tokens: RTE) applied to the spectra and polarized spectra emitted by the object. The RTE characterizes the interaction of the matter with the light that traverses through it. This interaction leaves its “fingerprints” in many different ways, for instance in the shape of the continuum of the spectra coming from the object, or in the presence or absence and the shape of spectral lines. Properly modeled, these features allow approximate characterization of the studied object. In recent decades, the advent of polarimetric observations has allowed the generalization of the RTE to polarized light ( Unno 1956 ; Rachkovsky 1967 ; Landi Degl’Innocenti Landi Degl’Innocenti 1972 ). This step was of great significance, as the polarization of the light encodes information on the magnetic field configuration as well as the geometry of the system, which allows a deeper insight into the system being studied. In solar physics, there are different approaches to solving the polarized RTE depending on the magnetic field regime adopted: atomic, Hanle, Zeeman, and/or Paschen (see e.g., Landi Degl’Innocenti Landolfi 2004 ). In this work, we focus on the solution of the polarimetric RTE under the Zeeman magnetic regime, which is usually the dominant one at this atmosphere layer. There are already several methods to address the solution of the RTE, each with its respective accuracy (see, e.g., del Toro Iniesta Ruiz Cobo 2016 ). There are several computational codes that allow one to infer the optical depth ( τ ) dependence of the physical properties in the solar atmosphere; for example, SIR ( Ruiz Cobo del Toro Iniesta 1992 ), SPINOR ( Frutiger et al. 2000 ), NICOLE ( Socas-Navarro et al. 2015 ), SNAPI ( Milić van Noort 2018 ), and STIC ( de la Cruz Rodríguez et al. 2019 ). These are of particular relevance here as they allow the furthest insight into the properties of the solar atmosphere in a three-dimensional volume. In these cases, the conversion between optical depth τ and geometrical height z is then performed by considering the relation d τ = − ρ κ c d z , where ρ is the density and κ c the continuum opacity, with the latter being a nonlinear function of the temperature T and gas pressure P g . Since the proper calculation of the gas pressure (and density) involves the whole three-dimensional volume, for which there is no account in the aforementioned codes, the gas pressure and density inferred by them are unrealistic, and hence also the conversion between τ and z . Deviations from hydrostatic equilibrium involve, among others, time-variation of the velocity, advection and viscous terms and, the most relevant at this atmospheric layer, the Lorentz force. The latter is responsible for the Wilson depression, a depression of the height at which photospheric spectral lines are formed with respect to the quiet-Sun because of the presence of magnetic field. Because the geometrical scale z is then inaccurate, so is the calculation of the spatial derivatives, such as those
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