Stochastic Analysis of the Soil Water Content Standard Deviation‐Mean Value Relationships: On the Physical Significance of the Critical Mean Soil Water Content

Abstract

AbstractThe spatial heterogeneity in the soil hydraulic properties was considered here as the main cause of the spatial variability in soil water content, θ. The aim of the study was (i) to identify the critical mean soil water content, Θcr, below which the standard deviation of the soil water content, σθ, can only diminish, and (ii) to provide a mathematical tool capable of linking Θcr to inherent soil hydraulic properties. The relationships between σθ and the mean value of θ, Θ, were analyzed by a first‐order analysis, based on a stochastic continuum presentation of steady‐state flow in 3‐D, spatially hetrogeneous, unsaturated soils, using the Gardner‐Russo model to describe the constitutive relations locally. Novel results of the study suggested that the mean pressure head, H, associated with Θcr, Hcr = H (Θcr), is an inflection point of the mean soil water capacity function, C(H) = dΘ/dH. Results of numerical simulations of flow in 3‐D, spatially heterogeneous, unsaturated soils, using the van Genuchten (1980, https://doi.org/10.2136/sssaj1980.03615995004400050002x) model to describe the constitutive relations locally, suggested that the results of the first‐order analysis might be applicable to more realistic situations, involving transient, nonmonotonous flows and more complicated descriptions of the local constitutive relations.