Long-Term Trends in Extreme Environmental Events with Changepoint Detection
Authors: Lee Mintaek 
Published: December 2022

This dissertation examines long-term trends in extreme environmental events with considerations for changepoints and autocorrelation. Due to changes in measurement location, observer, instrument, sampling protocol, local ecosystem, etc., many environmental time series often contain inhomogeneous changes in their distributions. If ignored in the modeling process, these inhomogeneities could produce misleading estimation of the long-term trends in these environmental extremes. Because documentations for these changepoint-inducing events could be incomplete or missing in many cases, those changepoints need to be estimated from the data. Here, we use a genetic algorithm to estimate the number and times of changepoints in the environmental extremes as a data homogenization procedure before estimating their long-term trends and return levels. We illustrate our methods using two different extreme environmental series: monthly maximum coastal sea levels and weekly maximum ozone concentrations.

Increase in extreme sea levels can bring disastrous outcomes to people living in coastal regions by increasing flood
risk or inducing stronger storm surges. With a substantial portion of the global community living in low elevation regions,
it is crucial to understand how extreme sea levels have been changing over time. Therefore, we first study long-term trends
in monthly maximum sea levels from coastal regions around the world. As strong periodicity and autocorrelation are pertinent
to the sea level data, bootstrap techniques are used to obtain more realistic confidence intervals to the estimated trends and
return levels. We find that the consideration of changepoints changed the estimated long-term trends of 89 tide gauges (approximately
30% of tide gauges considered) by more than 20 cm century-1.

Next, we examine another, but equally important environmental extreme event: extreme ozone concentrations. Specifically, we study long-term
trends in weekly maximum ozone concentrations from the contiguous United States. Because exposure to an unhealthy level of ozone (even for a
short period of time) can adversely affect one's health, understanding how extreme ozone events have changed over time can be of public health
interest. Whereas monthly maximum sea levels in many locations exhibit weak autocorrelation, the weekly maximum ozone concentrations in many
locations show non-ignorable autocorrelation even at two distant time points. For more accurate estimation of changepoints in the presence of
long-memory autocorrelation, we develop a genetic algorithm based changepoint detection method for extreme value series with long-memory
autocorrelation. This method is subsequently applied to detect changepoints in extreme ozone series. We find that the consideration of
changepoints changed the long-term trend estimates in 78 counties (approximately 20% of the counties considered) by more than 0.03 ppm
century-1. Lastly, we find that almost all counties considered in the study are projected to experience unhealthy levels of
ozone concentrations exceeding the EPA threshold at least once within 10 years.

Our results for these two extreme environmental events are summarized in maps with estimated long-term linear trends and return levels.