# Titles and abstracts

*Can We Perform Extreme Event Attribution with the Current Generation of Climate Models?*

There is considerable interest in being able to assess the extent to which recent extreme weather events can be linked to anthropogenic climate change. As a result, a number of groups around the world are producing near real-time attribution analyses. But are current generation climate models up to the job? I will argue that they are not - as manifest by the unreliability of monthly and seasonal forecasts. The importance of such reliability diagnostics has been misunderstood in the climate attribution community. I will try to show with an explicit but idealised example why information about monthly/seasonal forecast reliability must be considered central to the question of building climate models that can not only attribute real-time weather events, but can also provide society with reliable information to adapt to climate change. I will discuss some ideas on why current generation climate models are deficient and what we should do to improve them.

**Francesco Fedele (Georgia Tech)**

*Real world ocean rogue waves explained without the modulational instability*

Since the 1990s, the modulational instability has commonly been used to explain the occurrence of rogue waves that appear from nowhere in the open ocean. However, the importance of this instability in the context of ocean waves is not well established. This mechanism has been successfully studied in laboratory experiments and in mathematical studies, but there is no consensus on what actually takes place in the ocean. In this talk, we question the oceanic relevance of this paradigm. In particular, we present the analysis of the Andrea, Draupner and Killard rogue waves and find that the main generation mechanism for rogue waves is the constructive interference of elementary waves enhanced by second-order bound nonlinearities and not the modulational instability. This implies that rogue waves are likely to be rare occurrences of weakly nonlinear random seas. This is a joint with Frederic Dias, John Dudley, Joseph Brennan and Sonia Ponce de Leon.

**Combining intermittency, autoregression and censoring to model daily precipitation**

Daily precipitation is investigated in this presentation in terms of simple first order autoregressive models. The methodology is based on combining theory from censored processes with continuous autoregressive processes to model intermittent phenomena. The choice of short-memory autoregressive models is corroborated further by recent findings on scaling properties of daily precipitation records. The theory and application to synthetic models are presented then applied to Northern Ireland daily precipitation using both zero- and non zero-mean processes. The model does capture well seasonality reflecting in part the effect of large scale for example in winter season. It is suggested, in particular, that the process mean can be used as a measure to quantify dryness or wetness of a given region. Ways of model improvement, including power transformation, based on the square root, to represent extremes using exploratory quantile–quantile plots better are also discussed.

**Dispersion in rectangular networks: effective diffusivity and large-deviation rate function**

The dispersion of a diffusive scalar in a fluid flowing through a network has many applications including to biological flows, porous media, water supply and urban pollution. Motivated by this, we develop a large-deviation theory that predicts the evolution of the concentration of a scalar released in a rectangular network in the limit of large time . This theory provides an approximation for the concentration that remains valid for large distances from the centre of mass, specifically for distances up to $O(t)$ and thus much beyond the $O(t^{1/2})$ range where a standard Gaussian approximation holds. A byproduct of the approach is a closed-form expression for the effective diffusivity tensor that governs this Gaussian approximation. Monte Carlo simulations of Brownian particles confirm the large-deviation results and demonstrate their effectiveness in describing the scalar distribution when $t$ is only moderately large.

(Joint work with Jacques Vanneste)

**Weather generators to separate dynamical and thermodynamical contributions in climate event attribution**

Detection and Attribution of singular events (DASE) consists in estimating the difference of occurrence probabilities of a rare events in two different worlds. Such worlds can be a factual world (where all anthropogenic and natural forcings are at play) and a counterfactual world (where there are only natural forcings). DASE has required the use of huge computer resources in order to produced a large amount of model simulations, with and without anthropogenic forcings, to produce such probability estimates. This requirement somewhat hinders a systematic and quick investigation of extreme events. In this presentation, I propose an alternative to such an approach of DASE by using a stochastic weather generator based on analogues of the atmospheric circulation. Such a weather generator can mimic trajectories of the atmospheric system from observations. In particular, this methodology can be used to decompose the probability of extreme events into contributions from atmospheric circulation changes and thermodynamical terms. The methodology will be illustrated on a flood event that struck southern UK and northwestern France in January 2014. I will argue that the results obtained with this stochastic approach are consistent with large ensembles of model simulations.

**Charles-Edouard Bréhier (Lyon)**

**Mathematical analysis of Adaptive Multilevel Splitting algorithms**

Adaptive Multilevel Splitting (AMS) algorithms allow to sample efficiently rare events such as transitions between metastable states of SDE or SPDE systems, using interacting replicas with selection and mutations procedures. I will focus mainly on the estimation of the probability of such transitions. First, I will review efficiency and consistency results in an idealized case, i.e. when the optimal order parameter (or reaction coordinate) is known. I will then present how the AMS strategy should be implemented in the general case. The main result is the absence of bias of the associated estimator, and I will discuss the consequences of this property with numerical simulations.

**Hurricanes and Global Warming**

Tropical sea surface temperatures (SSTs), including in the Atlantic, have been increasing along with global temperature, with a likely contribution from increasing greenhouse gases. The question arises whether this warming has led to any detectable change in Atlantic or global hurricane activity, and what changes might be expected with continued warming over the 21st century.

Initial consideration of historical hurricane data suggests a possible strong sensitivity of hurricanes to global warming, including their frequency, intensity, and power dissipation. However, my talk will address why this is currently not the consensus view, and will show that model-projected increases in hurricane activity overall over the coming century are considerably more modest than suggested by an initial examination of observations. In short, it remains uncertain whether any past changes in hurricane activity have exceeded the levels expected from natural variability alone, particularly after considering the effects of changes in observing system capabilities. In addition to the possible influence of greenhouse gas warming, a related and unresolved question concerns the roles of natural variability vs. aerosol forcing in producing the observed epoch of low Atlantic hurricane activity from the late 1960s through the early 1990s.

Dynamical model simulations of Atlantic basin and global-scale hurricane (tropical cyclone) activity for the present-day climate have been improving in terms of simulating climatological behavior and past interannual variability of hurricane activity. These models have been used to project late 21st century hurricane activity through dynamical downscaling of climate change conditions obtained from multi-model ensembles of CMIP3 and CMIP5 global climate models. Among the most robust results of these dynamical downscaling studies is a projected increase in precipitation rates for hurricanes (13%), as the warmer atmosphere holds more water vapor, which enhances moisture convergence into the storm center. The average intensity of tropical cyclones in the warmer climate increases slightly (4%) in most, but not all, tropical cyclone basins. There is a strong tendency for our downscaling framework to produce fewer tropical storms and hurricanes overall in the warmer climate in most basins and in the global

average (-16%), although there is some divergence among modeling studies on this finding, with at least one recent study projecting an increase in global and Atlantic tropical storm frequency. In terms of the most intense hurricanes, we simulate an increasing frequency of category four and five hurricanes in the Atlantic and globally (+28%), although an increase is not simulated for all of the 10 individual climate models we have downscaled for the Atlantic. Thus, this is a less robust projection across our model studies than the projected decrease in frequency of all tropical storms and hurricanes combined. Sea level rise will increase the risk of storm surges from hurricanes, all other conditions (intensity, frequency, tracks of storms) being equal.

**Atmospheric circulation, climate change, and extremes**

Pretty much all that is known with any confidence about climate change concerns its energetic and thermodynamic aspects. Atmospheric circulation, which also involves consideration of dynamics, is much more uncertain yet plays a critical role in climate change at the regional scale. How to approach this issue represents a major scientific challenge. Implications for extremes, and extreme-event attribution, will be discussed.

**Studying transient turbulence in a model of Boundary layer type flow**

The coexistence of laminar flow with transient turbulence is a feature of many wall bounded flows such as pipe

flow [1] or stably stratified atmospheric boundary layers [2]. In this regime, turbulence is extremely intermittent and

the flow can visit extremely low values of turbulent kinetic energy, leading to a complete re-laminarisation of the flow.

Inversely, turbulence can build up in a laminar flow if one stimulates it with persistent finite amplitude perturbations

which have the optimal shape [3]. This high complexity is the main hindrance of modeling of such flows, while the

wide range of scale, processes and areas of physics involved makes the understanding of this regime very difficult.

So far, one had to do relatively long numerical or laboratory experiments in order to measure the properties of

the flow, such as the rate of transition from turbulence down to laminar flow T [1]. One can understand the origin

of transient temporal chaos in small systems, with few effective degrees of freedom [4] or do every efficient modeling

of the flow [5]. However, the ability to study efficiently large systems, where several physical process can compete in

a possibly complex geometry is lacking. This would typically be the case of a stably stratified planetary boundary

layer where orography and additional physical effects such as internal waves are taken into account. Moreover, one

still needs a theoretical framework in which to describe and understand the lifetime of extended transitional turbulent

flows.

We turn to theories of rare events and methods of computations of rare events that can greatly accelerate numerical

computations. We focus on the study of two models of turbulence in pipe flow (a chaotic and a stochastic one) [5]. We

use an algorithm called Adaptive multilevel splitting on these models [6], which calculates the specific trajectories of

multistability (collapse or build-up of turbulence) as well as the rate of transition T for them to happen. This method

has already proven very efficient in the study of multistability in gradient stochastic differential equations [7] and made

it possible to compare numerical results to theory. In particular, we can verify Large Deviations type predictions as to

the structure of the trajectory and the dependence of the transition rate on the low noise amplitude ǫ → 0. It takes

the form −ǫ ln(T ) = ∆Φ(✁ ǫ), where ∆Φ can be computed from the dynamical properties of the system.

We compute Trelam as a function of Reynolds number r and size L, and find a large deviation principle for T as

size goes to infinity −(1/L) ln(T ) = f (r). This was expected from the behaviour of the probability density functions

of kinetic energy in Couette flow [8]. This motivates us to study the Reynolds number dependence of the lifetime

of turbulence in a Large Deviations form f (r), 1/L → 0, focusing on the faster than linear growth of f (r) [1]. This

could hopefully be explained by theory on the collapse of turbulent puffs as Reynolds number determines their size,

amplitude and number in the flow, as well as locus of the separatrix between laminar and turbulent flow in phase

space.

References

[1] K. Avila, D. Moxey, A. de Lozar, M. Avila, D. Barkley, B. Hof, Science 333, 192–196(2011).

[2] C. Ansorge, J. P. Mellado, Boundary-Layer Meteorol. 153, pp. 89–116 (2014).

[3] S.M.E. Rabin, C.P. Caulfield, R.R. Kerswelln, J. Fluid Mech. 712, 244–272 (2012).

[4] B. Eckhardt, T.M. Schneider, B. Hof, J. Westerweel, Ann. Rev. Fluid Mech. 39, 447–468 (2007).

[5] D. Barkley, Phys. Rev. E84, 016309, J. Phys.: Conf. Ser. 318 032001 (2011).

[6] F. C ́erou, A. Guyader, T. Leli'evre, D. Pommier, J. Chem. Phys.134, 054108 (2011).

[7] J. Rolland, F. Bouchet, E. Simonnet, J. Stat. Phys. 162, 277-311 (2016).

[8] J. Rolland, Eur. Phys. J. B, 88: 66 (2015).

**Extreme phenomena in the solar atmosphere**

The atmosphere of the Sun is a highly dynamical physical system, with a huge variety of extreme and nonlinear phenomena operating in a broad range of time scales, from a fraction of a second to several years. Some of these processes, for example coronal mass ejections (CME) and solar flares directly affect the Earth and near-Earth space, and hence are considered as drivers of extreme geo-effective events of space weather. Other, for example magnetohydrodynamic oscillations of various plasma non-uniformities, have much lower direct impact on the Earth, but provide us with an important diagnostic tool, allowing for remote probing of solar atmospheric plasmas and physical processes operating there. This knowledge is crucial for the development of the CME and flare forecasting. One of such tools are quasi-periodic pulsations that are often detected in the lightcurves of solar, and more recently stellar flares. The typical periods range from a few seconds to several minutes. Flares with quasi-periodic variation

of the emission intensity may be of enhanced geo-effectiveness if the periodicity matches a natural periodicity of one of the geophysical (e.g., magnetospheric, ionospheric or upper-atmospheric) systems. The pulsations are interpreted either in terms of magnetohydrodynamic oscillations triggering or modulating the energy releases, or self-oscillatory regimes of the energy releases. The similarity of quasi-periodic pulsations detected in solar flares and stellar “super-flares” indicates the common mechanism for the energy releases, and hence contributes to the assessment of the probability of a potentially devastating solar super-flare.

**Noise-induced transitions between meta-stable atmospheric jet configurations**

We consider barotropic flows forced by a random white-in-time Gaussian noise, in particular the quasi-linear approximation of the 2D barotropic quasi-geostrophic equation in the beta-plane. For suitable parameters, this model allows for meta-stable zonal jet solutions. In the limit of large time-scale separation between the inertial scale

and the spin-up time (which is equivalent to the limit of vanishing Ekman-damping), rare transitions between these meta-stable jet configurations are described by a large deviation principle. In theory, the minimizer of the associated rate function allows statements about the stability and lifetime of atmospheric jets as well as the most likely trajectories leading to creation or destruction of atmospheric jets. In this talk, the associated large deviation principle is presented and the phase space landscape for atmospheric jets is investigated. Meta-stable jet configurations and the transition states for jet creation and destruction are computed numerically.

**The parallel replica algorithm: mathematical foundations and recent developments**

I will present the parallel replica algorithm, which is an accelerated dynamics method proposed by A.F. Voter in 1998. The aim of this technique is to efficiently generate trajectories of a metastable stochastic process. Recently, we propose a mathematical framework to understand the efficiency and the error associated with this technique. Generalizations of the original method in order to widen its applicability have been proposed.

References:

D. Aristoff, T. Lelièvre and G. Simpson, The parallel replica method for simulating long trajectories of Markov chains, AMRX, 2, 332-352, (2014)

A. Binder, T. Lelièvre and G. Simpson, A Generalized Parallel Replica Dynamics, Journal of Computational Physics, 284, 595-616, (2015).

**Xiang Zhou (City University of Hong Kong)**

**Recent Development of Numerical Methods for Transition Path and Transition State**

In this talk, I will focus on the study of optimal transition paths and transition bottlenecks for randomly perturbed dynamic system. The large deviation theory based minimum action method and the eigenvector-following based numerical method (gentlest ascent dynamics) for saddle points will be reviewed. These deterministic numerical tools are applicable to non-gradient spatially extended systems and effective to study noise-induced transitions in small noise limit. I might also discuss importance sampling of extreme events for dynamics and static problem very briefly.

**Introduction to large deviation theory and applications to climate dynamics**

For some aspects of climate dynamics, rare dynamical events may play a key role. A first class of problems are extreme events that have huge impacts, for instance specifically study such rare events. Those approaches are based on large deviation theory for complex dynamical systems. During this talk I will review basic aspects of large deviation theory for dynamical systems and stress their potential interest for climate applications. I will summarize the Europe, in a comprehensive climate model.

**A large deviation approach for computing rare transitions in multi-stable stochastic turbulent flows**

Many turbulent flows undergo sporadic random transitions, after long periods of apparent statistical stationarity. The understanding of this phenomena is extremely difficult due to the complexity, the large number of degrees of freedom, and the non-equilibrium nature of these turbulent flows. It is however, a key issue for many geophysical problems. One recent approach has been based on a large deviation approach, whereby transition paths are characterized through a path integral representation of their transition probability. In this talk, we will focus on this method to compute rare transition paths in the two-dimensional Navier-Stokes and quasi-geostrophic equations for both equilibrium (Langevin) and non-equilibrium dynamics. We shall show, that in the equilibrium case, a generalized detailed balance statement allows us to compute rare transition paths via deterministic relaxation paths of a dual system, while, for non-equilibrium problems require the use numerical optimization schemes.

**Efficient sampling of rare events by splitting**

Standard (or crude) Monte Carlo (MC) simulation is known to be inefficient for simulating rare events. For events with low probability, the squared relative error on estimates obtained from straightforward MC simulation is inversely proportional to the number of samples, so that an excessively large number of samples may be required to reach a desired accuracy for the estimation of rare event probabilities. Multilevel splitting is a broad class of techniques designed to improve the efficiency of MC sampling for rare events. I will discuss how results from large deviations theory can help to construct a suitable importance function for splitting.

**Characterizing hazardous convective weather risk**

Hazardous convective weather (HCW) events associated with severe thunderstorms include tornadoes, hail and damaging winds. Although relatively rare, these events cause substantial property damage and loss of life. The central U.S. is particularly prone to tornadoes, but severe thunderstorms occur in many regions worldwide. Quantification of HCW risk is important both in the short term (forecasters warning the public of eminent peril) and longer term (insurers assessing exposure to hazards). A changing climate complicates estimates of both current and future HCW risk. In this talk I will describe statistical approaches that combine data and physical understanding, and its application to prediction and variability questions.

**Michael Wilkinson (Open University)**

**Using large deviation theory to understand rain showers**

Understanding the mechanism of rainfall from ice-free cumulus clouds is a challenging problem, because of the low rate of collisions between microscopic water droplets settling under gravity. It has been proposed that turbulence may facilitate collisions between droplets, but despite intensive efforts this mechanism appears to be insufficient to explain rainfall.

An alternative approach is required. Recently, I showed that large deviation theory can explain how raindrops result from a succession of unusually rapid collisions. The onset of rain showers can be surprisingly rapid, much faster than the mean time required for a single collision.

The results are quite general, and are applicable to atmospheres on other planets. I introduce a hypothesis about the ability of light to penetrate clouds to the reach the surface of a solid planet, which is relevant to estimating the probability for life to evolve on other worlds.

The talk is based upon a recent paper, Large Deviation Analysis of Rapid Onset of Rain Showers, M. Wilkinson, Phys. Rv. Lett. 116, 018501, (2016), and a review article, Collisional Aggregation due to Turbulence, A. Pumir and Michael

Wilkinson, Ann. Rev. Cond. Matter Phys., 7, 141, (2016).

**Extreme events in atmospheric transport problems**

It is sometimes of interest to calculate the transport of an atmospheric trace gas between a localised source and localised measurement site (e.g. if a harmful chemical is released near a population centre). Here, importance sampling strategies for the efficient calculation of such transport are discussed. Two idealised but relevant problems are considered. The first is long-distance (i.e. hemispheric-scale) transport in the so-called chaotic advection regime. The second concerns short-range transport within the atmospheric boundary layer. In the latter case, the effect of using increasingly realistic stochastic models of turbulent transport is explored.

**Francesco Ragone (Hamburg and ENS-Lyon)**

**Simulation of heat waves in climate models using large deviation algorithms**

We will discuss here a new genealogical algorithm, based on large deviation theory, that allows to efficiently sample very rare events in complex climate models. A large ensemble of realizations are run in parallel, and selection and cloning procedures are applied in order to oversample the trajectories leading to the extremes of an observable of interest. The statistics and characteristic dynamics of the extremes can then be computed and analyzed on a much larger sample of events. This kind of importance sampling method belongs to a class of genealogical algorithms that have been successfully applied in other scientific fields (statistical mechanics, complex biomolecular dynamics), allowing to decrease by orders of magnitude the numerical cost required to sample extremes with respect to standard direct numerical sampling.

We study the applicability of this method to the computation of the statistics of European surface temperatures with the Planet Simulator (Plasim), an intermediate complexity general circulation model of the atmosphere. We demonstrate the efficiency of the method by comparing its performances against standard approaches. We show that with this method the relative errors on the estimate of composite averages of the extreme events are orders of magnitude smaller than with a direct numerical sampling. The dynamics of the paths leading to heat waves events are also studied. Eventually we discuss the feasibility of this method for applications with state of the art climate models, and the potential of this new approach for the study of extreme events, which allows to study their dynamics extensively at a reasonable computational cost, in more realistic settings.

**Efim Pelinovsky (Nizhny Novgorod)**

**Tsunamis of the meteoric origin**

At the turn of the XX and XXI centuries there was a substantial reassessment of the threat of falling of small solar system bodies to the Earth. This was due to the accumulation of serious fundamental knowledge of physical and dynamic evolution of the solar system as a whole. As the systematization of knowledge grew, the subject of the interaction of the planet with large celestial bodies has started to attract more and more attention. Currently, this topic is paid special attention to, and the fall of the meteorite in the Chelyabinsk region (Russia) on February 15, 2013 further fueled this interest.

Increasingly, information about the rapprochement of celestial bodies in size from a few tens of meters to kilometers with the Earth began to appear. Many of these objects fly in close proximity to the Earth at a distance comparable with the distance to the Moon. In this regard, forecasts of asteroids dangerously approaching the Earth began to be worked out for the coming decades and even centuries, and in science the term symbolizing the threat - the asteroid-comet hazard (ACH) is firmly entrenched.

The collision with the Earth of large celestial bodies with a diameter of a few kilometers is quite a rare event, but the clashes with small and medium-sized bodies repeatedly occurred in the past. Our planet has repeatedly collided with celestial bodies, and the number of proved impact craters was more than a hundred with the expected redoubling every 5.8 years. To date, the number of craters is about two hundred, although, most likely, this figure can easily double due to the inconsistency of some data.

Approaches to modeling a tsunami of meteoric origin are discussed. A brief overview of the asteroid and meteorite danger to the Earth is given. Formulas assessing the parameters of the tsunami caused by an asteroid entering the water are derived. The results of the numerical simulation of the effect of the angle of entry of the body into water on the characteristics of the resulting waves in the near field are given. The model based on the Navier-Stokes equations for multiphase flows with a free surface is used in calculations. The dimensions of perturbation are studied and the regularities of changes in the parameters of the source are discovered.

Acknowledgement. These results are obtained with the support of grant of Russian President for leading scientific schools NS-6637.2016.5, State Contract № 2014/133 and the RFBR grants (14-05-00092, 15-45-02061, 16-01-00267).

Publications:

1. Kharif, Ch., and Pelinovsky, E., Asteroid impact tsunamis. Comptes Rendus Physique, 2005, vol. 6, 361-366.

2. Kozelkov, A.S., Kurkin, A.A., and Pelinovsky, E.N. Tsunami of cosmogenic origin. Transactions of Nizhni Novgorod State Technical University, 2014, No. 2(104), 26-35.

3. Kozelkov, A.S., Kurkin, A.A., Pelinovskii, E.N., and Kurulin, V.V. Modeling the cosmogenic tsunami within the framework of the Navier–Stokes equations with sources of different types. Fluid Dynamics, 2015, vol. 50, No. 2, 306–313.

4. Kozelkov, A.S., Kurkin, A.A., Pelinovskii, E.N., Kurulin, V.V., and Tyatyushkina, E.S. Modeling the disturbances in the lake Chebarkul caused by the fall of the meteorite in 2013. Fluid Dynamics, 2015, vol. 50, No. 6, 828-840.

5. Kozelkov, A.S., Kurkin, A.A., and Pelinovskii, E.N. Effect of the angle of water entry of a body on the generated wave heights. Fluid Dynamics, 2016, vol. 51, No. 2, 288-298.

**Alexey Slunyaev (Nizhny Novgorod)**

**Rogue waves and coherent patterns**

The overview of recent and ongoing research on strongly nonlinear dynamics of gravity waves over deep water will be given. The weakly nonlinear framework for weakly modulated wave trains is based on the nonlinear Schrodinger equation (NLSE), which is integrable in the unidirectional setting. The integrable NLSE possesses a set of solitary solutions: envelope solitons on the zero background, and breathers propagating over the plane wave background. Solitons preserve energy and interact elastically with other waves. Breathers correspond to modes of modulational instability. Thus, solitons and breathers represent convenient elements of understanding and description of essentially nonlinear wave dynamics including so-called rogue waves.

It was generally believed that in the strongly nonlinear regime of water waves weakly nonlinear solutions of the NLSE totally failed to describe nonlinear wave dynamics. We have performed a series of investigations based on fully nonlinear numerical simulations of the Euler equations and also with laboratory tests aiming at revealing the limits of applicability of the NLSE and studying the dynamics of soliton-like wave patterns in the limit of strong nonlinearity. Besides, the weakly nonlinear theory is constructed for trapped surface waves propagating against jet currents. Weakly nonlinear soliton-like solutions for trapped waves on jet currents have been derived; they were tested in numerical simulations of the Euler equations. We show that in many cases the weakly nonlinear theory for weakly modulated water waves is able to provide reasonable description even in situations of steep strongly modulated waves.

The soliton-like patterns change the appearance, dynamics and statistics of surface waves essentially. Precursors of extreme wave occurrence and dangerous sea states could be detected in advance, providing the basis for a short-term rogue wave forecasting. New representative wave patterns should be taken into account in procedures of marine structure design.

References

1. A.V. Slunyaev, Numerical simulation of “limiting” envelope solitons of gravity waves on deep water. JETP 109, No.4, 676-686 (2009).

2. L. Shemer, A. Sergeeva, A. Slunyaev, Applicability of envelope model equations for simulation of narrow-spectrum unidirectional random field evolution: experimental validation. Phys. Fluids 22, 016601 (2010).

3. A. Slunyaev, Freak wave events and the wave phase coherence. Eur. Phys. J. Special Topics 185, 67-80 (2010).

4. A. Chabchoub, N. Hoffmann, M. Onorato, A. Slunyaev, A. Sergeeva, E. Pelinovsky, and N. Akhmediev, Observation of a hierarchy of up to fifth-order rogue waves in a water tank. Phys. Rev. E 86, 056601-1–6 (2012).

5. A. Slunyaev, G.F. Clauss, M. Klein, M. Onorato, Simulations and experiments of short intense envelope solitons of surface water waves. Phys. Fluids 25, 067105,1-17 (2013).

6. A. Slunyaev, E. Pelinovsky, A. Sergeeva, A. Chabchoub, N. Hoffmann, M. Onorato, N. Akhmediev, Super rogue waves in simulations based on weakly nonlinear and fully nonlinear hydrodynamic equations. Phys. Rev. E 88, 012909–1-10 (2013).

7. A.V. Slunyaev, V.I. Shrira, On the highest non-breaking wave in a group: fully nonlinear water wave breathers vs weakly nonlinear theory. J. Fluid Mech. 735, 203-248 (2013).

8. V.I. Shrira, A.V. Slunyaev, Trapped waves on jet currents: asymptotic modal approach. J. Fluid Mech. 738, 65-104 (2014).

9. V. Shrira, A. Slunyaev, Nonlinear dynamics of trapped waves on jet currents and rogue waves. Phys. Rev. E. 89, 041002(R) (2014).

10. A. Slunyaev, A. Sergeeva, and E. Pelinovsky, Wave amplification in the framework of forced nonlinear Schrödinger equation: the rogue wave context. Physica D 303, 18–27 (2015).

**Rogue waves in the coastal zone**

For a long time rogue waves have been a part of marine folklore, as extreme sea waves, which appear from nowhere, cause danger and destruction and disappear at once. Nowadays the existence of rogue waves is proved and they are registered all over the World by different instruments (range finders installed on offshore platforms, deployed buoys, radars including SAR, etc.). A number of ship accidents has also been related to rogue waves. They may occur at the surface of a relatively calm sea, reach not very high amplitudes, but be fatal for ships and crew due to their unexpectedness and abnormal features. The serious studies of the phenomenon started about 20–30 years ago and have been intensified during the last decade.

Rogue waves are often thought to form only in the deep ocean causing ship accidents and damaging offshore platforms, but indeed they occur in the coastal zone and even at the coast where they may provoke coastal flooding and high splashes over steep banks and coastal constructions. The formation mechanisms of coastal rogue waves differ from the generation in the deep water and are mainly due to nonlinear wave-wave and wave-coast (sea bottom) interaction. The factors influencing the probability of rogue wave occurrence at the coast have been the subject of investigation both theoretically within the shallow-water theory and through field and laboratory experiments.

**Michael Wehner (Laurence Berkeley National Laboratory)**

**Very extreme event attribution**

Many extreme weather events are not or cannot be simulated well by CMIP5 class climate models. We present a methodology based on shorter, but higher resolution hindcast models that is “fit for purpose” to make more defensible attribution statements about the role of anthropogenic forcing of the climate system. Two examples illustrate the strengths and weaknesses of the approach.

**Data-driven prediction of extremes and critical transitions in weather and climate science**

The talk discusses data-based approaches for predicting extreme events and critical transitions in weather and climate.

The first part deals with statistical post-processing of forecast ensembles. Despite impressive improvements in the forecast skill of numerical weather prediction in the past decades there are still limitations due to model error and problems in generating ensembles. Forecast ensembles are biased both in location and dispersion. They tend to be underdispersive, leading to overconfident uncertainty estimates and an underestimation of extreme weather events. The raw ensemble distribution can thus not be expected to convert directly into a predictive distribution for a variable of interest. Advanced statistical post-processing techniques are studied with a particular view on extreme weather events.

In the second part approaches to modelling critical transitions from time series data are discussed. A non-stationary low-order stochastic dynamical system of appropriate complexity to capture the transition mechanism under consideration is estimated from data. Integrations with the model are performed beyond the learning data window to predict the nature and timing of future critical transitions. The technique is generic, not requiring detailed a priori knowledge about the underlying dynamics of the system. The problem of quantifying the likelihood of meridional overturning circulation collapse is studied. The method is exemplified on the Stommel box model; then a data set from a fully coupled climate model, subject to a freshwater hosing experiment, is investigated. The contribution generally advocates the use of data-driven non-stationary low-order models for assessment of climate change and tipping point risk.

**Colm Connaughton (Warwick)**

**Fluxes, fluctuations and coherent structures in two-dimensional hydrodynamic models**

The energy flux plays a central role in the physics of turbulence as elucidated by Kolmogorov's classical theory. It is a highly fluctuating quantity in the sense that its fluctuations are typically much much larger than its mean. As a consequence, seemingly simple tasks like determining the direction of the energy flux or identifying the typical physical flow configurations responsible for scale-to-scale energy transfer are difficult to answer from experimental or numerical data. In this talk I will use some simple examples to explain some of these issues and look at how the presence of coherent structures can lead to confusing results if metrics designed to quantify homogeneous turbulence are applied carelessly.

**Eric Simonnet (Nice)**

**Computation of rare transitions between turbulent atmospheric jets**

Zonal atmospheric jets are known to naturally emerge from beta-plane turbulence due to the arrest of inverse energy cascade by Rossby waves. Transitions between jets of different wavenumbers are indeed observed in a weakly dissipative barotropic quasigeostrophic model forced by a weak noise. It shows a striking example of bimodality in the context of 2-D turbulence. By using an adaptive version of multilevel splitting algorithm, we are able to compute large statistical ensembles of trajectories connecting jets of different wavenumbers. We show that at very low probability regimes, these so-called reactive trajectories concentrate on a narrow region of phase space suggesting the existence of instantons. Moreover, these transitions are strongly irreversible as expected in non-gradient systems. The phenomenology of these transitions appears to be very robust and is driven by a subtil play between nucleation and coalescence of the zonal jets. The algorithm is also able to show some large-deviation behavior as the Ekman damping is becoming small.

**Tools for identifying resolved-scale turbulence in convection simulations**

The Met Office and the Natural Environment Research Council (NERC) have funded a new Research programme on Understanding and Representing Atmospheric Convection across Scales. An essential part of this programme will be high-resolution reference simulations, in particular sub-kilometre resolution simulations, the scale below which the dynamics of three-dimensional turbulence become important. The atmospheric models often do not converge to the observed rainfall in radar data as the resolution is improved and can over-predict the rainfall in the most intense storms. This does not occur when comparisons with 100 m radar data show that resolved-scale turbulence is being simulated, but for this programme we need to make this identification when radar data is not available. Tools for making such predictions when small-scale observations are not available will be presented.