Equation for Extending Water‐Retention Curves to Dryness

TLDR

Current water‑retention functions fail to predict zero water content at oven dryness. The study examined a modification of the Campbell equation to ensure the water‑retention curve terminates at a suction of 1000 MPa, approximating oven dryness. They derived a modified Campbell equation that forces the curve to terminate at ψ₀ = 1000 MPa and fitted it to water‑retention data from Australia, the UK, and the USA, comparing it with the unmodified form. The modified equation fit the data slightly better than the original (mean SD = 0.014 m³ m⁻³) and its parameters can be derived from the unmodified equation, making it preferable to extrapolation when data are scarce, though predictions for dry soils remain uncertain.

Abstract

Abstract Simple water‐retention functions in current use do not predict zero water content at oven dryness. Using the Campbell equation θ = a ψ ‐c = θ s (ψ ‐c − ψ ‐c 0 ) relating volumetric water content, θ, to matric suction, ψ, as an example, we examined a modification to ensure that the curve terminates in a suction ψ 0 = 1000 MPa, approximating oven dryness. The new equation is θ = a (ψ ‐c − ψ ‐c 0 ) = θ s (ψ ‐c − ψ ‐c 0 )/(ψ ‐c c − ψ ‐c 0 . It was compared with the unmodified equation by fitting to water‐retention data from Australia, the UK, and the USA. Results showed not only that the new equation fit the data slightly better than the original equation, with a mean standard deviation of 0.014 m 3 m −3 about the regression, but also that its parameters could be calculated from those of the unmodified equation if original water‐content data were unavailable for fitting. Although lack of data hampered assessment of its predictions of water content in dry soils, its use appears preferable to extrapolating the unmodified equation.