Data analysis
To investigate how the risk of each event type occurring within a year has changed between the two time periods, we plotted the change in the number of events between 1961–1988 and 1989–2016 on a gridded map of the UK, using output from the following model:
Single extreme weather event models: Generalized Additive Models or GAMs (Wood, 2017) were adopted as the modelling framework to characterise the trends in extreme event frequency. This well-established class of models allows for flexible characterisation of the spatio-temporal variability of a modelled environmental variable and has been used extensively to characterise natural hazards (Youndman and Economou, 2017) and in modelling environmental variables more generally (Wood, 2017). The data extracted relates to counts of events \(y_{s,t}\)in grid cell \(s\) and year \(t\). To capture the variability of these counts in space and time, we assume a Poisson distribution with mean\(\mu_{s,t}\): the mean count in cell \(s\) and year \(t\). This mean is then characterised as a function of \(s\) and \(t\) in the following way:
log(μs,t ) = µ0 +fT (t ) + fS (s ) + fS,T (s,t )
The three unknown functions f (.) were all assumed smooth in the sense of capturing spatial and temporal variation that does not change too extremely in neighbouring locations or points in time. Much more extreme variation was captured by the random element of the model (i.e. the Poisson variability). The one dimensional function fT (t ) of time (in years) was used to capture the overall temporal trend in the counts across space, whereas fS (s ), a two-dimensional function of longitude and latitude was used to capture overall spatial variability (across time). Lastly, the three dimensionalfS,T (s,t ) captured spatio-temporal variability, in the sense of allowing for different spatial patterns for each time point (year). This captured inter-annual variability in the spatial patterns exhibited by ys,t . Such models were estimated using the statistical language R (R Core Team, 2019) and the package mgcv (Wood et al., 2016).
The model was used to estimate event counts ys,t using the simulation from the predictive distributionp (ys,t ). This distribution captures both the Poisson variability in the counts as well as the uncertainty in estimating the three unknown functions. From this, we computed the distribution of the difference in mean counts between the two time periods, i.e. mean count in 1989-2016 less the mean count in 1961-1988. This difference was plotted as a Z score in figure 1 and figure 2 and figure S1. Probabilities where this difference is not zero at the 5% significance level are termed significant (analogous to a p value < 0.05).
The impact of rainfall on soil moisture is controlled to some extent by seasonality of resource use. Additionally, the impact of soil moisture deficit on plant response is related to growth stage. Therefore, we also investigated the change in dry spells at the seasonal time scale. To do this, we split each year into four, three-month time periods; Spring (March, April, May), Summer (June, July, August), Autumn (September, October, November) and Winter (December, January, February), and carried out the above data analysis on the defined threshold for low rainfall in each season.