4.3. Soil Surface State¶

ADELM diagnoses two quantities that drive potential soil surface evaporation: the soil-surface conductance to water vapour, and the soil-to-air vapour pressure gradient.

Coupling to other components

Soil Hydrology provides soil_moisture.
Soil Hydraulics provides soil_water_potential.
Potential Evapotranspiration uses soil_surface_conductance and soil_to_air_vapour_pressure_gradient.

1. Soil surface resistance¶

Potential surface evaporation uses the soil-surface conductance soil_surface_conductance [m s-1; Diagnostic: soil surface conductance to water vapour]:

(4.3.1)¶\[g_{\mathrm{ss}} = \frac{1}{r_{\mathrm{ss}}}\]

The soil surface resistance \(r_{\mathrm{ss}}\) follows an exponential formulation:

(4.3.2)¶\[r_{\mathrm{ss}} = f_{\mathrm{snow}} \cdot 1 + (1 - f_{\mathrm{snow}}) \exp\!\bigl(8.25 - k_{\mathrm{ss}}\,B_{\mathrm{evap}}\bigr)\]

where \(f_{\mathrm{snow}}\) is snow_cover_fraction [Diagnostic: fraction of the ground surface covered by snow], \(k_{\mathrm{ss}}\) is soil_surface_resistance_moisture_sensitivity [default: 4.225; Fixed parameter: exponential sensitivity coefficient of soil surface resistance to top-layer soil moisture], and \(B_{\mathrm{evap}}\) is the top-layer relative soil wetness:

(4.3.3)¶\[B_{\mathrm{evap}} = \mathrm{clamp}\!\left(\frac{\theta_1}{\theta_{\mathrm{sat},1}},\,0,\,1\right)\]

Snow-covered ground is assigned \(r_{\mathrm{ss}} = 1\;\mathrm{s\,m^{-1}}\) so that sublimation is handled separately. The resistance is further clamped to \([1,\,10000]\;\mathrm{s\,m^{-1}}\).

Symbol	ADELM variable
\(\theta_1\)	`soil_moisture` [m3 m-3; State: volumetric water content of each soil layer] (layer 0)
\(\theta_{\mathrm{sat},1}\)	`soil_saturated_moisture` [m3 m-3; Derived parameter: saturated volumetric soil moisture content] (layer 0)
\(k\)	`soil_surface_resistance_moisture_sensitivity` [default: 4.225; Fixed parameter: exponential sensitivity coefficient of soil surface resistance to top-layer soil moisture]
\(f_{\mathrm{snow}}\)	`snow_cover_fraction` [Diagnostic: fraction of the ground surface covered by snow]

2. Soil-to-air vapour pressure gradient¶

The soil-to-air vapour pressure gradient soil_to_air_vapour_pressure_gradient [kPa; Diagnostic: difference between soil-surface vapour pressure and near-surface air vapour pressure] drives the aerodynamic transport of water vapour from the soil surface to the canopy air:

(4.3.4)¶\[\Delta e = \max(e_{\mathrm{soil}} - e_{\mathrm{a}},\,0)\]

The air vapour pressure \(e_{\mathrm{a}}\) is recovered from the saturation vapour pressure and VPD:

(4.3.5)¶\[e_{\mathrm{a}} = e_{\mathrm{s,air}} - \mathrm{VPD}\]

where \(\mathrm{VPD}\) is vpd_kPa [kPa; Driver: vapour pressure deficit], and \(e_{\mathrm{s,air}}\) is the mean saturation vapour pressure evaluated at daily maximum and minimum temperatures:

(4.3.6)¶\[e_{\mathrm{s}}(T) = 0.6108\,\exp\!\left(\frac{17.27\,T}{T + 237.3}\right), \qquad e_{\mathrm{s,air}} = \tfrac{1}{2}\bigl[e_{\mathrm{s}}(T_{\max}) + e_{\mathrm{s}}(T_{\min})\bigr]\]

Here \(T_{\max}\) is ta_max_degC [degC; Driver: daily maximum near-surface air temperature], and \(T_{\min}\) is ta_min_degC [degC; Driver: daily minimum near-surface air temperature].

The soil-surface vapour pressure \(e_{\mathrm{soil}}\) is suppressed below saturation by soil water potential via the Kelvin equation:

(4.3.7)¶\[e_{\mathrm{soil}} = e_{\mathrm{s,air}}\,\exp\!\left( \frac{10^6\,\psi_{\mathrm{soil},1}\,V_w}{R\,T_{\mathrm{a},K}} \right)\]

where \(\psi_{\mathrm{soil},1}\) is the water potential of the first soil layer from soil_water_potential [MPa; Diagnostic: soil water potential across all soil layers], \(V_w\) is partial_molar_volume_of_water [default: 1.805e-05 m3 mol-1; Constant: partial molar volume of water at 20°C], \(R\) is universal_gas_constant [default: 8.3144 J mol-1 K-1; Constant: universal gas constant], and \(T_{\mathrm{a},K} = T_{\mathrm{a}} + T_0\) with \(T_{\mathrm{a}}\) being ta_degC [degC; Driver: near-surface air temperature] and \(T_0\) being absolute_zero_offset [default: 273.15 K; Constant: zero degrees Celsius expressed in Kelvin].