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. 2019 Sep 11;9:13165. doi: 10.1038/s41598-019-49822-6

Figure 3.

Figure 3

Stronger upper tail dependence relative to complete dependence increases the likelihood of compound flood events: Proof-of-concept illustrations of unconditional (left panel) and conditional (on high coastal CWL; right panel) flood hazards in UK Rivers along the North shields TG: River Ribble (a, top panel) a tidally influenced river located at a geodesic distance of 157 km and in the River South Tyne (b, bottom panel), non-tidally influenced, located at a geodesic distance of 69 km from the TG. (a) Kendall’s τ correlation between Annual maxima CWL and peak discharge for River Ribble is 0.16 with p-value = 0.12 [the p-value indicates the evidence against the null hypothesis of independence: the smaller (larger) the p-value, the stronger is the evidence against (for) the null hypothesis; however, a p-value does not indicate the probability that the null hypothesis is true], while empirical upper tail dependence coefficients are λCFGObs = 0.28 (p-value = 0.0054) and λLOGObs = 0.44 (p-value = 0.011). (b) Kendall’s τ correlation associated with compound event pairs in River South Tyne is 0.25 with p-value = 0.018, while empirical upper tail dependence coefficients are λCFGObs = 0.35 (p-value = 0.001) and λLOGObs = 0.44 (p-value = 0.013). While circles with shades in yellow and red denote the year of occurrence of the compound event, the one in gray indicates copula-simulated samples. For clarity, return level estimates are rounded to their nearest decimal numbers. Maps are generated using MATLAB 2015a (Version 8.5, http://www.mathworks.com), and then organized and labelled in Adobe Photoshop CS6 Desktop (Version 13.0.1 × 32, http://www.adobe.com) [Software].