Mean values in inhomogeneous atmospheres

A brief summary of observations of inhomogeneities in the solar atmosphere and progress in the theoretical analysis of two-dimensional model atmospheres is given. In particular, it is asserted that reliable reference models of the mean temperature, pressure, etc. may be derived only by averaging over the horizontal coordinates of a two- or three-dimensional model. In discussion of a wide variety of cases including strong chromospheric lines, weak photospheric lines, and continuum radiation, it is shown that although the derivation of mean values by first averaging over the fluctuations in the data and then applying a one-dimension analysis is an obvious first approximation, it may lead to errors of a gross qualitative nature. Thus the recent deductions by several authors of very small temperature gradients in the upper regions of sunspots are shown to be subject to considerable doubt.