  We investigate the relationship between spectral solar irradiance (SSI) and
ozone in the tropical upper stratosphere. We find that solar cycle (SC) changes
in ozone can be well approximated by considering the ozone response to SSI
changes in a small number individual wavelength bands between 176 and 310 nm,
operating independently of each other. Additionally, we find that the ozone
varies approximately linearly with changes in the SSI. Using these facts, we
present a Bayesian formalism for inferring SC SSI changes and uncertainties
from measured SC ozone profiles. Bayesian inference is a powerful,
mathematically self-consistent method of considering both the uncertainties of
the data and additional external information to provide the best estimate of
parameters being estimated. Using this method, we show that, given measurement
uncertainties in both ozone and SSI datasets, it is not currently possible to
distinguish between observed or modelled SSI datasets using available estimates
of ozone change profiles, although this might be possible by the inclusion of
other external constraints. Our methodology has the potential, using wider
datasets, to provide better understanding of both variations in SSI and the
atmospheric response.
