This is the publisher's version, also available electronically from http://onlinelibrary.wiley.com.It has been suggested that galactic shock asymmetry induced by our galaxy's infall toward the Virgo Cluster may be a source of periodicity in cosmic ray exposure as the solar system oscillates perpendicular to the galactic plane, thereby, inducing an observed terrestrial periodicity in biodiversity. There are a number of plausible mechanisms by which cosmic rays might affect terrestrial biodiversity. Here we investigate one of these mechanisms, the consequent ionization and dissociation in the atmosphere, resulting in changes in atmospheric chemistry that culminate in the depletion of ozone and a resulting increase in the dangerous solar UVB flux on the ground. We use a heuristic model of the cosmic ray intensity enhancement originally suggested by Medvedev and Melott (2007) to compute steady state atmospheric effects. This paper is a reexamination of an issue we have studied before with a simplified approximation for the distribution of incidence angles. The new results are based on an improved ionization background computation averaged over a massive ensemble (about 7 × 10^(5)) shower simulations at various energies and incidence angles. We adopt a range with a minimal model and a fit to full exposure to the postulated extragalactic background. The atmospheric effects are greater than they were with our earlier, simplified ionization model. At the lower end of the intensity range, we find that the effects are too small to be of serious consequence. At the upper end of this range, ∼6% global average loss of ozone column density exceeds that currently experienced due to anthropogenic effects such as accumulated chlorofluorocarbons. We discuss some of the possible effects. The intensity of the atmospheric effects is less than those of a nearby supernova or galactic γ ray burst, but the duration of the effects would be about 106 times longer. Present UVB enhancement from current ozone depletion ∼3% is a documented stress on the biosphere, but a depletion of the magnitude found at the upper end of our range would approximately double the global average UVB flux. We conclude that for estimates at the upper end of the reasonable range of the cosmic ray variability over geologic time, the mechanism of atmospheric ozone depletion may provide a major biological stress, which could easily bring about major loss of biodiversity. It is possible that future high-energy astrophysical observations will resolve the question of whether such depletion is likely