Full Macropore Flow

Macropores are defined as a secondary, additional continuous pore domain in the unsaturated zone, besides the matrix pore domain representing the microporous bulk soil. Macropore flow is initiated when the capillary head in the micropore domain is higher than a threshold matrix pressure head, y_t ; corresponding to the minimum pore size that is considered as belonging to the macropore domain. Water flow in the macropores is assumed to be lami­nar and not influenced by capillarity, corresponding to gravitational flow. The vertical volumetric flux (positive upwards) q_mp is then given by

(28.30)   

where K_mp(q_mp) is the hydraulic conductivity of the macropores depending on the volumetric soil moisture content of the macropores, q_mp. The continuity equation is expressed as

(28.31)   

where S_mp is a sink term for water exchange with the surrounding matrix. Combining (28.30) and (28.31) yields the governing equation for the macrop­ores

(28.32)   

The term S_mp becomes a source/sink term in Richards equation used in the matrix domain. This term is given by

(28.33)   

where y_mp and y_matrix are the capillary heads in the macropores and in the matrix, respectively, and K(q_matrix) is the hydraulic conductivity in the matrix depending on the volumetric soil moisture content of the matrix, q_matrix. The exchange flow from matrix to macropore is only considered when the capil­lary head in the matrix, y_{matrix ,} exceeds the threshold pressure, y_t. b_mp is a first-order linear water transfer coefficient, which is expected to increase with decreasing distance between macropores and with increasing hydraulic matrix-macropore contact. It can be expressed as

(28.34)   

where d is an effective diffusion path length in metres. C_f is a dimensionless contact factor to take care of coatings on the interior walls of the macropores. Such a coating could be present due to, for example, root remnants, worm slime or mineral precipitation and can decrease the contact between matrix and macropore significantly. The contact factor ranges from 0.0 (no contact) to 1.0 (full contact).

In the macropores, a simple power law function is assumed to represent the conductivity relation

(28.35)   

where K_s,mp is the saturated hydraulic conductivity of the macropores, q_s,mp is the macroporosity, and n is an empirical exponent accounting for size distri­bution, tortuosity, and continuity of the macropores. n may vary from two to six, according to Jarvis (1994). The lower values represent soils of coarse structure with macropore networks of narrow pore size distribution and little tortuosity, whereas the higher values apply to soils with a wider macropore size distribution and larger tortuosity. If macropores are included in the simu­lation the hydraulic conductivity used to represent the soil matrix should exclude the effect of macropores.

The actual size, form and number of macropores are not explicitly considered in the model. Instead the macropore characteristics appear indirectly from y_t, n and b_mp that in the present formulation are dependent on soil type. The cap­illary pressure in the macropores, y_mp, is supposed to vary linearly with the macropore moisture content q_mp between zero (at q_mp = q_s,mp) and y_t (at q_mp = 0). Neither root water uptake nor soil evaporation are considered to take place from the macropore domain.

The infiltration process description includes water entering the macropores, as well as the soil matrix at the soil surface. In this case, water is only ponded on the ground surface when the infiltration capacities of both pore regions are exceeded. Water flow into the macropores commences as the matrix infiltra­tion capacity is surpassed.

The bottom boundary condition for flow in the macropores is a vertical flux at a unit hydraulic gradient. This flux is input to the saturated zone. A coupling of the saturated zone and the unsaturated zone is necessary when the ground­water level fluctuates. During groundwater rise, the water present in the mac­ropores in the bottom unsaturated zone layer is released instantaneously to the groundwater and during groundwater decline, the macropores are exposed as empty.