Describing Soil Hydraulic Properties with Sums of Simple Functions

Abstract Simple functions do not adequately describe the hydraulic properties of many field soils, particularly those with substantial macroporosity. By considering the soil pore‐size distribution f (ψ) = Σ N i = 1 ψ i f i (ψ) corresponding to the effective saturation S (ψ) = Σ N i = 1 ψ i S i (ψ), where ψ is matric pressure head, the ψ i are fractions of effective porosity, the S i (ψ) are simple water retention functions in common use, and f i (ψ) = S ' i (ψ), we show that the relative hydraulic conductivity according to the Mualem model is K r (ψ) = S p ΣΣ N i = 1 ψ i g i (ψ)/Σ N i = 1 ψ i g i (0) 2 , where g i (ψ) = ε ψ ‐x ψ −1 f i (ψ) dψ and p is a pore interaction index. If the pores of the distributions do not interact, the appropriate relation is K (ψ) = Σ N i = 1 K si K ri (ψ), where K si is the saturated conductivity of distribution i and K ri = S p g i (ψ)/ g i (0) 2 . We note that the van Genuchten function S (ψ) = 1 + (−αψ) n − m with the restriction m = 1 − 1/ n leads to an infinite slope K '(ψ) at ψ = 0 unless n ≥ 2, which is unrealistic for field soils if a wide range of matric pressure heads is considered. Hydraulic conductivity near saturation is often expressed as K (ψ) = K s exp( a ψ). We introduce the function S (ψ) = (1 − αψ) exp(αψ), which gives, according to Mualem's model, a conductivity K (ψ) = K s (1 − αψ) p exp( p + 2)αψ that approximates K s exp(αψ) near saturation if a = 2α and is exactly equal if p = 0. As an example, a function using this model for one pore‐size distribution and the van Genuchten model for the other was compared with a function using two van Genuchten distributions. The latter gave a slightly improved fit to water content and conductivity data for an aggregated soil.