A scale invariant property of the water retention curve in weakly heterogeneous vadose zones

Abrupt changes of hydraulic properties in a vadose zone are modelled within a stochastic framework, which regards the saturated conductivity and parameters related to the distribution of soil pores as stationary, log‐normally distributed, random space functions. As a consequence, flow variables become random fields, and we aim at deriving an effective Richards equation. To obtain the latter, we adopt a perturbation expansion truncated at the first order (weakly heterogeneous media), which leads to the effective hydraulic conductivity and water retention curves. Overall, the effective properties are scale dependent. However, within the proposed framework, we demonstrate that the inflection point of the laboratory scale retention curve is not affected by the heterogeneity of the vadose zone. Finally, to illustrate the quantitative implications of our results, we consider a monitoring experiment at field scale, and we show how our approach leads to an effective water retention curve, which differs significantly from that which would be obtained without accounting for the above scale‐invariance property.