Linking transpiration reduction to rhizosphere salinity using a 3D coupled soil-plant model

Abstract

Aims

Soil salinity can cause salt plant stress by reducing plant transpiration and yield due to very low osmotic potentials in the soil. For predicting this reduction, we present a simulation study to (i) identify a suitable functional form of the transpiration reduction function and (ii) to explain the different shapes of empirically observed reduction functions.

Methods

We used high resolution simulations with a model that couples 3D water flow and salt transport in the soil towards individual roots with flow in the root system.

Results

The simulations demonstrated that the local total water potential at the soil-root interface, i.e. the sum of the matric and osmotic potentials, is for a given root system, uniquely and piecewise linearly related to the transpiration rate. Using bulk total water potentials, i.e. spatially and temporally averaged potentials in the soil around roots, sigmoid relations were obtained. Unlike for the local potentials, the sigmoid relations were non-unique functions of the total bulk potential but depended on the contribution of the bulk osmotic potential.

Conclusions

To a large extent, Transpiration reduction is controlled by water potentials at the soil-root interface. Since spatial gradients in water potentials around roots are different for osmotic and matric potentials, depending on the root density and on soil hydraulic properties, transpiration reduction functions in terms of bulk water potentials cannot be transferred to other conditions, i.e. soil type, salt content, root density, beyond the conditions for which they were derived. Such a transfer could be achieved by downscaling to the soil-root interface using simulations with a high resolution process model.

Appendix: model description

The model R-SWMS simulates both, soil and root water flow. Soil water flow is defined by the Richards equation (Richards 1931)

$$ \frac{\partial \theta }{\partial t}=\nabla \left[\mathbf{K}(h)\nabla \left(h+z\right)\right]-S\left(x,y,z\right)\kern0.5em $$

(9)

where θ [L³ L⁻³] is the volumetric water content, t [T] is time, K [L T⁻¹] is the hydraulic conductivity tensor, h [L] is the matric potential, S [T⁻¹] is a sink term representing the root water uptake, and z [L] is the vertical coordinate positive upward. The model of (Doussan et al. 1998) is coupled to the soil water flow. This model calculates water flow inside the roots based on a root network architecture, which is described as a network of connected root nodes. The axial xylem flow J _x [L³ T⁻¹] in a root segment describes water flow within the root xylem by

$$ {J}_x=-{K}_x^{\ast }{A}_x\left(\frac{\varDelta {h}_{xylem}}{l_{seg}}+\frac{\varDelta z}{l_{seg}}\right) $$

(10)

where K _x ^* [L T⁻¹] is the xylem conductivity, A _x [L²] is the xylem cross-sectional area, z [L] the vertical coordinate, l _seg [L] the root segment length, and h _xylem [L] the water pressure potential in the xylem.

The radial water flow J_r [L³ T⁻¹] between the soil-root interface and the root xylem is defined by Doussan et al. (1998) and used in R-SWMS as

$$ {J}_r={K}_r^{\ast }{A}_r\left({H}_{int}-{H}_{xylem}\right) $$

(11)

with the radial root conductance K _r ^* [T⁻¹], the root outer surface A _r [L²] and the water potential at the soil–root interface H _int [L] and in the xylem H _xylem [L].

The calculations of soil and root water flow inside R-SWMS are coupled as described in Javaux et al. (2008) via the water sink term S in the Richards equation and defined for one soil voxel by

$$ {S}_j=\frac{{\displaystyle {\sum}_{k=1}^{n_k}{J}_{r,k}}}{V_j} $$

(12)

where J_k is the radial fluxes into the root segment k, located in a soil voxel j. Here, V _j is the voxel volume, and n _k is the number of root segments within voxel j.

The solute movement inside the soil is described by the convection–dispersion equation (CDE)

$$ \frac{\partial \theta c}{\partial t}=\nabla \left(\theta D\cdot \nabla c\right)-\nabla \left(\theta uc\right)-S\prime c $$

(13)

where c [M L⁻³] is the solute concentration, u [L T⁻¹] is the pore water velocity, S ^′ [T⁻¹] is the solute sink term and D [L² T⁻¹] is the dispersion coefficient tensor, defined as

$$ {D}_{ij}={\lambda}_T\left\Vert u\right\Vert {\delta}_{ij}+\left({\lambda}_T-{\lambda}_L\right)\frac{u_j{u}_i}{\left\Vert u\right\Vert }+{D}_w\tau {\delta}_{ij} $$

(14)

where $\left\Vert u\right\Vert =\sqrt{u{u}^T}$ is the Euclidean norm of the pore water velocity vector, α_L and α_T are the longitudinal and transverse dispersivities, respectively, D _W [L² T⁻¹] is the molecular diffusion coefficient and τ [−] is the tortuosity factor.

The CDE is solved by the model PARTRACE (Bechtold et al. 2011; Schröder et al. 2012). PARTRACE solves a random walk particle tracking algorithm, where an equivalent stochastic differential definition of the CDE is used, which contains the velocity provided by R-SWMS and a random displacement which accounts for the dispersion. A large number of solute particles represent the solute mass and are moved through the system according to this equation.

With an interface between R-SWMS and PARTRACE, velocity and water sink term profiles are updated in every time step and provided to the solute transport code. In addition, after the concentration profile is calculated by PARTRACE, a feedback coupling supply the concentration values, which are transformed to osmotic potentials, to the soil and root water module of the model (R-SWMS).