On the Relationship Between Mean and Variance of Soil Moisture Fields¹

Abstract

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.

Spatial-temporal variability of soil water content in a cropland-shelterbelt-desert site in an arid inland river basin of Northwest China

“…Furthermore, there was a threshold in the shelterbelt with the value of approximately 22.0%. Pan and Peters-Lidard (2008) indicated that the variance decreased with SWC when it exceeded the threshold, and the variance increased with SWC if it was less than the threshold. In contrast, no evidence of a threshold effect was found in the cropland, desert or cropland-shelterbelt-desert land use pattern.…”

Soil Moisture for Hydrological Applications: Open Questions and New Opportunities

“…The values of the first two statistical moments of absolute soil moisture data (in volumetric units, m 3 /m 3 ), i.e., mean and variance, as well as their mutual relationship, were largely investigated (e.g., [79]). In most cases, a convex upward relationship is obtained between mean and variance thus concluding that soil moisture variability peaks for intermediates wetness conditions (e.g., [2,75,80,81]).…”

Spatial Pattern and Temporal Stability of Root-Zone Soil Moisture during Growing Season on a Larch Plantation Hillslope in Northwest China

“…When the mean VSM decreases to a threshold, the dominant process controlling soil drying is switched from drainage to evapotranspiration. With further reduction of mean VSM, CVs are decreased by the effect of evapotranspiration, showing a positive correlation with mean VSM in dry soils [48]. The VSM threshold depends on soil, topography, climate, and vegetation, and is typically between 15% and 25% [48,49].…”

“…The CVs are mainly controlled by soil hydraulic conductivity and porosity under (extreme) wet conditions. When the mean VSM starts to decrease due to the drainage and evapotranspiration, the variability of saturated hydraulic conductivity, particle size distribution, and air entry pressure will result in an increase in CVs, thus CVs are negatively correlated with the mean VSM in relatively wet conditions [47,48]. When the mean VSM decreases to a threshold, the dominant process controlling soil drying is switched from drainage to evapotranspiration.…”