  Detecting changepoints in functional data has become an important problem as
interest in monitoring of climate phenomenon has increased, where the data is
functional in nature. The observed data often contains both amplitude
($y$-axis) and phase ($x$-axis) variability. If not accounted for properly,
true changepoints may be undetected, and the estimated underlying mean change
functions will be incorrect. In this paper, an elastic functional changepoint
method is developed which properly accounts for these types of variability. The
method can detect amplitude and phase changepoints which current methods in the
literature do not, as they focus solely on the amplitude changepoint. This
method can easily be implemented using the functions directly or can be
computed via functional principal component analysis to ease the computational
burden. We apply the method and its non-elastic competitors to both simulated
data and observed data to show its efficiency in handling data with phase
variation with both amplitude and phase changepoints. We use the method to
evaluate potential changes in stratospheric temperature due to the eruption of
Mt.\ Pinatubo in the Philippines in June 1991. Using an epidemic changepoint
model, we find evidence of a increase in stratospheric temperature during a
period that contains the immediate aftermath of Mt.\ Pinatubo, with most
detected changepoints occurring in the tropics as expected.
