Multiple extreme weather event models
To quantify the correlation between the counts of the various stress events we used the single event models to detrend the data for each event metric and create a transformed data set which does not exhibit spatio-temporal variability. Using the transformed data, the dependency across the various event metrics was quantified using correlation. The single event Poisson models were used to transform the original datays,t (for each stress) to the scale of a Gaussian random variable with mean zero and variance one. At that scale, all spatial and temporal variability has been factored out and the sample correlations between the transformed counts for each event are estimates of the dependency between each event.
A modified simulation technique was employed to sample from the predictive distribution of the counts for each event, allowing for the correlation between them. Firstly, we generated random samples of the data at the detrended scale, respecting the correlation between the event metrics at this scale. Then, we transformed these samples back to original scale of the data to obtain a set of simulated counts in each grid cell and year, thus maintaining both the spatio-temporal variability in each event but also the correlation between event metrics.
The thresholds were set as the sample mean of each event metric across all grid cells and years. The joint probability that the annual mean count of two or more event categories exceeds a particular threshold was then determined. Comparison of differences in these probabilities between 1961–1988 and 1989–2016 lie in the region between -1 and 1, and conveys information about whether the risk of two or more stress events occurring within one year has increased. Significant changes are ones that are above 0.05 or below -0.05.