The energy of waves in the photosphere and lower chromosphere: III.   Inversion setup for Ca II H spectra in local thermal equilibrium
  The Ca II H line is one of the strongest lines in the solar spectrum and provides continuous information on the solar atmosphere from the photosphere to the lower chromosphere. We describe an inversion approach that reproduces observed Ca II H spectra assuming LTE. We developed an inversion strategy based on the SIR code. The approach uses a two-step procedure with an archive of pre-calculated spectra to fit the line core and a subsequent iterative modification to improve the fit in the line wing. Simultaneous spectra in the 630nm range can optionally be used to fix the continuum temperature. The method retrieves 1D temperature stratifications neglecting lateral radiative transport. LOS velocities are included by an empirical approach. An archive of about 300.000 pre-calculated spectra is more than sufficient to reproduce the line core of observed Ca II H spectra both in quiet Sun and in active regions. The final thermodynamical stratifications match observed and best-fit spectra to a level of about 0.5 (1) % of Ic in the line wing (core). Inversion schemes based on pre-calculated spectra allow one a reliable and relatively fast retrieval of solar properties from observed chromospheric spectra. The approach can be easily extended to an 1D NLTE case by a simple exchange of the pre-calculated archive spectra. 
C. Beck, R. Rezaei, K.G. Puschmann
astro-ph.SR