Multivariate Max-stable Processes with Application to the Forecasting of Multiple Hazards

Lead Research Organisation: University of Reading
Department Name: Mathematics and Statistics


Due to climate change, extreme meteorological phenomena such as heavy precipitation, extreme temperature, strong winds and sea level rise, seem to be growing more severe and frequent, but the actual estimation of this evolution in extreme weather events remains subject to large uncertainty. For example, in December 2015 when storm Desmond hit the UK, several communities were badly affected by water level rises. Rainfall in this storm crept up to new record levels and provided us with critical lessons on how we can better prepare to withstand similar hazards. However, these lessons learned are in hindsight. When looking at the occurrence probability of such an extreme event that out-spans the range of previously recorded data, Extreme Value Theory (EVT) is the most appropriate branch of probability theory to be implemented as risk assessment and forecasting have a strong probabilistic foundation. In many operational settings, risk mitigation measures are required to balance costs with safety. For example, in insuring systems and infrastructure against extreme events, it might not be enough to sift through extreme record events that emerge from historical data, but it would also be nonsensical to channel most resources into a safety system so robust that it would spectacularly exceed the actual risk being protected against. EVT offers an appropriate statistical toolkit for forecasting extreme outcomes to a high degree of accuracy, thus providing critical evidence for assessing risk more accurately in preparing a proportionate response.

There are varying layers of complexity in EVT enveloped in the recently introduced class of multivariate max-stable processes. These are promising models for the structural components that capture how extremes from multiple phenomena (hence the prefix multivariate) are likely to manifest themselves jointly across a certain region over time (hence the so-called space-time processes, also termed random fields). Real life applications abound in the multivariate infinite-dimensional max-stable processes frameworks. For example, the Fukushima nuclear disaster in 2011 was ignited by the combination of a huge earthquake followed by a tsunami.

The main goal of this research proposal is to develop a general theory for multivariate infinite-dimensional extremes (extremes of two or more random fields) that will culminate in the development of statistical methodology for modelling interactions of two or more related extreme events. Recent studies have found that there exists significant long-term impact of climate change on storms that combine wind speed and precipitation, deeming it critically important that any fragility analysis be conducted in such a way as to ensure probabilistic safety levels of a nuclear power plant for extreme weather events. For example, the sting jet phenomena often unleashes very extreme local wind speeds, heavy rainfall and extreme temperatures on a nuclear plant. This is therefore the first application area of the developed statistical methodology. It is intended that this research programme will not only lead to improvement in safety standards and operational reliability of the nuclear energy fleet but also carries with it the potential of reducing costs in expensive overprotection measures that could run into millions of pounds.
In addition to the nuclear energy sector other application areas will be explored. Energy supply and renewables power systems are so unwieldy that people are still trying to unravel some intriguing aspects of time dependent peak demands. The statistical methodology developed as part of this research programme will enable a better understanding to be gained of the characteristic features in smart-meter data, which will ultimately give people access to more affordable energy, providing more interaction and safety and thus more choice.

Planned Impact

An EPSRC Innovation Fellowship will help to establish a dedicated research program, which is uniquely positioned to tackle real world problems on rare events. While the immediate impact of the project will be academic (through the development of a rigorous probabilistic underpinning to the modelling of multiple hazards), this will be a crucial component in the pathway to industrial impact.
Following development of the methodology, the first users of the planned research are planned to be the nuclear industry. The nuclear energy sector is a major hazard industry and this proposed research programmes sits ideally within this context: forecasting the joint development of extreme weather events posing catastrophic threat is critically important in evaluating site installation and safety infrastructure. Nuclear power plants are subject to strict safety measures, being closely regulated by national nuclear safety authorities. The Office for Nuclear Regulation Strategic Plan (2016-2020) highlights ''the importance of engaging with the broader science and research community to improve understanding of known nuclear hazards and to gain insight into potential hazards and risks''. This research programme can improve the hazard characterisation used within EDF Energy, enabling more accurate and feasible risk estimation, which will in turn provide direct input to regulatory bodies worldwide and be of influence in advising on complex safety issues. In addition to specific application to the nuclear sector via EDF Energy, I will focus on profile raising and networking activities in the following areas:

1. Energy sector
Solar panels and electric batteries reduce pressure on the electricity grid, but the increasing number of electric vehicles and charging stations for these vehicles are pressuring the demand. Rarely, though inevitably, businesses and households may experience power outages. Understanding the interplay of solar radiation with electricity consumption will help to forecast peak energy demands. It is envisaged that this research proposal will assist SSE Scottish Southern Energy in designing fit-to-purpose solutions for meeting their target of a 10% reduction in the uncertainty in risk estimation of a power outage. The described activity can be used to assist other companies in the energy sector, such as Centrica and TenneT in identifying-cost effective energy efficient opportunities, reaching out to other providers with interest in batteries (Western Power).

2. Meteorological services
The statistical methodology developed as part of this research proposal, drawing on the semi-parametric estimation of a time-space trend in extreme outcomes, will be potentially useful in improving ensemble-based forecasts of extreme events which, in the current state-of-the-art Met Office's practice, tend to infer optimistically extreme occurrences. The main research findings in the analysis of extreme values can be a valuable resource in identifying and mapping those risk regions capable of generating similar extreme weather events. It will be possible to develop a systematic statistical procedure for mapping those regions with similar vulnerability to water level rise, whose implementation could feed into optimal alarm systems of flood-warning, particularly those aligned with the Met Office-National Severe Weather Warning Service. The proposed research programme tackles statistical estimation and testing for random fields at their extreme levels by drawing on data readings from sources scattered across different points (sites) within a region. Thus, there is potential to collaborate with the ECMWF-European Centre for Medium-range Weather Forecasts on their new probabilistic point-rainfall product for supporting the prediction of flash floods across the globe, and develop it further into the forecasting of various levels of storminess which involve the combination of strong winds with very heavy rainfall.


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Description The are two main discoveries as part of this funded programme of work, which are outlined as follows:

(i) New fundamental probability underpinning to the modelling of more than one extreme events at a time has been developed. This lead to a novel statistical methodology to tackle the modelling of extreme events whose frequency is evolving on the space-time domain due to an accelerating climate change.

(ii) Development of an interesting solution (with a firm probabilistic underpinning) to the challenging problem of selecting a non-stationary threshold for characterising extreme exceedances on a circular domain. Essential the proposed statistical methodology solved a critical problem identified in Forristall's paper (On the use of directional wave criteria, Journal of waterway, port, coastal, and ocean engineering, 2004) that a directional partitions is not compatible with the omni-directional approach.
Exploitation Route Likely uptake by applied sciences as there is accompanying software coupled with illustrative application to real-world data sets. This also ensures reproducibility of the research findings as part of this grant.
Sectors Energy,Environment

Title Statistical methodology for non-stationary multivariate extremes 
Description General functions for performing the extreme value analysis as part of the application in the paper "Spatial dependence and space-time trend in extremes" have been wholly implemented in R and are available at 
Type Of Technology New/Improved Technique/Technology 
Year Produced 2021 
Impact Reproducibility of the results with enhanced uptake by applied sciences, notably meteorology, energy systems modelling and ocean engineering. 
Title circularEV - Automatic selection of a non-stationary threshold for extreme values on a circular domain 
Description The R-package circularEV is made up of the code and data for reproducing the results for extreme value analysis on a circular domain as part of the statistical methodology in the paper by Konzen, E., Neves, C., and Jonathan, P. (2021). Modelling non-stationary extremes of storm severity: comparing parametric and semi-parametric inference. Environmetrics 
Type Of Technology New/Improved Technique/Technology 
Year Produced 2021 
Open Source License? Yes  
Impact This software has been designed in such a way as to be made fit-for-purpose to solve a challenging problem within ocean engineering context. It is currently being used by Philip Jonathan and their team of statistical and physical modellers working at Shell R&D. 
Description Research showcase meeting at SSE Networks, Reading 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Industry/Business
Results and Impact Meeting at SSE Networks for raising awareness to the recently developed work as part of the research project for this EPSRC UKRI Fellowship (technical report available at This meeting provided a valuable opportunity to consult with energy industry and receive input about impending applied developments for addressing operational needs.
Year(s) Of Engagement Activity 2020
Description Workshop Interfaces in extreme value theory 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact This workshop had strong industrial engagement, the main interest being in the modelling of hazards with potentially catastrophic impact to the nuclear energy fleet. The two talks I have given on the work developed as part of this EPSRC-UKRI award, encouraged my academic colleagues to reflect on the relative merits of different modelling approaches (both parametric and semi-parametric), potentially influencing their own practice. I received laudatory and enthusiastic feedback from Industrial representatives (EDF Energy and Shell) and was praised by attendees.
Year(s) Of Engagement Activity 2019