Inversions of spectropolarimetric observations of penumbral filaments deliver the stratification of different physical quantities in an optical depth scale .
However , without establishing a geometrical height scale their three-dimensional geometrical structure can not be derived .
This is crucial in understanding the correct spatial variation of physical properties in the penumbral atmosphere and to provide insights into the mechanism capable of explaining the observed penumbral brightness .
The aim of this work is to determine a global geometrical height scale in the penumbra by minimizing the divergence of the magnetic field vector and the deviations from static equilibrium as imposed by a force balance equation that includes pressure gradients , gravity and the Lorentz force .
Optical depth models are derived from the SIR inversion of spectropolarimetric data of an active region observed with SOT on-board the Hinode satellite .
We use a genetic algorithm to determine the boundary condition for the inference of geometrical heights .
The retrieved geometrical height scale permits the evaluation of the Wilson depression at each pixel and the correlation of physical quantities at each height .
Our results fit into the uncombed penumbral scenario , i.e. , a penumbra composed of flux tubes with channelled mass flow and with a weaker and more horizontal magnetic field as compared with the background field .
The ascending material is hotter and denser than their surroundings .
We do not find evidence of overturning convection or field free regions in the inner penumbral area analyzed .
The penumbral brightness can be explained by the energy transfer of the ascending mass carried by the Evershed flow , if the physical quantities below z = -75 km are extrapolated from the results of the inversion .