Turbulent fluxes

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Overview

Turbulent motion in the atmosphere transports heat away from the surface. Two primary mechanisms are involved: the sensible heat flux due to the temperature gradient between the atmosphere and land surface, and the latent heat flux (from evaporation, transpiration, and sublimation).

The surface energy budget partitioning strongly depends on the strength of these fluxes:

Strong winds and atmospheric instability → large turbulent fluxes
Calm conditions and stable boundary layer → weak turbulent fluxes

The coupling between the turbulent fluxes and atmospheric conditions are primarily captured through aerodynamic resistance (or equivalently conductance) terms that approximate the instantaneous resistance of the land surface to energy losses due to turbulent effects.

Implementations

Terrarium.PrescribedTurbulentFluxes — Type

struct PrescribedTurbulentFluxes{NF} <: Terrarium.AbstractTurbulentFluxes{NF}

Represents the simplest case where the turbulent (sensible and latent) heat fluxes are prescribed via input variables.

Terrarium.DiagnosedTurbulentFluxes — Type

struct DiagnosedTurbulentFluxes{NF} <: Terrarium.AbstractTurbulentFluxes{NF}

Represents the standard case where the turbulent (sensible and latent) heat fluxes are diagnosed from atmosphere and soil conditions.

Sensible heat flux

Sensible heat is transported by the mean wind and turbulent eddies using bulk aerodynamic theory:

\[\begin{equation} H_s = c_a \rho_a \frac{\Delta T}{r_a} \end{equation}\]

where $c_a$ is the specific heat capacity of moist air (J/kg/K) and $\rho_a$ is the moist air density (kg/m³), both computed dynamically based on the local atmosphere state using Thermodynamics.jl. $\Delta T = T_s - T_a$ is the temperature difference (K) (positive if surface warmer than air), and $r_a$ is the aerodynamic resistance (s/m). $H_s$ is positive when surface is warmer than air (heat flows upward), and negative when surface is cooler (heat flows downward).

Latent heat flux

Evaporation and sublimation remove heat from the surface through the latent heat pathway. It is driven by the specific humidity difference $\Delta q$ (kg/kg), equivalent with the vapor pressure difference $\Delta e$ (Pa), between the surface and atmosphere. Under the typical assumption that the land surface is saturated (see e.g. [29]), the vapor pressure difference is computed as:

\[\begin{equation} \Delta e = e_s - e_a = e_{\text{sat}}(T_s) - e_a(q_a, p) \end{equation}\]

with $T_s$ the skin temperature. The specific humidity difference $\Delta q$ is

\[\begin{equation} \Delta q = q_s - q_a = q_{\text{sat}}(T_s) - q_a \end{equation}\]

with $q_{\text{sat}}$ the saturation specific humidity at the surface temperature and $q_a$ the specific humidity of the atmosphere.

The latent heat flux is then computed as:

\[\begin{equation} H_l = L \rho_a \frac{\Delta q}{r_a} \end{equation}\]

where $L$ is the latent heat of vaporization or sublimation (J/kg). $H_l$ represents energy lost due to evaporation, transpiration, or sublimation. While negative values of $H_l$ are theoretically possible when $\Delta q$ is negative, condensation is currently neglected so mass will not be conserved under such conditions.

The latent heat flux is directly tied to:

Vegetation: Transpiration through stomata (see Photosynthesis)
Soil moisture: Availability of water for evaporation (see Soil hydrology)
Surface roughness: Vegetation height affects aerodynamic properties

Diagnosed turbulent fluxes

Terrarium.DiagnosedTurbulentFluxes — Type

struct DiagnosedTurbulentFluxes{NF} <: Terrarium.AbstractTurbulentFluxes{NF}

Represents the standard case where the turbulent (sensible and latent) heat fluxes are diagnosed from atmosphere and soil conditions.

Prescribed turbulent fluxes

Terrarium.PrescribedTurbulentFluxes — Type

struct PrescribedTurbulentFluxes{NF} <: Terrarium.AbstractTurbulentFluxes{NF}

Represents the simplest case where the turbulent (sensible and latent) heat fluxes are prescribed via input variables.

Process interface

Terrarium.compute_auxiliary! — Method

compute_auxiliary!(
    state,
    grid,
    tur::DiagnosedTurbulentFluxes,
    seb::Terrarium.AbstractSurfaceEnergyBalance,
    constants::PhysicalConstants,
    atmos::Terrarium.AbstractAtmosphere,
    args...
)

Methods

Sensible heat flux

Terrarium.compute_sensible_heat_flux — Function

compute_sensible_heat_flux(
    _::DiagnosedTurbulentFluxes,
    Q_T,
    ρₐ,
    cₐ
) -> Any

Compute the sensible heat flux [W/m²] as a function of the bulk aerodynamic temperature gradient Q_T [K m/s] and the density ρₐ [kg/m³] and specific heat capacity cₐ [J/kg K] of air.

compute_sensible_heat_flux(
    i,
    j,
    grid,
    fields,
    tur::DiagnosedTurbulentFluxes,
    skinT::Terrarium.AbstractSkinTemperature,
    constants::PhysicalConstants,
    atmos::Terrarium.AbstractAtmosphere
) -> Any

Compute the sensible heat flux at i, j based on the current skin temperature and atmospheric conditions.

Latent heat flux

The latent heat flux is computed via a unified interface for both standalone flux calculations as well as coupling with evapotranpsiration:

Terrarium.compute_latent_heat_flux — Method

compute_latent_heat_flux(
    i,
    j,
    grid,
    fields,
    tur::DiagnosedTurbulentFluxes,
    skinT::Terrarium.AbstractSkinTemperature,
    constants::PhysicalConstants,
    atmos::Terrarium.AbstractAtmosphere
) -> Any
compute_latent_heat_flux(
    i,
    j,
    grid,
    fields,
    tur::DiagnosedTurbulentFluxes,
    skinT::Terrarium.AbstractSkinTemperature,
    constants::PhysicalConstants,
    atmos::Terrarium.AbstractAtmosphere,
    evtr::Union{Nothing, Terrarium.AbstractEvapotranspiration}
) -> Any
compute_latent_heat_flux(
    i,
    j,
    grid,
    fields,
    tur::DiagnosedTurbulentFluxes,
    skinT::Terrarium.AbstractSkinTemperature,
    constants::PhysicalConstants,
    atmos::Terrarium.AbstractAtmosphere,
    evtr::Union{Nothing, Terrarium.AbstractEvapotranspiration},
    snow::Union{Nothing, Terrarium.AbstractSnow}
) -> Any

Compute the latent heat flux at i, j based on the current skin temperature and atmospheric conditions. When an evapotranspiration scheme is provided, uses the ET-aware humidity flux; otherwise uses bare ground evaporation.

With a snow component, the flux is partitioned by snow-covered area fraction f_snow: the snow-free fraction (1 − f_snow) evaporates from the ground/canopy (latent heat of vaporization), while the snow-covered fraction sublimates from the snowpack (latent heat of sublimation, see compute_snow_sublimation_flux). Without snow it reduces to the bare ground/canopy latent flux.

Terrarium.compute_latent_heat_flux — Method

compute_latent_heat_flux(
    _::DiagnosedTurbulentFluxes,
    Q_h,
    ρₐ,
    L
) -> Any

Compute the latent heat flux as a function of the humidity flux Q_h [m/s], the density ρₐ [kg/m³] of air, and the specific latent heat of vaporization or sublimation L [J/kg].

Terrarium.vapor_pressure_difference — Function

vapor_pressure_difference(
    c::ThermodynamicConstants,
    p,
    q_air,
    T
) -> Any

Computes the difference in vapor pressure between a saturated surface at temperature T [°C] and the atmosphere, defined by its specific humidity q_air [kg/kg] and pressure p [Pa]. Relies on Thermodynamics.jl via partial_pressure_vapor and saturation_vapor_pressure.

Terrarium.specific_humidity_difference — Function

specific_humidity_difference(
    c::ThermodynamicConstants,
    p,
    q_air,
    T
) -> Any

Computes the difference in specific humidity between a saturated surface at temperature T [°C] and the atmosphere, defined by its specific humidity q_air [kg/kg] and pressure p [Pa].

Kernel functions

The fused surface-energy-balance kernel stores the turbulent fluxes through compute_turbulent_fluxes!: the DiagnosedTurbulentFluxes variant computes and stores the sensible and latent heat fluxes, while the PrescribedTurbulentFluxes variant is a no-op because the fluxes are supplied as input fields.

Terrarium.compute_turbulent_fluxes! — Function

compute_turbulent_fluxes!(
    out,
    i,
    j,
    grid,
    fields,
    tur::DiagnosedTurbulentFluxes,
    skinT,
    constants,
    atmos,
    evtr,
    snow
)

Compute the turbulent (sensible and latent) heat fluxes from the current skin temperature and store them into the auxiliary output fields out.

compute_turbulent_fluxes!(
    out,
    i,
    j,
    grid,
    fields,
    _::PrescribedTurbulentFluxes,
    skinT,
    constants,
    atmos,
    evtr,
    snow
)

Prescribed turbulent fluxes are input fields supplied by an external coupler (already present in fields), so there is nothing to compute or store.

Terrarium.compute_vapor_pressure_difference — Method

compute_vapor_pressure_difference(
    i,
    j,
    grid,
    fields,
    atmos::Terrarium.AbstractAtmosphere,
    c::PhysicalConstants,
    T
) -> Any

Computes the vapor pressure difference [Pa] between a saturated surface at temperature T [°C] and the current atmospheric fields.

Terrarium.compute_specific_humidity_difference — Method

compute_specific_humidity_difference(
    i,
    j,
    grid,
    fields,
    atmos::Terrarium.AbstractAtmosphere,
    c::PhysicalConstants,
    T
) -> Any

Computes the specific humidity difference [kg/kg] between a saturated surface at temperature T [°C] and the current atmospheric fields.

References

[29]: S. Zhou and B. Yu. Physical basis of the potential evapotranspiration and its estimation over land. Journal of Hydrology 641, 131825 (2024).