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.
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
In order to make a cereal root generated by ArchiSimple match the biomass of that one generated by FSPM-GroIMP, the biomass limiting factor function in ArchiSimple 9.1 was evaluated. The file that contains the maximum root biomass value allowed for growth in ArchiSimple is called biomrac.txt and it is given in grams at each time step, daily in this case. Figure 1 shows the evolution of a cereal root dry biomass generated by FSPM-GroIMP for a period of 94 days with the Beta factor and without it (no limitation).
The driven data for plant growth, i.e., the potential evapotranspiration (m.s-1) was set constant in 2.0×e-8 m.s-1 in order to speed up the performance of Min3P – ArchiSimple and reduce CPU time but without impacting the final result. Potential evapotranspiration only impacts root water uptake calculated from Min3P, which is not being evaluated in this simulation. This simulation only evaluates the impact of the variable biomrac on dry root biomass generated by ArchiSimple.
The impact of the Beta function on dry root biomass generated by FSPM-GroIMP is in the order of -50% at the end of the simulation on day 94. In reality, Figure 1 shows a delay in root growth, i.e., while the root system starts growing substantially around day 20 without water limitation being considered, the same is only observed 30 days later when water scarcity in the soil is taken into account.
Both values of dry root biomass were from FSPM-GroIMP were used to limit plant growth in ArchiSimple through the biomrac variable, and the results are shown in Figure 2. In these simulation the soil variables in ArchiSimple were set to: Croiss = 6.0; Ramif = 1.0; iCMeca = 0.07; and Orientation = 1.
The Beta function presents little or no impact on root system growth with depth. However, the Beta function impacts root surface density and the ‘spread’ of the root system throughout the horizontal layers of the soil.
Figure 3 shows the integrated root surface density (m-2.m-3) of a cereal root for 94 days without Beta function and with Beta function. It is possible to notice that the impact of the Beta function of root surface density is in the order of -70%.
This sensitivity analysis indicates that for this set of variables used in FSPM-GroIMP without soil water limitation, the root biomass generated is larger than the one generated by ArchiSimple and, therefore, the Croiss variable had to be set much higher than 1.0 in order to generate a larger root system. As well as the root system was set to grow to a larger size, the soil mechanic constraint had to be set to a higher value as well, once the cereal root was growing too deep (deeper than 2 m) and giving unrealistic biomass vertical profiles.
Models of root system architecture are often used for studying plant-soil interactions. These models are required to simulate the structural and spatial distribution of the root system, the integration of root level processes (e.g., elongation, branching) with soil properties, and root interaction with the airborne part of a plant. Only a few of them, however, have been integrated into larger crop or ecosystem models because they are too difficult to parameterise and they require large amounts of computational power.
ArchiSimple has been designed to enable the representation of the architectural diversity coming from various plant species interacting with environmental conditions (Pagès et al., 2014). It is a dynamic architectural and functional model, in which the root system is represented as a set of small segments and meristems. The root system is modified by functions describing their development, including emission of new roots from the shoot, elongation of existing roots, acropetal branching, radial growth, and self-pruning following root decay. Model parameters can be estimated independently from observations or from the literature. Calibration and evaluation for 6 species (Musa spp., Pisum sativum, Prunus persica, Teucrium botrys, Thlaspi perfoliatum, and Zea mays) are described in Pagès et al. (2014).
In order to make a cereal root generated by ArchiSimple match the biomass of that one generated by FSPM-GroIMP, a group of variables related to the soil, as described in ArchiSimple, were evaluated in a sensitivity analysis.
The file that contains the description of soil properties within ArchiSimple has a group of 4 variables: Croiss (favours growth); Ramif (favours ramification); iCMeca (intensity of constraint); and Orientation (0 – iso; 1 – vertical).
Croiss (favours growth)
Croiss = variable; Ramif = 1.0; iCMeca = 0.00; Orientation = 0 (iso).
Ramif (favours ramification)
Croiss = 0.5; Ramif = variable; iCMeca = 0.00; Orientation = 0 (iso).
iCMeca (intensity of constraint)
Croiss = 1.0; Ramif = 1.0; iCMeca = variable; Orientation = 0 (iso).
Orientation = 0 (iso) and 1 (vertical)
Croiss = 0.5; Ramif = 1.0; iCMeca = 0.00; Orientation = variable.
Pagès, L., Bécel, C., Boukcim, H., Moreau, D., Nguyen, C., & Voisin, A. S. (2014). Calibration and evaluation of ArchiSimple, a simple model of root system architecture. Ecological Modelling. https://doi.org/10.1016/j.ecolmodel.2013.11.014