Evapotranspiration

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Overview

Evapotranspiration ($\text{ET}$) (m/s) is the combined process of water evaporation from soil and open water surfaces, evaporation of water intercepted by the canopy, and transpiration through leaf stomata. These processes remove water from the surface, driving latent heat flux and competing with sensible heat and ground heat fluxes in the surface energy balance.

All evapotranspiration pathways are primarily driven by the vapor pressure gradient or specific humidity gradient at the surface $\Delta q = q_{\text{sat}}(T_s) - q_a$, where $q_{\text{sat}}(T_s)$ is the saturation specific humidity at surface temperature $T_s$ (kg/kg) and $q_a$ is the atmospheric specific humidity (kg/kg) at a particular reference height.

Each pathway is also modulated by aerodynamic resistance(s) $r_a$ (s/m) (between surface and atmosphere) and possibly stomatal resistance $r_s$ (s/m) (in the case of transpiration).

Terrarium.AbstractEvapotranspiration — Type

Base type for evapotranspiration processes.

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subtypes(Terrarium.AbstractEvapotranspiration)

2-element Vector{Any}:
 BareGroundEvaporation
 PALADYNCanopyEvapotranspiration

Bare ground evaporation

The simplest case where no vegetation is considered.

Terrarium.BareGroundEvaporation — Type

BareGroundEvaporation{NF, GR} <: AbstractEvapotranspiration

Evaporation scheme for bare ground that calculates the humidity flux as

\[E = \beta \frac{\Delta q}{r_a}\]

where Δq is the specific humidity difference, rₐ is aerodynamic resistance, and β is an evaporation limiting factor.

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variables(BareGroundEvaporation(Float32))

Variables
├─ Prognostic: 
├─ Auxiliary: 
├── evaporation_ground [m s^-1] on XY{Center, Center}
├─ Inputs: 
├── skin_temperature [°C] on XY{Center, Center}
├─ Namespaces:

Vegetated land evapotranspiration

A big-leaf approach that combines canopy evaporation, transpiration and ground evaporation in parallel.

Terrarium.PALADYNCanopyEvapotranspiration — Type

struct PALADYNCanopyEvapotranspiration{NF, GR<:Terrarium.AbstractGroundEvaporationResistanceFactor} <: Terrarium.AbstractEvapotranspiration{NF}

Canopy evapotranspiration scheme from PALADYN ([11, Eq. (5)]) that includes a canopy evaporation term based on the saturation fraction of canopy water defined by the canopy hydrology scheme.

\[E_{\text{ground}} = \beta \frac{\Delta q}{r_a + r_e}\]

\[E_{\text{can}} = f_{\text{can}} \frac{\Delta q}{r_a}\]

\[T_{\text{can}} = \frac{\Delta q}{r_a + r_s}\]

Properties:

C_can: Drag coefficient for the transfer of heat and water between the ground and canopy
ground_resistance: Parameterization for ground resistance to evaporation/sublimation

References

[11] Willeit and Ganopolski, Geoscientific Model Development (2016)

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variables(PALADYNCanopyEvapotranspiration(Float32))

Variables
├─ Prognostic: 
├─ Auxiliary: 
├── evaporation_canopy [m s^-1] on XY{Center, Center}
├── evaporation_ground [m s^-1] on XY{Center, Center}
├── transpiration [m s^-1] on XY{Center, Center}
├─ Inputs: 
├── skin_temperature [°C] on XY{Center, Center}
├── ground_temperature [°C] on XY{Center, Center}
├─ Namespaces:

Evaporation from the canopy

Evaporation of water intercepted by the canopy $E_{\text{can}}$ (m/s) depends on the saturation state of the canopy (fraction of leaves wet),

\[\begin{equation} E_{\text{can}} = f_{\text{can}} \frac{\Delta q}{r_a}\,, \end{equation}\]

where $f_{\text{can}}$ is the canopy saturation fraction (0 = dry, 1 = saturated) (-) and $\Delta q$ is the vapor pressure gradient (kg/kg).

When $f_{\text{can}} = 0$ (completely dry canopy), $E_{\text{can}} = 0$. When $f_{\text{can}} = 1$ (wet canopy), evaporation proceeds at the potential rate.

Ground evaporation

Evaporation from exposed soil or under-canopy surfaces $E_{\text{ground}}$ (m/s) is limited by soil water availability,

\[\begin{equation} E_{\text{ground}} = \beta \frac{\Delta q}{r_a + r_e}\,, \end{equation}\]

where $\beta$ is the ground evaporation resistance factor (0 to 1) (-) and $r_e$ is the aerodynamic resistance between ground and canopy (s/m).

The resistance factor $\beta$ is computed from soil moisture in the upper layer: $\beta = 1$ when soil is wet (at field capacity) and $\beta \to 0$ as soil dries.

Transpiration

Plant transpiration occurs through stomata and is controlled by stomatal conductance,

\[\begin{equation} T_{\text{can}} = \frac{\Delta q}{r_a + r_s}\,, \end{equation}\]

where $r_s = 1 / g_w$ is the stomatal resistance (s/m) and $g_w$ is the stomatal conductance (m/s) (computed from photosynthesis; see Stomatal conductance).

High stomatal conductance (when photosynthetically active) leads to low stomatal resistance and high transpiration. This creates a strong coupling between carbon uptake (photosynthesis) and water loss (transpiration).

Total evapotranspiration

The PALADYN approach combines all three pathways in parallel,

\[\begin{equation} \text{ET} = E_{\text{can}} + E_{\text{ground}} + T_{\text{can}}\,, \end{equation}\]

to obtain a total surface humidity flux $\text{ET}$ (m/s) that can be converted into the [latent heat flux][@ref "Turbulent fluxes"] expressed in W/m² for use in the surface energy balance.

Process interface

Terrarium.compute_auxiliary! — Method

compute_auxiliary!(
    state,
    grid,
    evaporation::BareGroundEvaporation,
    ::NoCanopyInterception,
    constants::PhysicalConstants,
    atmos::Terrarium.AbstractAtmosphere
)
compute_auxiliary!(
    state,
    grid,
    evaporation::BareGroundEvaporation,
    ::NoCanopyInterception,
    constants::PhysicalConstants,
    atmos::Terrarium.AbstractAtmosphere,
    soil::Union{Nothing, Terrarium.AbstractSoil},
    args...
)

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Terrarium.compute_auxiliary! — Method

compute_auxiliary!(
    state,
    grid,
    evapotranspiration::PALADYNCanopyEvapotranspiration,
    canopy_interception::Terrarium.AbstractCanopyInterception,
    constants::PhysicalConstants,
    atmos::Terrarium.AbstractAtmosphere,
    soil::Terrarium.AbstractSoil,
    vegetation::Terrarium.AbstractVegetation,
    args...
)

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Ground resistance parameterizations

Terrarium.ConstantEvaporationResistanceFactor — Type

struct ConstantEvaporationResistanceFactor{NF} <: Terrarium.AbstractGroundEvaporationResistanceFactor

Represents a spatiotemporally constant ground evaporation resistance factor.

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Terrarium.SoilMoistureResistanceFactor — Type

struct SoilMoistureResistanceFactor{NF} <: Terrarium.AbstractGroundEvaporationResistanceFactor

Implements the soil moisture limiting resistance factor of [22],

\[\beta = \frac{1}{4} \left[1 - \cos\left(π \theta_1/\theta_{\text{fc}} \right)\right] \quad \text{for } \theta_1 < \theta_{\text{fc}}\]

otherwise $\beta=1$.

References

[22] Lee and Pielke, Journal of Applied Meteorology (1992)

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Coupling to soil hydrology

Subtypes of AbstractEvapotranpsiration automatically inherit an implementation of the forcing interface for SoilHydrology, which computes the contribution of ET to the soil moisture tendency in each soil layer. The default implementation draws the rescaled surface humidity flux only from the uppermost soil layer.

Terrarium.forcing — Method

forcing(i, j, k, grid, clock, fields, evapotranspiration::AbstractEvapotranspiration, ::AbstractSoilHydrology)

Compute and return the evapotranspiration forcing for soil moisture at the given indices i, j, k. The ET forcing is just the surface_humidity_flux rescaled by the thickness of layer k.

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Kernel functions

Terrarium.surface_humidity_flux — Function

surface_humidity_flux(i, j, grid, fields, ::AbstractEvapotranspiration)

Compute the surface humidity flux [m/s] at cell i, j based on the current state.

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Terrarium.compute_transpiration — Function

compute_transpiration(
    _::PALADYNCanopyEvapotranspiration{NF},
    Δq,
    rₐ,
    gw_can
) -> Any

Compute transpiration from the given humidity gradient, aerodynamic resistance rₐ and stomatal conductance gw_can.

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Terrarium.compute_evaporation_ground — Function

compute_evaporation_ground(
    _::PALADYNCanopyEvapotranspiration,
    Δq,
    β,
    rₐ,
    rₑ
) -> Any

Compute evaporation from the ground below the canopy, following [11, Eq. (5)]; Δq is the humidity gradient, β is the ground evaporation resistance factor, rₐ is aerodynamic resistance, and rₑ is aerodynamic resistance between the ground and canopy.

References

[11] Willeit and Ganopolski, Geoscientific Model Development (2016)

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Terrarium.compute_evaporation_canopy — Function

compute_evaporation_canopy(
    _::PALADYNCanopyEvapotranspiration,
    Δq,
    f_can,
    rₐ
) -> Any

Compute evaporation of water intercepted by the canopy from humidity gradient Δq, canopy saturation fraction f_can, and aerodynamic resistance rₐ.

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Terrarium.ground_evaporation_resistance_factor — Function

ground_evaporation_resistance_factor(i, j, grid, fields, :AbstractGroundEvaporationResistanceFactor, args...)

Compute the resistance factor against ground evaporation [-] based on the current state and implementation-specific process dependencies in args.

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