Renato Vitolo

University of Exeter | UoE · College of Engineering, Mathematics and Physical Sciences

Tropical cyclones have been a major cause of reef coral decline during recent decades, including on the Great Barrier Reef (GBR). While cyclones are a natural element of the disturbance regime of coral reefs, the role of temporal clustering has previously been overlooked. Here, we examine the consequences of different types of cyclone temporal dist...

This article examines whether the temporal clustering of flood events can be explained in terms of climate variability or time‐varying land‐surface state variables. The point process modelling framework for flood occurrence is based on Cox processes, which can be represented as Poisson processes with randomly varying rate of occurrence. In the spec...

Het onvoorspelbare venijn van de staart De statistische theorie van extreme waarden biedt een handvat voor de studie van meteorolo-gische extremen zoals orkanen en hittegolven. De klassieke theorie voor extreme waarden richt zich op onafhankelijke stochasten, later uitgebreid naar afhankelijke (bijvoorbeeld tijdsgecor-releerde) stochasten. Een rece...

This study aims at quantifying the most important factors affecting variations in downward surface shortwave radiation (DSW) in Europe including cloud cover and atmospheric circulation patterns. The role of observed cloud cover on DSW was analyzed through generalized linear models using DSW measurements obtained from the Global Energy Balance Archi...

Extreme value theory in deterministic systems is concerned with unlikely large (or small) values of an observable evaluated along evolutions of the system. In this paper we study the finite-time predictability of extreme values, such as convection, energy, and wind speeds, in three geophysical models. We study whether finite-time Lyapunov exponents...

This paper investigates the long-term variability of specific weather types that are associated with damaging hailstorms in Germany for past (1971-2000) and future (2011-2050) time periods. Forty large-scale weather types are determined by the objective weather type classification scheme of German Weather Service. This scheme is applied to both rea...

Tipping points associated with bifurcations (B-tipping) or induced by noise (N-tipping) are recognized mechanisms that may potentially lead to sudden climate change. We focus here on a novel class of tipping points, where a sufficiently rapid change to an input or parameter of a system may cause the system to 'tip' or move away from a branch of att...

Extreme value theory for chaotic dynamical systems is a rapidly expanding area of research. Given a system and a real function (observable) defined on its phase space, extreme value theory studies the limit probabilistic laws obeyed by large values attained by the observable along orbits of the system. Based on this theory, the so-called block maxi...

Tropical cyclones have massive economic, social, and ecological impacts, and models of their occurrence influence many planning activities from setting insurance premiums to conservation planning. Most impact models allow for geographically varying cyclone rates but assume that individual storm events occur randomly with constant rate in time. This...

Observations and model studies provide ample evidence for the presence of multidecadal variability in the North Atlantic sea-surface temperature known as the Atlantic Multidecadal Oscillation (AMO). This variability is characterised by a multidecadal time scale, the westward propagation of temperature anomalies, and a phase difference between the a...

Infinite cascades of periodicity hubs were predicted and very recently observed experimentally to organize stable oscillations of some dissipative flows. Here we describe the global mechanism underlying the genesis and organization of networks of periodicity hubs in control parameter space of a simple prototypical flow, namely a Rössler's oscillato...

Annual maximum daily rainfall time series from 221 rain gages in the Midwest United States with a record of at least 75 years are used to study extreme rainfall from a regional perspective. The main topics of this study are: (i) seasonality of extreme rainfall; (ii) temporal stationarity and long-term persistence of annual maximum daily rainfall; (...

This paper first summarizes the theory of quasi-periodic bifurcations for dissipative dynamical systems. Then it presents algorithms for the computation and continuation of invariant circles and of their bifurcations. Finally several applications are given for quasiperiodic bifurcations of Hopf, saddle-node and period-doubling type. Keywordsbifurc...

This paper provides an overview of the universal study of families of dynamical systems undergoing a Hopf-Neĭmarck-Sacker bifurcation as developed in [1–4]. The focus is on the local resonance set, i.e., regions in parameter space for which periodic dynamics occurs. A classification of the corresponding geometry is obtained by applying Poincaré-Tak...

High resolution dynamical models of the global climate system - such as HiGEM and NUGAM, developed through the UK High Resolution Global Environmental Modelling (HiGEM) project and the UK Japan Climate Collaboration (UJCC) - are able to simulate important aspects of extreme weather events in a global climate context. This ability holds value for th...

This paper focuses on the parametric abundance and the ’Cantorial’ persistence under perturbations of a recently discovered class of strange attractors for diffeomorphisms, the so-called quasi-periodic Hénon-like. Such attractors were first detected in the Poincaré map of a periodically driven model of the atmospheric flow: they were characterised...

Dynamical phenomena are studied near a Hopf-saddle-node bifurcation of fixed points of 3D-diffeomorphisms. The interest lies in the neighbourhood of weak resonances of the complex conjugate eigenvalues. The 1 : 5 case is chosen here because it has the lowest order among the weak resonances, and therefore it is likely to have a most visible influenc...

This paper studies the dynamical mechanisms potentially involved in the so-called atmospheric low-frequency variability, occurring at midlatitudes in the Northern Hemisphere. This phenomenon is characterised by recurrent non-propagating and temporally persistent flow patterns, with typical spatial and temporal scales of 6000–10 000 km and 10–50 day...

The spatial and temporal structure of rainfall is fundamental for correctly assess the flood hazard and risk of large areas. The occurrence of multiple catastrophic events within a given time span affecting the same portfolio of insured properties may induce enhanced loss. Therefore in the insurance industry it is of interest to characterize not on...

We propose a new approach to the creation of a stochastic event set for tropical cyclone risk assessment in West Pacific, for use in the insurance industry in the catastrophe modelling process. The event set is based on both available observational data and a database of tropical cyclones dynamically simulated by a state-of-the-art Global Climate M...

Risk assessment, in the form if catastrophe modelling, is used by the insurance industry to estimate potential loss from hazardous events, such as tropical cyclones (TCs). Probability distributions of potential loss are generated using available information about the location, severity and frequency of the hazard in question, coupled with informati...

We investigate the spatial dependence of and the large-scale atmospheric and climatic effects on the clustering of tropical cyclones in the North Atlantic Ocean. Tropical cyclone tracks from the HURDAT database are examined. We study the transit of tropical cyclones near points belonging to a grid covering the North Atlantic Ocean. Clustering is ch...

Following several recent, large-scale flood events in the UK (including central and eastern England in Easter 1998; northern England in autumn 2000; northern and central England in 2007; and Scotland and northern England in 2009), research to explain their occurrence has shifted away from "searching for a trend". Instead, new studies have demonstra...

This paper introduces the notion of robust extremes in deterministic chaotic systems, presents initial theoretical results, and outlines associated inferential techniques. A chaotic deterministic system is said to exhibit robust extremes under a given observable when the associated statistics of extreme values depend smoothly on the system's contro...

This paper deals with families of planar diffeomorphisms undergoing a Hopf–Neĭmarck–Sacker bifurcation and focuses on bifurcation diagrams of the periodic dynamics. In our universal study the corresponding geometry is classified using Lyapunov–Schmidt reduction and contact-equivalence singularity theory, equivariant under an appropriate cyclic grou...

This study has investigated how the clustering of wintertime extra-tropical cy-clones depends on the vorticity intensity of the cyclones, and the sampling time period over which cyclone transits are counted. Clustering is characterized by the dispersion (ratio of the variance and the mean) of the counts of eastward transits of cyclone tracks obtain...

The possibility that multiple catastrophic events occur within a given timespan and affect the same portfolio of insured properties may induce enhanced risk. For this reason, in the insurance industry it is of interest to characterise not only the point probability of catastrophic events, but also their spatial structure. As far as floods are conce...

This study aims at quantifying the most important factors for the decadal variations in the surface shortwave downward radiation. With reports describing global variations of this radiation parameter using surface and satellite-derived measurements, emphasis has recently been placed on regional studies to further understand the mechanisms that are...

Low-frequency behaviour is investigated in a low-order atmospheric model derived from the 2-layer shallow water equations on a β-plane channel with bottom topography. The low-order model has a 46-dimensional state space and is obtained from the shallow water equations by a Galerkin projection retaining only the Fourier modes with lowest wave number...

A chaotic deterministic system is said to exhibit robust extremes under an observable when the associated extreme value statistics depend smoothly on the system's control parameters. Such robustness can be exploited to enhance the precision and accuracy of statistical estimators of extreme value distributions. It is conjectured here that robust cha...

Natural catastrophes are particularly threatening for the insurance industry when they occur in temporal clusters, that is groups of events within a short time period. We present work combining knowledge and techniques from two distinct disciplines, hydrology and meteorology, to explore the role of large-scale atmospheric flow patterns in the tempo...

ABSTRACTA statistical methodology is proposed and tested for the analysis of extreme values of atmospheric wave activity at mid-latitudes. The adopted methods are the classical block-maximum and peak over threshold, respectively based on the generalized extreme value (GEV) distribution and the generalized Pareto distribution (GPD). Time-series of t...

A model map $Q$ for the Hopf-saddle-node (HSN) bifurcation of fixed points of diffeomorphisms is studied. The model is constructed to describe the dynamics inside an attracting invariant two-torus which occurs due to the presence of quasi-periodic Hopf bifurcations of an invariant circle, emanating from the central HSN bifurcation. Resonances of th...

The understanding of atmospheric and oceanic low-frequency variability is an old problem having both theoretical interest and practical importance, e.g., for the assessment of climate change. In this paper possible relations with dynamical systems theory are given, in particular through bifurcation theory. Firstly, a specific type of oceanic low fr...

The dynamics near a Hopf saddle-node bifurcation of fixed points of diffeomorphisms is analysed by means of a case study: a two-parameter model map G is constructed, such that at the central bifurcation the derivative has two complex conjugate eigenvalues of modulus one and one real eigenvalue equal to 1. To investigate the effect of resonances, th...

A quasi-geostrophic intermediate complexity model of the mid-latitude atmospheric circulation is considered, featuring simplified baroclinic conversion and barotropic convergence processes. The model undergoes baroclinic forcing towards a given latitudinal temperature profile controlled by the forced equator-to-pole temperature difference TE. As TE...

A quasi-geostrophic intermediate complexity model of the mid-latitude atmospheric circulation is considered, featuring simplified baroclinic conversion and barotropic convergence processes. The model undergoes baroclinic forcing towards a given latitudinal temperature profile controlled by the forced equator-to-pole temperature difference TE. As TE...

A baroclinic model for the atmospheric jet at middle-latitudes is used as stochastic generator of non-stationary time series of the total energy of the system. A linear time trend is imposed on the parameter $T_E$, descriptive of the forced equator-to-pole temperature gradient and responsible for setting the average baroclinicity in the model. The...

A baroclinic model for the atmospheric jet at middle-latitudes is used as a stochastic generator of time series of the total energy of the system. Statistical inference of extreme values is applied to yearly maxima sequences of the time series, in the rigorous setting provided by extreme value theory. In particular, the Generalized Extreme Value (G...

A quasi-geostrophic intermediate complexity model is considered, providing a schematic representation of the baroclinic conversion processes which characterize the physics of the mid-latitudes atmospheric circulation. The model is relaxed towards a given latitudinal temperature profile, which acts as baroclinic forcing, controlled by a parameter TE...

A low-dimensional model of general circulation of the atmosphere is investigated. The differential equations are subject to periodic forcing, where the period is one year. A three-dimensional Poincaré mapping P depends on three control parameters F, G, and ε, the latter being the relative amplitude of the oscillating part of the forcing. This paper...

Statistical properties of vortices are examined in a simplified model for the atmospheric baroclinic jet at midlatitudes. The model is derived from the two-layer quasi-geostrophic equations. Examined properties are: 1) the average vorticity on the vortex centres; 2) the impact rate of vortex tracks on selected gridpoints; 3) return periods of the m...

The research presented in this PhD thesis within the framework of nonlinear deterministic dynamical systems depending on parameters. The work is divided into four Chapters, where the first is a general introduction to the other three. Chapter two deals with the investigation of a time-periodic three-dimensional system of ordinary differential equat...