5.4. Soil Hydrology

ADELM updates the multi-layer soil-water store from surface liquid input, infiltration, evapotranspiration removal, gravitational drainage, runoff, and bottom-boundary underflow.

Notation

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

Coupling to other components

1. Column water balance

See also

model.processes.hydrology.calculate_soil_hydrology()

For the full soil column, the total storage change satisfies

(5.4.1)\[\sum_{i=1}^{N_{\mathrm{soil}}} S_{\mathrm{soil},i,t+1} = \sum_{i=1}^{N_{\mathrm{soil}}} S_{\mathrm{soil},i,t} + P_{\mathrm{liq,surf}} - E_{\mathrm{soil}} - E_{\mathrm{tr}} - Q_{\mathrm{surf}} - Q_{\mathrm{deep}}\]

where \(P_{\mathrm{liq,surf}}\) is the surface liquid input, \(E_{\mathrm{soil}}\) is actual soil evaporation (soil_evaporation_mmday [mm day-1; Flux: water flux evaporated from the top soil layer]), \(E_{\mathrm{tr}}\) is total transpiration (canopy_transpiration_mmday [mm day-1; Flux: water flux from the soil column to the atmosphere through plants]), \(Q_{\mathrm{surf}}\) is surface runoff (runoff_mmday [mm day-1; Flux: water flux leaving the land surface as runoff]), and \(Q_{\mathrm{deep}}\) is bottom-boundary underflow (underflow_mmday [mm day-1; Flux: downward water flux leaving the base of the soil column]).

The surface liquid input combines throughfall and snowmelt:

(5.4.2)\[P_{\mathrm{liq,surf}} = P_{\mathrm{through}} + M_{\mathrm{snow}}\]

where \(P_{\mathrm{through}}\) is throughfall_from_canopy_mmday [mm day-1; Flux: liquid precipitation reaching the soil surface without canopy interception] and \(M_{\mathrm{snow}}\) is snowmelt_mmday [mm day-1; Flux: water flux released from the snowpack by melting].

2. Layer storage update

The soil column is discretized into \(N_{\mathrm{soil}}\) layers. The upper \(N_{\mathrm{run}}\) layers (user-defined num_runoff_generation_layers) form the runoff-generation zone where surface runoff \(Q_{\mathrm{surf}}\) is diagnosed. Surface runoff leaves the system before entering the soil column; only \(W_{\mathrm{inf}}\) infiltrates into the layers (Section 4).

Surface layer (\(i = 1\)):

(5.4.3)\[S_{\mathrm{soil},1,t+1} = S_{\mathrm{soil},1,t} + I_1 - E_{\mathrm{soil}} - RWU_1 - D_1\]

Runoff-generation layers (\(2 \le i \le N_{\mathrm{run}}\)):

(5.4.4)\[S_{\mathrm{soil},i,t+1} = S_{\mathrm{soil},i,t} + I_i + D_{i-1} - RWU_i - D_i\]

Deep layers (\(N_{\mathrm{run}} < i \le N_{\mathrm{soil}}\)):

(5.4.5)\[S_{\mathrm{soil},i,t+1} = S_{\mathrm{soil},i,t} + D_{i-1} - RWU_i - D_i\]

where \(I_i\) is infiltration added to layer \(i\) (Section 4), \(D_{i-1}\) is gravitational drainage received from the layer above (\(D_0 = 0\) for the surface layer), \(RWU_i\) is root water uptake (Section 5), \(D_i\) is gravitational drainage leaving layer \(i\) downward (Section 6), and \(E_{\mathrm{soil}}\) is actual soil evaporation applied to the surface layer only (Section 3). Deep layers receive no direct infiltration: \(W_{\mathrm{inf}}\) is bounded by the total pore space of the runoff-generation zone and is fully absorbed there. Water reaches deep layers only through gravitational drainage \(D_{i-1}\). For the bottom layer, \(D_{N_{\mathrm{soil}}}\) leaves the column as underflow \(Q_{\mathrm{deep}}\).

3. Surface evaporation

Soil evaporation soil_evaporation_mmday [mm day-1; Flux: water flux evaporated from the top soil layer] is applied to the first layer only:

(5.4.6)\[E_{\mathrm{soil}} = \min(E_{\mathrm{soil}}^\ast,\;S_{\mathrm{soil},1})\]

where \(E_{\mathrm{soil}}^\ast\) is the surface-evaporation demand. This demand is the residual atmospheric capacity after snow sublimation has already been served:

(5.4.7)\[E_{\mathrm{soil}}^\ast = \max(E_{\mathrm{surf}}^\ast - E_{\mathrm{snow}},\;0)\]

where \(E_{\mathrm{surf}}^\ast\) is potential_surface_evaporation [mm day-1; Diagnostic: atmospheric demand for evaporation from the snow-free soil surface] and \(E_{\mathrm{snow}}\) is snow_sublimation_mmday [mm day-1; Flux: water flux sublimated from the ground snowpack].

4. Infiltration

Total infiltrating water. Surface runoff \(Q_{\mathrm{surf}}\) and total infiltrating water \(W_{\mathrm{inf}}\) are diagnosed from the aggregated state of the upper \(N_{\mathrm{run}}\) runoff-generation layers:

(5.4.8)\[W_{\mathrm{run}} = \sum_{i=1}^{N_{\mathrm{run}}} S_{\mathrm{soil},i}, \qquad W_{\mathrm{run,max}} = \sum_{i=1}^{N_{\mathrm{run}}} \theta_{\mathrm{sat},i}\,z_i\]

The relative wetness of the runoff-generation zone is \(W_{\mathrm{run}}/W_{\mathrm{run,max}}\). The maximum infiltration capacity is

(5.4.9)\[I_{\mathrm{cap,max}} = (1 + b_{\mathrm{inf}})\,W_{\mathrm{run,max}}\]

where \(b_{\mathrm{inf}}\) is soil_infiltration_shape_parameter [default: 0.2; Fixed parameter: shape parameter of the variable infiltration capacity curve]. The initial curve capacity is

(5.4.10)\[W_{\mathrm{cap,0}} = I_{\mathrm{cap,max}}\left[1 - \left(1 - \frac{W_{\mathrm{run}}}{W_{\mathrm{run,max}}}\right)^{1/(1+b_{\mathrm{inf}})}\right]\]

When the runoff-generation zone is unsaturated (\(W_{\mathrm{run}} < W_{\mathrm{run,max}}\)), infiltration follows the variable-infiltration-capacity curve:

(5.4.11)\[W_{\mathrm{inf}} = W_{\mathrm{run,max}}\left[1 - \left(1 - \frac{W_{\mathrm{cap,0}} + P_{\mathrm{liq,surf}}}{I_{\mathrm{cap,max}}}\right)^{1+b_{\mathrm{inf}}}\right] - W_{\mathrm{run}}\]

When the zone is saturated, infiltration is limited by the remaining pore space:

(5.4.12)\[W_{\mathrm{inf}} = \min\!\left(P_{\mathrm{liq,surf}},\;W_{\mathrm{run,max}} - W_{\mathrm{run}}\right)\]

Layer-by-layer distribution. \(W_{\mathrm{inf}}\) is passed top-down through the \(N_{\mathrm{run}}\) runoff-generation layers, with \(W_{\mathrm{inf},1}^\downarrow = W_{\mathrm{inf}}\) and \(W_{\mathrm{inf},i}^\downarrow = W_{\mathrm{inf},i-1}^\downarrow - I_{i-1}\). The addition to layer \(i\) is

(5.4.13)\[I_i = \min\!\left(W_{\mathrm{inf},i}^\downarrow,\;(\theta_{\mathrm{sat},i} - \theta_i)\,z_i\right)\]

where \(W_{\mathrm{inf},i}^\downarrow\) is the remaining infiltrating water reaching layer \(i\). Layer-wise additions are stored in infiltration_mmday [mm day-1; Flux: water flux entering each soil layer from above].

Surface runoff is the residual liquid input not absorbed by the soil column:

(5.4.14)\[Q_{\mathrm{surf}} = P_{\mathrm{liq,surf}} - W_{\mathrm{inf}}\]

5. Root water uptake

Potential transpiration potential_canopy_transpiration [mm day-1; Diagnostic: maximum water vapour flux from canopy leaves to the atmosphere] is distributed across all layers using the hydraulic uptake fractions water_uptake_fraction [Diagnostic: fraction of total root water uptake in each soil layer]:

(5.4.15)\[RWU_i = \min\!\left(E_{\mathrm{tr}}^\ast\,\zeta_i,\;S_{\mathrm{soil},i}\right)\]

where \(E_{\mathrm{tr}}^\ast\) is potential_canopy_transpiration [mm day-1; Diagnostic: maximum water vapour flux from canopy leaves to the atmosphere]. Layer uptake is stored in root_water_uptake_mmday [mm day-1; Flux: water flux extracted from each soil layer by roots], and the profile sum gives canopy_transpiration_mmday [mm day-1; Flux: water flux from the soil column to the atmosphere through plants].

6. Drainage

Field capacity \(\theta_{\mathrm{fc},i}\) is provided to the hydrology step as the derived parameter soil_field_capacity [m3 m-3; Derived parameter: volumetric soil moisture content at field capacity]. In the default ADELM setup this quantity comes from the pedotransfer routine together with soil_saturated_moisture [m3 m-3; Derived parameter: saturated volumetric soil moisture content], soil_saturated_hydraulic_conductivity [mm h-1; Derived parameter: saturated hydraulic conductivity], and soil_brooks_corey_b [Derived parameter: pore-size distribution index in the Brooks-Corey soil water retention curve]:

See also

model.parameterization.pedotransfer.calculate_soil_parameters_pedotransfer()

Gravitational drainage from layer \(i\) assumes a unit hydraulic gradient (free drainage) so that the Darcy flux equals the unsaturated conductivity:

(5.4.16)\[D_i = \min\!\left(K(\theta_i)\,\Delta t_{\mathrm{day}},\; (\theta_i - \theta_{\mathrm{fc},i})^{+}\,z_i\right)\]

where \(K(\theta_i)\) is the Brooks-Corey conductivity, \(\Delta t_{\mathrm{day}}\) is the length of the daily time step, and \((\cdot)^{+}\) denotes the positive part. For layers \(i < N_{\mathrm{soil}}\), drainage is additionally bounded by the available pore space of the layer below:

(5.4.17)\[D_i \le (\theta_{\mathrm{sat},i+1} - \theta_{i+1})^{+}\,z_{i+1}\]

Drainage is zero when \(T_{\mathrm{a}} < T_{\mathrm{freeze}}\), where \(T_{\mathrm{freeze}}\) is freezing_point [default: 0 degC; Constant: temperature at which water freezes]. For the bottom layer, \(D_{N_{\mathrm{soil}}}\) leaves the column as underflow underflow_mmday [mm day-1; Flux: downward water flux leaving the base of the soil column].