Modelling Short- and Long-Term Dependencies of Clustered High-Threshold Exceedances in Significant Wave Heights

The peaks-over-threshold (POT) method has a long tradition in modelling extremes in environmental variables. However, it has originally been introduced under the assumption of independently and identically distributed (iid) data. Since environmental data often exhibits a time series structure, this assumption is likely to be violated due to short- and long-term dependencies in practical settings, leading to clustering of high-threshold exceedances. In this paper, we first review popular approaches that either focus on modelling short- or long-range dynamics explicitly. In particular, we consider conditional POT variants and the Mittag–Leffler distribution modelling waiting times between exceedances. Further, we propose a new two-step approach capturing both short- and long-range correlations simultaneously. We suggest the autoregressive fractionally integrated moving average peaks-over-threshold (ARFIMA-POT) approach, which in a first step fits an ARFIMA model to the original series and then in a second step utilises a classical POT model for the residuals. Applying these models to an oceanographic time series of significant wave heights measured on the Sefton coast (UK), we find that neither solely modelling short- nor long-range dependencies satisfactorily explains the clustering of extremes. The ARFIMA-POT approach, however, provides a significant improvement in terms of model fit, underlining the need for models that jointly incorporate short- and long-range dependence to address extremal clustering, and their theoretical justification.

Performance Evaluation of a Nowcasting Modelling Chain Operatively Employed in Very Small Catchments in the Mediterranean Environment for Civil Protection Purposes

The Hydro-Meteorological Centre (CMI) of the Environmental Protection Agency of Liguria Region, Italy, is in charge of the hydrometeorological forecast and the in-event monitoring for the region. This region counts numerous small and very small basins, known for their high sensitivity to intense storm events, characterised by low predictability. Therefore, at the CMI, a radar-based nowcasting modelling chain called the Small Basins Model Chain, tailored to such basins, is employed as a monitoring tool for civil protection purposes. The aim of this study is to evaluate the performance of this model chain, in terms of: (1) correct forecast, false alarm and missed alarm rates, based on both observed and simulated discharge threshold exceedances and observed impacts of rainfall events encountered in the region; (2) warning times respect to discharge threshold exceedances. The Small Basins Model Chain is proven to be an effective tool for flood nowcasting and helpful for civil protection operators during the monitoring phase of hydrometeorological events, detecting with good accuracy the location of intense storms, thanks to the radar technology, and the occurrence of flash floods.

Robust Management of Systemic Risks and Food-Water-Energy-Environmental Security: Two-Stage Strategic-Adaptive GLOBIOM Model

Critical imbalances and threshold exceedances can trigger a disruption in a network of interdependent systems. An insignificant-at-first-glance shock can induce systemic risks with cascading catastrophic impacts. Systemic risks challenge traditional risk assessment and management approaches. These risks are shaped by systemic interactions, risk exposures, and decisions of various agents. The paper discusses the need for the two-stage stochastic optimization (STO) approach that enables the design of a robust portfolio of precautionary strategic and operational adaptive decisions that makes the interdependent systems flexible and robust with respect to risks of all kinds. We established a connection between the robust quantile-based non-smooth estimation problem in statistics and the two-stage non-smooth STO problem of robust strategic–adaptive decision-making. The coexistence of complementary strategic and adaptive decisions induces systemic risk aversion in the form of Value-at-Risk (VaR) quantile-based risk constraints. The two-stage robust decision-making is implemented into a large-scale Global Biosphere Management (GLOBIOM) model, showing that robust management of systemic risks can be addressed by solving a system of probabilistic security equations. Selected numerical results emphasize that a robust combination of interdependent strategic and adaptive solutions presents qualitatively new policy recommendations, if compared to a traditional scenario-by-scenario decision-making analysis.