Lars Rosén,et al.  On Modelling Discrete Geological Structures as Markov Random Fields , 2002 .

[11]  W. Schwarzacher,et al.  The use of Markov chains in the study of sedimentary cycles , 1969 .

[12]  John W. Crawford,et al.  An Efficient Markov Chain Model for the Simulation of Heterogeneous Soil Structure , 2004 .

[13]  Weidong Li,et al.  Markov Chain Random Fields for Estimation of Categorical Variables , 2007 .

[14]  G. Fogg,et al.  Transition probability-based indicator geostatistics , 1996 .

[15]  Li Weidong.  Transiogram: A spatial relationship measure for categorical data , 2006 .

[16]  Weidong Li,et al.  A Fixed-Path Markov Chain Algorithm for Conditional Simulation of Discrete Spatial Variables , 2007 .

[17]  G. Fogg,et al.  Modeling Spatial Variability with One and Multidimensional Continuous-Lag Markov Chains , 1997 .

[18]  Graham E. Fogg,et al.  Multi-scale alluvial fan heterogeneity modeled with transition probability geostatistics in a sequence stratigraphic framework , 1999 .