Terminology

This section defines the key concepts and formulae used to process atmospheric profiles.

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.