  We present here 21 cm predictions from high dynamic range simulations for a
range of reionization histories that have been tested against available
Lyman-alpha and CMB data. We assess the observability of the predicted spatial
21 cm fluctuations by ongoing and upcoming experiments in the late stages of
reionization in the limit in which the hydrogen spin temperature is
significantly larger than the CMB temperature. Models consistent with the
available Lyman-alpha data and CMB measurement of the Thomson optical depth
predict typical values of 10--20 mK^2 for the variance of the 21 cm brightness
temperature at redshifts z=7--10 at scales accessible to ongoing and upcoming
experiments (k < 1 h/cMpc). This is only a factor of a few below the
sensitivity claimed to have been already reached by ongoing experiments in the
signal rms value. Our different models for the reionization history make
markedly different predictions for the redshift evolution and thus frequency
dependence of the 21 cm power spectrum and should be easily discernible by
LOFAR (and later HERA and SKA1) at their design sensitivity. Our simulations
have sufficient resolution to assess the effect of high-density Lyman limit
systems that can self-shield against ionizing radiation and stay 21 cm bright
even if the hydrogen in their surroundings is highly ionized. Our simulations
predict that including the effect of the self-shielded gas in highly ionized
regions reduces the large scale 21 cm power by about 30%.
