Bypass flow in macropores

An optional switch (Crack) to account for bypass flow has been included in the model to consider rapid flow in macropores during conditions when smaller pores are only partially filled with water (see below). The amount of water in the macropores is not accounted for explicitly. Instead, the infiltration flow rate at the soil surface or the vertical flow in the macropores at any depth in the soil profile, q_in, determines the partitioning of the total liquid water flow (q_w – q_v) into ordinary Darcy flow, q_mat, and bypass flow, q_bypass. (see Figure 2.1).

Figure 2.1. Matrix and bypass flow in the model.

 

              (2.3)

 

and

                               (2.4)

where k(θ) is the unsaturated conductivity at a given water content, ψ is the water tension and z is the depth co-ordinate. At the soil surface, q_in is the infiltration rate. At other depths in the soil, q_in is the vertical flow rate in the macropores, q_bypass, from the layer immediately above. S_mat is the sorption capacity rate, i.e. the threshold value for bypass flow in the macropores, defined as:

                                                      (2.5)

where k_mat  is the maximum conductivity of smaller pores (i.e. matric pores), a_r is the ratio between compartment thickness, ∆z, and the unit horizontal area represented by the model, pF is ¹⁰log of ψ and a_scale is an empirical scaling coefficient accounting for the geometry of aggregates.

The calculated water flow in the matric pores, q_mat, is used to update the water contents and the water tensions in the numerical solution, whereas q_bypass is directed without delay to the next soil compartment. However, q_bypass can never reach layers below the water table depth, which is the lower boundary condition for the use of Richard’s equation.