  Computing the return times of extreme events and assessing the impact of
climate change on such return times is fundamental to extreme event attribution
studies. However, the rarity of such events in the observational record makes
this task a challenging one, even more so for "record-shattering" events that
have not been previously observed at all. While climate models could be used to
simulate such extremely rare events, such an approach entails a huge
computational cost: gathering robust statistics for events with return time of
centuries would require a few thousand years of simulation.
  In this study, we use an innovative tool, rare event algorithm, that allows
to sample numerous extremely rare events at a much lower cost than direct
simulations. We employ the algorithm to sample extreme heatwave seasons,
corresponding to large anomalies of the seasonal average temperature, in a
heatwave hotspot of South Asia using the global climate model Plasim. We show
that the algorithm estimates the return levels of extremely rare events with
much greater precision than traditional statistical fits. It also enables the
computation of various composite statistics, whose accuracy is demonstrated
through comparison with a very long control run. In particular, our results
reveal that extreme heatwave seasons are associated with an anticyclonic
anomaly embedded within a large-scale hemispheric quasi-stationary
wave-pattern. Additionally, the algorithm accurately represents the
intensity-duration-frequency statistics of sub-seasonal heatwaves, offering
insights into both seasonal and sub-seasonal aspects of extreme heatwave
seasons. This innovative approach could be used in extreme event attribution
studies to better constrain the changes in event's probability and intensity
with global warming, particularly for events with return times spanning
centuries or millennia.
