  Nitrate ion spikes in polar ice cores are contentiously used to estimate the
intensity, frequency, and probability of historical solar proton events,
quantities that are needed to prepare for potentially society-crippling space
weather events. We use the Whole Atmosphere Community Climate Model to
calculate how large an event would have to be to produce enough odd nitrogen
throughout the atmosphere to be discernible as nitrate peaks at the Earth's
surface. These hypothetically large events are compared with probability of
occurrence estimates derived from measured events, sunspot records, and
cosmogenic radionuclides archives. We conclude that the fluence and spectrum of
solar proton events necessary to produce odd nitrogen enhancements equivalent
to the spikes of nitrate ions in Greenland ice cores are unlikely to have
occurred throughout the Holocene, confirming that nitrate ions in ice cores are
not suitable proxies for historical individual solar proton events.
