Eleanor D'Arcy

Max-autogressive moving average (Max-ARMA) processes are powerful tools for modelling time series data with heavy-tailed behaviour; these are a non-linear version of the popular autoregressive moving average models. River flow data typically have features of heavy tails and non-linearity, as large precipitation events cause sudden spikes in the data that then exponentially decay. Therefore, stationary Max-ARMA models are a suitable candidate for capturing the unique temporal dependence structure exhibited by river flows. This paper contributes to advancing our understanding of the extremal properties of stationary Max-ARMA processes. We detail the first approach for deriving the extremal index, the lagged asymptotic dependence coefficient, and an efficient simulation of a general Max-ARMA process. We use the extremal properties, coupled with the belief that Max-ARMA processes provide only an approximation to extreme river flow, to fit such a model which can describe key features of river flow behaviour over a high threshold. We make our inference under a reparametrisation which gives a simpler parameter space that excludes cases where any parameter is non-identifiable. We illustrate results for river flow data from UK rivers Thames and Lune, that exhibit different response characteristics to extreme rainfall events.

Coastal flooding is already one of the most dangerous and costly natural hazards that humanity faces globally and yet it will become even more frequent and challenging to manage because of climate change and other factors. In densely populated estuarine settings, a storm surge barrier is often an attractive and economical solution for flood protection. There are currently many storm surge barriers in operation around the world protecting tens of millions of people and trillions of pounds of property and infrastructure. However, with accelerating rates of sea-level rise being observed, along with changes in storminess, tides and river discharge, surge barriers are closing increasingly often, and closures are now occurring in months when they typically have not occurred in the past. Increased use of surge barriers in the future has critical implications for barrier management, maintenance and operation. In this paper we develop, validate and apply a novel statistical approach to assess how the number of storm surge barrier closures will likely increase in the future and change in frequency throughout the year, that can be used for different climate change scenarios and accounting for forecast errors in water levels. As representative case study examples, we focus on the Eastern Scheldt storm surge Barrier in the Netherlands and the Thames Barrier in the UK. We validate the method, demonstrating it accurately predicts past closure statistics for the Eastern Scheldt and the Thames Barriers over the 38 and 42 years they have been operational, respectively. Then we apply the method to estimate the potential future numbers of barrier closures considering a range of different projections of sea-level rise, along with changes in storm surges, tides and river discharge. We show that there is very likely to be a rapid acceleration in the number of barrier closures in the future, dominated by sea-level rise, with strong influence of the 18.6-year lunar nodal cycle, at both case study barriers. Finally, we illustrate how the tool can be used to help guide future barrier management, maintenance, operation and upgrade/replacement planning and inform adaptative flood management approaches. The tool we have developed could easily be extended to other storm surge barriers around the world.

Max-autogressive moving average (Max-ARMA) processes are powerful tools for modelling time series data with heavy-tailed behaviour; these are a non-linear version of the popular autoregressive moving average models. River flow data typically have features of heavy tails and non-linearity, as large precipitation events cause sudden spikes in the data that then exponentially decay. Therefore, stationary Max-ARMA models are a suitable candidate for capturing the unique temporal dependence structure exhibited by river flows. This paper contributes to advancing our understanding of the extremal properties of stationary Max-ARMA processes. We detail the first approach for deriving the extremal index, the lagged asymptotic dependence coefficient, and an efficient simulation for a general Max-ARMA process. We use the extremal properties, coupled with the belief that Max-ARMA processes provide only an approximation to extreme river flow, to fit such a model which can broadly capture river flow behaviour over a high threshold. We make our inference under a reparametrisation which gives a simpler parameter space that excludes cases where any parameter is non-identifiable. We illustrate results for river flow data from the UK River Thames.

Max-autogressive moving average (Max-ARMA) processes are powerful tools for modelling time series data with heavy-tailed behaviour; these are a non-linear version of the popular autoregressive moving average models. River flow data typically have features of heavy tails and non-linearity, as large precipitation events cause sudden spikes in the data that then exponentially decay. Therefore, stationary Max-ARMA models are a suitable candidate for capturing the unique temporal dependence structure exhibited by river flows. This paper contributes to advancing our understanding of the extremal properties of stationary Max-ARMA processes. We detail the first approach for deriving the extremal index, the lagged asymptotic dependence coefficient, and an efficient simulation for a general Max-ARMA process. We use the extremal properties, coupled with the belief that Max-ARMA processes provide only an approximation to extreme river flow, to fit such a model which can broadly capture river flow behaviour over a high threshold. We make our inference under a reparametrisation which gives a simpler parameter space that excludes cases where any parameter is non-identifiable. We illustrate results for river flow data from the UK River Thames.

This paper details a methodology proposed for the EVA 2021 conference data challenge. The aim of this challenge was to predict the number and size of wildfires over the contiguous US between 1993 and 2015, with more importance placed on extreme events. In the data set provided, over 14% of both wildfire count and burnt area observations are missing; the objective of the data challenge was to estimate a range of marginal probabilities from the distribution functions of these missing observations. To enable this prediction, we make the assumption that the marginal distribution of a missing observation can be informed using non-missing data from neighbouring locations. In our method, we select spatial neighbourhoods for each missing observation and fit marginal models to non-missing observations in these regions. For the wildfire counts, we assume the compiled data sets follow a zero-inflated negative binomial distribution, while for burnt area values, we model the bulk and tail of each compiled data set using non-parametric and parametric techniques, respectively. Cross validation is used to select tuning parameters, and the resulting predictions are shown to significantly outperform the benchmark method proposed in the challenge outline. We conclude with a discussion of our modelling framework, and evaluate ways in which it could be extended.

This paper details a methodology proposed for the EVA 2021 conference data challenge. The aim of this challenge was to predict the number and size of wildfires over the contiguous US between 1993 and 2015, with more importance placed on extreme events. In the data set provided, over 14\% of both wildfire count and burnt area observations are missing; the objective of the data challenge was to estimate a range of marginal probabilities from the distribution functions of these missing observations. To enable this prediction, we make the assumption that the marginal distribution of a missing observation can be informed using non-missing data from neighbouring locations. In our method, we select spatial neighbourhoods for each missing observation and fit marginal models to non-missing observations in these regions. For the wildfire counts, we assume the compiled data sets follow a zero-inflated negative binomial distribution, while for burnt area values, we model the bulk and tail of each compiled data set using non-parametric and parametric techniques, respectively. Cross validation is used to select tuning parameters, and the resulting predictions are shown to significantly outperform the benchmark method proposed in the challenge outline. We conclude with a discussion of our modelling framework, and evaluate ways in which it could be extended.

Extreme sea level estimates are fundamental for mitigating coastal flooding as they provide insight for defence engineering. As the global climate changes, rising sea levels combined with increases in storm intensity and frequency pose an increasing risk to coastline communities. We present a new method for estimating extreme sea levels that accounts for the effects of climate change on extreme events that are not accounted for by mean sea level trends. We follow a joint probabilities methodology, considering skew surge and peak tides as the only components of sea levels. We model extreme skew surges using a non-stationary generalised Pareto distribution (GPD) with covariates accounting for climate change, seasonality and skew surge–peak tide interaction. We develop methods to efficiently test for extreme skew surge trends across different coastlines and seasons. We illustrate our methods using data from four UK tide gauges and estimate sea level return levels when accounting for these long-term trends.

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.References: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.