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In the quiet solar photosphere, the mixed polarity fields form a magneticcarpet, which continuously evolves due to dynamical interaction between theconvective motions and magnetic field. This interplay is a viable source toheat the solar atmosphere. In this work, we used the line-of-sight (LOS)magnetograms obtained from the Helioseismic and Magnetic Imager (HMI) on the\textit{Solar Dynamics Observatory} (\textit{SDO}), and the ImagingMagnetograph eXperiment (IMaX) instrument on the \textit{Sunrise} balloon-borneobservatory, as time dependent lower boundary conditions, to study theevolution of the coronal magnetic field. We use a magneto-frictional relaxationmethod, including hyperdiffusion, to produce time series of three-dimensional(3D) nonlinear force-free fields from a sequence of photospheric LOSmagnetograms. Vertical flows are added up to a height of 0.7 Mm in the modelingto simulate the non-force-freeness at the photosphere-chromosphere layers.Among the derived quantities, we study the spatial and temporal variations ofthe energy dissipation rate, and energy flux. Our results show that the energydeposited in the solar atmosphere is concentrated within 2 Mm of thephotosphere and there is not sufficient energy flux at the base of the coronato cover radiative and conductive losses. Possible reasons and implications arediscussed. Better observational constraints of the magnetic field in thechromosphere are crucial to understand the role of the magnetic carpet incoronal heating.

Nonlinear Force-Free Field Modeling of the Solar Magnetic Carpet and Comparison with SDO/HMI and Sunrise/IMaX Observations