  The energy input into the lower solar corona by flare evaporation events has
been modeled according to the available observations for quiet regions. The
question is addressed whether such heating events can provide the observed
average level of the coronal emission measure and thus of the observed flux of
extreme ultraviolet (EUV) and X-ray emission without contradicting the observed
average power spectrum of the emission measure, the typical emission measure
variations observed for individual pixels and the observed flare energy
distribution. As the assumed flare height influences the derived flare energy,
the mathematical foundations of nanoflare distributions and their conversion to
different height assumptions are studied first. This also allows a comparison
with various published energy distributions differing in height assumptions and
to relate the observations to the input parameters of the heating model. An
analytic evaluation of the power spectrum yields the relationship between the
average time profile of nanoflares (or microflares), assumed to be self-similar
in energy, and the power spectrum. We find that the power spectrum is very
sensitive to the chosen time profile of the flares. Models are found by
numerical simulation that fit all available observations. They are not unique
but severely constrained. We concentrate on a model with a flare height
proportional to the square root of the flare area. The existence of a fitting
model demonstrates that nanoflare heating of the corona is a viable and
attractive mechanism.
