On the relationship between mean and variance of soil moisture fields

The objective of this work was to explain an apparent contradiction in the literature related to the relationship between mean and variance (or standard deviation) of soil moisture fields. Some studies found an increase in soil moisture variance with decreasing mean soil moisture, while others showed a decrease. The evidence of maximum variance in the mid-range of mean soil moisture was also reported in the literature. In this paper, we focus on the effects of spatial variability of soil texture on the relationship between variance and mean of soil moisture during soil dry-down processes. Soil texture influences soil moisture mean and variance through its direct effects on evaporation and drainage, which are two main factors controlling soil drying. A differential equation describing soil moisture dry down is proposed and studied. Our study shows that as mean soil moisture is greater than a threshold, variance increases with decreasing mean soil moisture. If mean soil moisture is less than the threshold, variance decreases with decreasing mean soil moisture. The threshold depends on soil texture and is between the field capacity and the wilting point. The soil moisture dry-down equation is also applied to explain the apparent contradiction with regard to the relationship between mean and variance of soil moisture fields reported in the literature.