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

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.

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.