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Introduction

Introduction#

Assumptions#

The air is assumed to behave as an ideal gas, i.e. a collection of point particles without interactions between one another. It is in thermodynamic equilibrium, it is not chemically reacting and it obeys the ideal gas state equation:

(1)#\[p = n \, k \, T\]

where:

  • \(p\) stands for the air pressure \([ML^{-1}T^{-2}]\),

  • \(n\) stands for the air number density \([L^{-3}]\),

  • \(k\) is the Bolzmann constant \([ML^{2}T^{-2}\Theta^{-1}]\) and

  • \(T\) stands for the air temperature \([\Theta]\).

Air can usually be treated as an ideal gas within reasonable tolerance over a wide parameter range around standard temperature and pressure (273 K, 100 kPa) and the approximation generally gets better with lower pressure and higher temperature.

Atmosphere modelling#

Eradiate represents the atmosphere as a participating medium (the air) whose envelope is defined by a geometric shape. The shape is either a cuboid or a spherical shell, depending on the geometry used. The participating medium is specified by its radiative properties, i.e. the scattering phase function \(p\), single scattering albedo \(\varpi\) and volume extinction coefficient \(\sigma_{\mathrm{t}}\) of its constituents, for each point \(P \,(x, y, z)\) in the participating medium:

(2)#\[x, y, z \longrightarrow p(x, y, z), \varpi(x, y, z), \sigma_{\mathrm{t}}(x, y, z)\]

In the one-dimensional approximation, atmospheric radiative properties are invariant with respect to \(x\) and \(y\), and we can rewrite (2) as:

(3)#\[x, y, z \longrightarrow p(z), \varpi(z), \sigma_{\mathrm{t}}(z)\]

If the participating medium is uniform, then (2) reduces to:

\[x, y, z \longrightarrow p_0, \varpi_0, \sigma_{\mathrm{t}, 0}\]

where \(p_0\), \(\varpi_0\), \(\sigma_{\mathrm{t}, 0}\) are constants.

The structure of the participating medium is assumed to be isotropic, i.e. the properties of the medium embedded in one cell is invariant to rotation of the cell.

Atmospheric constituents#

Atmospheric constituents are divided into two broad categories:

  • molecules : particles in gaseous state, e.g. H₂O, CO₂, O₃, N₂O, CO, CH₄, O₂, NO, SO₂, NO₂.

  • particles : solid or liquid state particles, e.g. water droplets, ice crystals, dust particles.

Atmosphere types#

Atmosphere types are defined based on radiative properties uniformness and nature of atmospheric constituents.

Constituents

Uniform radiative properties

Non-uniform radiative properties

Molecules

N/A

MolecularAtmosphere

Particles

N/A

ParticleLayer

Both

HomogeneousAtmosphere

HeterogeneousAtmosphere

Volume interactions#

The modelling of the interaction of radiation with molecules through scattering and absorption is built in Eradiate. By default, air scattering is modeled using the Rayleigh scattering model. Computation of molecular absorption is described here.

The modelling of the interaction of radiation with particles is not provided. When working with particles, you must either:

  • specify yourself the particle radiative properties,

  • use pre-defined particle radiative properties.

Note

So far, two pre-defined particle radiative properties data sets are provided. We are currently working on adding more data sets.

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