Diagnostics

PotentialTemperature(model, flavor=:specific)

Return a KernelFunctionOperation representing the (mixture) potential temperature $θ$.

The potential temperature is defined as the temperature a parcel would have if adiabatically brought to a reference pressure $p₀$:

\[θ = \frac{T}{Π}\]

where $T$ is temperature and $Π = (p/p₀)^{Rᵐ/cᵖᵐ}$ is the mixture Exner function, computed using the moist air gas constant $Rᵐ$ and heat capacity $cᵖᵐ$.

Arguments

• model: An AtmosphereModel instance.
• flavor: Either :specific (default) to return $θ$, or :density to return $ρ θ$.

Examples

using Breeze

grid = RectilinearGrid(size=(1, 1, 8), extent=(1, 1, 1e3))
model = AtmosphereModel(grid)
set!(model, θ=300, qᵗ=0.01)

θ = PotentialTemperature(model)
Field(θ)

# output
1×1×8 Field{Center, Center, Center} on RectilinearGrid on CPU
├── grid: 1×1×8 RectilinearGrid{Float64, Periodic, Periodic, Bounded} on CPU with 1×1×3 halo
├── boundary conditions: FieldBoundaryConditions
│   └── west: Periodic, east: Periodic, south: Periodic, north: Periodic, bottom: ZeroFlux, top: ZeroFlux, immersed: Nothing
├── operand: KernelFunctionOperation at (Center, Center, Center)
├── status: time=0.0
└── data: 3×3×14 OffsetArray(::Array{Float64, 3}, 0:2, 0:2, -2:11) with eltype Float64 with indices 0:2×0:2×-2:11
    └── max=300.0, min=300.0, mean=300.0

VirtualPotentialTemperature(model, flavor=:specific)

Return a KernelFunctionOperation representing virtual potential temperature $θᵛ$.

Virtual potential temperature is the temperature that dry air would need to have in order to have the same density as moist air at the same pressure. To define virtual potential temperature, we first note the definition of virtual temperature:

\[Tᵛ = T \left( 1 + δᵛ qᵛ - qˡ - qⁱ \right)\]

where $δᵛ ≡ Rᵛ / Rᵈ - 1$. This follows from the ideal gas law for a mixture, $p = ρ Rᵐ T$, the mixture gas constant $Rᵐ = qᵈ Rᵈ + qᵛ Rᵛ = Rᵈ \left( 1 + δᵛ qᵛ - qˡ - qⁱ \right)$, and the definition of virtual temperature, $p = ρ Rᵈ Tᵛ$, which leads to

\[Tᵛ = T rac{Rᵐ}{Rᵈ} = T \left( 1 + δᵛ qᵛ - qˡ - qⁱ \right)\]

The virtual potential temperature is defined analogously,

\[θᵛ = θ \left( 1 + δᵛ qᵛ - qˡ - qⁱ \right)\]

where $θ$ is potential temperature. Note that $Rᵛ / Rᵈ ≈ 1.608$ for water vapor and a dry air mixture typical to Earth's atmosphere, and that $δᵛ ≈ 0.608$.

using Breeze

grid = RectilinearGrid(size=(1, 1, 8), extent=(1, 1, 1e3))
model = AtmosphereModel(grid)
set!(model, θ=300, qᵗ=0.01)

θᵛ = VirtualPotentialTemperature(model)
Field(θᵛ)

# output
1×1×8 Field{Center, Center, Center} on RectilinearGrid on CPU
├── grid: 1×1×8 RectilinearGrid{Float64, Periodic, Periodic, Bounded} on CPU with 1×1×3 halo
├── boundary conditions: FieldBoundaryConditions
│   └── west: Periodic, east: Periodic, south: Periodic, north: Periodic, bottom: ZeroFlux, top: ZeroFlux, immersed: Nothing
├── operand: KernelFunctionOperation at (Center, Center, Center)
├── status: time=0.0
└── data: 3×3×14 OffsetArray(::Array{Float64, 3}, 0:2, 0:2, -2:11) with eltype Float64 with indices 0:2×0:2×-2:11
    └── max=301.824, min=301.824, mean=301.824

EquivalentPotentialTemperature(model, flavor=:specific)

Return a KernelFunctionOperation representing equivalent potential temperature $θᵉ$.

Equivalent potential temperature is conserved during moist adiabatic processes (including condensation and evaporation) and is useful for identifying air masses and tracking convective processes. Following Emanuel1994 equation 4.5.11:

\[θᵉ = T \left(\frac{p₀}{p}\right)^{Rᵈ/cᵖᵐ} \exp\left(\frac{ℒˡ qᵛ}{cᵖᵐ T}\right) ℋ^γ\]

where $ℒˡ$ is the latent heat of vaporization, $qᵛ$ is the vapor mass fraction, $ℋ$ is the relative humidity, and $γ = -Rᵛ qᵛ / cᵖᵐ$.

Arguments

• model: An AtmosphereModel instance.
• flavor: Either :specific (default) to return $θᵉ$, or :density to return $ρ θᵉ$.

Examples

using Breeze

grid = RectilinearGrid(size=(1, 1, 8), extent=(1, 1, 1e3))
model = AtmosphereModel(grid)
set!(model, θ=300, qᵗ=0.01)

θᵉ = EquivalentPotentialTemperature(model)
Field(θᵉ)

# output
1×1×8 Field{Center, Center, Center} on RectilinearGrid on CPU
├── grid: 1×1×8 RectilinearGrid{Float64, Periodic, Periodic, Bounded} on CPU with 1×1×3 halo
├── boundary conditions: FieldBoundaryConditions
│   └── west: Periodic, east: Periodic, south: Periodic, north: Periodic, bottom: ZeroFlux, top: ZeroFlux, immersed: Nothing
├── operand: KernelFunctionOperation at (Center, Center, Center)
├── status: time=0.0
└── data: 3×3×14 OffsetArray(::Array{Float64, 3}, 0:2, 0:2, -2:11) with eltype Float64 with indices 0:2×0:2×-2:11
    └── max=326.162, min=325.849, mean=326.005

References

• Emanuel, K. A. (1994). Atmospheric Convection. Oxford University Press.

LiquidIcePotentialTemperature(model, flavor=:specific)

Return a KernelFunctionOperation representing liquid-ice potential temperature $θˡⁱ$.

Liquid-ice potential temperature is a conserved quantity under moist adiabatic processes that accounts for the latent heat associated with liquid water and ice:

\[θˡⁱ = θ \left(1 - \frac{ℒˡᵣ qˡ + ℒⁱᵣ qⁱ}{cᵖᵐ T}\right)\]

where $θ$ is the mixture potential temperature, $ℒˡᵣ$ and $ℒⁱᵣ$ are the reference latent heats for liquid and ice, and $qˡ$, $qⁱ$ are the liquid and ice mass fractions.

Arguments

• model: An AtmosphereModel instance.
• flavor: Either :specific (default) to return $θˡⁱ$, or :density to return $ρ θˡⁱ$.

Examples

using Breeze

grid = RectilinearGrid(size=(1, 1, 8), extent=(1, 1, 1e3))
model = AtmosphereModel(grid)
set!(model, θ=300, qᵗ=0.01)

θˡⁱ = LiquidIcePotentialTemperature(model)
Field(θˡⁱ)

# output
1×1×8 Field{Center, Center, Center} on RectilinearGrid on CPU
├── grid: 1×1×8 RectilinearGrid{Float64, Periodic, Periodic, Bounded} on CPU with 1×1×3 halo
├── boundary conditions: FieldBoundaryConditions
│   └── west: Periodic, east: Periodic, south: Periodic, north: Periodic, bottom: ZeroFlux, top: ZeroFlux, immersed: Nothing
├── operand: KernelFunctionOperation at (Center, Center, Center)
├── status: time=0.0
└── data: 3×3×14 OffsetArray(::Array{Float64, 3}, 0:2, 0:2, -2:11) with eltype Float64 with indices 0:2×0:2×-2:11
    └── max=300.0, min=300.0, mean=300.0

StabilityEquivalentPotentialTemperature(model, flavor=:specific)

Return a KernelFunctionOperation representing stability-equivalent potential temperature $θᵇ$.

Stability-equivalent potential temperature is a moist-conservative variable suitable for computing the moist Brunt-Väisälä frequency. It follows from the derivation in the paper by Durran and Klemp (1982), who show that the moist Brunt-Väisälä frequency $Nᵐ$ is correctly expressed in terms of the vertical gradient of a moist-conservative variable.

The formulation is based on equation (17) by Durran and Klemp (1982):

\[θᵇ = θᵉ \left( \frac{T}{Tᵣ} \right)^{cˡ qˡ / cᵖᵐ}\]

where $θᵉ$ is the equivalent potential temperature, $T$ is temperature, $Tᵣ$ is the energy reference temperature, $cˡ$ is the heat capacity of liquid water, $qᵗ$ is the total moisture specific humidity, and $cᵖᵐ$ is the moist air heat capacity.

This quantity is conserved along moist adiabats and is appropriate for use in stability calculations in saturated atmospheres.

Arguments

• model: An AtmosphereModel instance.
• flavor: Either :specific (default) to return $θᵇ$, or :density to return $ρ θᵇ$.

Examples

using Breeze

grid = RectilinearGrid(size=(1, 1, 8), extent=(1, 1, 1e3))
model = AtmosphereModel(grid)
set!(model, θ=300, qᵗ=0.01)

θᵇ = StabilityEquivalentPotentialTemperature(model)
Field(θᵇ)

# output
1×1×8 Field{Center, Center, Center} on RectilinearGrid on CPU
├── grid: 1×1×8 RectilinearGrid{Float64, Periodic, Periodic, Bounded} on CPU with 1×1×3 halo
├── boundary conditions: FieldBoundaryConditions
│   └── west: Periodic, east: Periodic, south: Periodic, north: Periodic, bottom: ZeroFlux, top: ZeroFlux, immersed: Nothing
├── operand: KernelFunctionOperation at (Center, Center, Center)
├── status: time=0.0
└── data: 3×3×14 OffsetArray(::Array{Float64, 3}, 0:2, 0:2, -2:11) with eltype Float64 with indices 0:2×0:2×-2:11
    └── max=326.162, min=325.849, mean=326.005

References

• Durran, D. R. and Klemp, J. B. (1982). On the effects of moisture on the Brunt-Väisälä frequency. Journal of the Atmospheric Sciences 39, 2152–2158.

StaticEnergy(model, flavor=:specific)

Return a KernelFunctionOperation representing moist static energy $e$.

Moist static energy is a conserved quantity in adiabatic, frictionless flow that combines sensible heat, gravitational potential energy, and latent heat:

\[e = cᵖᵐ T + g z - ℒˡᵣ qˡ - ℒⁱᵣ qⁱ\]

where $cᵖᵐ$ is the moist air heat capacity, $T$ is temperature, $g$ is gravitational acceleration, $z$ is height, and $ℒˡᵣ qˡ + ℒⁱᵣ qⁱ$ is the latent heat content of condensate.

This is the prognostic thermodynamic variable used in StaticEnergyThermodynamics.

Arguments

• model: An AtmosphereModel instance.
• flavor: Either :specific (default) to return $e$, or :density to return $ρ e$.

Examples

using Breeze

grid = RectilinearGrid(size=(1, 1, 8), extent=(1, 1, 1e3))
model = AtmosphereModel(grid)
set!(model, θ=300)

e = StaticEnergy(model)
Field(e)

# output
1×1×8 Field{Center, Center, Center} on RectilinearGrid on CPU
├── grid: 1×1×8 RectilinearGrid{Float64, Periodic, Periodic, Bounded} on CPU with 1×1×3 halo
├── boundary conditions: FieldBoundaryConditions
│   └── west: Periodic, east: Periodic, south: Periodic, north: Periodic, bottom: ZeroFlux, top: ZeroFlux, immersed: Nothing
├── operand: KernelFunctionOperation at (Center, Center, Center)
├── status: time=0.0
└── data: 3×3×14 OffsetArray(::Array{Float64, 3}, 0:2, 0:2, -2:11) with eltype Float64 with indices 0:2×0:2×-2:11
    └── max=3.03055e5, min=3.02663e5, mean=3.02859e5

SaturationSpecificHumidity(
    model
) -> KernelFunctionOperation{Center, Center, Center, _A, _B, K, Tuple{}} where {_A, _B, K<:Breeze.AtmosphereModels.Diagnostics.SaturationSpecificHumidityKernelFunction}
SaturationSpecificHumidity(
    model,
    flavor_symbol
) -> KernelFunctionOperation{Center, Center, Center, _A, _B, K, Tuple{}} where {_A, _B, K<:Breeze.AtmosphereModels.Diagnostics.SaturationSpecificHumidityKernelFunction}

Return a KernelFunctionOperation representing the specified flavor of saturation specific humidity $qᵛ⁺$.

Flavor options

• :prognostic

  Return the saturation specific humidity corresponding to the model's prognostic state. This is the same as the equilibrium saturation specific humidity for saturated conditions and a model that uses saturation adjustment microphysics.

• :equilibrium

  Return the saturation specific humidity in potentially-saturated conditions, using the model.specific_moisture. This is equivalent to the :total_moisture flavor under saturated conditions with no condensate; or in other words, if model.specific_moisture happens to be equal to the saturation specific humidity.

• :total_moisture

  Return saturation specific humidity in the case that the total specific moisture is equal to the saturation specific humidity and there is no condensate. This is useful for manufacturing perfectly saturated initial conditions.