4.1. Atmospheric Thermodynamics

ADELM diagnoses the atmospheric state variables required by the Penman-Monteith evapotranspiration and conductance formulations: air density, latent heat, psychrometric and vapour pressure slope coefficients, and air-side transport properties.

See also

model.parameterization.surface_exchange.calculate_timestep_and_thermodynamics()

Coupling to other components

1. Atmospheric state

Air temperature \(T_{\mathrm{a}}\) (ta_degC [degC; Driver: near-surface air temperature]) is first converted to kelvin:

(4.1.1)\[T_{\mathrm{a},K} = T_{\mathrm{a}} + T_0\]

where \(T_0\) is absolute_zero_offset [default: 273.15 K; Constant: zero degrees Celsius expressed in Kelvin]. Air density (air_density [kg m-3; Diagnostic: mass of air per unit volume]) follows from the ideal gas approximation:

(4.1.2)\[\rho_{\mathrm{a}} = \frac{353}{T_{\mathrm{a},K}}\]

The molar conductance conversion factor air_molar_density [mol m-3; Diagnostic: molar concentration of air] converts conductances from velocity units to molar units via the ideal gas law:

(4.1.3)\[g_{\mathrm{mol}} = \frac{p_0}{R\,T_{\mathrm{a},K}}\]

where \(p_0\) is standard_air_pressure [default: 101325 Pa; Constant: reference air pressure] and \(R\) is universal_gas_constant [default: 8.3144 J mol-1 K-1; Constant: universal gas constant].

2. Latent heat and psychrometric coefficients

The latent heat of vaporization latent_heat_of_vaporization [J kg-1; Diagnostic: energy required to vaporize one kilogram of liquid water] is the energy cost of evaporating water, approximated as a linear function of temperature:

(4.1.4)\[\begin{split}\lambda_{\mathrm{v}} = \begin{cases} 2{,}501{,}000 - 2364\,T_{\mathrm{a}} & T_{\mathrm{a}} \ge 1\,^{\circ}\mathrm{C} \\ 2{,}835{,}000 & T_{\mathrm{a}} < 1\,^{\circ}\mathrm{C} \end{cases}\end{split}\]

The psychrometric constant psychrometric_constant [kPa K-1; Diagnostic: ratio of sensible to latent heat flux for a wet surface at constant pressure] relates the sensible and latent heat fluxes of a wet surface:

(4.1.5)\[\gamma = 0.0646\,\exp\!\left(0.00097\,T_{\mathrm{a}}\right)\]

The slope of the saturation vapour pressure curve saturation_vapour_pressure_slope [kPa K-1; Diagnostic: rate of change of saturation vapour pressure with temperature] controls how strongly evaporative demand responds to available energy:

(4.1.6)\[s = \frac{2502.94\,\exp\!\left(\dfrac{17.269\,T_{\mathrm{a}}}{T_{\mathrm{a}} + 237.3}\right)} {\left(T_{\mathrm{a}} + 237.3\right)^2}\]

3. Transport properties

The molecular diffusivity of water vapour in air water_vapour_diffusivity [m2 s-1; Diagnostic: molecular diffusivity of water vapour in air] follows a temperature-dependent power law:

(4.1.7)\[D_{\mathrm{v}} = 2.42 \times 10^{-5} \left(\frac{T_{\mathrm{a},K}}{293.2}\right)^{1.75}\]

The kinematic viscosity of air kinematic_viscosity_of_air [m2 s-1; Diagnostic: ratio of dynamic viscosity to air density] is derived from the dynamic viscosity \(\mu\) via the Sutherland approximation:

(4.1.8)\[\mu = \frac{1.4963 \times 10^{-6}\,T_{\mathrm{a},K}^{1.5}}{T_{\mathrm{a},K} + 120}\]
(4.1.9)\[\nu = \frac{\mu}{\rho_{\mathrm{a}}}\]