Academic literature on the topic 'Bivariate Failure Return Period'

Bivariate modeling and hazard assessment of low flows are performed exploiting copulas. 7-day low flows observed, respectively, in the upper, middle and lower parts of the Çoruh basin (Turkey) are examined, considering three pairs of certified stations located in different sub-basins. A thorough statistical analysis indicates that the GEV distribution can be used to model the marginal behavior of the low-flow. The joint distributions at each part are modeled via a dozen of copula families. As a result, the Husler–Reiss copula adequately fits the joint low flows in the upper part, while the t-Student copula turns out to best fit the other parts. In order to assess the low-flow hazard, these copulas are then used to compute joint return periods and failure probabilities under a critical bivariate “AND” hazard scenario. The results indicate that the middle and lower parts of the Çoruh basin are likely to experience the largest drought hazards. As a novelty, the statistical tools used allow to objectively quantify drought threatening in a thorough multivariate perspective, which involves distributional analysis, frequency analysis (return periods) and hazard analysis (failure probabilities).

Abstract. The Paris Agreement sets a long-term temperature goal to hold global warming to well below 2.0 ∘C and strives to limit it to 1.5 ∘C above preindustrial levels. Droughts with either intense severity or a long persistence could both lead to substantial impacts such as infrastructure failure and ecosystem vulnerability, and they are projected to occur more frequently and trigger intensified socioeconomic consequences with global warming. However, existing assessments targeting global droughts under 1.5 and 2.0 ∘C warming levels usually neglect the multifaceted nature of droughts and might underestimate potential risks. This study, within a bivariate framework, quantifies the change in global drought conditions and corresponding socioeconomic exposures for additional 1.5 and 2.0 ∘C warming trajectories. The drought characteristics are identified using the Standardized Precipitation Evapotranspiration Index (SPEI) combined with the run theory, with the climate scenarios projected by 13 Coupled Model Inter-comparison Project Phase 5 (CMIP5) global climate models (GCMs) under three representative concentration pathways (RCP 2.6, RCP4.5 and RCP8.5). The copula functions and the most likely realization are incorporated to model the joint distribution of drought severity and duration, and changes in the bivariate return period with global warming are evaluated. Finally, the drought exposures of populations and regional gross domestic product (GDP) under different shared socioeconomic pathways (SSPs) are investigated globally. The results show that within the bivariate framework, the historical 50-year droughts may double across 58 % of global landmasses in a 1.5 ∘C warmer world, while when the warming climbs up to 2.0 ∘C, an additional 9 % of world landmasses would be exposed to such catastrophic drought deteriorations. More than 75 (73) countries' populations (GDP) will be completely affected by increasing drought risks under the 1.5 ∘C warming, while an extra 0.5 ∘C warming will further lead to an additional 17 countries suffering from a nearly unbearable situation. Our results demonstrate that limiting global warming to 1.5 ∘C, compared with 2 ∘C warming, can perceptibly mitigate the drought impacts over major regions of the world.

The interaction between oceanographic, meteorological, and hydrological factors can result in an extreme flooding scenario in the low-lying coastal area, called compound flooding (CF) events. For instance, rainfall and storm surge (or high river discharge) can be driven by the same meteorological forcing mechanisms, tropical or extra-tropical cyclones, resulting in a CF phenomenon. The trivariate distributional framework can significantly explain compound events’ statistical behaviour reducing the associated high-impact flood risk. Resolving heterogenous dependency of the multidimensional CF events by incorporating traditional 3D symmetric or fully nested Archimedean copula is quite complex. The main challenge is to preserve all lower-level dependencies. An approach based on decomposing the full multivariate density into simple local building blocks via conditional independence called vine or pair-copulas is a much more comprehensive way of approximating the trivariate flood dependence structure. In this study, a parametric vine copula of a drawable (D-vine) structure is introduced in the trivariate modelling of flooding events with 46 years of observations of the west coast of Canada. This trivariate framework searches dependency by combining the joint impact of annual maximum 24-h rainfall and the highest storm surge and river discharge observed within the time ±1 day of the highest rainfall event. The D-vine structures are constructed in three alternative ways by permutation of the conditioning variables. The most appropriate D-vine structure is selected using the fitness test statistics and estimating trivariate joint and conditional joint return periods. The investigation confirms that the D-vine copula can effectively define the compound phenomenon’s dependency. The failure probability (FP) method is also adopted in assessing the trivariate hydrologic risk. It is observed that hydrologic events defined in the trivariate case produce higher FP than in the bivariate (or univariate) case. It is also concluded that hydrologic risk increases (i) with an increase in the service design life of the hydraulic facilities and (ii) with a decrease in return periods.