Aerosol / particles (Aer)

Aer-Core v2 [aer_core_v2]

This data format is derived from libRadtran’s aerosol data format. It features an adaptive scattering angle (θ) grid that allows for an optimal positioning of samples depending on the wavelength.

The number of angular samples can vary across wavelengths up to a maximum equal to the size of the iangle dimension. The per-wavelength count is stored in nangles; entries beyond nangles[iw] in theta, mu, and phase are NaN-padded.

Similarly, the number of Legendre coefficients can vary across wavelengths up to a maximum equal to the size of the imom dimension. When pmom is present, nmom stores the per-wavelength count; entries beyond nmom[iw] in pmom are NaN-padded.

Format

xarray.Dataset (in-memory), NetCDF (storage)

Dimensions

• w: radiation wavelength

• phamat: nonzero coefficients in the phase matrix

• iangle: angular data points

• imom: Legendre coefficients for the (1,1) phase matrix component

Coordinates

When relevant, units are required and specified in the “units” metadata field.

• w(w) float [length]: wavelength

• phamat(phamat) str [—]: row and column indices of the phase matrix coefficient (e.g. “11”, “12”, etc.)

• theta(w, iangle) float [angle]: scattering angle θ; NaN-padded beyond nangles[iw]

• mu(w, iangle) float [—]: value of cos θ; NaN-padded beyond nangles[iw]

Data variables

When relevant, units are required and specified in the “units” metadata field.

• ext(w) float [1 / length]: extinction coefficient per unit concentration

• ssa(w) float [—]: single-scattering albedo

• phase(phamat, w, iangle) float [1 / sr]: value of the phase matrix; NaN-padded beyond nangles[iw]

• nangles(w) int [—]: number of valid angular samples per wavelength; must be consistent with the NaN padding of theta, mu, and phase

• pmom(w, imom) float [—], optional: Legendre expansion coefficients of the (1,1) phase matrix element; NaN-padded beyond nmom[iw]

• nmom(w) int [—], required if pmom is present: number of valid Legendre coefficients per wavelength; must be consistent with the NaN padding of pmom

Note

pmom stores only the Legendre expansion of the (1,1) element \(p_{11}\). Legendre expansions of the other phase matrix components are not part of this format.

Normalization conventions

The (1,1) element of the phase matrix \(p_{11} (\mu)\) follows the 4π-normalized convention, normalizing the µ-parametrized phase function to 2:

\[\frac{1}{4\pi} \int_{4\pi} p_{11}(\Omega)\, \mathrm{d}\Omega = 1 \Longleftrightarrow \int_{-1}^{1} p_{11}(\mu)\, \mathrm{d}\mu = 2,\]

where \(p_{11} (\mu)\) is in sr⁻¹.

The pmom variable stores the Legendre expansion coefficients \(p_l = (2l + 1) \xi_l\), where

\[\xi_l = \frac{1}{2} \int_{-1}^{1} p_{11}(\mu)\, P_l(\mu)\, \mathrm{d}\mu,\]

and \(P_l\) is the Legendre polynomial of degree \(l\). The phase function is thus recovered as

\[p_{11}(\mu) = \sum_{l=0}^{L} \mathtt{pmom}[l]\, P_l(\mu).\]

For a normalized phase function, \(\mathtt{pmom}[0] = 1\) and \(\mathtt{pmom}[1] = 3g\), where \(g\) is the asymmetry parameter.

Note

• Data are sorted in ascending order of w and mu

• Valid phamat values are (in that order): ["11", "12", "33", "34", "22", "44"]

• The number of phamat values implicitly defines whether the data describes light polarization: 1 means without polarization, 2+ means with polarization

• The number of phamat values implicitly defines the scattering particle shape: 1 or 4 means spherical particles, 6 means spheroidal particles

Mapping of dimensions in the Aer-Core v2 format to the libRadtran equivalent.

	Eradiate	libRadtran
Spectral dimension	w	nlam
Phase matrix coefficients	phamat	phamat
Angular data points (maximum)	iangle	nthetamax
Angular data points (per wavelength)	nangles	ntheta
Legendre coefficients	imom	nmommax

Aer v1 (legacy) [aer_v1]

The original aerosol / particle single-scattering radiative property format. This format uses dense phase matrix storage and a fixed mu grid. It was replaced by the more storage-efficient Aer-Core v2 format. Data provided in this format can be converted to the Aer-Core v2 format using the aer_v1_to_aer_core_v2() function.

Format

xarray.Dataset (in-memory), NetCDF (storage)

Dimensions

• w: radiation wavelength

• mu: scattering angle cosine

• i: scattering phase matrix row index

• j: scattering phase matrix column index

Coordinates

All dimension coordinates; when relevant, units are required and specified in the “units” metadata field.

• w(w) float [length]: wavelength

• mu(mu) float [—]: scattering angle cosine

• i(i), j(j) int [—]: phase matrix row and column indices

Data variables

When relevant, units are required and specified in the “units” metadata field.

• sigma_t(w) float [1 / length]: volume extinction coefficient

• albedo(w) float [—]: single-scattering albedo

• phase(w, mu, i, j) float [1 / sr]: scattering phase matrix

Normalization conventions

The intended normalization for the (1,1) element of the phase matrix is the same 4π-normalized convention used by Aer-Core v2:

\[\int_{-1}^{1} p_{11} (\mu) \, \mathrm{d}\mu = 2\]

In practice, datasets in this format may not conform to this convention. The phase_scale parameter of aer_v1_to_aer_core_v2() can be used to rescale the phase function during conversion in order to enforce the correct normalization. It should be noted that this has no impact on the correctness of Monte Carlo simulations using the Mitsuba radiometric kernel, as Mitsuba-level phase function components all enforce internally a correct normalization of statistical distributions, including tabulated phase functions.

Conventions

• Phase matrix coefficients use C-style indexing (from 0).

Conversion

The following conversion components are provided:

List of scattering particle property converters

Function	Source format	Target format
aer_v1_to_aer_core_v2()	Aer v1	Aer-Core v2
libradtran_to_aer_core_v2()	libRadtran / MOPSMAP	Aer-Core v2
libradtran_to_aer_v1()	libRadtran / MOPSMAP	Aer v1