Hysteresis effects on water retention and conductivity

The hysteresis may be assumed in the water retention curve and in the unsaturated conductivity function depending on the switch Hysteresis (the water retention curve and the unsaturated conductivity are described in detail in section Soil hydraulic properties).

The calculation of hysteresis is based on three multiplicative functions considering (1) the time since start of sorption loop, R_hage, (2) the shift point pF-value, R_hshift, and (3) the accumulated rate of water content increase, R_hacc. These three functions are governed by common parameter values for all layers and they can all vary between zero and unity. In addition for each layer one parameter p_hysmax gives the maximal effect.

Thus:

                                                           (2.6)

where ψ^* is the reference value of water tension (i.e. the estimated value before any corrections), and R_h is the hysteresis effect calculated as:

                                                       (2.7)

The age response is given as:

                                                           (2.8)

where ∆t_shift is the time elapsed since last major shift from a desorption to a sorption process and a_hysk is a parameter.

The shift point response is:

                           (2.9)

were a_PF1 and a_PF2 are parameters.

Finally the function of accumulated change of water content is defined as:

                                                  (2.10)

where the ∆θ_sorp is the accumulated increase of water content at a rate that exceeds the threshold value a_θD since the last major shift from desorption to sorption and a_thetm is the maximum moisture parameter value. The ∆θ_sorp is reset to a value that corresponds to continuous change in the total hysteresis response when a new sorption process starts.

Similar to the water tension the hydraulic conductivity is given as:

                                                         (2.11)

where p_hysmaxc is a parameter defined for each layer of the soil.