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Item type:Publication, Access status: without files , Non-asymptotic distributions of water extremes: much ado about what?Non-asymptotic (NA) probability distributions of block maxima (BM) have been proposed as an alternative to asymptotic distributions of BM derived by means of classic extreme-value theory (EVT). Their advantage should be the inclusion of moderate quantiles, as well as of extremes, in the inference procedures. This would increase the amount of information used and reduce the uncertainty characterizing the inference based on short samples of BM or peaks over high thresholds. In this study, we show that the NA distributions of BM suffer from two main drawbacks that make them of little usefulness for practical applications. Firstly, unlike classic EVT distributions, NA models of BM imply the preliminary definition of their conditional parent distributions, which explicitly appears in their expression. However, when such conditional parent distributions are known or estimated, the unconditional parent distribution is readily available, and the corresponding NA distribution of BM is no longer needed as it is just an approximation of the upper tail of the parent. Secondly, when declustering procedures are used to remove autocorrelation characterizing hydroclimatic records, NA distributions of BM devised for independent data are strongly biased even if the original process exhibits low or moderate autocorrelation. On the other hand, NA distributions of BM accounting for autocorrelation are less biased but still of little practical usefulness. Such conclusions are supported by theoretical arguments, Monte Carlo simulations, and re-analysis of sea level data.Publicationtype: Journal Article11 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Sailing synthetic seas: Stochastic simulation of benchmark sea state time seriesCoastal and offshore engineering relies on the analysis of sea state parameters, such as significant wave height (Hm₀), zero-crossing mean wave period (Tm₀₂), and mean wave direction (Θm). Since observed records of these parameters usually span only a few years, proper uncertainty assessment requires the simulation of unobserved but equally plausible time series. This study suggests a simple stochastic method, named SyntheSeas, to generate synthetic sequences that preserve marginal distributions and power spectra along with power cross-spectra of Hm₀, Tm₀₂, and Θm. SyntheSeas is a tailored version of the multivariate Iterative Amplitude Adjusted Fourier Transform (IAAFT) method, and has several desirable properties: (i) it relies on minimal assumptions, (ii) it accounts for the limiting steepness condition that constrains the relationship between Hm₀ and Tm₀₂without using ad hoc parametrisation, and (iii) it accounts for the modelling problems due to the circular behaviour of Θ<inf>m</inf> with satisfactory approximation. Thanks to its simplicity and transparency, SyntheSeas (i) allows the identification of the key properties required to simulate realistic time series of Hm₀, Tm₀₂, and Θm, (ii) provides a benchmark to test parametric models and their components, and (iii) enables quick applications, such as preliminary uncertainty and sensitivity analyses, without requiring advanced expertise in stochastic modelling. As a proof of concept, we discuss an application to data recorded from four wave buoys deployed around the United Kingdom.Publicationtype: Journal Article9 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Testing tests before testing data: an untold tale of compound events and binary dependenceIn any statistical investigation, we deal with the applications of probability theory to real problems, and the conclusions are inferences based on observations. To obtain plausible inferences, statistical analysis requires careful understanding of the underlying probabilistic model, which constrains the extraction and interpretation of information from observational data, and must be preliminarily checked under controlled conditions. However, these very first principles of statistical analysis are often neglected in favor of superficial and automatic application of increasingly available ready-to-use software, which might result in misleading conclusions, confusing the effect of model constraints with meaningful properties of the process of interest. To illustrate the consequences of this approach, we consider the emerging research area of so-called ‘compound events’, defined as a combination of multiple drivers and/or hazards that contribute to hydro-climatological risk. In particular, we perform an independent validation analysis of a statistical testing procedure applied to binary series describing the joint occurrence of hydro-climatological events or extreme values, which is supposed to be superior to classical analysis based on Pearson correlation coefficient. To this aim, we suggest a theoretically grounded model relying on Pearson correlation coefficient and marginal rates of occurrence, which enables accurate reproduction of the observed joint behavior of binary series, and offers a sound simulation tool useful for informing risk assessment procedures. Our discussion on compound events highlights the dangers of renaming known topics, using imprecise definitions and overlooking or misusing existing statistical methods. On the other hand, our model-based approach reveals that consistent statistical analyses should rely on informed stochastic modeling in order to avoid the proposal of flawed methods, and the untimely dismissal of well-devised theories.Publicationtype: Journal Article7 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , All in order: Distribution of serially correlated order statistics with applications to hydrological extremesClassic extreme value theory provides asymptotic distributions of block maxima (BM) Y or peaks over threshold (POT). However, as BM and POT are relatively small subsets of the values assumed by the parent process Z, alternative approaches have been proposed to make inferences on extremes by using intermediate values and non-asymptotic models. In this study, we investigate the finite sample theory of extremes based on order statistics, and present a set of results enabling the analysis of the properties of non-asymptotic distributions of BM in finite-size blocks of data under the assumption that the parent process Z has stationary temporal dependence. In particular, we suggest the beta-binomial distribution ( F β B ) as a suitable approximation of the marginal distribution of order statistics and BM under dependence, thus generalizing the theoretical results available under independence. We demonstrate the usefulness of the F β B distribution in three conceptual applications of hydrological interest. Firstly, we review the so-called Complete Time-series Analysis (CTA) framework, showing that the differences between FY and FZ are due to the inherent theoretical nature of the processes Y and Z and the different probabilistic failure scenarios described by FY and FZ. Secondly, we provide a theoretical rule to select the number of the largest maxima (LM) and over-threshold exceedances (OT) required to approximate the desired portion of the upper tail of FZ with specified accuracy. Finally, we discuss how the F β B distribution offers an interpretation and generalization of the so-called metastatistical extreme value (MEV) framework and its simplified version (SMEV), avoiding the use of high-dimensional joint distributions and preliminary data thresholding and declustering. All methodological results are validated by Monte Carlo simulations involving widely used stochastic processes with persistence. Real-world stream flow data are also analyzed as proof of concept.Publicationtype: Journal Article2 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Dissecting innovative trend analysisInvestigating the nature of trends in time series is one of the most common analyses performed in hydro-climate research. However, trend analysis is also widely abused and misused, often overlooking its underlying assumptions, which prevent its application to certain types of data. A mechanistic application of graphical diagnostics and statistical hypothesis tests for deterministic trends available in ready-to-use software can result in misleading conclusions. This problem is exacerbated by the existence of questionable methodologies that lack a sound theoretical basis. As a paradigmatic example, we consider the so-called Şen’s ‘innovative’ trend analysis (ITA) and the corresponding formal trend tests. Reviewing each element of ITA, we show that (1) ITA diagrams are equivalent to well-known two-sample quantile-quantile (q–q) plots; (2) when applied to finite-size samples, ITA diagrams do not enable the type of trend analysis that it is supposed to do; (3) the expression of ITA confidence intervals quantifying the uncertainty of ITA diagrams is mathematically incorrect; and (4) the formulation of the formal tests is also incorrect and their correct version is equivalent to a standard parametric test for the difference between two means. Overall, we show that ITA methodology is affected by sample size, distribution shape, and serial correlation as any parametric technique devised for trend analysis. Therefore, our results call into question the ITA method and the interpretation of the corresponding empirical results reported in the literature.Publicationtype: Journal Article5 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Flood propagation and duration in large river basins: a data-driven analysis for reinsurance purposes(European Geophysical Society, 2018-10-01); ; Bast, HubertDuration is a key characteristic of floods influencing the design of protection infrastructures for prevention, deployment of rescue resources during the emergency, and repartition of damage costs in the aftermath. The latter financial aspect mainly relies on the insurance industry and allows the transfer of damage costs from the public sector to the private capital market. In this context, the cost of catastrophes affecting a large amount of insured properties is partly or totally transferred from insurance companies to reinsurance companies by contracts that define the portion of transferred costs according to the temporal extent of the flood events synthesized in the so-called hours clause. However, hours clauses imply standard flood event durations, such as 168 h (1 week), regardless of the hydrological properties characterizing different areas. In this study, we firstly perform a synoptic-scale exploratory analysis to investigate the duration and magnitude of large flood events that occurred around the world and in Europe between 1985 and 2016, and then we present a data-driven procedure devised to compute flood duration by tracking flood peaks along a river network. The exploratory analysis highlights the link of flood duration and magnitude with flood generation mechanism, thus allowing the identification of regions that are more or less prone to long-lasting events exceeding the standard hours clauses. The flood tracking procedure is applied to seven of the largest river basins in Central and Eastern Europe (Danube, Rhine, Elbe, Weser, Rhone, Loire, and Garonne). It correctly identifies major flood events and enables the definition of the probability distribution of the flood propagation time and its sampling uncertainty. Overall, we provide information and analysis tools readily applicable to improve reinsurance practices with respect to spatiotemporal extent of flooding hazard.Publicationtype: Journal Article4 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Unsurprising surprises: The frequency of record-breaking and overthreshold hydrological extremes under spatial and temporal dependenceRecord-breaking (RB) events are the highest or lowest values assumed by a given variable, such as temperature and precipitation, since the beginning of the observation period. Research in hydroclimatic fluctuations and their link with this kind of extreme events recently renewed the interest in RB events. However, empirical analyses of RB events usually rely on statistical techniques based on too restrictive hypotheses such as independent and identically distributed (i/id) random variables or nongeneral numerical methods. In this study, we propose some exact distributions along with accurate approximations describing the occurrence probability of RB and peak-over-threshold (POT) events under general spatiotemporal dependence, which enable analyses based on more appropriate assumptions. We show that (i) the Poisson binomial distribution is the exact distribution of the number of RB events under i/id, (ii) equivalent binomial distributions are accurate approximations under i/id, (iii) beta-binomial distributions provide the exact distribution of POT occurrences under spatiotemporal dependence, and (iv) equivalent beta-binomial distributions provide accurate approximations for the distribution of RB occurrences under spatiotemporal dependence. To perform numerical validations, we also introduce a generator of spatially and temporally correlated binary processes, called BetaBitST. As examples of application, we study RB and POT occurrences for monthly precipitation and temperature over the conterminous United States and reanalyze Mauna Loa daily temperature data. Results show that accounting for spatiotemporal dependence yields strikingly different conclusions, making the observed frequencies of RB and POT events much less surprising than expected and calling into question previous results reported in the literature.Publicationtype: Journal Article2 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Untenable nonstationarity: An assessment of the fitness for purpose of trend tests in hydrologyThe detection and attribution of long-term patterns in hydrological time series have been important research topics for decades. A significant portion of the literature regards such patterns as ‘deterministic components’ or ‘trends’ even though the complexity of hydrological systems does not allow easy deterministic explanations and attributions. Consequently, trend estimation techniques have been developed to make and justify statements about tendencies in the historical data, which are often used to predict future events. Testing trend hypothesis on observed time series is widespread in the hydro-meteorological literature mainly due to the interest in detecting consequences of human activities on the hydrological cycle. This analysis usually relies on the application of some null hypothesis significance tests (NHSTs) for slowly-varying and/or abrupt changes, such as Mann-Kendall, Pettitt, or similar, to summary statistics of hydrological time series (e.g., annual averages, maxima, minima, etc.). However, the reliability of this application has seldom been explored in detail. This paper discusses misuse, misinterpretation, and logical flaws of NHST for trends in the analysis of hydrological data from three different points of view: historic-logical, semantic-epistemological, and practical. Based on a review of NHST rationale, and basic statistical definitions of stationarity, nonstationarity, and ergodicity, we show that even if the empirical estimation of trends in hydrological time series is always feasible from a numerical point of view, it is uninformative and does not allow the inference of nonstationarity without assuming a priori additional information on the underlying stochastic process, according to deductive reasoning. This prevents the use of trend NHST outcomes to support nonstationary frequency analysis and modeling. We also show that the correlation structures characterizing hydrological time series might easily be underestimated, further compromising the attempt to draw conclusions about trends spanning the period of records. Moreover, even though adjusting procedures accounting for correlation have been developed, some of them are insufficient or are applied only to some tests, while some others are theoretically flawed but still widely applied. In particular, using 250 unimpacted stream flow time series across the conterminous United States (CONUS), we show that the test results can dramatically change if the sequences of annual values are reproduced starting from daily stream flow records, whose larger sizes enable a more reliable assessment of the correlation structures.Publicationtype: Journal Article7 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , A blueprint for full collective flood risk estimation: Demonstration for European river floodingFloods are a natural hazard evolving in space and time according to meteorological and river basin dynamics, so that a single flood event can affect different regions over the event duration. This physical mechanism introduces spatio-temporal relationships between flood records and losses at different locations over a given time window that should be taken into account for an effective assessment of the collective flood risk. However, since extreme floods are rare events, the limited number of historical records usually prevents a reliable frequency analysis. To overcome this limit, we move from the analysis of extreme events to the modeling of continuous stream flow records preserving spatio-temporal correlation structures of the entire process, and making a more efficient use of the information provided by continuous flow records. The approach is based on the dynamic copula framework, which allows for splitting the modeling of spatio-temporal properties by coupling suitable time series models accounting for temporal dynamics, and multivariate distributions describing spatial dependence. The model is applied to 490 stream flow sequences recorded across 10 of the largest river basins in central and eastern Europe (Danube, Rhine, Elbe, Oder, Waser, Meuse, Rhone, Seine, Loire, and Garonne). Using available proxy data to quantify local flood exposure and vulnerability, we show that the temporal dependence exerts a key role in reproducing interannual persistence, and thus magnitude and frequency of annual proxy flood losses aggregated at a basin-wide scale, while copulas allow the preservation of the spatial dependence of losses at weekly and annual time scales.Publicationtype: Journal Article5 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Irreversibility and complex network behavior of stream flow fluctuationsExploiting the duality between time series and networks, directed horizontal visibility graphs (DHVGs) are used to perform an unprecedented analysis of the dynamics of stream flow fluctuations with focus on time irreversibility and long range dependence. The analysis relies on a large quality-controlled data set consisting of 699 daily time series recorded in the continental United States (CONUS) that are not affected by human activity and primarily reflects meteorological conditions. DHVGs allow a clear visualization and quantification of time irreversibility of flow dynamics, which can be interpreted as a signature of nonlinearity, and long range dependence resulting from the interaction of atmospheric, surface and underground processes acting at multiple spatio-temporal scales. Irreversibility is explored by mapping the time series into ingoing, outgoing, and undirected graphs and comparing the corresponding degree distributions. Using surrogate data preserving up to the second order linear temporal dependence properties of the observed series, DHVGs highlight the additional complexity introduced by nonlinearity into flow fluctuation dynamics. We show that the degree distributions do not decay exponentially as expected, but tend to follow a subexponential behavior, even though sampling uncertainty does not allow a clear distinction between apparent or true power law decay. These results confirm that the complexity of stream flow dynamics goes beyond a linear representation involving for instance the combination of linear processes with short and long range dependence, and requires modeling strategies accounting for temporal asymmetry and nonlinearity.Publicationtype: Journal Article6