APPLICATION OF THE MARKOV CHAIN THEORY TO DESCRIBE SPATIAL DISTRIBUTION OF TEXTURAL LAYERS

Abstract

The spatial distributions (thickness and layer composition) of textural layers of alluvial soils are needed to quantify water and solute transport in a field. The purpose of this study was to quantify the thickness probability distributions and vertical change of textural layers in 2 m soil profiles using conventional statistical techniques and Markov chain theory. A 15-km² alluvial soil region was selected, and 139 sampling points were distributed on a grid for observing the thickness and vertical change of textual layers. The soil was divided into six textural types: sand, sandy loam, light loam, medium loam, clay loam, and clay. The thickness probability distributions of the six types of textural layers were counted, and the observed distributions were nearly lognormal. This result was verified by the χ² test and the skew state and peak state coefficient tests. The coefficients of variation (CVs) ranged from 0.57 to 0.98, expressing a moderate variation in thickness of textural layers. The Markov chain theory was used to characterize the state transition of a dispersed state sequence changing with time (or space), and the transition probability matrix (TPM) was the main tool used for the characterization. The vertical change of textural layers along soil profiles may be defined as a Markov chain. The transition frequency matrices (TFMs) and transition probability matrices were calculated for the vertical change of layers of different textural types and 5-cm thickness, respectively. The Markov characteristic and the near stability of the vertical change of textural layers were verified by the χ² test. The TFM and TPM of layers with different textural types showed that the major textural layers are clay and sand. Furthermore, the main layer was composed of clay-sand, sand-clay, clay-sand-clay, and sand-clay-sand in the research region. The TPMs from the east and west subregions indicated differences in soil-depositing environments between the two subregions. The TPM was found to be a very useful tool for characterizing quantitatively the vertical change of textural layers in a region, and it is expected to be a useful tool in the future.