  The purpose of this paper is to illustrate new techniques for computing
multiday extreme precipitation taken from recent theoretical advancements in
extreme value theory in the framework of dynamical systems, using historical
precipitation data along the eastern coast of Australia as a case study. We
explore the numerical pitfalls of applying standard extreme value techniques to
model multiday extremes. Then, we illustrate that our data conforms to the
appropriate setting for the application of recently derived extreme value
distributions for runs of extremes in the dynamical framework and adapt these
to the non-stationary setting. Finally, we use these distributions to make more
informed predictions on the return times and magnitudes of consecutive daily
extreme precipitation and find changes in the dependence of increasing
consecutive daily rainfall extremes on the Southern Oscillation Index. Although
our case study is focused on extreme precipitation across eastern Australia, we
emphasize that these techniques can be used to model expected returns and
magnitudes of consecutive extreme precipitation events across many locations.
