Scaling of the hydraulic properties

Spatial variability of the soil hydraulic properties within a material is described by a set of linear scaling transformations that relate the individual functions θ(h) and K(h) of a node to reference functions θ(h) and K(h) of its material Vogel et al. (1991); Šimůnek et al. (2009):

with the three independent scaling factors α_θ, α_K and α_h of the node (the quantities Scaling αθ, αK, αh of the soil profile). The approach is a generalization of the similar-media scaling of Miller and Miller (1956), in which α_h and α_K follow from a single characteristic length λ (α_h = 1/λ, α_K = λ², α_θ = 1).

All factors equal to 1 mean no scaling. With hysteresis the scaling applies to both branches. Scaling factors are used, for example, to describe stochastic fields of hydraulic properties or gradual changes within a layer.

Literature cited in this topic

• Miller, E. E., and R. D. Miller (1956). Physical theory for capillary flow phenomena. Journal of Applied Physics 27(4): 324–332. doi:10.1063/1.1722370
• Vogel, T., M. Císlerová, and J. W. Hopmans (1991). Porous media with linearly variable hydraulic properties. Water Resources Research 27(10): 2735–2741. doi:10.1029/91WR01676
• Šimůnek, J., M. Šejna, H. Saito, M. Sakai, and M. Th. van Genuchten (2009). The HYDRUS-1D Software Package for Simulating the One-Dimensional Movement of Water, Heat, and Multiple Solutes in Variably-Saturated Media, Version 4.08. HYDRUS Software Series 3, Department of Environmental Sciences, University of California Riverside, Riverside, CA, USA, 330 pp. https://www.pc-progress.com/en/Default.aspx?h1d-description

All sources: References.