Serinaldi, FrancescoFrancescoSerinaldi2026-03-112026-03-112013-10-01Water Resources Research 49 (10): 6527-6547 (2013)https://hdl.handle.net/11420/61990Moving from univariate to multivariate frequency analysis, this study extends the Klemeš' critique of the widespread belief that the increasingly refined mathematical structures of probability functions increase the accuracy and credibility of the extrapolated upper tails of the fitted distribution models. In particular, we discuss key aspects of multivariate frequency analysis applied to hydrological data such as the selection of multivariate design events (i.e., appropriate subsets or scenarios of multiplets that exhibit the same joint probability to be used in design applications) and the assessment of the corresponding uncertainty. Since these problems are often overlooked or treated separately, and sometimes confused, we attempt to clarify properties, advantages, shortcomings, and reliability of results of frequency analysis. We suggest a selection method of multivariate design events with prescribed joint probability based on simple Monte Carlo simulations that accounts for the uncertainty affecting the inference results and the multivariate extreme quantiles. It is also shown that the exploration of the p-level probability regions of a joint distribution returns a set of events that is a subset of the p-level scenarios resulting from an appropriate assessment of the sampling uncertainty, thus tending to overlook more extreme and potentially dangerous events with the same (uncertain) joint probability. Moreover, a quantitative assessment of the uncertainty of multivariate quantiles is provided by introducing the concept of joint confidence intervals. From an operational point of view, the simulated event sets describing the distribution of the multivariate p-level quantiles can be used to perform multivariate risk analysis under sampling uncertainty. As an example of the practical implications of this study, we analyze two case studies already presented in the literature. Key Points Refined multivariate distributions do not improve extrapolation Joint confidence intervals are introduced Appropriate multivariate design events are derived ©2013. The Authors. Water Resources Research published by Wiley on behalf of American Geophysical Union.en1944-797320131065276547WileycopulasJoint confidence intervalsMonte Carlo simulationmultivariate design eventsmultivariate frequency analysisuncertaintyNatural Sciences and Mathematics::577: EcologyNatural Sciences and Mathematics::551: Geology, Hydrology MeteorologyJournal Article10.1002/wrcr.20531