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The role of magnetic fields in the chromospheric heating problem remainsgreatly unconstrained. Most theoretical predictions from numerical models relyon a magnetic configuration, field strength and connectivity whose details havenot been well established with observational studies. High-resolution studiesof chromospheric magnetic fields in plage are very scarce or non-existent ingeneral. Our aim is to study the stratification of the magnetic field vector inplage regions. We use high-spatial resolution full-Stokes observations acquiredwith CRISP instrument at the Swedish 1-m Solar Telescope in the Mg I$\lambda$5173, Na I $\lambda$5896 and Ca II $\lambda$8542 lines. We havedeveloped a spatially-regularized weak-field approximation (WFA) method basedon the idea of spatial regularization. This method allows for a fastcomputation of magnetic field maps for an extended field of view. The fidelityof this new technique has been assessed using a snapshot from a realistic 3Dmagnetohydrodynamics simulation. We have derived the depth-stratification ofthe line-of-sight component of the magnetic field from the photosphere to thechromosphere in a plage region. The magnetic fields are concentrated in theintergranular lanes in the photosphere and expand horizontally toward thechromosphere, filling all the space and forming a canopy. Our results suggestthat the lower boundary of this canopy must be located around 400-600 km fromthe photosphere. The mean canopy total magnetic field strength in the lowerchromosphere ($z\approx760$ km) is 658 G. At $z=1160$ km we estimate$<B_\parallel>\approx 417$ G. We propose a modification to the WFA thatimproves its applicability to data with worse signal-to-noise ratio. Thesemethods provide a quick and reliable way of studying multi-layer magnetic fieldobservations without the many difficulties inherent to other inversion methods.

Stratification of canopy magnetic fields in a plage region. Constraints from a spatially-regularized weak-field approximation method