Statistical modelling of extreme daily rainfall over Aotearoa New Zealand

Extreme rainfall in New Zealand, and how best to characterise expected changes in those extremes as the climate warms, is investigated using very large ensembles of regional climate model simulations at five different ‘epochs’ of climate change (pre-industrial, present-day, and three future states at 1.5 °C, 2.0 °C, and 3.0 °C above pre-industrial). Different constructs of non-stationary Generalised Extreme Value (GEV) models are explored to determine which provides the most accurate estimates of extreme rainfall for the minimum model complexity. The different GEV model constructs vary the number of parameters (location, scale and shape) that are assumed to vary as climate changes, summarised as a linear dependence on Southern Hemisphere mean land surface temperature. Non-stationarity is also explored a different way, with a stationary GEV fitted separately within each of the five ’epochs’. These different models are applied to annual maximum one-day rainfall at eight locations around the country, chosen to be broadly representative of the various rainfall regimes countrywide. In situations with fair but not enormous sample sizes, such as with long historical records, the model in which only the location and scale, but not the shape, parameters vary with warming has the tightest sampling uncertainty without introducing substantial bias. According to this GEV model, 1-in-100-year rainfall increases with warming at all eight locations, ranging from about 5%/${}^{\circ }$C in most of the country to 8%/${}^{\circ }$C in the north. The change arises from an increase in the location parameter, with only a proportional increase in the scale parameter, consistent with extreme rainfall increases dictated by anthropogenic increases in specific humidity.