The energy of waves in the photosphere and lower chromosphere

Context. Most semi-empirical static one-dimensional (1D) models of the solar atmosphere in the magnetically quiet Sun (QS) predict an increase in temperature at chromospheric layers. Numerical simulations of the solar chromosphere with a variable degree of sophistication, i.e. from 1D to three-dimensional (3D) simulations; assuming local thermal equilibrium (LTE) or non-LTE (NLTE), on the other hand, only yielded an increase in the brightness temperature without any stationary increase in the gas temperature.