Evaluating the impact of hydraulic head on soil moisture in Min3P

Min3P was developed to simulate three-dimensional flow and multicomponent reactive transport in variably saturated media involving a set of homogeneous and heterogeneous reactions. The model also simulates networks of equilibrium and kinetic reactions. Several geochemical processes can be considered within Min3P including: aqueous speciation, mineral dissolution-precipitation, intra-aqueous kinetic reactions, gas exchange, ion exchange, surface complexation, and linear sorption (Gérard et al., 2008).

The basic version of the model includes Richard’s equation for the solution of variably-saturated flow, as well as it solves mass balance equations for advective-diffusive solute transport and diffusive gas transport. Min3P has been used to support multiple field and laboratory investigations including reactions of inorganic and organic substances and has been developed to account for plant-soil interactions (Mayer et al., 2012).

Min3P can also simulate water and solute dynamics in the root zone of soils and the underlying vadose zone. To this end, several processes have been implemented including physical evaporation, plant transpiration, solute uptake by plants, and preferential flow (equilibrium scheme). The implementation of plant transpiration and preferential flow was required to accurately simulate soil moisture variations in a soil of a forest (Gérard et al., 2004). Plant uptake of solutes was added to support the modelling investigation of the cycle of Si (Gérard et al., 2008).

The initial conditions in the solution domain for the physical flow problem is specified by the hydraulic head for a fully saturated flow and by the pressure head distribution for variably-saturated flow. The distribution of this parameter can be discretised across the model domain by means of zones.

The distribution of hydraulic head through an aquifer determines where groundwater will flow. In a hydrostatic example, where the hydraulic head is constant, there is no flow. However, if there is a difference in hydraulic head from the top to bottom due to draining from the bottom, the water will flow downward, due to the difference in head, also called the hydraulic gradient (read more about in here).

It is important to understand and determine the behaviour of soil moisture availability in order to further perform experiments relating plant growth and water in the soil.

In order to evaluate the impact of the hydraulic head depth on soil moisture in Min3P, a box of clay soil with porosity 0.428 and dimensions 2 m x 2 m x 2 m was brought to hydraulic equilibrium by varying the high of the hydraulic head in 4 different depths: 4 m, 6 m, 10 m, and 100 m, using the the hydraulic head depth of 5 m as control for comparison.

Figure 1. Vertical profile of soil moisture availability for two different values of hydraulic head depth: -4 m (left) and -5 m (right).

Figure 2. Vertical profile of soil moisture availability for two different values of hydraulic head depth: -6 m (left) and -5 m (right).

Figure 3. Vertical profile of soil moisture availability for two different values of hydraulic head depth: -10 m (left) and -5 m (right).

Figure 4. Vertical profile of soil moisture availability for two different values of hydraulic head depth: -100 m (left) and -5 m (right).

The top layer of the soil, at 2 m, presents a smaller soil moisture availability than the bottom layer, at 0 m, because by capillarity part of the moisture from the saturated zone humidifies the bottom part of the soil, but gravity acts on the opposite direction creating a gradient of moisture pointing to the position of the hydraulic head. The deeper the hydraulic head the dryier the soil, keeping the gradient pointing down, execept for the case where the hydraulic head is in 100 m below the ground (Fig. 4). In this case, the hydraulic head is located so deep that capillarity is not strong enough to take water to the upper 2 m of the soil, leaving it with soil moisture availability values under 0.16.


Gérard, F., Tinsley, M., & Mayer, K. U. (2004). Preferential Flow Revealed by Hydrologic Modeling Based on Predicted Hydraulic Properties. Soil Science Society of America Journal. https://doi.org/10.2136/sssaj2004.1526

Gérard, F., Mayer, K. U., Hodson, M. J., & Ranger, J. (2008). Modelling the biogeochemical cycle of silicon in soils: Application to a temperate forest ecosystem. Geochimica et Cosmochimica Acta. https://doi.org/10.1016/j.gca.2007.11.010

U. Mayer, K., T. Amos, R., Molins, S., & Gerard, F. (Eds.). (2012). Reactive Transport Modeling in Variably Saturated Media with MIN3P: Basic Model Formulation and Model Enhancements. In Groundwater Reactive Transport Models (pp. 186–211). https://doi.org/10.2174/978160805306311201010186