Using Probability Distributions to Quantify Soil Development Variability with Time.

Soils develop as the result of a complex suite of biogeochemical and physical processes; however, effective modeling of soil development over pedogenic time scales and the resultant soil property variability is limited to individual chronosequence studies or overly broad generalizations.  Traditional soil chronosequence studies do not account for uncertainty in soil development. Here we develop a probabilistic approach to quantify the distribution of probable soil property values based on a review of soil chronosequence studies to examine the changes in the distributions of soil texture and depth with increasing time and influx of pedogenic energy from climate and biological forcing.  We found the greatest variability in maximum measured clay content occurred between 10³ to 10⁵ years, with convergence of clay contents in soils older than 10⁶ years.  Conversely, we found that the variability in maximum sand content increased with increasing time, with the greatest variability in soils between 10⁵ to 10⁶ years old; we did not find distributional changes in maximum silt content with time.  Bivariate normal probability distributions were parameterized using the chronosequence data, from which univariate distributions based on the total pedogenic energy (age x rate of energy flux) were calculated, allowing determination of a probable range of soil properties for a given age and energy flux.  For maximum clay content, the bivariate distribution was capable of effectively representing the measured maximum clay content values with an r² of 0.53.  By taking a distributional approach to quantifying soil development and variability, we can quantitatively represent the full state factor model, while explicitly quantifying the uncertainty in soil development.