spectral_rad_srcvec_pathFromPropmat

Workspace.spectral_rad_srcvec_pathFromPropmat(self, spectral_rad_srcvec_path: SourceVector = self.spectral_rad_srcvec_path, spectral_propmat_path: ArrayOfPropmatVector = self.spectral_propmat_path, spectral_nlte_srcvec_path: ArrayOfStokvecVector = self.spectral_nlte_srcvec_path, spectral_propmat_jac_path: ArrayOfPropmatMatrix = self.spectral_propmat_jac_path, spectral_nlte_srcvec_jac_path: ArrayOfStokvecMatrix = self.spectral_nlte_srcvec_jac_path, freq_grid_path: ArrayOfAscendingGrid = self.freq_grid_path, atm_path: ArrayOfAtmPoint = self.atm_path, jac_targets: JacobianTargets = self.jac_targets) → None

Gets the source term along the path.

Per Stokvec element (single frequency, single temperature, single derivative target), the source term is computed as:

\[\vec{J} = B(T, f) + \mathbf{K}^{-1} \vec{S}\]

and the Jacobian is computed as:

\[\frac{\partial \vec{J}}{\partial x} = \frac{\partial B(T, f)}{\partial x} - \mathbf{K}^{-1} \left( \frac{\partial \mathbf{K}}{\partial x} \mathbf{K}^{-1} - \frac{\partial \vec{S}}{\partial x} \right)\]

where:

Variable	Extracted from ARTS parameter	Meaning
\(\vec{J}\)	spectral_rad_srcvec_path J	The spectral radiance source term along the path.
\(B(T, f)\)	None - this is computed locally	The Planck function at the temperature and frequency.
\(\mathbf{K}\)	spectral_propmat_path	The propagation matrix along the path.
\(\vec{S}\)	spectral_nlte_srcvec_path	The non-LTE source vector along the path.
\(\frac{\partial \vec{J}}{\partial x}\)	spectral_rad_srcvec_path dJ	The Jacobian of the spectral radiance source term with respect to the jac_targets.
\(\frac{\partial B(T, f)}{\partial x}\)	None - this is computed locally	The Jacobian of the Planck function with respect to the jac_targets. Only tempertature is supported.
\(\frac{\partial \mathbf{K}}{\partial x}\)	spectral_propmat_jac_path	The Jacobian of the propagation matrix with respect to the jac_targets.
\(\frac{\partial \vec{S}}{\partial x}\)	spectral_nlte_srcvec_jac_path	The Jacobian of the non-LTE source vector with respect to the jac_targets.
\(x\)	jac_targets	The targets for the Jacobian computation.
\(T\)	atm_path	The temperature at the atmospheric point along the path.
\(f\)	freq_grid_path	The frequency grid at the atmospheric point along the path.

The output dimensions are:

• spectral_rad_srcvec_path: freq_grid x ray_path, freq_grid x ray_path x jac_targets (target count)

Author: Richard Larsson

Used by wrapper methods

spectral_radClearskyEmission() spectral_radClearskyRayleighScattering() spectral_radClearskyScattering()

Parameters:

• spectral_rad_srcvec_path (~pyarts3.arts.SourceVector, optional) – Source vectors along the propagation path. Defaults to self.spectral_rad_srcvec_path. [OUT]

• spectral_propmat_path (~pyarts3.arts.ArrayOfPropmatVector, optional) – Propagation matrices along the propagation path. Defaults to self.spectral_propmat_path. [IN]

• spectral_nlte_srcvec_path (~pyarts3.arts.ArrayOfStokvecVector, optional) – Additional non-LTE along the propagation path. Defaults to self.spectral_nlte_srcvec_path. [IN]

• spectral_propmat_jac_path (~pyarts3.arts.ArrayOfPropmatMatrix, optional) – Propagation derivative matrices along the propagation path. Defaults to self.spectral_propmat_jac_path. [IN]

• spectral_nlte_srcvec_jac_path (~pyarts3.arts.ArrayOfStokvecMatrix, optional) – Additional non-LTE derivative along the propagation path. Defaults to self.spectral_nlte_srcvec_jac_path. [IN]

• freq_grid_path (~pyarts3.arts.ArrayOfAscendingGrid, optional) – All freq_grid along the propagation path. Defaults to self.freq_grid_path. [IN]

• atm_path (~pyarts3.arts.ArrayOfAtmPoint, optional) – Atmospheric points along the propagation path. Defaults to self.atm_path. [IN]

• jac_targets (~pyarts3.arts.JacobianTargets, optional) – A list of targets for the Jacobian Matrix calculations. Defaults to self.jac_targets. [IN]