### Changes of Variability, Probability Distributions and Statistical Entropy of Soil Properties under Anthropogenic Formation.

Irina V. Mikheeva, Institute of Soil Science and Agrochemistry of Siberian Branch of Russian Academy of Sciences, 18, Sovetskaya Street, Novosibirsk, 630099, Russia

Continuous quantitative variability of soil properties is one of the basic features of soils so far as they are complex systems and it has fundamental significance, because it is the ground of the diversity of conditions of existence of soil organisms and plants. Reliable quantitative evaluation of anthropogenic processes in soils can be carried out only taking into account their variability. Variability of parameters may be considered as quantitative uncertainty, which measure may be evaluated by entropy index. Entropy index in modern science often is used as criterion for evaluation of evolution and self-organization of complex systems, so it is grounded to use this index as criterion for evaluation of soil forming and evolution of soil cover. Meaning of entropy h for random value x may be calculated on the basis of function of its probability distribution f(x), consequently the entropy may be considered as one of statistical characteristics of soil variability. We defined probability distributions of properties of chestnut soils in Kulunda steppe in the south of West Siberia. Data, received by four soil surveys, repeated on the same territory in the last third of twentieths century, have been grouped using soil - genetic principles before doing statistical analysis. Parameters of the maximal likelihood were estimated for several tens of well known mathematical functions of distributions by using of factual data. Optimal grouping of the data within individual samples before calculation of histograms provided robustness of estimations of parameters. Hypotheses about the consent of suspected and theoretical distribution were checked by six parametric and nonparametric criteria's (Pearson's, relations of likelihood, Kolmogorov's, Smirnov's, and two criteria's of Mizes). Probability distributions, which approximate the histograms most closely, were defined on combination of values of these criteria's. This approach was applied to description of variability of properties of chestnut soils within their series (Mikheeva, 2001 in Russian). After this we calculated the entropy. Results of our statistical analysis showed, that dynamics, evolution and continuous geographical trend of soils often occur without changes of interval of variation of soil properties, but under transformation of soilforming factors and processes, including anthropogenic processes, original “wave” of probability distributions of attributes is watched. It is connected with changes of frequencies of values of properties, and it is reflected by gradual modification of shift, dispersion and form of their probability distributions. For example, with growth of clay content in lithocatena, and with intensifying of hydromorphism in catena and with growth of humidity in geographical zones in the north direction not only shift of probability distribution of humus content is watched, but increasing of dispersion and change of form of statistical distribution too. It similar to overflowing of frequencies of values, but in the same time, intervals of variations of properties in close soils essentially intersect. The entropy of humus content in investigated soils at dry steppe and steppe oscillate from 0.15 to 1.15, and values of this index in these geographical zones are close and most of all it depends on texture of rocks, at which the soils were formed. The value of entropy of humus content in soils at forestry steppe is more significant. Highest values of entropy in chestnut soils are inherent to boundaries of genetic horizons, especially of illuvial horizons, also dust and sand fractions contents. It is consequence of alluvial genesis of territory and numerous periods of wind erosion. Wind erosion, ploughing and irrigation reduce the entropy of humus content, but soil-protective strip agriculture raises it. Irrigation by low-mineralized water raises the entropy of chemical properties and reduces the entropy of clay content in high horizon.