  The ventilation of carbon dioxide within subterranean caves regulates the
growth of speleothems --- mineral deposits found in caves that provide
important clues about past climate. While previous studies have used internal
temperature measurements to predict ventilation rates, such data would not be
available for the task of climate reconstruction. Here, we develop a
parsimonious model to predict ventilation rates from knowledge of outside
temperatures and the cave's physical dimensions only. In the model, ventilation
arises from buoyancy-driven flows created in passageways that connect to the
outside. A few key simplifications leads to a system amenable to perturbation
analysis, resulting in explicit expressions for ventilation rates. We compare
these predictions to time-resolved, in-situ measurements of transported cave
gases (carbon dioxide and radon). The theory accurately accounts for the timing
and magnitude of seasonal and synoptic variations of these gases, and is
therefore diagnostic of seasonal bias in speleothem growth.
