2.1. Soil Hydraulics¶

Soil hydraulics in ADELM diagnoses how water supply is distributed across the soil profile and made available to the plant. The main outputs are the layer soil conductivity \(K_i\), the layer soil water potential \(\psi_{\mathrm{soil},i}\), the normalized root fraction \(f_{\mathrm{root},i}\), the layer uptake fraction \(\zeta_i\), and the root-zone soil water potential \(\psi_{\mathrm{root}}\).

Notation

subscript \(i\) denotes soil layer index (\(1\) = topmost)

Coupling to other components

Soil Hydrology uses water_uptake_fraction.
Stomatal Conductance uses root_zone_soil_water_potential.

Root-distribution geometry¶

The layer root distribution weight (unnormalized) in each layer is

(2.1.1)¶\[r_i = \beta^{z_{\mathrm{top},i}} - \beta^{z_{\mathrm{bottom},i}}\]

where \(\beta\) (plant_root_distribution_shape [PFT-based parameter: shape parameter of the exponential vertical root-fraction distribution]) controls the root profile shape, and \(z_{\mathrm{top},i}\) and \(z_{\mathrm{bottom},i}\) are the top and bottom depth of layer \(i\) in centimetres.

Normalizing over the full profile gives root_fraction [Derived parameter: normalised root fraction per soil layer]:

(2.1.2)¶\[f_{\mathrm{root},i} = \frac{r_i}{\sum_j r_j}\]

Soil hydraulic state¶

By default, the Brooks-Corey parameters used below are provided by the pedotransfer parameterization.

See also

model.parameterization.pedotransfer.calculate_soil_parameters_pedotransfer()

Soil hydraulic conductivity¶

The unfrozen hydraulic conductivity is

(2.1.3)¶\[K_{i,\mathrm{unf}} = K_{\mathrm{sat},i} \left(\frac{\theta_i}{\theta_{\mathrm{sat},i}}\right)^{3 + 2 B_i}\]

where \(\theta_i\) is soil_moisture [m3 m-3; State: volumetric water content of each soil layer], \(K_{\mathrm{sat},i}\) is soil_saturated_hydraulic_conductivity [mm h-1; Derived parameter: saturated hydraulic conductivity], \(\theta_{\mathrm{sat},i}\) is soil_saturated_moisture [m3 m-3; Derived parameter: saturated volumetric soil moisture content], and \(B_i\) is soil_brooks_corey_b [Derived parameter: pore-size distribution index in the Brooks-Corey soil water retention curve].

The freeze-reduction factor is

(2.1.4)¶\[f_{\mathrm{freeze}} = \frac{1}{1 + \exp\left[-k_f\left(T_{\mathrm{g}} - T_f\right)\right]}\]

where \(T_{\mathrm{g}}\) is soil temperature, \(T_f\) (soil_freeze_transition_temperature [default: 1 degC; Fixed parameter: temperature threshold below which freezing reduces soil hydraulic conductivity]) is the freeze transition temperature, and \(k_f\) (soil_freeze_transition_sharpness [default: 5; Fixed parameter: sharpness of the temperature-driven freeze reduction of soil hydraulic conductivity]) controls transition sharpness.

Attention

In the current ADELM version, \(T_{\mathrm{g}} = T_{\mathrm{a}}\) (ta_degC [degC; Driver: near-surface air temperature]).

The effective conductivity soil_conductivity [mm h-1; Diagnostic: effective hydraulic conductivity of each soil layer] is

(2.1.5)¶\[K_i = f_{\mathrm{freeze}}\,K_{i,\mathrm{unf}}\]

Soil water potential¶

The layer soil water potential uses a two-zone formulation. For dry conditions (\(\theta_i \le \theta_{\mathrm{fc},i}\)):

(2.1.6)¶\[\psi_{\mathrm{soil},i} = A_i\,\theta_i^{-B_i}\]

For wet conditions (\(\theta_i > \theta_{\mathrm{fc},i}\)), a linear interpolation between field capacity and bubbling-head potential is used:

(2.1.7)¶\[\psi_{\mathrm{soil},i} = \psi_{\mathrm{fc}} + \frac{(\theta_i - \theta_{\mathrm{fc},i})\,(\psi_{\mathrm{e},i} - \psi_{\mathrm{fc}})} {\theta_{\mathrm{sat},i} - \theta_{\mathrm{fc},i}}\]

where \(A_i\) is soil_brooks_corey_a [MPa; Derived parameter: air-entry pressure coefficient in the Brooks-Corey soil water retention curve] (\(\le 0\)), \(B_i\) is soil_brooks_corey_b [Derived parameter: pore-size distribution index in the Brooks-Corey soil water retention curve], \(\psi_{\mathrm{e},i}\) is soil_brooks_corey_bubbling_head [MPa; Derived parameter: brooks-Corey air-entry (bubbling) water potential of the soil] (\(\le 0\)), \(\theta_{\mathrm{fc},i}\) is soil_field_capacity [m3 m-3; Derived parameter: volumetric soil moisture content at field capacity], and \(\psi_{\mathrm{fc}} = -0.033\;\mathrm{MPa}\) is the fixed field-capacity water potential. The result is stored as soil_water_potential [MPa; Diagnostic: soil water potential across all soil layers].

Soil-plant water supply¶

For each layer, the soil-to-leaf water potential gradient is

(2.1.8)¶\[\Delta\psi_{\mathrm{soil},i} = \max(\psi_{\mathrm{soil},i} - \psi_{\mathrm{leaf,min}},\; 0)\]

where \(\psi_{\mathrm{leaf,min}}\) is plant_minimum_leaf_water_potential [MPa; PFT-based parameter: minimum leaf water potential below which soil-plant water transport ceases]. Only positive gradients drive upward water flow.

The layer-wise soil-plant water supply is

(2.1.9)¶\[S_i = f_{\mathrm{root},i}\,K_i\,\Delta\psi_{\mathrm{soil},i}\]

The fractional contribution of each layer to total supply is water_uptake_fraction [Diagnostic: fraction of total root water uptake in each soil layer]:

(2.1.10)¶\[\zeta_i = \frac{S_i}{\sum_j S_j}\]

The uptake-weighted root-zone soil water potential root_zone_soil_water_potential [MPa; Diagnostic: mean soil water potential of the root zone] is

(2.1.11)¶\[\psi_{\mathrm{root}} = \sum_i \zeta_i\,\psi_{\mathrm{soil},i}\]

When total supply is negligible (\(\sum_i S_i \approx 0\)), uptake fractions fall back to a unit weight on the top soil layer:

(2.1.12)¶\[\psi_{\mathrm{root}} = \psi_{\mathrm{soil},1}\]