  Increases in extreme weather events are a potentially important consequence
of anthropogenic climate change (ACC), yet, are difficult to attribute to ACC
because the record length is often similar to, or shorter than, extreme-event
return periods. This study is motivated by the ``World Weather Attribution
Project'' (WWAP) and their approach of fitting extreme value distribution
functions to local observations. The approach calculates the dependence of
distribution parameters on the global mean surface temperature (GMST) and uses
this dependence to attribute extreme events to ACC. Applying the WWAP method to
a large ensemble of climate simulations run without anthropogenic forcing, we
still find a strong dependence of distribution parameters on GMST. This
dependence results from internal climate variability, such as ENSO, affecting
both extreme events and GMST. Therefore, dependence on GMST does not
necessarily imply an effect of ACC on extremes.
  We next re-examine three WWAP attribution cases. We consider whether an
extreme value, normal, or log-normal distribution better represents the data;
if a GMST-dependence of distribution parameters is justified using a likelihood
ratio test; and if a meaningful attribution can be made given errors in GMST
dependence. The effects of natural variability on both GMST and extremes make
it impossible to attribute the 2020 Siberian Heatwave and Australia's
2020--2021 bushfires to ACC. The small number of data points for the 2019--2021
drought in Madagascar precludes a meaningful attribution analysis. Overall,
natural variability and the uncertain relationship between GMST and extremes
make attribution using the WWAP approach challenging.

Atmospheric and Oceanic Physics