  We model the deepest observable layers of dark sunspot umbral atmospheres in
terms of an empirical model which equally describes observed near infrared
continuum intensities and line profiles. We use the umbral continuum intensity
at 1.67 nm and the three C I lines at 1,6888, 1,7449 and 1,7456 nm to model the
deep layers near the minimum of H- absorption. We find that a radiative
equilibrium stratification yields the best compromise between continuum and C I
line observations. We determine the effective temperature from the umbral and
photospheric flux ratio by down-scaling the monochromatic photospheric flux
with the umbral contrast for each frequency. The thus obtained monochromatic
umbral flux and the photospheric one are integratied over the whole frequency
range, yielding the ratio of total umbral and photospheric flux, which gives
3560 K < T_eff < 3780 K. We assume for our model M3 T_eff=3750 K and fit M3 to
the theoretical model by Meyer et al. (1974). Comparison of the model's 'nabla'
gradient with the adiabatic one shows that umbral convection, if existing at
all, can only occur at considerably deeper layers than in the photosphere.
