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

The spatial distributions (thickness and layer composition) of textura l layers of alluvial soils are needed to quantify water and solute tra nsport in a field. The purpose of this study was to quantify the thick ness probability distributions and vertical change of textural layers in 2 m soil profiles using conventional statistical techniques and Mar kov chain theory. A 15-km(2) alluvial soil region was selected, and 13 9 sampling points were distributed on a grid for observing the thickne ss and vertical change of textual layers. The soil was divided into si x textural types: sand, sandy loam, light loam, medium loam, clay loam , and clay. The thickness probability distributions of the six types o f textural layers were counted, and the observed distributions were ne arly lognormal. This result was verified by the chi(2) test and the sk ew state and peak state coefficient tests. The coefficients of variati on (CVs) ranged from 0.57 to 0.98, expressing a moderate variation in thickness of textural layers. The Markov chain theory was used to char acterize the state transition of a dispersed state sequence changing w ith time (or space), and the transition probability matrix (TPM) was t he main tool used for the characterization. The vertical change of tex tural layers along soil profiles may be defined as a Markov chain. The transition frequency matrices (TFMs) and transition probability matri ces were calculated for the vertical change of layers of different tex tural types and 5-cm thickness, respectively. The Markov characteristi c and the near stability of the vertical change of textural layers wer e verified by the chi(2) test. The TFM and TPM of layers with differen t textural types showed that the major textural layers are clay and sa nd. Furthermore, the main layer was composed of clay-sand, sand-clay, clay-sand-clay, and sand-clay-sand in the research region. The TPMs fr om the east and west subregions indicated differences in soil-depositi ng 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 too l in the future.