Dependence of drivers affects risks associated with compound events

Abstract

Compound climate extremes are receiving increasing attention because of their disproportionate impacts on humans and ecosystems. However, risks assessments generally focus on univariate statistics. We analyze the co-occurrence of hot and dry summers and show that these are correlated, inducing a much higher frequency of concurrent hot and dry summers than what would be assumed from the independent combination of the univariate statistics. Our results demonstrate how the dependence structure between variables affects the occurrence frequency of multivariate extremes. Assessments based on univariate statistics can thus strongly underestimate risks associated with given extremes, if impacts depend on multiple (dependent) variables. We conclude that a multivariate perspective is necessary to appropriately assess changes in climate extremes and their impacts and to design adaptation strategies.

Keywords: CMIP5; Climate Change; Climate extremes; compound events; risk.

Fig. 1. Correlation between temperature and precipitation during the warm season.

The warm season is determined as the hottest 3-month period in the temperature climatology. The correlation is computed as the interannual correlation of the yearly averaged values of temperature and precipitation over the considered 3-month period. (A) Model mean of correlations of all CMIP5 models (1870–1969). Stippling is shaded according to the fraction of models that show significant correlations at the 0.05 level if this fraction is larger than 0.5. (B) Mean of the correlations of the observation-based data sets CRU (1901–2013), Princeton (1901–2012), and Delaware (1901–2012). Oceans and areas, where less than two of the three data sets show significant correlations at the 0.05 level, are colored in gray.

Fig. 2. Dependence affects the likelihood of bivariate extremes.

(A) Temperature and negative precipitation averaged across June, July, and August (warm season) at 56.25°E, 51.25°N in CRU for the time period 1901–2013 (red). Data where the values of temperature are randomly permutated are shown in gray. (B) Same data as in (A) transformed into normalized ranks. The regions where both variables concurrently exceed both 78th (solid), 86th (dashed), and 90th percentiles (dotted), corresponding to 20-year (p = 0.05), 50-year (p = 0.02), and 100-year (p = 0.01) bivariate return periods for independent data under the condition that temperature and negative precipitation exceed the same quantile (u = v), are depicted. Return periods of the original, correlated data based on the same thresholds correspond to approximately 8 years (p ≈ 0.13), 13 years (p ≈ 0.08), and 18 years (p ≈ 0.05). (C) Comparison between estimating changes in the likelihood of bivariate extremes by counting extremes (light bars) and modeling the extremes with copulas (dark bars) for different coefficients of correlation. The increase in likelihood due to the correlation is shown, taking an event in which both variables are independent and exceed their 90th percentile as reference (that is, a 100-year event). Whiskers represent 1 SD over 83 repetitions.

Fig. 3. Increase in likelihood of extremely hot and dry warm seasons due to dependence.

Starting from a 100-year event with independent temperature and negative precipitation (that is, both exceed their 90th percentile), the increase in likelihood of these events due to the dependence between temperature and correlation is shown. (A) Average of the increases in likelihood across all CMIP5 models. (B) Average of the increases in likelihood in the data sets CRU, Princeton, and Delaware. (C) Increases in likelihood were averaged over CMIP5 models across the regions central North America (CNA), Amazon (AMZ), central Europe (CEU), South Africa (SAF), East Asia (EAS), and South Asia (SAS). Whiskers represent 1 SD over all models. (D) As in (C) but averaged over observation-based data sets CRU, Princeton, and Delaware. Whiskers represent 1 SD over all three data sets.

Fig. 4. Future projections.

(A) Increase in likelihood of concurrently exceeding the historical 90th percentiles of temperature and negative precipitation averaged over the warm season during the 21st century. The average over all CMIP5 models is shown. (B) Change in interannual correlation between temperature and precipitation averaged over the warm season between 1870–1969 and the 21st century. The average over all CMIP5 models is shown. (C) Change in likelihood that an extremely hot and dry warm season with a return period of 100 years during 1870–1969 will occur during the 21st century. The average across all CMIP5 models is shown. Stippling highlights locations where models show a significant increase in likelihood in the 21st century (P < 0.1). For (B) and (C), temperature and precipitation during the warm season were linearly detrended in both time periods before further analysis.