  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=-75km are extrapolated from the results of the inversion.
