2.1. Hydraulic functions
Three pairs of hydraulic functions are widely used in hydrological modelling, namely those developed by Brooks and Corey (1964), Campbell (1974), and van Genuchten (1980.
The Brooks and Corey (BC) (1964) water retention function is given by:
[1]
where α is the reciprocal of the air entry value (or bubbling pressure) [cm-1], n is a dimensionless shape parameter [-] (related to 1/b for the original Brooks-Coreyb parameter), h is the pressure head [cm], andSe is the effective saturation [-] given by:
\(S_{e}=\frac{\theta-\theta_{r}}{\theta_{s}-\ \theta_{r}\ }\)[2]
where θ is the actual water content [cm3cm-3], θr is the residual water content [cm3 cm-3], andθs is the saturated water content [cm3 cm-3].
The unsaturated hydraulic conductivity is given by:
[3]
where Ks is the saturated hydraulic conductivity [cm d-1].
The Campbell (1974) water retention function is a modification of that introduced by Brooks and Corey (1964), with θrset to 0.
The Mualem van Genuchten function (MvG) (van Genuchten, 1980) is given by:
[4]
where m is a shape factor related to n by m = 1-1/n .
For the VGM model, the unsaturated hydraulic conductivity is calculated by:
[5]
where λ is the tortuosity factor [-].