  Extreme event attribution characterizes how anthropogenic climate change may
have influenced the probability and magnitude of selected individual extreme
weather and climate events. Attribution statements often involve quantification
of the fraction of attributable risk (FAR) or the risk ratio (RR) and
associated confidence intervals. Many such analyses use climate model output to
characterize extreme event behavior with and without anthropogenic influence.
However, such climate models may have biases in their representation of extreme
events. To account for discrepancies in the probabilities of extreme events
between observational datasets and model datasets, we demonstrate an
appropriate rescaling of the model output based on the quantiles of the
datasets to estimate an adjusted risk ratio. Our methodology accounts for
various components of uncertainty in estimation of the risk ratio. In
particular, we present an approach to construct a one-sided confidence interval
on the lower bound of the risk ratio when the estimated risk ratio is infinity.
We demonstrate the methodology using the summer 2011 central US heatwave and
output from the Community Earth System Model. In this example, we find that the
lower bound of the risk ratio is relatively insensitive to the magnitude and
probability of the actual event.
