Theory and equations

Root solute uptake

Root solute (nutrient) uptake follows Šimůnek and Hopmans (2009) as the sum of a passive and an active part.

Passive uptake

Solutes taken up passively move with the water into the roots, up to a maximum concentration c_max (cRoot):

P_a(x, t) = S(x, t) min[c(x, t), c_max]

with the root water uptake S. c_max = 0 means no passive uptake; a large c_max means that the solute is taken up with the water at its full concentration.

Active uptake

The potential active uptake A_p is the part of the potential (demand) uptake rate that the passive uptake does not cover:

A_p(t) = max[ S_pot ω_w − ∫ P_a dx, 0 ]

where S_pot is the potential solute uptake rate [M/L²/T] (with time-variable boundary conditions from the cBot column of the solute) and ω_w the water stress index when reduced potential solute uptake due to reduced water uptake is on (otherwise 1). It is distributed over the root zone with Michaelis–Menten kinetics:

A_a(x, t) = b(x) A_p(t) (c − c_min) / (K_m + c − c_min)

with the Michaelis–Menten constant K_m and the minimum concentration c_min below which no active uptake occurs. As for water, the active uptake can be compensated: with the solute stress index ω_s = ∫ A_a dx / A_p and the critical index ω_s,c, the uptake is divided by max(ω_s, ω_s,c).

The total uptake P_a + A_a is a sink term of the solute transport equation of the solute. HYDRUS-1D 2009 allows active uptake of a single solute only; HYDRUS 4.17 and Rusteau let you choose the solute Šimůnek et al. (2016).

Literature cited in this topic

Šimůnek, J., and J. W. Hopmans (2009). Modeling compensated root water and nutrient uptake. Ecological Modelling 220(4): 505–521. doi:10.1016/j.ecolmodel.2008.11.004
Šimůnek, J., M. Th. van Genuchten, and M. Šejna (2016). Recent developments and applications of the HYDRUS computer software packages. Vadose Zone Journal 15(7). doi:10.2136/vzj2016.04.0033

All sources: References.