Flood quantile estimation is of great importance for many engineering studies and policy decisions. However, practitioners must often deal with small data available. Thus, the information must be used optimally. In the last decades, to reduce the waste of data, inferential methodology has evolved from annual maxima modeling to peaks over a threshold one. To mitigate the lack of data, peaks over a threshold are sometimes combined with additional information - mostly regional and historical information. However, whatever the extra information is, the most precious information for the practitioner is found at the target site. In this study, a model that allows inferences on the whole time series is introduced. In particular, the proposed model takes into account the dependence between successive extreme observations using an appropriate extremal dependence structure. Results show that this model leads to more accurate flood peak quantile estimates than conventional estimators. In addition, as the time dependence is taken into account, inferences on other flood characteristics can be performed. An illustration is given on flood duration. Our analysis shows that the accuracy of the proposed models to estimate the flood duration is related to specific catchment characteristics. Some suggestions to increase the flood duration predictions are introduced.
Flood risk estimation via geometric extremal graphical models
STOR-i Centre for Doctoral Training, Lancaster University（兰卡斯特大学 STOR-i 博士培训中心）；School of Mathematical Sciences, Lancaster University（兰卡斯特大学数学科学学院）；Department of Mathematics, University of Oslo（奥斯陆大学数学系）
We re-consider Leadbetter's extremal index for stationary sequences. It has interpretation as reciprocal of the expected size of an extremal cluster above high thresholds. We focus on heavy-tailed time series, in particular on regularly varying stationary sequences, and discuss recent research in extreme value theory for these models. A regularly varying time series has multivariate regularly varying finite-dimensional distributions. Thanks to results by Basrak and Segers we have explicit representations of the limiting cluster structure of extremes, leading to explicit expressions of the limi…
We derive some key extremal features for $k$th order Markov chains that can be used to understand how the process moves between an extreme state and the body of the process. The chains are studied given that there is an exceedance of a threshold, as the threshold tends to the upper endpoint of the distribution. Unlike previous studies with $k>1$, we consider processes where standard limit theory describes each extreme event as a single observation without any information about the transition to and from the body of the distribution. Our work uses different asymptotic theory which results in no…
The hazard of pluvial flooding is largely influenced by the spatial and temporal dependence characteristics of precipitation. When extreme precipitation possesses strong spatial dependence, the risk of flooding is amplified due to catchment factors that cause runoff accumulation such as topography. Temporal dependence can also increase flood risk as storm water drainage systems operating at capacity can be overwhelmed by heavy precipitation occurring over multiple days. While transformed Gaussian processes are common choices for modeling precipitation, their weak tail dependence may lead to un…
With the use of empirical data, this paper focuses on solving financial and investment issues involving extremal dependence of ten pairwise combinations of the five BRICS (Brazil, Russia, India, China, and South Africa) stock markets. Daily closing equity indices from 5 January 2010 to 6 August 2018 are used in the study. Unlike previous literature, we use bivariate point process and conditional multivariate extreme value models to investigate the extremal dependence of the stock market returns. However, it is observed that the point process was able to model many more extreme observations or …
Hydrological post-processing using quantile regression algorithms constitutes a prime means of estimating the uncertainty of hydrological predictions. Nonetheless, conventional large-sample theory for quantile regression does not apply sufficiently far in the tails of the probability distribution of the dependent variable. To overcome this limitation that could be crucial when the interest lies on flood events, hydrological post-processing through extremal quantile regression is introduced here for estimating the extreme quantiles of hydrological model's responses. In summary, the new hydrolog…
Uncertainty in return level estimates for rare events, like the intensity of large rainfall events, makes it difficult to develop strategies to mitigate related hazards, like flooding. Latent spatial extremes models reduce uncertainty by exploiting spatial dependence in statistical characteristics of extreme events to borrow strength across locations. However, these estimates can have poor properties due to model misspecification: many latent spatial extremes models do not account for extremal dependence, which is spatial dependence in the extreme events themselves. We improve estimates from l…
In this chapter, we show how to efficiently model high-dimensional extreme peaks-over-threshold events over space in complex non-stationary settings, using extended latent Gaussian Models (LGMs), and how to exploit the fitted model in practice for the computation of long-term return levels. The extended LGM framework assumes that the data follow a specific parametric distribution, whose unknown parameters are transformed using a multivariate link function and are then further modeled at the latent level in terms of fixed and random effects that have a joint Gaussian distribution. In the extrem…
Multivariate extreme value models are used to estimate joint risk in a number of applications, with a particular focus on environmental fields ranging from climatology and hydrology to oceanography and seismic hazards. The semi-parametric conditional extreme value model of Heffernan and Tawn (2004) involving a multivariate regression provides the most suitable of current statistical models in terms of its flexibility to handle a range of extremal dependence classes. However, the standard inference for the joint distribution of the residuals of this model suffers from the curse of dimensionalit…
To disentangle the complex non-stationary dependence structure of precipitation extremes over the entire contiguous U.S., we propose a flexible local approach based on factor copula models. Our sub-asymptotic spatial modeling framework yields non-trivial tail dependence structures, with a weakening dependence strength as events become more extreme, a feature commonly observed with precipitation data but not accounted for in classical asymptotic extreme-value models. To estimate the local extremal behavior, we fit the proposed model in small regional neighborhoods to high threshold exceedances,…
Inference on the extremal behaviour of spatial aggregates of precipitation is important for quantifying river flood risk. There are two classes of previous approach, with one failing to ensure self-consistency in inference across different regions of aggregation and the other imposing highly restrictive assumptions. To overcome these issues, we propose a model for high-resolution precipitation data, from which we can simulate realistic fields and explore the behaviour of spatial aggregates. Recent developments have seen spatial extensions of the Heffernan and Tawn (2004) model for conditional …
Understanding the spatial extent of extreme precipitation is necessary for determining flood risk and adequately designing infrastructure (e.g., stormwater pipes) to withstand such hazards. While environmental phenomena typically exhibit weakening spatial dependence at increasingly extreme levels, limiting max-stable process models for block maxima have a rigid dependence structure that does not capture this type of behavior. We propose a flexible Bayesian model from a broader family of (conditionally) max-infinitely divisible processes that allows for weakening spatial dependence at increasin…
