Unsaturated Conductivity

There are three optional ways of determining the unsaturated hydraulic conductivity in the model (see switch Conductivity Function).

Following Mualem (1976), the unsaturated conductivity, kw*, is given by:

                                                        (2.26)

If the Brooks & Corey function for water retention is used, eq.(2.19), the unsaturated conductivity, kw*, can then be expressed as:

                                                   (2.27)

where kmat is the saturated matrix conductivity and n is a parameter accounting for pore correlation and flow path tortuosity. Eqs. (2.26)- (2.28) are used for water contents in the matric pores.

See viewing functions Measured Unsaturated Conductivity, Pressure Head, single layers, Measured Unsaturated Conductivity, Water Content, single layers and Modelled Unsaturated Hydraulic Conductivity, profile.

In case of using the van Genuchten equation, eq. (2.21), the corresponding equation for the unsaturated conductivity is given by:

                          (2.28)

where the coefficients α, gn and gm are the same parameters as used in eq (2.21)..

As alternative options to the equations of Mualem eqs. (2.26)- (2.28)   the unsaturated hydraulic conductivity, kw*, can either be caluclated as a simple power function of relative saturation:

                                                         (2.29)

or as a simple power function of effective saturation:

                                                             (2.30)

where pnr and pne are parameters, kmat is the saturated matrix conductivity, θs is the water content at saturation, θ is the actual water content and Se is the effective saturation.

Figure 2.4. The unsaturated conductivity for a clay soil calculated with the parameter values given above.

To account for the conductivity in the macropores, an additional contribution to the hydraulic conductivity is considered when water content exceeds θs - θm, i.e. at ψmat (see Figure 2.4 above). The total hydraulic conductivity close to saturation is thus calculated as:

                                  (2.31)

where ksat is the saturated total conductivity, which includes the macropores, and kw*(θs - θm) is the hydraulic conductivity below θs - θm (i.e. at ψmat) calculated from eqs (2.26)- (2.28).

All the hydraulic conductivities are scaled with respect to temperature. The scaling is related to the viscosity of water and is simplified to a linear response in the normal range around 20 °C, which is used as a reference temperature. In addition to this dependence a minimum unsaturated conductivity is also applied. Thus the actual unsaturated hydralic conductivity after temperature corrections, kw, is given by:

                                   (2.32)

where rAOT, rA1T and kminuc are parameter values. kw* is the conductivity according to eqs. (2.26)-(2.31). See viewing function Hydraulic conductivity, temperature function.