# Preface: Advances in extreme value analysis and application to natural hazards

Yasser Hamdi, Ivan Haigh, Sylvie Parey, Tomas Wahl

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Yasser Hamdi, Ivan Haigh, Sylvie Parey, Tomas Wahl. Preface: Advances in extreme value analysis and application to natural hazards. Natural Hazards and Earth System Sciences, 2021, 21 (5), pp.1461-1465. 10.5194/nhess-21-1461-2021. hal-03397624

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# Preface: Advances in extreme value analysis and application to natural hazards

Yasser Hamdi<fnref n="1" />, Ivan D. Haigh<fnref n="2" />, Sylvie Parey<fnref n="3" />, and Thomas Wahl<fnref n="4" />

**Correspondence:** Yasser Hamdi (yasser.hamdi@irsn.fr)

Published: 10 May 2021

Natural extreme events are infrequently observed events that occur with low probability, often referred to as rare or exceptional events that have widespread impact and devastating economic and social consequences. Natural extreme events encompass hazards such as floods, hurricanes, extreme temperatures and heat spells, earthquakes, tsunamis, and debris flows. Extreme value analysis (EVA) refers to efforts to characterize a hazard by estimating the intensity and the frequency of occurrence of the event. Statistically speaking, EVA is the branch of statistics dealing with the extreme deviations from the mean or the median of probability distributions. It seeks to assess, from a given sample of a random variable, the probability of a certain extreme value of the variable to occur. Such analysis may include a wide range of approaches, including, most notably, frequentist and Bayesian statistical models derived from historical event data in order to describe the behavior of extreme values. The estimation of the frequency of occurrence of extreme events using probability functions has been a common issue for many decades (e.g., Dalrymple, 1960; Cunnane, 1987; Haigh et al., 2016; Wahl et al., 2017; Hamdi et al., 2019; Parey et al., 2019).

Engineers, for example, generally need to determine the extreme value of a given return period *T*, i.e., the quantile $X_T$ or design value. For instance, EVA is widely used in the field of hydrology to estimate the probability of an unusually large flooding event, such as the 100-year flood. Similarly, for the design of a protection structure against coastal flooding, a coastal engineer would seek to estimate the 100-year storm

surge, or similar. Traditional methods for analyzing and estimating the frequency of extreme events have been generally based on available local observations from the systematic record alone. However, it seems that these methods are not really suitable for relatively short data sets often characterized by the presence of gaps. This is just one of the challenges the EVA community is facing; others include, for example, the incorporation of non-stationarity, multiple correlated variables or hazards, and spatial and temporal clustering.

The fourth biennial Advances in Extreme Value Analysis and Application to Natural Hazards (EVAN) international conference was organized in Paris from 17 to 19 September 2019 and followed earlier conferences in Germany (2013), Spain (2015), and Southampton (2017). The conference brought together research scientists, students, practitioners, and stakeholders concerned with the complex and inter-disciplinary topic of natural hazard characterization. The conference was organized around the theme of extreme value analysis, covering a wide range of geophysical variables (flows, rainfall, snow, temperature, winds, sea level, storm surge, surface ocean waves, etc.) and development and description of probabilistic approaches useful in natural hazard characterization. The topics covered at the EVAN conference included univariate and multivariate extreme value analysis, local and regional frequency/Bayesian analysis, stationary and non-stationary extreme value analysis, multi-hazard risk analysis and compound effects, spatial analysis, extreme value analysis from a climate perspective,

<footnote n="1">¹Institute for Radiological Protection and Nuclear Safety, Fontenay-aux-Roses, France</footnote>

<footnote n="2">²School of Ocean and Earth Sciences, National Oceanography Centre,
University of Southampton, European Way, Southampton, UK</footnote>

<footnote n="3">³EDF R & D, Saclay, France</footnote>

<footnote n="4">⁴Department of Civil, Environmental, and Construction Engineering, National Center for Integrated Coastal Research,
University of Central Florida, Orlando, USA</footnote>
<table><caption>**Table 1.** The special issue thematic areas.</caption><thead><tr><th>Paper</th><th>Regional/ spatial</th><th>Non- stationary</th><th>Multivariate</th><th>Probabilistic/ risk evaluation</th><th>Multi-hazard/ compound effects</th><th>From climate perspective</th></tr></thead><tbody><tr><td>Turki et al. (2020)</td><td>X</td><td>X</td><td></td><td></td><td></td><td>X</td></tr><tr><td>Kudryavtseva et al. (2021)</td><td></td><td>X</td><td></td><td></td><td>X</td><td></td></tr><tr><td>Jane et al. (2020)</td><td>X</td><td></td><td>X</td><td></td><td>X</td><td></td></tr><tr><td>Le Roux et al. (2020)</td><td></td><td>X</td><td></td><td>X</td><td></td><td></td></tr><tr><td>Orcel et al. (2021)</td><td></td><td></td><td>X</td><td></td><td>X</td><td></td></tr><tr><td>Ben Daoued et al. (2020)</td><td></td><td></td><td></td><td>X</td><td>X</td><td></td></tr><tr><td>Tilloy et al. (2020)</td><td></td><td></td><td>X</td><td>X</td><td>X</td><td></td></tr><tr><td>Lu et al. (2020)</td><td>X</td><td></td><td></td><td>X</td><td></td><td></td></tr><tr><td>Ji et al. (2020)</td><td>X</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Rohmer et al. (2020)</td><td></td><td>X</td><td></td><td>X</td><td></td><td></td></tr><tr><td>Stephens et al. (2020)</td><td>X</td><td></td><td></td><td></td><td>X</td><td></td></tr><tr><td>Luo et al. (2020)</td><td>X</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Andreevsky et al. (2020)</td><td>X</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Pecelj et al. (2020)</td><td>X</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Fu et al. (2020)</td><td>X</td><td></td><td></td><td>X</td><td></td><td></td></tr></tbody></table>

estimation of aleatory and epistemic uncertainties, and probabilistic risk analysis.

The main objective of this special issue is to provide an overview of the different perspectives on this complex and inter-disciplinary topic from research scientists, students, practitioners, and stakeholders who participated in the conference. It outlines the breadth of methods currently used for analyzing and estimating the extreme events to characterize natural hazards. This special issue encompasses 15 papers, all based on talks given at the fourth EVAN conference. A common objective of the contributions to this special issue is to characterize natural hazards by conducting frequency/Bayesian analysis of extreme events to establish a relationship between the magnitude and frequency of occurrence (return period) of these extreme events and for estimating the design value (the r-year return level) at a given location of interest.

The special issue summarized herein has been grouped under seven thematic areas of the statistics of extreme events.

1. *Regional/spatial information.* This approach is used to mitigate the paucity of data and the influence of outliers. A regional frequency analysis model assumes a homogenous behavior of the variable of interest at a regional scale.

2. *Non-stationary statistical modeling.* Estimating extreme values and associated uncertainties under the non-stationary assumption is a key research question, since the extreme value theory is often used to assess risks in the context of climate change.

3. *Multivariate analysis.* This includes the extension of univariate models to incorporate multiple variables.

4. *Probabilistic.* Many scenarios are used and injected to assess risk.

5. *Multi-hazard/compound effects.* The combination of two or more hazards/drivers in the analysis.

6. *From a climate perspective.* This includes all aspects of climate change, incorporated into EVA.

Table 1 summarizes all the papers published in the special issue according to these seven themes. Overall, the papers illustrate the multi-disciplinary composition of the special issue and multi-disciplinary aspects related to EVA in the context of natural hazard research.

Table 1 shows that the approaches proposed in this special issue were implemented locally (at-site frequency analysis) (most of the papers) or regionally (regional frequency analysis), which is used to limit unreliable extrapolation when available data record lengths are short compared to the recurrence interval of interest (Andreevsky et al., 2020), or for predicting extremes at locations where no observed data are available.

Extreme value characterization needs long and homogeneous time series, which do not exist for some variables and/or geographical areas. In such cases, it may be interesting to use gridded or reanalysis products. However, these products are produced with spatial interpolations or climate model assimilation techniques and may present biases, especially for the highest values. Luo et al. (2020) compared four bias correction approaches applied to the Asian Precipitation Highly Resolved Observational Data Integration Towards Evaluation of Water Resources (APHRODITE) data set in order to study extreme precipitation in the Yarlung Tsangpo-Brahmaputra River basin. The analysis of the risk associated with extreme temperatures and heat waves was
also part of this special issue. In order to characterize the
biothermal heat hazard, Pecelj et al. (2020) assessed the bio-
climatic conditions in Serbia during summer. The driver used
in this study is the bioclimatic index UTCI (Universal Ther-
mal Climate Index). Thresholds of this driver were compared
to those of daily maximum air temperatures. The heat wave
events which occurred in 2007, 2012, 2015, and 2017 in Ser-
bia were used as case studies. Most of these events were
of the longest durations and are considered to be the indi-
cators of biothermal heat hazard. It was concluded that the
UTCI associated with very strong heat stress can be consid-
ered a good indicator of heat waves. By using southwestern
China as a case study, Ji et al. (2020) evaluated the formation
and impact of debris flows using their susceptibility factor. A
large number of typical debris flow gullies, distributed along
five rivers, were evaluated to predict the susceptibility to de-
bris flows through the establishment of a factor index sys-
tem using nine indexes. The authors then developed a Type I
quantification-theory-based model to predict the debris flows
susceptibility factors. The reliability of the proposed model
was analyzed using 10 debris flow gullies upstream of the
Dadu River. The comparison of predicted and measured ac-
tual susceptibility shows that the model is right in 90% of
cases.

Despite the fact that both local and regional frequency
analyses are mature disciplines and consolidated methodolo-
gies are available in the literature, Andreevsky et al. (2020)
proposed a distinctive and interesting aspect in the regional
frequency analysis. The authors use the spatial extremogram
technique to form physically and statistically homogeneous
regions centered on the target site. It quantifies the pairwise
closeness between sites based on the extremal dependence
between a given target site and all the other sites in the whole
region.

As is mentioned earlier, almost all the papers included
in this special issue have opted for the local analysis but
are applied at different stations. As can be seen in Table 1,
four papers deal with non-stationary extreme value analy-
sis. Turki et al. (2020) investigated the nonstationary dy-
namics of extreme surges along the English Channel coasts
to gain insights into the physical mechanisms relating the
global atmospheric circulation to the local-scale variability
of extreme surges. It was concluded that this relation signifi-
cantly improves the perdition of extremes, with 30 % exhibit-
ing their non-linear relationship with climate mechanisms.
Kudryavtseva et al. (2021) assessed the non-stationarity of
extreme water levels in the eastern Baltic Sea with a par-
ticular focus on the Gulf of Riga. The analysis uses tide
gauge observations from 1961 to 2018 and the block max-
ima method to identify extreme events. The authors then an-
alyze the changes in the parameters of the generalized ex-
treme value (GEV) distribution through time. Changes in lo-
cation and scale parameters are found to be coherent in the
Gulf of Riga with linear upward trends but are different from
the Baltic proper, where one station was also included in the

study. The shape parameter shows significant variation, with
a pronounced dip in the late 1980s indicating a change from
a Fréchet to Weibull distribution.

Minimizing the risk of structure collapse in many high-
latitude areas worldwide requires an assessment of extreme
snow loads. Le Roux et al. (2020) utilized non-stationary
extreme value models to analyze trends in the 50-year re-
turn level of ground snow load for the French Alps. Their
results show a temporal decrease in the 50-year return lev-
els of snow load between 1959 and 2019. However, despite
these reductions, levels still exceed return levels designed
for French building standards under a stationary assumption.
The magnitude-frequency relation can also be established
by using a probabilistic risk assessment approach. Rohmer
et al. (2020) present a “seismic probabilistic safety assess-
ments” which was performed at the level of a nuclear power
plant. This approach used non-stationary frequency estima-
tions as boundary conditions of a dynamic model to com-
pute hazard and fragility curves. It provides a comprehensive
framework for assessing extremes in different fields of en-
vironmental studies. The main strength of the paper is that it
covers a large number of EVA fields and features. Indeed, the
approach uses frequency estimations and can be extended to
a Bayesian inference to better estimate uncertainties. Further-
more, it can be implemented locally in univariate and multi-
variate contexts, and the approach uses both stationary and
non-stationary variables.

As was mentioned earlier, the special issue also aimed to
promote probabilistic approaches useful in natural hazard
characterization in a multi-hazard context and considering
compounding effects. As shown in Table 1, several contribu-
tions in this special issue deal with probabilistic hazard ap-
proaches (e.g., Le Roux et al., 2020; Ben Daoued et al., 2020;
Tilloy et al., 2020; Lu et al., 2020; Rohmer et al., 2020; Fu
et al., 2020) and multi-hazard risk evaluation with compound
effects (Stephens et al., 2020). Ben Daoued et al. (2020) de-
veloped a new method for modeling dependence and coinci-
dence of extreme storm surges with high tide, using the city
of Le Havre in France as a case study. Their paper highlights
a bias in the maximum instantaneous storm surge-based pro-
cedure compared to the direct statistics on sea levels, and
this bias is more important for high return periods. The study
concluded that an appropriate coincidence probability con-
cept, considering the dependence structure between extreme
storm surges, is needed for a better assessment of the risk.
Based on a case study, Lu et al. (2020) suggested a method
for a quantitative assessment of the risk linked to landslides
for highways. The method uses an analysis of the annual fail-
ure probability of the slope, combined with empirical corre-
lations with the geometry of the slope, in order to assess the
consequences based on a probabilistic modeling of the traf-
fic on the highway. This approach, developed using a case
study in Hong Kong, can be adapted to other regions. Fu
el al. (2020) used a scenario-based probabilistic approach to
evaluate the risk associated with the landslide hazard and to
estimate spatial, temporal, and size probabilities. The spa-
tial probabilities (calculated from susceptibility mapping) al-
lowed the identification of the major controlling factors in the
study area (western Hubei, China). The analysis of the haz-
ard maps revealed that most building areas are at the foot of
major slopes with very high hazard probabilities. It was then
concluded that more than 1500 people and USD 18 million
worth of property are threatened by landslides (i.e., a 50-year
return level equivalent to a landslide volume of 50 000 m³).

In the contribution on compound effects and using tide
gauge data from 1900 onwards, Stephens et al. (2020) iden-
tify 85 extreme sea level events and 135 extreme skew surge
events, which are then considered for a spatiotemporal anal-
ysis along the coastline of New Zealand. Their findings high-
light that most extreme sea level events are the result of
moderate skew surges and high perigean spring tides and
that events are typically at least 10 d apart because of the
spring-neap cycle. They also identified the parts of the coun-
try where extreme events are more likely to occur (such as
the east coast of the North Island) and assessed the role of
seasonality, including mean sea level anomalies.

The final three contributions also deal with compound ef-
fects and hazard drivers but in a multivariate extreme value
analysis context and by considering the structure of the de-
pendence between the explanatory variables or drivers. In-
deed, as was mentioned earlier, extreme events may result
from a combination of different drivers which can present
various types of dependence. Jane et al. (2020) analyzed the
dependence structure between the principal flooding drivers
at three locations across Miami-Dade County in southeast
Florida. They identified the best-performing models for cap-
turing the dependence between the principal drivers of com-
pound flooding which leads to recommendations for revised
future design frameworks. Orcel et al. (2021) introduce a
copula-based approach to overcome the limitations in the
widely applied DEFRA (UK Department for Environment,
Food and Rural Affairs) method when assessing joint proba-
bilities between multiple variables. Their proposed approach
first identifies the most suitable bivariate copula which is fit
to the variable pairs with the strongest dependence, before
the function is extended to the trivariate case, and proof is
provided that this function satisfies the mathematical prop-
erties of the copula. Tilloy et al. (2020) evaluate six distinct
bivariate modeling approaches in a framework that consid-
ers 60 synthetic data sets. The results indicate that no sin-
gle approach leads to the best results for all data sets con-
sidered, but rather highlights the strengths and weaknesses
of the different approaches, depending on the application at
hand. Two real-world data sets are also included to demon-
strate that the modeling approaches selected from the sys-
tematic framework lead to good results.

Overall, the paper collection in this special issue provides
a starting point for solving some of the most critical chal-
lenges surrounding EVA and its application to assess a wide
range of natural hazards. The EVAN conference series will

continue to provide a platform for scientists and practitioners
to engage in conversations and initiate collaborations which
ultimately benefit our society; the fifth conference will take
place in Miami in 2022 and we hope to see you there. We
would like to thank all the authors and reviewers who were
involved in this special issue, and we hope you enjoy reading
it.

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