Unsurprising Surprises: The Frequency of Record‐breaking and Overthreshold Hydrological Extremes Under Spatial and Temporal Dependence

Describing the space‐time variability of hydrologic extremes in relation to climate is important for scientific and operational purposes. Many studies demonstrated the role of large‐scale modes of climate variability such as the El Niño–Southern Oscillation (ENSO) or the North Atlantic Oscillation (NAO), among many others. Climate indices have hence frequently been used as predictors in probabilistic models describing hydrologic extremes. However, standard climate indices such as ENSO/NAO are poor predictors in some regions. Consequently, this paper describes an innovative method to avoid relying on standard climate indices, based on the following idea: the relevant climate indices are effectively unknown (they are hidden), and they should therefore be estimated directly from hydrologic data. In statistical terms, this corresponds to a Bayesian hierarchical model describing extreme occurrences, with hidden climate indices treated as latent variables. This approach is illustrated using three case studies. A synthetic case study first shows that identifying hidden climate indices from occurrence data alone is feasible. A second case study using flood occurrences at 42 east Australian sites confirms that the model correctly identifies their ENSO‐related climate driver. The third case study is based on 207 sites in France, where standard climate indices poorly predict flood occurrence. The hidden climate indices model yields a reliable description of flood occurrences, in particular their clustering in space and their large interannual variability. Moreover, some hidden climate indices are linked with specific patterns in atmospheric variables, making them interpretable in terms of climate variability and opening the way for predictive applications.

“…On any given year t , the number of stations with a flood occurrence corresponds to the number of successes among n t trials, with varying success probabilities

((),, π_{1} \dots π_{n_{t}})

Section: Resultsmentioning

confidence: 99%

Revealing Hidden Climate Indices from the Occurrence of Hydrologic Extremes

Renard

Thyer

2019

“…On the other hand, spatial correlations were not explicitly accounted for in the method. The occurrence of more floods than expected within any given space‐time window may be less surprising when spatial correlations are considered (Serinaldi & Kilsby, 2018). Analyses of the flood discharge records (not shown here) suggest that there is some spatial correlation.…”

Section: Discussionmentioning

confidence: 99%

Detecting Flood‐Rich and Flood‐Poor Periods in Annual Peak Discharges Across Europe

Lun

Fischer

Viglione

et al. 2020

This paper proposes a method from Scan statistics for identifying flood‐rich and flood‐poor periods (i.e., anomalies) in flood discharge records. Exceedances of quantiles with 2‐, 5‐, and 10‐year return periods are used to identify periods with unusually many (or few) threshold exceedances with respect to the reference condition of independent and identically distributed random variables. For the case of flood‐rich periods, multiple window lengths are used in the identification process. The method is applied to 2,201 annual flood peak series in Europe between 1960 and 2010. Results indicate evidence for the existence of flood‐rich and flood‐poor periods, as about 2 to 3 times more anomalies are detected than what would be expected by chance. The frequency of the anomalies tends to decrease with an increasing threshold return period which is consistent with previous studies, but this may be partly related to the method and the record length of about 50 years. In the northwest of Europe, the frequency of stations with flood‐rich periods tends to increase over time and the frequency of stations with flood‐poor periods tends to decrease. In the east and south of Europe, the opposite is the case. There appears to exist a turning point around 1970 when the frequencies of anomalies start to change most clearly. This turning point occurs at the same time as a turning point of the North Atlantic Oscillation index. The method is also suitable for peak‐over‐threshold series and can be generalized to higher dimensions, such as space and space‐time.

“…Furthermore, the long-term behavior of the hydrological cycle and its driving forces provide the context to understand that correlations between hydrological samples not only occur, but they also can persist for a long time (see O'Connell et al, 2016, for a recent review). While Leadbetter (1974Leadbetter ( , 1983) demonstrated that distributions based on dependent events (with limited long-term persistence at extreme levels) share the same asymptotic properties of distributions based on independent trials, there is evidence that correlation has strong influence on the exact statistical properties of extreme values and it slows down the already slow rate of convergence (e.g., Bogachev & Bunde, 2012;Eichner et al, 2011;Serinaldi & Kilsby, 2016;Volpi et al, 2015). In essence, correlation inflates the variability of the expected values and the width of confidence intervals due to information redundancy, and a typical effect is reflected in the tendency of hydrological extremes to cluster in space and time (e.g., Serinaldi & Kilsby, 2018, and references therein).…”

Section: Introductionmentioning

confidence: 99%

“…Then, correlation structures and variability of hydrological processes might easily be underestimated, further compromising the attempt to draw conclusions about trends spanning the period of records (see Serinaldi et al, , for detailed discussion). In other words, the lately growing body of publications examining “nonstationarity” in hydrological extremes (see Salas et al, , and references therein) may likely reflect time dependence of such extremes within a stationary setting, as observed patterns are usually compatible with stationary correlated random processes (Koutsoyiannis & Montanari, ; Luke et al, ; Serinaldi & Kilsby, ).…”

Section: Introductionmentioning

confidence: 99%

On the Exact Distribution of Correlated Extremes in Hydrology

Lombardo

Napolitano

Russo

et al. 2019

The analysis of hydrological hazards usually relies on asymptotic results of extreme value theory, which commonly deals with block maxima or peaks over threshold (POT) data series. However, data quality and quantity of block maxima and POT hydrological records do not usually fulfill the basic requirements of extreme value theory, thus making its application questionable and results prone to high uncertainty and low reliability. An alternative approach to better exploit the available information of continuous time series and nonextreme records is to build the exact distribution of maxima (i.e., nonasymptotic extreme value distributions) from a sequence of low-threshold POT. Practical closed-form results for this approach do exist only for independent high-threshold POT series with Poisson occurrences. This study introduces new closed-form equations of the exact distribution of maxima taken from low-threshold POT with magnitudes characterized by an arbitrary marginal distribution and first-order Markovian dependence, and negative binomial occurrences. The proposed model encompasses and generalizes the independent-Poisson model and allows for analyses relying on significantly larger samples of low-threshold POT values exhibiting dependence, temporal clustering, and overdispersion. To check the analytical results, we also introduce a new generator (called Gen2Mp) of proper first-order Markov chains with arbitrary marginal distributions. An illustrative application to long-term rainfall and streamflow data series shows that our model for the distribution of extreme maxima under dependence takes a step forward in developing more reliable data-rich-based analyses of extreme values.