Joint probability of changes in mean sea level, tides, and skew surges around Australia

The frequency of sea level exceedances depends not only changing mean sea level, but also on changing tides and surges. Global studies have shown that the tide and surge components of observed sea level are not necessarily stationary and can contribute to the likelihood of sea level threats. The way tide and surge variables are measured is key for determining changes in their behaviour. Measuring tides by a few harmonic constituents can underestimate their real amplitudes, especially spring tides. This is significant because sea level exceedances are typically a consequence of larger tides coinciding with a surge. Measuring surges by the non-tidal residual retains any dependency between the tide and surge variables, whereas the skew surge measure reduces dependence necessary for computing the joint probability distribution. The joint probability method is well adopted in sea level studies for estimating extremes, where the mean sea level is typically included as a constant or linear trend. But the interannual variability in mean sea level can be an influential contributor to sea level threats. Here we describe a method to combine the probability distributions of all three components: 1) annual relative mean sea level, 2) high water tide levels, and 3) skew surges, to compute the joint probability of sea level exceedances. We estimate the increasing exceedance probability for tide gauges around the Australian coastline from 1991-2022. Characterising the combined influence of changing sea level factors on the likelihood of exceedances provides a technique for understanding the unique sea level threats in diverse coastal environments.