Development And Application Of A Transiogram Modeling System

Categorical geographical variables, such as soil types, land cover/use classes and lithofacies, usually exhibit complex spatial variability. Besides complex autocorrelations within individual categories, there are also complex interclass relationships existing among different categories.For describing the spatial variability of categorical spatial variables, conventional methods usually used are Markov transition probability matrices and indicator variograms from indicator geostatistics. Although being effective, they have apparent limitations in some respects:First, they may conceal some spatial correlation information, and second, they lack intuition.Recently, Markov chain geostatistics and its accompanying spatial measure, the transiogram, were proposed. The transiogram can be used as an independent spatial measure for characterizing spatial variability of discrete variables. It not only has strong describing ability and is easy to understand, but also has the support of the perfect Markov chain theory. In addition, as far as mathematical models used for fitting experimental transiograms, the transiogram method not only can utilize existing mathematical models proposed for variogram modeling in geostatistics, but also innovated new mathematical models. The innovated new models also can be used for fitting experimental variograms with similar features and improve their fitting accuracy.This thesis is mainly focused on the introduction of the transiogram theory and its application in characterizing the spatial variability of soil types, and the development of a transiogram modeling system using the popular Python language. A part of the soil type map of the Yiling District, Yichang City, was used as the original data to calculate various transiograms for characterizing the spatial variability of soil types, and demonstrate their features and advantages in charactering spatial variability of categorical spatial variables. The results show that:1. The developed modeling system functions well, and may accurately estimate experimental transiograms and characterize the transiogram theory.2. As a spatial correlation measure for describing the spatial variability of soil types, the transiogram has its advantages. For example, it can effectively capture the feature of neighboring relationships existing among a number of categories.3. Compared with indicator variograms, transiograms indicate obvious advantages in charactering the spatial variability of soil types. The physical meaning of transiograms is clear and easy to understand. Because of the irreversibility and asymmetry properties, unidirectional cross-transiograms can capture the asymmetry and juxtaposition relationships of soil types in their spatial distributions.This transiogram modeling system currently did not consider the estimation of anisotropic transiograms with a tolerance angle and width (this does not include uni-directional transiograms), nor consider the use of nested models.