On the emergence of rainfall extremes from ordinary events

Zorzetto, Enrico; Botter, Gianluca; Marani, Marco

doi:10.1002/2016gl069445

Cited by 116 publications

(153 citation statements)

References 38 publications

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“…For very small samples with lengths below roughly 14 years, the GEV leads to unacceptably large errors of 200%, while the MEV provides useful estimations, even for the largest quantiles. These findings nicely corroborate results of Zorzetto et al (), who showed that the MEV outperforms the GEV even when a POT approach was used for fitting the GEV.…”

Section: Resultssupporting

confidence: 90%

“…For samples with more than 35 years, Figure indicates a slightly better performance of the GEV, albeit the improvement is only about 2.5%. Again this was also shown by Zorzetto et al (), where for larger return periods above ∼40 years, some evidence can be found that the GEV (fitted via POT) is slightly superior to the MEV.…”

Section: Resultssupporting

confidence: 80%

“…The cumulative distribution function of the distribution of block maxima is obtained by the use of the total probability theorem:

ζ false(x false) = true \sum_{n = 1}^{\infty} \int_{Ω_{\overset{Θ}{true}}} F {false(x; \overset{θ}{true} false)}^{n} g false(n, \overset{θ}{true} false) normald \overset{θ}{true} for x \in double-struckR

where

g false(n, \overset{θ}{true} false)

is the joint probability distribution of N and

\overset{Θ}{true}

and

Ω_{\overset{Θ}{true}}

is the set of all possible values of the parameters of the parent distribution. Following Zorzetto et al () and Wilson and Toumi (), we adopt the Weibull distribution

F false(x; C_{j}, w_{j} false) = 1 - \exp^{- {false(\frac{x}{C_{j}} false)}^{w_{j}}}

to model the ordinary rainfall events, that is, the nonzero daily rainfall in each year j =1,…, T , thereby, C j >0 is the scale and w j >0 the shape parameter , and compute a sample average approximation to based on T realizations of

false(\overset{Θ}{true}, N false)

F_{MEV} false(x; \overset{C}{true}, \overset{w}{true}, \overset{n}{true} false) = \frac{1}{T} true \sum_{j = 1}^{T} {([], 1 - \exp^{- {false(\frac{x}{C_{j}} false)}^{w_{j}}})}^{n_{j}} .

for

x \in double-struckR

, where

\overset{C}{true} = false(C_{1}, ⋯, C_{T} false)

and the same ap...…”

Section: Theoretical Frameworkmentioning

confidence: 99%

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Error Structure of Metastatistical and Generalized Extreme Value Distributions for Modeling Extreme Rainfall in Austria

Schellander

Lieb

Hell

2019

Earth and Space Science

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Incorrect estimation of extreme values of daily precipitation can have severe consequences in hydrological and engineering applications. Recent advances in the study of extreme precipitation have shown that the Metastatistical Extreme Value Distribution (MEV) is superior to the Generalized Extreme Value Distribution (GEV) whenever the length of the available record is small compared to the average recurrence time. This paper provides a detailed examination of the relative performance of MEV and GEV for both point estimates and spatial modeling. An analysis for a large number of sample years and return periods for daily precipitation in Austria shows that the MEV exceeds the GEV if the number of sample years is smaller, and the estimated return period is larger than 35 years. This advantage disappears almost entirely if the MEV is used for spatially smooth extreme value modeling instead of the GEV. However, the computational effort is drastically reduced in comparison to spatial modeling with the GEV if a simplified version of the MEV is used.

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Section: Resultssupporting

confidence: 90%

Section: Resultssupporting

confidence: 80%

“…The cumulative distribution function of the distribution of block maxima is obtained by the use of the total probability theorem:

ζ false(x false) = true \sum_{n = 1}^{\infty} \int_{Ω_{\overset{Θ}{true}}} F {false(x; \overset{θ}{true} false)}^{n} g false(n, \overset{θ}{true} false) normald \overset{θ}{true} for x \in double-struckR

where

g false(n, \overset{θ}{true} false)

is the joint probability distribution of N and

\overset{Θ}{true}

and

Ω_{\overset{Θ}{true}}

is the set of all possible values of the parameters of the parent distribution. Following Zorzetto et al () and Wilson and Toumi (), we adopt the Weibull distribution

F false(x; C_{j}, w_{j} false) = 1 - \exp^{- {false(\frac{x}{C_{j}} false)}^{w_{j}}}

false(\overset{Θ}{true}, N false)

F_{MEV} false(x; \overset{C}{true}, \overset{w}{true}, \overset{n}{true} false) = \frac{1}{T} true \sum_{j = 1}^{T} {([], 1 - \exp^{- {false(\frac{x}{C_{j}} false)}^{w_{j}}})}^{n_{j}} .

for

x \in double-struckR

, where

\overset{C}{true} = false(C_{1}, ⋯, C_{T} false)

and the same ap...…”

Section: Theoretical Frameworkmentioning

confidence: 99%

See 1 more Smart Citation

Error Structure of Metastatistical and Generalized Extreme Value Distributions for Modeling Extreme Rainfall in Austria

Schellander

Lieb

Hell

2019

Earth and Space Science

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show abstract

“…Recently proposed metastatistical extreme value (MEV) approaches do not require such a threshold, and are based on the statistical distribution of finite sample maxima, i.e., the probability distribution of the maximum value for a finite number of events (Marani and Ignaccolo , Zorzetto et al. ). In the MEV framework, the occurrence and size of future events, and the parameters of their distributions are treated as random variables which together imply a distribution for extremes.…”

Section: Introductionmentioning

confidence: 99%

Spatiotemporal prediction of wildfire size extremes with Bayesian finite sample maxima

Joseph

Rossi

Mietkiewicz

et al. 2019

Ecological Applications

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Wildfires are becoming more frequent in parts of the globe, but predicting where and when wildfires occur remains difficult. To predict wildfire extremes across the contiguous United States, we integrate a 30‐yr wildfire record with meteorological and housing data in spatiotemporal Bayesian statistical models with spatially varying nonlinear effects. We compared different distributions for the number and sizes of large fires to generate a posterior predictive distribution based on finite sample maxima for extreme events (the largest fires over bounded spatiotemporal domains). A zero‐inflated negative binomial model for fire counts and a lognormal model for burned areas provided the best performance. This model attains 99% interval coverage for the number of fires and 93% coverage for fire sizes over a six year withheld data set. Dryness and air temperature strongly predict extreme wildfire probabilities. Housing density has a hump‐shaped relationship with fire occurrence, with more fires occurring at intermediate housing densities. Statistically, these drivers affect the chance of an extreme wildfire in two ways: by altering fire size distributions, and by altering fire frequency, which influences sampling from the tails of fire size distributions. We conclude that recent extremes should not be surprising, and that the contiguous United States may be on the verge of even larger wildfire extremes.

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“…The GPDs for the construction of the MEVD are fitted on a 3‐year basis using PWMs as described earlier. Differently from other EVT applications (e.g., rainfall; see Zorzetto et al, ), in this case of extreme hurricanes, the MEVD uses, for parameter fitting, the same observational information used in the GEV‐POT approach: The thresholds used in the two approaches are both set at u = 33.4 m/s, slightly lower than thresholds used in Jagger and Elsner (). Differences in performance between the MEVD and the GEV distribution that may be found should thus be ascribed to the different underlying hypotheses, rather than to a more effective use of data.…”

Section: Methodsmentioning

confidence: 99%

Extreme Atlantic Hurricane Probability of Occurrence Through the Metastatistical Extreme Value Distribution

Hosseini

Scaioni

Marani

2020

Geophysical Research Letters

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The estimation of extreme hurricane probability is hampered by small samples and by limitations in our models of extreme tropical storms. Current best estimates of extreme hurricane probability based on the traditional extreme value theory assume hurricane arrivals to be a homogeneous Poisson process. We reformulate here, for application to Atlantic hurricanes, the Metastatistical Extreme Value Distribution (MEVD) that relaxes this key assumption in the traditional extreme value theory and uses all available observations. The MEVD application to the 1886–2017 observational record improves the accuracy of extreme Atlantic hurricane estimation by about 50% with respect to current best estimates. The MEVD allows trends to emerge above estimation uncertainty: A sliding‐window analysis shows a significant increase in extreme hurricane likelihood in the past century. This trend, previously uncertain and controversial, remains significant after correcting for hurricane underdetection in the presatellite era and when focusing only on the modern observational period (1970–2017).

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On the emergence of rainfall extremes from ordinary events

Cited by 116 publications

References 38 publications

Error Structure of Metastatistical and Generalized Extreme Value Distributions for Modeling Extreme Rainfall in Austria

Error Structure of Metastatistical and Generalized Extreme Value Distributions for Modeling Extreme Rainfall in Austria

Spatiotemporal prediction of wildfire size extremes with Bayesian finite sample maxima

Extreme Atlantic Hurricane Probability of Occurrence Through the Metastatistical Extreme Value Distribution

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