Gauging mixed climate extreme value distributions in tropical cyclone regions

Abstract

In tropical cyclone (TC) regions, tide gauge or numerical hindcast records are usually of insufficient length to have sampled sufficient cyclones to enable robust estimates of the climate of TC-induced extreme water level events. Synthetically-generated TC populations provide a means to define a broader set of plausible TC events to better define the probabilities associated with extreme water level events. The challenge is to unify the estimates of extremes from synthetically-generated TC populations with the observed records, which include mainly non-TC extremes resulting from tides and more frequently occurring atmospheric-depression weather and climate events. We find that extreme water level measurements in multiple tide gauge records in TC regions, some which span more than 100 years, exhibit a behaviour consistent with the combining of two populations, TC and non-TC. We develop an equation to model the combination of two populations of extremes in a single continuous mixed climate (MC) extreme value distribution (EVD). We then run statistical simulations to show that long term records including both historical and synthetic events can be better explained using MC than heavy-tailed generalised EVDs. This has implications for estimating extreme water levels when combining synthetic cyclone extreme sea levels with hindcast water levels to provide actionable information for coastal protection.

The Influence of Future Changes in Tidal Range, Storm Surge, and Mean Sea Level on the Emergence of Chronic Flooding

“…It is notable that the Australian locations with large tidal ranges and less variability due to how tide and surge extremes coincide are all subject to tropical cyclone driven storm surges at present. Tropical cyclones are very often the focus when considering coastal flood risk in these locations (e.g., Haigh, MacPherson, et al., 2014; O’Grady et al., 2022). The most extreme future floods will continue to be driven by tropical cyclones.…”

Understanding uncertainties in contemporary and future extreme wave events for broad-scale impact and adaptation planning

“…To further support our results, we determined the Akaike information criterion (corrected for small samples) (AICc) ( 68 ) for both GUM-AMAX and GEV-AMAX. The AICc is an estimator of prediction error used across different scientific research fields ( 69 , 70 ), which asymptotically selects the extreme value distribution that minimizes the mean squared errors of the estimation. The AIC corrected for small sample sizes ( N / W < 40) is provided byAICc=−2logLfalse(normalθfalse^false)+2W+2Wfalse(W+1false)N−W−1with Lfalse(normalθfalse^false) representing the maximized log-likelihood, W representing the number of estimated parameters used to achieve that log-likelihood, and N representing the sample size.…”

“…To further support our results, we determined the Akaike information criterion (corrected for small samples) (AICc) ( 68 ) for both GUM-AMAX and GEV-AMAX. The AICc is an estimator of prediction error used across different scientific research fields ( 69 , 70 ), which asymptotically selects the extreme value distribution that minimizes the mean squared errors of the estimation. The AIC corrected for small sample sizes ( N / W < 40) is provided by with representing the maximized log-likelihood, W representing the number of estimated parameters used to achieve that log-likelihood, and N representing the sample size.…”

Observational and model evidence together support wide-spread exposure to noncompensable heat under continued global warming

“…We did so by identifying the stations exhibiting annual block maxima that could be appropriately described by a nonstationary generalized extreme value (GEV) distribution, wherein the distribution location is parameterized as a linear function of global average temperature (full details in Materials and Methods). Nonstationary GEV distributions have a long history of application to the projection of future climate extremes from both observational and modeled data (25)(26)(27)(28), including the projection of lethal heat extremes (10). Estimated return periods were then calculated from each station's respective GEV distribution for a year with at least 1 day of 6-hour exposure to noncompensable heat stress under six different warming regimes: global average temperatures at 0.5°C increments between 1°and 3.5°C warmer than the preindustrial average (Fig.…”