Describing Soil Hydraulic Properties with Sums of Simple Functions
- Peter J. Ross and
- Keith R. J. Smettem
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) = ΣNi = 1 ψi fi (ψ) corresponding to the effective saturation S(ψ) = ΣNi = 1 ψi Si(ψ), where ψ is matric pressure head, the ψi are fractions of effective porosity, the Si(ψ) are simple water retention functions in common use, and fi(ψ) = S'i(ψ), we show that the relative hydraulic conductivity according to the Mualem model is Kr(ψ) = Sp[ΣΣNi = 1 ψi gi(ψ)/ΣNi = 1 ψi gi(0)]2, where gi(ψ) = εψ-xψ−1 fi(ψ) dψ and p is a pore interaction index. If the pores of the distributions do not interact, the appropriate relation is K(ψ) = ΣNi = 1 KsiKri(ψ), where Ksi is the saturated conductivity of distribution i and Kri = Sp[gi(ψ)/gi(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) = Ks exp(aψ). We introduce the function S(ψ) = (1 − αψ) exp(αψ), which gives, according to Mualem's model, a conductivity K(ψ) = Ks(1 − αψ)p exp[(p + 2)αψ] that approximates Ks 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.
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