## 1. Introduction

[2] Soil moisture is a key variable controlling hydrological and energy fluxes in soils. Due to the heterogeneity of soils, atmospheric forcing, vegetation, and topography, soil moisture is spatially variable. Understanding and characterizing this spatial variability is one of the major challenges within hydrological sciences. Especially the relationship *σ*_{θ}(〈θ〉) between mean soil moisture content, 〈θ〉, and its standard deviation *σ*_{θ}, has received considerable attention in the hydrological community. This relationship is important to understand the contribution of soil moisture variability at smaller scales towards the effective soil moisture observed at larger scales or its role in the parametrization of, e.g., climate and watershed models (upscaling/downscaling [e.g., *Famiglietti et al.*, 1999; *Crow et al.*, 2005; *Ryu and Famiglietti*, 2005]). Some studies report an increase in *σ*_{θ} with decreasing 〈θ〉 [e.g., *Bell et al.*, 1980; *Famiglietti et al.*, 1998; *Oldak et al.*, 2002], while others report the opposite behaviour [*Famiglietti et al.*, 1999; *Choi and Jacobs*, 2007]. Re-examination of recent experimental work [*Ryu and Famiglietti*, 2005; *Choi and Jacobs*, 2007; *Choi et al.*, 2007] and of results from simulations and stochastic analysis of water flow in heterogeneous soils [*Roth*, 1995; *Harter and Zhang*, 1999] shows that *σ*_{θ}(〈θ〉) increases during drying from a very wet stage, reaches a maximum value at a specific or critical mean moisture content, and then decreases during further drying (Figure 1). The observed unimodal shape of *σ*_{θ}(〈θ〉) has been explained mostly based on empirical [*Hu and Islam*, 1998] and/or statistical analysis of field data [e.g., *Famiglietti et al.*, 1998; *Ryu and Famiglietti*, 2005; *Choi and Jacobs*, 2007]. To date, an explicit mathematical analysis of *σ*_{θ}(〈θ〉) is lacking. In this letter, we use analytical stochastic work by *Zhang et al.* [1998], to show that *σ*_{θ}(〈θ〉) is directly related to the soil hydraulic properties and their statistical moments and that inverse modelling can be used to estimate these properties from moisture data. Our results show that the relationship between soil moisture variability and mean moisture content is controlled by soil hydraulic properties, their statistical moments and their spatial correlation. The unimodal shape of *σ*_{θ}(〈θ〉) observed in the field and in simulation data is well explained by existing stochastic theories.