A case study of a “Dragon-King”: The 1999 Venezuelan catastrophe

Süveges, M.; Davison, A. C.

doi:10.1140/epjst/e2012-01566-6

Cited by 21 publications

(18 citation statements)

References 28 publications

(23 reference statements)

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“…Of special concern are the statistics of extremes, which have received much attention among hydrologists (Katz et al, 2002) and others concerned with a wide range of phenomena including snow avalanches on mountain slopes (Ancey, 2012); rupture events associated with the propagation of cracks or sliding along faults in brittle materials including rock failure, landslides and earthquakes (Amitrano, 2012;Lei, 2012;Main and Naylor, 2012) as well as volcanic eruptions, landslides, wildfires and floods (Sachs et al, 2012;Schoenberg and Patel, 2012;Süveges and Davison, 2012); demographic and financial crises (Akaev et al, 2012;Janczura and Weron, 2012); neuronal avalanches and coherence potentials in the mammalian cerebral cortex (de Arcangelis, 2012;Plenz, 2012); citations of scientific papers (Golosovsky and Solomon, 2012); and distributions of city sizes (Pisarenko and Sornette, 2012). Extreme values cluster around heavy tails of data frequency distributions which are often modeled as stretched exponential, lognormal or power functions.…”

Section: Published By Copernicus Publications On Behalf Of the Europementioning

confidence: 99%

Scalable statistics of correlated random variables and extremes applied to deep borehole porosities

Guadagnini

Neuman

Nan

et al. 2015

Hydrol. Earth Syst. Sci.

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Abstract. We analyze scale-dependent statistics of correlated random hydrogeological variables and their extremes using neutron porosity data from six deep boreholes, in three diverse depositional environments, as example. We show that key statistics of porosity increments behave and scale in manners typical of many earth and environmental (as well as other) variables. These scaling behaviors include a tendency of increments to have symmetric, non-Gaussian frequency distributions characterized by heavy tails that decay with separation distance or lag; power-law scaling of sample structure functions (statistical moments of absolute increments) in midranges of lags; linear relationships between log structure functions of successive orders at all lags, known as extended self-similarity or ESS; and nonlinear scaling of structure function power-law exponents with function order, a phenomenon commonly attributed in the literature to multifractals. Elsewhere we proposed, explored and demonstrated a new method of geostatistical inference that captures all of these phenomena within a unified theoretical framework. The framework views data as samples from random fields constituting scale mixtures of truncated (monofractal) fractional Brownian motion (tfBm) or fractional Gaussian noise (tfGn). Important questions not addressed in previous studies concern the distribution and statistical scaling of extreme incremental values. Of special interest in hydrology (and many other areas) are statistics of absolute increments exceeding given thresholds, known as peaks over threshold or POTs. In this paper we explore the statistical scaling of data and, for the first time, corresponding POTs associated with samples from scale mixtures of tfBm or tfGn. We demonstrate that porosity data we analyze possess properties of such samples and thus follow the theory we proposed. The porosity data are of additional value in revealing a remarkable cross-over from one scaling regime to another at certain lags. The phenomena we uncover are of key importance for the analysis of fluid flow and solute as well as particulate transport in complex hydrogeologic environments.

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Section: Published By Copernicus Publications On Behalf Of the Europementioning

confidence: 99%

Scalable statistics of correlated random variables and extremes applied to deep borehole porosities

Guadagnini

Neuman

Nan

et al. 2015

Hydrol. Earth Syst. Sci.

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“…Süveges and Davison () studied a disastrous rainfall that occurred in coastal Venezuela in December 1999. As for the Burlington precipitation data that are considered here, standard extremal models failed to account for this catastrophe because clusters of heavy precipitation were not appropriately accounted for.…”

Section: Comparisons With Existing Modelsmentioning

confidence: 99%

“…Recall that a univariate stationary time series

(Y_{i} : i \in Z)

is said to be an M3‐process if, for each

i \in Z

, we can write

Y_{i} = {truemax}_{k \in Z} {truemax}_{l \in N} a_{l, k} X_{l, i - k}

in terms of mutually independent unit Fréchet random variables

(X_{l, k} : l \in N, k \in Z)

and a so‐called filter matrix

A = (a_{l, k} : l \in N, k \in Z)

of non‐negative constants summing to 1. It is typically assumed, as Süveges and Davison () did, that a l , k >0 only when l ∈ {1,…, L } and k ∈ {1,…, K } so that all profiles are of the same fixed length K . When normalized by the sum of its components, i.e.…”

Section: Comparisons With Existing Modelsmentioning

confidence: 99%

“…Süveges and Davison () argued that, when the threshold u is sufficiently high, any cluster

(Y_{j} : j \in C)

of extremes, once normalized by the sum of its components, i.e.

W = false(W_{j} : j \in scriptC false) = \frac{1}{\underset{j \in C}{false\sum} Y_{j}} false(Y_{j} : j \in scriptC false),

corresponds to a noisy version of one of the signatures. This intuition is rooted in a result of Zhang and Smith () stating that, if

(Y_{i} : i \in Z)

is an M3‐process, then, for each l ∈ {1,…, L },

Pr 2.047em2.047emtrue{\frac{(Y_{t + 1}, \dots, Y_{t + K})}{Y_{t + 1} + \dots + Y_{t + K}} = false(c_{l, 1}, \dots, c_{l, K} false) infinitely often 2.047em2.047emtrue} = 1 .

…”

Section: Comparisons With Existing Modelsmentioning

confidence: 99%

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Modelling Extreme Rain Accumulation with an Application to the 2011 Lake Champlain Flood

Jalbert

Murphy

Genest

et al. 2019

Journal of the Royal Statistical Society Series C: Applied Statistics

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Summary A simple strategy is proposed to model total accumulation in non‐overlapping clusters of extreme values from a stationary series of daily precipitation. Assuming that each cluster contains at least one value above a high threshold, the cluster sum S is expressed as the ratio S=M/P of the cluster maximum M and a random scaling factor P ∈ (0,1]. The joint distribution for the pair (M,P) is then specified by coupling marginal distributions for M and P with a copula. Although the excess distribution of M is well approximated by a generalized Pareto distribution, it is argued that, conditionally on P<1, a scaled beta distribution may already be sufficiently rich to capture the behaviour of P. An appropriate copula for the pair (M,P) can also be selected by standard rank‐based techniques. This approach is used to analyse rainfall data from Burlington, Vermont, and to estimate the return period of the spring 2011 precipitation accumulation which was a key factor in that year's devastating flood in the Richelieu Valley Basin in Québec, Canada.

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“…examine closely, in a special issue of the European Physical Journal, the nature of extreme-valued outliers associated with a wide range of phenomena including rainfall events (Peters et al, 2012); snow avalanches on mountain slopes (Ancey, 2012); rupture events associated with the propagation of cracks or sliding along faults in brittle materials including rock failure, landslides and earthquakes (Amitrano, 2012;Lei, 2012;Main and Naylor, 2012) as well as volcanic eruptions, landslides, wildfires and floods (Sachs et al, 2012;Schoenberg and Patel, 2012;Süveges and Davison, 2012); demographic and financial crises (Akaev et al, 2012;Janczura and Weron, 2012); neuronal avalanches and coherence potentials in the mammalian cerebral cortex (de Arcangelis, 2012;Plenz, 2012); citations of scientific papers (Golosovsky and Solomon, 2012); distributions of city sizes (Pisarenko and Sornette, 2012); and others. The prospect of predicting Dragon Kings has further motivated Janczura and Weron (2012) and Pisarenko and Sornette (2012) to propose statistical tests capable of identifying (not predicting) such outliers in a given data set.…”

Section: Published By Copernicus Publications On Behalf Of the Europementioning

confidence: 99%

On the identification of Dragon Kings among extreme-valued outliers

Riva

Neuman

Guadagnini

2013

Nonlin. Processes Geophys.

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Abstract. Extreme values of earth, environmental, ecological, physical, biological, financial and other variables often form outliers to heavy tails of empirical frequency distributions. Quite commonly such tails are approximated by stretched exponential, log-normal or power functions. Recently there has been an interest in distinguishing between extreme-valued outliers that belong to the parent population of most data in a sample and those that do not. The first type, called Gray Swans by Nassim Nicholas Taleb (often confused in the literature with Taleb's totally unknowable Black Swans), is drawn from a known distribution of the tails which can thus be extrapolated beyond the range of sampled values. However, the magnitudes and/or space–time locations of unsampled Gray Swans cannot be foretold. The second type of extreme-valued outliers, termed Dragon Kings by Didier Sornette, may in his view be sometimes predicted based on how other data in the sample behave. This intriguing prospect has recently motivated some authors to propose statistical tests capable of identifying Dragon Kings in a given random sample. Here we apply three such tests to log air permeability data measured on the faces of a Berea sandstone block and to synthetic data generated in a manner statistically consistent with these measurements. We interpret the measurements to be, and generate synthetic data that are, samples from α-stable sub-Gaussian random fields subordinated to truncated fractional Gaussian noise (tfGn). All these data have frequency distributions characterized by power-law tails with extreme-valued outliers about the tail edges.

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A case study of a “Dragon-King”: The 1999 Venezuelan catastrophe

Cited by 21 publications

References 28 publications

Scalable statistics of correlated random variables and extremes applied to deep borehole porosities

Scalable statistics of correlated random variables and extremes applied to deep borehole porosities

Modelling Extreme Rain Accumulation with an Application to the 2011 Lake Champlain Flood

On the identification of Dragon Kings among extreme-valued outliers

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