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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 , 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 , Can we tell more than we can know? The limits of bivariate drought analyses in the United StatesThe joint occurrence of extreme hydroclimatic events, such as simultaneous precipitation deficit and high temperature, results in the so-called compound events, and has a serious impact on risk assessment and mitigation strategies. Multivariate frequency analysis (MFA) allows a probabilistic quantitative assessment of this risk under uncertainty. Analyzing precipitation and temperature records in the contiguous United States (CONUS), and focusing on the assessment of the degree of rarity of the 2014 California drought, we highlight some critical aspects of MFA that are often overlooked and should be carefully taken into account for a correct interpretation of the results. In particular, we show that an informative exploratory data analysis (EDA) devised to check the basic hypotheses of MFA, a suitable assessment of the sampling uncertainty, and a better understanding of probabilistic concepts can help to avoid misinterpretation of univariate and multivariate return periods, and incoherent conclusions concerning the risk of compound extreme hydroclimatic events. Empirical results show that the dependence between precipitation deficit and temperature across the CONUS can be positive, negative or not significant and does not exhibit significant changes in the last three decades. Focusing on the 2014 California drought as a compound event and based on the data used, the probability of occurrence strongly depends on the selected variables and how they are combined, and is affected by large uncertainty, thus preventing definite conclusions about the actual degree of rarity of this event.Publicationtype: Journal Article7 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , The importance of prewhitening in change point analysis under persistenceThe presence of serial correlation in hydro-meteorological time series often makes the detection of deterministic gradual or abrupt changes with tests such as Mann–Kendall (MK) and Pettitt problematic. In this study we investigate the adverse impact of serial correlation on change point analyses performed by the Pettitt test. Building on methods developed for the MK test, different prewhitening procedures devised to remove the serial correlation are examined, and the effects of the sample size and strength of serial dependence on their performance are tested by Monte Carlo experiments involving the first-order autoregressive [AR(1)] process, fractional Gaussian noise (fGn), and fractionally integrated autoregressive [ARFIMA(1,d,0)] model. Results show that (1) the serial correlation affects the Pettitt test more than tests for slowly varying monotonic trends such as the MK test both for short-range and long-range persistence; (2) the most efficient prewhitening procedure based on AR(1) involves the simultaneous estimation of step change and lag-1 autocorrelation ρ, and bias correction of ρ estimates; (3) as expected, the effectiveness of the prewhitening procedure strongly depends upon the model selected to remove the serial correlation; (4) prewhitening procedures allow for a better control of the type I error resulting in rejection rates reasonably close to the nominal values. As ancillary results, (5) we show the ineffectiveness of the original formulation of the so-called trend-free prewhitening (TFPW) method and provide analytical results supporting a corrected version called TFPWcu; and (6) we propose an improved two-stage bias correction of ρ estimates for AR(1) signals.Publicationtype: Journal Article8 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Upper tail dependence in rainfall extremes: would we know it if we saw it?The simultaneous occurrence of extreme events, such as simultaneous storms and floods at different locations, has a serious impact on risk assessment and mitigation strategies. The joint occurrence of extreme events can be measured by the so-called upper tail dependence (UTD) coefficient λ U. In this study, we reconsider the properties of the most popular λ U estimators and show that their strong bias and uncertainty make most of the empirical results reported in the hydrological literature questionable. In order to overcome the limits of λ U analysis, we test several alternative tools such as a pool of formal statistical tests devised for recognizing upper tail independence and graphical diagnostics based on binary correlation and binary entropy. The reliability of all the methods is preliminarily checked by Monte Carlo experiments. Statistical tests and graphical diagnostics are therefore applied to three different rainfall data sets that allow us to explore the properties of the spatial dependence structure of rainfall extremes over a wide range of spatio-temporal scales ranging from 30 min and 1 km to 30 days and 3000 km. Results highlight that (1) classical estimators provide non zero tail dependence even for cases where it should be zero; (2) formal tests and binary correlation highlight that the pairwise spatial dependence structure can be weaker than Gaussian, thus excluding UTD calculated in a pairwise manner; (3) the binary entropy computed on triples of locations shows that the pairwise UTD is not enough to explain the spatial dependence structure of extreme rainfall, whose complexity becomes evident only after resorting to higher order correlation measures. The results concerning the bias and uncertainty of λ U estimators are fully general and suggest avoiding their use especially for the short time series usually available in hydrology.Publicationtype: Journal Article7 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Dismissing return periods!The concept of return period in stationary univariate frequency analysis is prone to misconceptions and misuses that are well known but still widespread. In this study we highlight how nonstationary and multivariate extensions of such a concept are affected by additional misconceptions, thus easily resulting in further ill-posed procedures and misleading conclusions. We also show that the concepts of probability of exceedance and risk of failure over a given design life period provide more coherent, general and well devised tools for risk assessment and communication.Publicationtype: Journal Article5 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Complexity–entropy analysis of daily stream flow time series in the continental United StatesComplexity–entropy causality plane (CECP) is a diagnostic diagram plotting normalized Shannon entropy (Formula presented.) that has been introduced in nonlinear dynamics analysis to classify signals according to their degrees of randomness and complexity. In this study, we explore the applicability of CECP in hydrological studies by analyzing 80 daily stream flow time series recorded in the continental United States during a period of 75 years, surrogate sequences simulated by autoregressive models (with independent or long-range memory innovations), Theiler amplitude adjusted Fourier transform and Theiler phase randomization, and a set of signals drawn from nonlinear dynamic systems. The effect of seasonality, and the relationships between the CECP quantifiers and several physical and statistical properties of the observed time series are also studied. The results point out that: (1) the CECP can discriminate chaotic and stochastic signals in presence of moderate observational noise; (2) the signal classification depends on the sampling frequency and aggregation time scales; (3) both chaotic and stochastic systems can be compatible with the daily stream flow dynamics, when the focus is on the information content, thus setting these results in the context of the debate on observational equivalence; (4) the empirical relationships between (Formula presented.) and Hurst parameter H, base flow index, basin drainage area and stream flow quantiles highlight that the CECP quantifiers can be considered as proxies of the long-term low-frequency groundwater processes rather than proxies of the short-term high-frequency surface processes; (6) the joint application of linear and nonlinear diagnostics allows for a more comprehensive characterization of the stream flow time series.Publicationtype: Journal Article5 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , On the relationship between the index of dispersion and Allan factor and their power for testing the Poisson assumptionSeveral statistical tests are available for testing the Poisson hypothesis and/or the equidispersion of a point process. The capability to discriminate between the Poissonian behaviour and more complex processes is fundamental in many areas of research including earthquake analysis, hydrology, ecology, biology, signal analysis and sociology. This study investigates the relationship between two indices often used for detecting departures from equidispersion, namely, the index of dispersion (ID) and the Allan factor (AF). Since an approximation of the sampling distribution of AF for Poisson data has been recently proposed in the literature, we perform a detailed analysis of its properties and its relationship with the asymptotic sampling distribution of ID. Moreover, the statistical power of the AF for testing the Poisson hypothesis is assessed by using an extensive Monte Carlo simulation, and the performances of AF and ID are compared. We propose a simplified version of the AF sampling distribution that does not depend on the rate of occurrence keeping the maximum errors of extreme percentiles always smaller than 2-3 %. The power study highlights that ID systematically outperforms AF for discriminating between equidispersed and under/over dispersed data. Both indices show the same lack of power for distinguishing between data drawn from equidispersed non-Poissonian distribution functions. Therefore, even though AF is a useful statistical tool for detecting the possible fractal behaviour of point processes, ID should be preferred when the analysis aims at assessing equidispersion. The lack of power for a small sample size confirms the difficulty of identifying the true nature of the occurrence process of rare events.Publicationtype: Journal Article10 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Copula-based mixed models for bivariate rainfall data: an empirical study in regression perspectiveA comprehensive parametric approach to study the probability distribution of rainfall data at scales of hydrologic interest (e.g. from few minutes up to daily) requires the use of mixed distributions with a discrete part accounting for the occurrence of rain and a continuous one for the rainfall amount. In particular, when a bivariate vector (X, Y) is considered (e.g. simultaneous observations from two rainfall stations or from two instruments such as radar and rain gauge), it is necessary to resort to a bivariate mixed model. A quite flexible mixed distribution can be defined by using a 2-copula and four marginals, obtaining a bivariate copula-based mixed model. Such a distribution is able to correctly describe the intermittent nature of rainfall and the dependence structure of the variables. Furthermore, without loss of generality and with gain of parsimony this model can be simplified by some transformations of the marginals. The main goals of this work are: (1) to empirically explore the behaviour of the parameters of marginal transformations as a function of time scale and inter-gauge distance, by analysing data from a network of rain gauges; (2) to compare the properties of the regression curves associated to the copula-based mixed model with those derived from the model simplified by transformations of the marginals. The results from the investigation of transformations' parameters are in agreement with the expected theoretical dependence on inter-gauge distance, and show dependence on time scale. The analysis on the regression curves points out that: (1) a copula-based mixed model involves regression curves quite close to some non-parametric models; (2) the performance of the parametric regression decreases in the same cases in which non-parametric regression shows some instability; (3) the copula-based mixed model and its simplified version show similar behaviour in term of regression for mid-low values of rainfall.Publicationtype: Journal Article7 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Analysis of inter-gauge dependence by Kendall's τ K, upper tail dependence coefficient, and 2-copulas with application to rainfall fieldsThe spatial dependence of rainfall is usually studied considering pairs of rain gauges and analysing the behaviour of Pearson's correlation coefficient with respect to the distance between the two devices. However, this measure of linear dependence involves the underlying hypothesis that the data follow a bivariate normal distribution. When the data are skewed, as in the case of rainfall, a preliminary transformation is often performed in an attempt to obtain the required bivariate normality. This approach does not always guarantee satisfactory results, resulting in correlation estimator that exhibits bias and high variance. In this work, the inter-gauge dependence is studied by applying the alternative non-parametric Kendall's rank correlation coefficient and the upper tail dependence coefficient. Exploiting the link between these two indices with copulas allows building an exploratory graphical method useful to drive the definition of a regional 2-copula suitable for the description of the data. Then, this copula is used to generalize the Shimizu's bivariate mixed model, providing some freedom in the choice of the dependence structure and marginals. The analysis is performed on seven years of rainfall observations with 30-min time resolution collected by 35 gauges located in Central Italy. The effect of zero-measurements and several aggregation time scales are considered as well. Results of this study support some conclusions previously appeared in literature; mainly that only positive contemporaneous pairs of rainfall observations correctly describe the inter-site dependence. © Springer-Verlag 2007.Publicationtype: Journal Article3