  We study the effects of box size on ENZO simulations of the intergalactic
medium (IGM) at z = 2. We follow statistics of the cold dark matter (CDM) and
the Lya absorption. We find that the larger boxes have fewer pixels with
significant absorption (flux < 0.96) and more pixels in longer stretches with
little or no absorption, and they have wider Lya lines. We trace these effect
back to the additional power in larger boxes from longer wavelength modes. The
IGM in our larger boxes is hotter, from increased pressure heating due to
faster hydrodynamical infall. When we increase the photoheating in smaller
boxes to compensate, their Lya statistics change to mimic those of a box of
twice the size. Statistics converge towards their value in the largest (76.8
Mpc) box, except for the most common value of the CDM density which continues
to rise. When we compare to errors with data, we find that our 76.8 Mpc box is
larger than we need for the mean flux, barely large enough for the column
density distribution and the power spectrum of the flux, and too small for the
line widths. This box with 75 kpc cells has approximately the same mean flux as
QSO spectra, but the Lya lines are too wide by 2.6 km/s, there are too few
lines with log H I column densities > 10^17 cm^-2, and the power of the flux is
too low by 20 - 50%, from small to large scales. Four times smaller cell size
does not resolve these differences, nor do simple changes to the ultraviolet
background that drives the H and He II ionization. It is hard to see how
simulations using popular cosmological and astrophysical parameters can match
Lyman-alpha forest data at z=2.
