Explanation

Terminology¶

Column number density¶

If \(n_{\mathrm{M}} (z)\) denotes the number density of molecule M at altitude \(z\), then the column number density of molecule M is

\[ N_{\mathrm{M}} = \int_{0}^{+\infty} n_{\mathrm{M}} (z) \, \mathrm{d} z \]

Column number density has dimensions of length^-2.

Column mass density¶

The column mass density is to mass density what column number density is to number density, i.e.,

\[ P_{\mathrm{M}} = \int_{0}^{+\infty} \rho_{\mathrm{M}} (z) \, \mathrm{d} z \]

where \(\rho_{\mathrm{M}} (z)\) is the mass density of molecule M at altitude \(z\).

Mass density is related with number density through:

\[ \rho_{\mathrm{M}} = m_{\mathrm{M}} \, n_{\mathrm{M}} \]

where \(m_{\mathrm{M}}\) is the molecular mass of molecule M.

Since molecular mass does not change with altitude, we simply have

\[ P_{\mathrm{M}} = m_{\mathrm{M}} \, N_{\mathrm{M}} \]

Column mass density has dimensions of mass * length^-2.

Number density at sea level¶

Sea level is defined by \(z=0\), hence the number density at sea level of molecule M is simply \(n_{\mathrm{M}}(0)\). Number density at sea level has dimensions of length^-3.

Mass density at sea level¶

Similarly, mass density at sea level is \(\rho_{\mathrm{M}}(0) = m_{\mathrm{M}} \, n_{\mathrm{M}}(0)\). Mass density at sea level has dimensions of mass * length^-3.

Dataset schema¶

Joseki produces atmospheric profile datasets in the NetCDF format using the xarray library which provides a comprehensive, robust and convenient interface to read, write, manipulate and visualise NetCDF data.

Metadata conventions¶

The NetCDF format allows to store metadata alongside data. Joseki's datasets metadata follow the conventions for Climate and Forecast (v1.10).

Standard names¶

The Climate and Forecast (CF) conventions define standard names to describe variables. Joseki's datasets comply with CF Standard Name Table Version 81, 25 April 2023 except for the following variables for which a standard name did not exist (hence we derived one):

Standard name	Long name	Units
`air_number_density`	`air number density`	`m^-3`

Structure¶

A dataset includes 4+ data variables:

Standard name	Long name	Symbol	Units
`air_pressure`	`air pressure`	`p`	`Pa`
`air_temperature`	`air temperature`	`t`	`K`
`air_number_density`	`air number density`	`n`	`m^-3`
`mole_fraction_of_M_in_air`	`mole fraction of M in air`	`x_M`	`dimensionless`

where M is the chemical formula of the given molecule (e.g. mole_fraction_of_H2O_in_air is associated the symbol x_H2O), and one of the two following coordinates variables:

Standard name	Long name	Symbol	Units
`altitude`	`altitude`	`z`	`km`
`layer_center_altitude`	`layer center altitude`	`z`	`km`

All data variables depend solely on the altitude (either altitude or layer_center_altitude).