[1] In this paper we provide a general theoretical framework exploiting copulas for studying the return periods of hydrological events; in particular, we consider events depending upon the joint behavior of two nonindependent random variables, an approach which can easily be generalized to the multivariate case. We show that using copulas may greatly simplify the calculations and may even yield analytical expressions for the isolines of the return periods, both in the unconditional and in the conditional case. In addition, we show how a new probability distribution may be associated with the return period of specific events and introduce the definitions of sub-, super-, and critical events as well as those of primary and secondary return periods. An illustration of the techniques proposed is provided by analyzing some case studies already examined in literature.
Sea level rise (SLR), a well-documented and urgent aspect of anthropogenic global warming, threatens population and assets located in low-lying coastal regions all around the world. Common flood hazard assessment practices typically account for one driver at a time (e.g., either fluvial flooding only or ocean flooding only), whereas coastal cities vulnerable to SLR are at risk for flooding from multiple drivers (e.g., extreme coastal high tide, storm surge, and river flow). Here, we propose a bivariate flood hazard assessment approach that accounts for compound flooding from river flow and coastal water level, and we show that a univariate approach may not appropriately characterize the flood hazard if there are compounding effects. Using copulas and bivariate dependence analysis, we also quantify the increases in failure probabilities for 2030 and 2050 caused by SLR under representative concentration pathways 4.5 and 8.5. Additionally, the increase in failure probability is shown to be strongly affected by compounding effects. The proposed failure probability method offers an innovative tool for assessing compounding flood hazards in a warming climate.sea level rise | coastal flooding | compound extremes | copula | failure probability F looding hazard, characterized by the intensity/frequency of flood events (1), is an important consideration in local level planning and adaptation (2). Coastal cities are especially demanding sites for flood hazard assessment because of exposure to multiple flood drivers such as coastal water level (WL), river discharge, and precipitation (3, 4). Furthermore, dependence among the flood drivers [e.g., coastal surge/tide, sea level rise (SLR), and river flow] can lead to compound events (5) in which the simultaneous or sequential occurrence of extreme or nonextreme events may lead to an extreme event or impact (6). For example, in estuarine systems, the interplay between coastal WL and freshwater inflow determines the surface WL (and hence the flood probability) at subtidal (7) and tidal (8-11) frequencies.In the United States, flood hazard assessment practices are typically based on univariate methods. For example, procedures for rivers often treat oceanic contributions (e.g., tides and storm surges) using static base flood levels (e.g., ref. 12), and do not consider the dynamic effects of coastal WL (e.g., ref. 13). Similarly, flood hazard procedures for coastal WLs (e.g., ref. 14) do not account for terrestrial factors such as river discharge or direct precipitation into urban areas. Previous studies indicate that univariate extreme event analysis may not correctly estimate the probability of a given hydrologic event (15,16). This points to the potential importance of multivariate analysis of extreme events in coastal/estuarine systems and consideration of compounding effects between flood drivers (6). Bivariate extreme event analysis has been explored in a coastal context with different variables and in different areas (5, 17-33) (see SI Appendix, Table S2 for more details). B...
This paper is the outcome of a community initiative to identify major unsolved scientific problems in hydrology motivated by a need for stronger harmonisation of research efforts. The procedure involved a public consultation through online media, followed by two workshops through which a large number of potential science questions were collated, prioritised, and synthesised. In spite of the diversity of the participants (230 scientists in total), the process revealed much about community priorities and the state of our science: a preference for continuity in research questions rather than radical departures or redirections from past and current work. Questions remain focused on the process-based understanding of hydrological variability and causality at all space and time scales. Increased attention to environmental change drives a new emphasis on understanding how change propagates across interfaces within the hydrological system and across disciplinary boundaries. In particular, the expansion of the human footprint raises a new set of questions related to human interactions with nature and water cycle feedbacks in the context of complex water management problems. We hope that this reflection and synthesis of the 23 unsolved problems in hydrology will help guide research efforts for some years to come. ARTICLE HISTORY
Abstract. Calculating return periods and design quantiles in a multivariate environment is a difficult problem: this paper tries to make the issue clear. First, we outline a possible way to introduce a consistent theoretical framework for the calculation of the return period in a multi-dimensional environment, based on Copulas and the Kendall's measure. Secondly, we introduce several approaches for the identification of suitable design events: these latter quantities are of utmost importance in practical applications, but their calculation is yet limited, due to the lack of an adequate theoretical environment where to embed the problem. Throughout the paper, a case study involving the behavior of a dam is used to illustrate the new concepts outlined in this work.
[1] Stochastic models of rainfall, usually based on Poisson arrivals of rectangular pulses, generally assume exponential marginal distributions for both storm duration and average rainfall intensity, and the statistical independence between these variables. However, the advent of stochastic multifractals made it clear that rainfall statistical properties are better characterized by heavy tailed Pareto-like distributions, and also the independence between duration and intensity turned out to be a nonrealistic assumption. In this paper an improved intensity-duration model is considered, which describes the dependence between these variables by means of a suitable 2-Copula, and introduces Generalized Pareto marginals for both the storm duration and the average storm intensity. Several theoretical results are derived: in particular, we show how the use of 2-Copulas allows reproducing not only the marginal variability of both storm average intensity and storm duration, but also their joint variability by describing their statistical dependence; in addition, we point out how the use of heavy tailed Generalized Pareto laws gives the possibility of modeling both the presence of extreme values and the scaling features of the rainfall process, and has interesting connections with the statistical structure of the process of rainfall maxima, which is naturally endowed with a Generalized Extreme Value law. Finally, a case study considering rainfall data is shown, which illustrates how the theoretical results derived in the paper are supported by the practical analysis.
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