My PhD is titled ‘Extreme Value Methods for Protecting and Maintaining Critical Infrastructure from Natural Hazards’. Here I detail some of the projects I have worked on as part of my PhD, as well as anywhere I have presented this work.

Extreme Value Modelling for Maintenance Scheduling of Flood Barriers

Flood barriers located at estuaries close under two scenarios; when extreme storm surge conditions are observed to mitigate against coastal flooding, and during periods of high river flow to prevent fluvial flood events. The number of barrier closures has increased dramatically in recent years due to anthropogenic global warming resulting in sea level rise and more frequent freak weather events. However, the number of barrier closures per year is often restricted due to maintenance and safety checks. Our aim is to predict the life expectancy of such barriers to aid with planning necessary upgrades. We do so by simulating realistic time series of surge and river flow that reflect their extremal behaviour and the dependence between them.

River flow exhibits a unique temporal dependence structure, as the time series exhibits sudden extreme events resulting from large precipitation events that descend exponentially, as the large volume of water takes time to propagate down the river. We capture this using a non-stationary copula model. We also propose a seasonal marginal model for extreme river flow using a non-stationary generalised Pareto distribution (GPD). Extreme surges are also modelled using a non-stationary GPD and we model the dependence structure between these variables. This ensures barriers are robust to individual flood risks, as well as the co-occurrence of such extreme events.


  • Workshop on environmental and ecological extremes (Lancaster)

  • STOR-i Extremes Workshop (Lancaster)

Accounting for Seasonality in Extreme Sea Level Estimation

Storm surges pose an increasing risk to coastline communities. These events, combined with high tide, can result in coastal flooding. To reduce the impact of storm surges, an accurate estimate of coastal flood risk is necessary. Specifically, estimates are required for the return level of sea levels (still water), which is the level with annual exceedance probability p. This estimate is used as an input to determine the height for a coastal defence, such as a sea wall. The return level estimation requires statistical analysis based on extreme value theory, as we need to know about the frequency of events that are more extreme than those previously observed.

Large storm surges exhibit seasonality, they are typically at their worst in the winter and least extreme in the summer. This seasonal pattern differs from that of the tide, whose seasonality is driven astronomically, resulting in tidal peaks at the spring and autumn equinoxes. Hence, the worst levels of these two components of still water level are likely to peak at different times in the year, and so statistical methods that treat them as independent variables are likely to over-estimate return levels.

We focus on the skew surge: the difference between the observed and predicted high water within a tidal cycle. Williams et al. (2016) show that tide and skew surge are independent conditional on the time of year. Batstone et al. (2013) used this property to derive estimates used for UK coastal flood defences. They used generalised Pareto distributions for the skew surge tail but did not account for the separate seasonality of tide and skew surge.

This work aims to model how the distribution of skew surges changes over a year and we combine our results with the known seasonality of tides to derive estimates of still water level return levels. We compare our results with the Batstone et al. (2013) approach at a few locations on the UK coastline.


  • Batstone, C., Lawless, M., Tawn, J., Horsburgh, K., Blackman, D., McMillan, A., Worth, D., Laeger, S. and Hunt, T., 2013. A UK best-practice approach for extreme sea-level analysis along complex topographic coastlines. Ocean Engineering, 71, pp.28-39.
  • Williams, J., Horsburgh, K.J., Williams, J.A. and Proctor, R.N., 2016. Tide and skew surge independence: New insights for flood risk. Geophysical Research Letters, 43(12), pp.6410-6417.


  • EGU General Assembly 2021 (online)
    D’Arcy, E., Tawn, J., Joly-Laugel, A., and Sifnioti, D.: Accounting for Seasonality in Extreme Sea Level Estimation, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-12276,, 2021.

  • EVA 2021University of Edinburgh (online)

  • RSC in Probability and Statistics 2021 Lancaster University (online)
  • STEM for Britain final  2022 – Houses of Parliament, London
  • EVAN 2022 – University of Central Florida
  • CEDS 2022 – Lancaster University 
  • CMStatistics – Kings College London


  • EVA 2023 – Bocconi University


  • D’Arcy E., Tawn J. A .and Sifnioti D. E. (2022). Accounting for Climate Change in Extreme Sea Level Estimation. Water. 14(19):2956.

  • D’Arcy, E., Tawn, J.A., Joly, A. and Sifnioti, D.E., (2022). Accounting for seasonality in extreme sea level estimation. arXiv preprint:2207.09870

  • D’Arcy, E. and Tawn, J. A. (2021). Discussion of towards using state-of-the-art climate models to help constrain estimates of unprecedented UK storm surges (by Howard, T. and Williams, S. D. P.). Natural Hazards and Earth System Sciences Discussions. 

Wildfire Modelling

This paper details the methodology proposed by the Lancaster Ducks team for the EVA 2021 conference data challenge. This aim of this challenge was to predict the number and size of wildfires over the contiguous US between 1993-2015, with more importance placed on extreme events. Our approach proposes separate methods for modelling the bodies and tails of the distributions of both wildfire variables. For the former, a hierarchical clustering technique is proposed to first group similar locations, with a non-parametric approach subsequently used to model the non-extreme data. To capture tail behaviour, separate techniques derived from univariate extreme value theory are proposed for both variables. For the count data, a generalised Pareto distribution with a generalised additive model structure is used to capture effects from covariates on values above a high threshold. For burnt area, a non-stationary generalised Pareto distribution enables us to capture the tail behaviour of proportions obtained through a transformation of observed area data. The resulting predictions are shown to perform reasonably well, improving on the benchmark method proposed in the challenge outline. We also provide a discussion about the limitations of our modelling framework and evaluate ways in which it could be extended.



  • D’Arcy, E., Murphy-Barltrop, C.J.R., Shooter, R. and Simpson, E.S., 2021. A marginal modelling approach for predicting wildfire extremes across the contiguous United States. arXiv preprint arXiv:2112.15372.