Atmospheric Temperature Profiles

Overview

The Thermodynamics.TemperatureProfiles module provides pre-defined atmospheric temperature profiles for testing and validation purposes, and to be used as reference states in atmosphere models. These profiles represent idealized atmospheric conditions commonly used in climate modeling and thermodynamic testing.

Available Profiles

Three temperature profiles are currently available:

1. IsothermalProfile: Constant temperature with height
2. DecayingTemperatureProfile: Temperature decreases smoothly with height
3. DryAdiabaticProfile: Temperature follows dry adiabatic lapse rate

Usage

Each profile constructor requires two arguments:

• param_set: A thermodynamic parameter set from ClimaParams.jl
• z: Altitude (height above surface)

The profiles return both temperature and pressure as a function of altitude.

Isothermal Profile

A constant temperature profile, useful for testing thermodynamic calculations under uniform conditions.

import Thermodynamics as TD
import Plots
import ClimaParams as CP
import Thermodynamics.Parameters as TP
FT = Float64
param_set = TP.ThermodynamicsParameters(FT)
z = range(FT(0), stop = FT(2.5e4), length = 50);

isothermal = TD.TemperatureProfiles.IsothermalProfile(param_set, FT);
args = isothermal.(Ref(param_set), z);
T = first.(args);
p = last.(args);

p1 = Plots.plot(T, z./10^3, xlabel="Temperature [K]");
p2 = Plots.plot(p./10^3, z./10^3, xlabel="Pressure [kPa]");
Plots.plot(p1, p2, layout=(1,2), title="Isothermal", ylabel="z [km]");
Plots.savefig("isothermal.svg");

"/home/runner/work/Thermodynamics.jl/Thermodynamics.jl/docs/build/isothermal.svg"

Decaying Temperature Profile

A profile where temperature decreases smoothly with height, representing typical atmospheric conditions.

import Thermodynamics as TD
import Plots
import ClimaParams as CP
import Thermodynamics.Parameters as TP
FT = Float64
param_set = TP.ThermodynamicsParameters(FT)
z = range(FT(0), stop = FT(2.5e4), length = 50);

decaying = TD.TemperatureProfiles.DecayingTemperatureProfile{FT}(param_set);
args = decaying.(Ref(param_set), z);
T = first.(args);
p = last.(args);

p1 = Plots.plot(T, z./10^3, xlabel="Temperature [K]");
p2 = Plots.plot(p./10^3, z./10^3, xlabel="Pressure [kPa]");
Plots.plot(p1, p2, layout=(1,2), ylabel="z [km]", title="Decaying");
Plots.savefig("decaying.svg")

"/home/runner/work/Thermodynamics.jl/Thermodynamics.jl/docs/build/decaying.svg"

Dry Adiabatic Profile

A profile following the dry adiabatic lapse rate, where potential temperature is constant with height.

import Thermodynamics as TD
import Plots
import ClimaParams as CP
import Thermodynamics.Parameters as TP
FT = Float64
param_set = TP.ThermodynamicsParameters(FT)
z = range(FT(0), stop = FT(2.5e4), length = 50);

dry_adiabatic = TD.TemperatureProfiles.DryAdiabaticProfile{FT}(param_set);
args = dry_adiabatic.(Ref(param_set), z)
T = first.(args)
p = last.(args)
θ_dry = TD.dry_pottemp_given_pressure.(Ref(param_set), T, p)

p1 = Plots.plot(T, z./10^3, xlabel="Temperature [K]");
p2 = Plots.plot(p./10^3, z./10^3, xlabel="Pressure [kPa]");
p3 = Plots.plot(θ_dry, z./10^3, xlabel="Potential temperature [K]");
Plots.plot(p1, p2, p3, layout=(1,3), ylabel="z [km]", title="Dry adiabatic")
Plots.savefig("dry_adiabatic.svg")

"/home/runner/work/Thermodynamics.jl/Thermodynamics.jl/docs/build/dry_adiabatic.svg"

Applications

These temperature profiles are useful for:

• Testing thermodynamic calculations under controlled conditions
• Benchmarking performance across different atmospheric conditions
• Educational purposes to understand atmospheric thermodynamics

Integration with Thermodynamic States

Temperature profiles can be combined with thermodynamic state calculations:

# Example: Create thermodynamic states along a temperature profile
z = range(0, 25e3, length=100)  # 0 to 25 km
profile = TD.TemperatureProfiles.DryAdiabaticProfile{Float64}(param_set)

# Get temperature and pressure at each altitude
T_pairs = profile.(Ref(param_set), z)
T = first.(T_pairs)
p = last.(T_pairs)

# Create thermodynamic states
ts_states = [TD.PhaseDry_pT(param_set, p[i], T[i]) for i in 1:length(z)]

Extending the Module

Additional temperature profiles can be added by:

1. Creating a struct containing the parameters needed for the profile
2. Implementing a functor that takes (param_set, z) and returns (T, p)

Example structure:

struct CustomProfile{FT} <: TemperatureProfile{FT}
    # Profile parameters
end

function (profile::CustomProfile{FT})(param_set, z) where {FT}
    # Calculate T and p based on z
    return (T, p)
end