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Workspace Method jacobianAddTemperature

Description

Includes atmospheric temperatures in the Jacobian.

The calculations are performed by (semi-)analytical expressions.
Hydrostatic equilibrium (HSE) can be included.

The analytical calculation approach neglects so far refraction
totally, but considers the local effect of HSE.
The later should be accaptable for observations around zenith and
nadir. There is no warning if the method is applied incorrectly, 
with respect to these issues. Note that the argument *hse* of this
WSM only refers to the Jacobian calculation, if the model and/or
retrieved atmosphere actually fulfils HSE or not is governed in
other manners.

The calculations (both options) assume that gas species are defined
in VMR (a change in temperature then changes the number density). 
This has the consequence that retrieval of temperatures and number
density can not be mixed. Neither any warning here!

The number of elements added to the state vector (x) is:
   n_g1 * n_g2 * n_g3
where n_g1, n_g2 and n_g3 are the length of GIN *g1*, *g2* and *g3*,
respectively. Here empty vectors should be considered to have a length 1.
The elements are sorted with pressure as innermost loop, followed by
latitude and longitude as outermost loop.

Authors: Mattias Ekstrom, Patrick Eriksson

Synopsis

jacobianAddTemperature(

jacobian_quantities, jacobian_agenda, atmosphere_dim, p_grid, lat_grid, lon_grid, g1, g2, g3, hse )

Variables

OUT+IN	jacobian_quantities	(ArrayOfRetrievalQuantity)	The retrieval quantities in the Jacobian matrix.
OUT+IN	jacobian_agenda	(Agenda)	Pure numerical Jacobian calculation agenda.
IN	atmosphere_dim	(Index)	The atmospheric dimensionality (1-3).
IN	p_grid	(Vector)	The pressure grid.
IN	lat_grid	(Vector)	The latitude grid.
IN	lon_grid	(Vector)	The longitude grid.
GIN	g1	(Vector)	Pressure retrieval grid.
GIN	g2	(Vector)	Latitude retrieval grid.
GIN	g3	(Vector)	Longitude retreival grid.
GIN	hse	(String, Default: "on")	Flag to assume HSE or not ("on" or "off").