4.4. Potential Evapotranspiration¶

Potential evapotranspiration represents the atmospheric demand for water vapour in the absence of supply limitation. ADELM evaluates it separately for five pathways: soil surface evaporation (potential_surface_evaporation), ground snow sublimation (potential_snow_sublimation), wet-canopy evaporation (potential_canopy_evaporation), canopy sublimation (potential_canopy_sublimation), and transpiration (potential_transpiration). The hydrology module then constrains each flux by available water storage.

Coupling to other components

Shortwave Radiation and Longwave Radiation provide soil_net_swrad_Wm2, canopy_net_swrad_Wm2, soil_net_lwrad_Wm2, and canopy_net_lwrad_Wm2.
Atmospheric Thermodynamics provides air_density, air_molar_density, latent_heat_of_vaporization, psychrometric_constant, and saturation_vapour_pressure_slope.
Soil Surface State provides soil_surface_conductance and soil_to_air_vapour_pressure_gradient.
Aerodynamic Exchange provides soil_aerodynamic_conductance, above_canopy_aerodynamic_conductance, leaf_boundary_layer_conductance, and canopy_aerodynamic_conductance.
Stomatal Conductance provides canopy_stomatal_conductance.
Snow Hydrology uses potential_snow_sublimation.
Canopy Hydrology uses potential_canopy_evaporation and potential_canopy_sublimation.
Soil Hydrology uses potential_transpiration.

1. Potential surface evaporation and sublimation¶

Potential surface evaporation potential_surface_evaporation [mm day-1; Diagnostic: atmospheric demand for evaporation from the snow-free soil surface] follows the Penman-Monteith form:

(4.4.1)¶\[E_{\mathrm{soil,pot}} = \frac{ s\,R^{\mathrm{n}}_{\mathrm{g}} + \rho_{\mathrm{a}} c_p \Delta e_{\mathrm{soil}}/r_{\mathrm{a,soil}} }{ \lambda_{\mathrm{v}} \left[ s + \gamma\left(1 + \dfrac{r_{\mathrm{ss}}}{r_{\mathrm{a,soil}}}\right) \right] }\]

The soil net radiation \(R^{\mathrm{n}}_{\mathrm{g}}\) (soil_net_radiation_Wm2 [W m-2; Flux: net radiative flux at the soil surface]) is

(4.4.2)¶\[R^{\mathrm{n}}_{\mathrm{g}} = R^{\mathrm{n}}_{\mathrm{lw},\mathrm{g}} + R^{\mathrm{n}}_{\mathrm{sw},\mathrm{g}}\]

Symbol	ADELM variables
\(R^{\mathrm{n}}_{\mathrm{lw},\mathrm{g}}\)	`soil_net_lwrad_Wm2` [W m-2; Flux: longwave radiative flux absorbed by the soil surface]
\(R^{\mathrm{n}}_{\mathrm{sw},\mathrm{g}}\)	`soil_net_swrad_Wm2` [W m-2; Flux: shortwave radiative flux absorbed by the soil surface (visible plus near-infrared)]
\(s\)	`saturation_vapour_pressure_slope` [kPa K-1; Diagnostic: rate of change of saturation vapour pressure with temperature]
\(\rho_{\mathrm{a}}\)	`air_density` [kg m-3; Diagnostic: mass of air per unit volume]
\(c_p\)	`specific_heat_capacity_air` [default: 1004.6 J kg-1 K-1; Constant: specific heat capacity of air]
\(\Delta e_{\mathrm{soil}}\)	`soil_to_air_vapour_pressure_gradient` [kPa; Diagnostic: difference between soil-surface vapour pressure and near-surface air vapour pressure]
\(r_{\mathrm{a,soil}}\)	`soil_aerodynamic_conductance` [m s-1; Diagnostic: aerodynamic conductance for water vapour transport between the soil surface and the canopy air]
\(r_{\mathrm{ss}}\)	`soil_surface_conductance` [m s-1; Diagnostic: soil surface conductance to water vapour]
\(\lambda_{\mathrm{v}}\)	`latent_heat_of_vaporization` [J kg-1; Diagnostic: energy required to vaporize one kilogram of liquid water]
\(\gamma\)	`psychrometric_constant` [kPa K-1; Diagnostic: ratio of sensible to latent heat flux for a wet surface at constant pressure]

Potential ground snow sublimation potential_snow_sublimation [mm day-1; Diagnostic: atmospheric demand for sublimation from the ground snowpack] uses a separate Penman-Monteith formulation for an ice surface, with ice-phase thermodynamic quantities replacing the liquid-water equivalents:

(4.4.3)¶\[E_{\mathrm{snow,pot}} = \frac{ s_{\mathrm{ice}}\,R^{\mathrm{n}}_{\mathrm{g}} + \rho_{\mathrm{a}} c_p \Delta e_{\mathrm{ice}}/r_{\mathrm{a,soil}} }{ \lambda_{\mathrm{s}}\left(s_{\mathrm{ice}} + \gamma_{\mathrm{s}}\right) }\]

where \(s_{\mathrm{ice}}\) is the slope of the saturation vapour pressure curve over ice, \(\Delta e_{\mathrm{ice}} = \max(e_{\mathrm{sat,ice}}(T_{\mathrm{a}}) - e_{\mathrm{a}},\,0)\) is the ice-surface vapour pressure deficit, \(\gamma_{\mathrm{s}} = \gamma\,\lambda_{\mathrm{v}}/\lambda_{\mathrm{s}}\) is the psychrometric constant for the sublimation pathway, and \(\lambda_{\mathrm{s}}\) is latent_heat_of_sublimation [default: 2.836e+06 J kg-1; Constant: latent heat of sublimation of water at 0°C].

2. Potential wet-canopy evaporation and sublimation¶

Potential wet-canopy evaporation demand potential_canopy_liquid_evaporation [mm day-1; Diagnostic: atmospheric demand for evaporation from wet canopy surfaces] is

(4.4.4)¶\[E_{\mathrm{can,liq,pot}} = \frac{ s\,R^{\mathrm{n}}_{\mathrm{v}} + \rho_{\mathrm{a}} c_p \mathrm{VPD}/r_{\mathrm{a}} }{ \lambda_{\mathrm{v}}\left[s + \gamma\left(1 + \dfrac{r_{\mathrm{b}}}{r_{\mathrm{a}}}\right)\right] }\]

where \(r_{\mathrm{a}} = 1/g_{\mathrm{a,above}}\) is the above-canopy aerodynamic resistance and \(r_{\mathrm{b}} = 1/g_{\mathrm{b}}\) is the leaf boundary layer resistance. In ADELM, the aerodynamic numerator uses the above-canopy path, and the denominator includes the extra leaf boundary layer resistance.

The canopy net radiation \(R^{\mathrm{n}}_{\mathrm{v}}\) (canopy_net_radiation_Wm2 [W m-2; Flux: net radiative flux at the canopy surface]) is

(4.4.5)¶\[R^{\mathrm{n}}_{\mathrm{v}} = R^{\mathrm{n}}_{\mathrm{lw},\mathrm{v}} + R^{\mathrm{n}}_{\mathrm{sw},\mathrm{v}}\]

Symbol	ADELM variables
\(R^{\mathrm{n}}_{\mathrm{lw},\mathrm{v}}\)	`canopy_net_lwrad_Wm2` [W m-2; Flux: longwave radiative flux absorbed by the canopy]
\(R^{\mathrm{n}}_{\mathrm{sw},\mathrm{v}}\)	`canopy_net_swrad_Wm2` [W m-2; Flux: shortwave radiative flux absorbed by the canopy]
\(\rho_{\mathrm{a}}\)	`air_density` [kg m-3; Diagnostic: mass of air per unit volume]
\(c_p\)	`specific_heat_capacity_air` [default: 1004.6 J kg-1 K-1; Constant: specific heat capacity of air]
\(\mathrm{VPD}\)	`vpd_kPa` [kPa; Driver: vapour pressure deficit]
\(g_{\mathrm{a,above}}\)	`above_canopy_aerodynamic_conductance` [m s-1; Diagnostic: aerodynamic conductance for water vapour transport from the canopy top to the reference height]
\(g_{\mathrm{b}}\)	`leaf_boundary_layer_conductance` [m s-1; Diagnostic: bulk conductance for water vapour across the laminar boundary layer of canopy leaves]

Potential canopy sublimation potential_canopy_sublimation [mm day-1; Diagnostic: atmospheric demand for sublimation of solid-phase water stored on the canopy] is then

(4.4.6)¶\[E_{\mathrm{sub,pot}} = E_{\mathrm{can,liq,pot}}\,\frac{\lambda_{\mathrm{v}}}{\lambda_{\mathrm{s}}}\]

where \(\lambda_{\mathrm{s}}\) is latent_heat_of_sublimation [default: 2.836e+06 J kg-1; Constant: latent heat of sublimation of water at 0°C]. Because \(\lambda_{\mathrm{s}} > \lambda_{\mathrm{v}}\), the sublimation demand is smaller than the corresponding wet-canopy evaporation demand.

4.4. Potential Evapotranspiration¶

1. Potential surface evaporation and sublimation¶

2. Potential wet-canopy evaporation and sublimation¶

3. Potential transpiration¶