## CliMathNet Conference Contributed Posters

#### David Armstrong McKay, University of Southampton

**Title: Reduced Earch system resilience across the Palaeocene-Eocene Thermal Maximum**

**David I. Armstrong M ^{c}Kay*^{1,2} **& Timothy M. Lenton

^{3}

^{1}*Ocean and Earth Science, University of Southampton*

^{2}*Geography and Environment, University of Southampton (current address)*

^{3}*College of Life and Environmental Sciences, University of Exeter*

*D.Armstrong-McKay@noc.soton.ac.uk

**Abstract:**

Several past episodes of rapid carbon cycle and climate change are hypothesised to be the result of the Earth system reaching a tipping point beyond which an abrupt transition to a new state occurs. At the Palaeocene-Eocene Thermal Maximum (PETM) ~55.5 Ma hypothesised tipping points involve the abrupt transfer of carbon from surface reservoirs to the atmosphere. Theory suggests that tipping points in complex dynamical systems should be preceded by early warning signals (EWS) due to critical slowing down of their dynamics, including increasing temporal autocorrelation and variability. However, detecting EWS in palaeorecords is challenging, with issues of data quality, false positives, and parameter selection potentially affecting reliability. Here we show that in the highest-resolution palaeorecord currently available, there is evidence of destabilisation of the carbon cycle prior to the PETM, elevated carbon cycle instability after the PETM in the lead up to Eocene Thermal Maximum 2 (ETM2), and further instability thereafter. This may reflect gradual forcing of the carbon cycle due to the North Atlantic Volcanic Province eruptions. Whilst our results do not prove the existence of a tipping point, they do indicate a loss of ‘resilience’ in the carbon-climate system with weakened stabilising negative feedbacks. We also present preliminary results of resilience analysis across other Cenozoic palaeoclimate perturbations, including the Cretaceous-Palaeogene boundary and the Eocene-Oligocene Transition.

*Linked to ReCoVER Early Career Research Project RFFECR002: “Can early warning signals be reliably detected in the Cenozoic palaeoclimate record?”*

#### Gualtiero Badin, University of Hamburg

Authors: Giovanni Conti and Gualiterio Badin

**Title: Hyperbolic Covariant Coherent Structures in two dimensional flows**

#### Tamas Bodai, University of Reading

**Title: On the importance of the convergence to climate attractors**

**Abstract:**

Ensemble approaches are becoming widely used in climate research. In contrast to weather forecast, however, in the climatic context one is interested in long-time properties, those arising on the scale of several decades. The well-known strong internal variability of the climate system implies the existence of a related dynamical attractor with chaotic properties. Under the condition of climate change this should be a snapshot attractor, naturally arising in an ensemble-based framework. Although ensemble averages can be evaluated at any instant of time, results obtained during the process of convergence of the ensemble towards the attractor are not relevant from the point of view of climate. In simulations, therefore, attention should be paid to whether the convergence to the attractor has taken place. We point out that this convergence is of exponential character, therefore, in a finite amount of time after initialization relevant results can be obtained. The role of the time scale separation due to the presence of the deep ocean is discussed from the point of view of ensemble simulations.

#### Aoibheann Brady, University of Bath

Authors: Aoibheann Brady, Ilaria Prosdocimi and Julian Faraway

**Title: Detection & attribution of large scale drivers for environmental change **

**Abstract:**

The UK has been hit by a number of large flood events in recent years, with concerns that the current infrastructure and level of protection of cities may not be fit for purpose. There is growing concern that climate change may result in an increased risk of flooding. The changes in flood risk, which are derived from climate change projections, are nevertheless not validated by the observed river flow data, from which no compelling evidence of increasing trends can be inferred. In fact, trend tests obtained from modelling each gauging station separately typically lead to some unclear signal. This might be largely due to the fact that river flow records typically cover a short period of time, and the site-by site tests to assess whether change can be detected in observed data are not very powerful (in a statistical sense) and cannot fully differentiate between possible confounders.

To overcome these issues, we propose a Bayesian hierarchical model where all stations are modelled together, thus allowing for the borrowing of information from other stations. We discuss the use of this approach to detect and attribute changes in flooding and other environmental variables. This will result in methods for the detection of spatially coherent trends in environmental data. We also investigate methods to make an assessment on the main drivers of higher river flows and flooding at a regional or national scale, with a focus on climates indices (such as the North Atlantic Oscillation), annual temperature and annual CO2 emissions.

#### Guilia Carigi, University of Reading

**Title: Rate-induced tipping in nonautonomous dynamical systems with bounded noises**

**Abstract: **

We talk about rate-induced tipping when a system is pushed across a bifurcation point through a nonautonomous change in the parameter that is a non-adiabatic, so that it cannot be regarded as a constant parameter in the dynamics. This project aims at providing a mathematical framework for rate-induced tipping in the presence of bounded noise. In many practical applications random perturbations of the physical system are bounded; it is proved that in such systems there can be more than one stationary measure and the assumption of bounded noise makes a more precise analysis of the bifurcation point possible.

#### Lesley De Cruz, Royal Meteorological Institute of Belgium

Authors:Maarten Reyniers * ^{1}*, Laurent Delobbe

*, Loris Foresta*

^{1}

^{2}*1*Royal Meteorological Institute of Belgium

^{2 }^{Swiss Federal Office of Meteorology and Climatology, Locano, Switzerland}^{}

**Title: Impact of blending high-frequency NWP precipitation forecasts in a stochastic nowcasting scheme**

#### Davide Faranda, CNRS

**Title: Dynamical systems proxies of atmospheric predictability and mid-latitude extremes**

Authors: Gabriele Messori, Rodrigo Caballero, Davide Faranda

**Abstract:**

Extreme weather ocurrences carry enormous social and economic costs and routinely garner widespread scientific and media coverage. Many extremes (for e.g. storms, heatwaves, cold spells, heavy precipitation) are tied to specific patterns of midlatitude atmospheric circulation. The ability to identify these patterns and use them to enhance the predictability of the extremes is therefore a topic of crucial societal and economic value.

We propose a novel predictability pathway for extreme events, by building upon recent advances in dynamical systems theory. We use two simple dynamical systems metrics − local dimension and persistence − to identify sets of similar large-scale atmospheric flow patterns which present a coherent temporal evolution. When these patterns correspond to weather extremes, they therefore afford a particularly good forward predictability. We specifically test this technique on European winter temperatures, whose variability largely depends on the atmospheric circulation in the North Atlantic region. We find that our dynamical systems approach provides predictability of large-scale temperature extremes up to one week in advance.

#### Andrey Gritsun, Russian Acadamy of Sciences

Authors: Perezhogin P.A. (1,2), Glazunov A.V.(1), Gritsun A.S.(1)

(1) Institute of Numerical Mathematics (Russian Academy of Sciences, Moscow, Russia)

(2) Moscow institute of Physics and Technology (Moscow, Russia)

**Title: Stochastic and deterministic kinetic energy backscatter parameterizations for the two-dimensional turbulence modeling**

In this work we are considering the problem of modeling 2D isotropic turbulence in a periodic rectangular domain excited by the forcing pattern of prescribed spatial scale. This setting could be viewed as the simplest analog of the large scale quasi 2D circulation of the ocean and the atmosphere. Since the direct numerical simulation (DNS) of this problem is usually not possible due to the high computational costs we are exploring several possibilities to construct coarse approximation models and corresponding subgrid closures (deterministic or stochastic). The necessity of subgrid closures is especially important when the forcing scale is close to the cutoff scale of the coarse model that leads to the significant weakening of the inverse energy cascade and large scale component of the system dynamics.

The construction of closures is based on the *a priori* analysis of the DNS solution and takes into account the form of a spatial discretization scheme used in a particular coarse model. We show that the statistics of a coarse model could be significantly improved provided a proper combination of deterministic and stochastic closures is used. As a result we are able to restore the shape of the energy spectra of the model. In addition the lagged autocovariance of the model solution as well its sensitivity to external perturbations fit the ones of the DNS experiment much better.

Acknowledgment: work was supported by the Russian foundation for Basic Research (project 16-55-12015).

#### Maria Jacob, University of Reading

**Title: Forecasting Peaks in Household Electric Load Profiles**

**Abstract:**

Low carbon technologies such as electric vehicles, heat pumps, solar and wind generation represent an exciting opportunity for a reduction in emissions of carbon dioxide into our atmosphere, but on the other hand represent a huge challenge to the electricity distribution organisations, in particular on the low voltage network level. The new loads created by these technologies in combination with their uptake result in the need for a detailed prediction of individual daily and seasonal loads several years in advance. With this in mind, the MRes will focus on two tasks: i) optimising forecasting techniques to model energy demand and, ii) deducing the properties of the tail behaviour of energy demands for both the present and the future, using Extreme Value Theory.

#### Frank Kwasniok, University of Exeter

**Title: Quantifying the likelihood of meridional overturning circulation collapse using non-stationary data-driven modelling**

**Abstract:**

The problem of quantifying the likelihood of meridional overturning circulation collapse is studied. A non-stationary low-order stochastic model is estimated from data. The model is propagated beyond the learning data window using its associated Fokker-Planck equation and the probability of tipping is calculated. The method is exemplified and verified on the Stommel box model. Then data from an intermediate-complexity ocean model subject to a ramped freshwater flux is analyzed; different climate forcing scenarios and their associated risk of AMOC collapse are studied. The proposed technique is generic, not requiring any detailed a priori knowledge about the underlying dynamics of the system; it is applicable to any system exhibiting two alternative states and a possible transition between them via a fold bifurcation. The contribution generally advocates the use of data-driven non-stationary low-order models for climate change and tipping point risk assessment.

#### Valerio Lembo, University of Hamburg

Authors: Valerio Lembo*^{1}* and Valerio Lucarini

*2*

1 University of Hamburg

2 University of Reading

**Title: A flexible tool for diagnosing water, energy and entropy budgets in climate models**

#### Peter Read, University of Oxford

**Title: Spectrally-resolved energetics of the Martian atmosphere**

A. Valeanu, **P. L. Read**, F. Tabataba-Vakili & R. M. B. Young

**Abstract:**

The dynamics and pattern of energy distribution across different scales of motion in the atmosphere are a key component in understanding the general atmospheric circulation, and in the validation of atmospheric models. Much work on measuring and diagnosing the spectra of kinetic and potential energy in the Earth’s atmosphere has been carried out over the past 30 years, together with derivations of turbulent structure functions and estimates of spectral fluxes, showing complex exchanges of energy. Until recently, however, such exchanges for other planetary atmospheres has remain largely unexplored. In the present work, we have analyzed the kinetic and potential energy spectra of the atmosphere of Mars, derived from an assimilated analysis of spacecraft observations of temperature over several Mars years. We will present results of an analysis of both energy spectra and the fluxes of kinetic and potential energy, based on an approach developed by Augier & Lindborg (2013), and examine both the annually averaged exchanges and their variation with season. The results indicate that Mars is in a rather different dynamical regime to the Earth, with upscale kinetic energy transfers at large scales but predominantly downscale energy transfers across much of the spectrum.

#### Luke Storer, University of Reading

**Title: Global Response of Clear-Air Turbulence to Climate Change**

Authors: Luke Storer (University of Reading), Paul Williams (University of Reading), Manoj Joshi (University of East Anglia)

**Abstract:**

Clear-air turbulence (CAT) is one of the largest causes of weather-related aviation incidents. Here we use climate model simulations to study the impact that climate change could have on global CAT by the period 2050-2080. We extend previous work by analyzing eight geographic regions, two flight levels, five turbulence strength categories, and four seasons. We find large relative increases in CAT, especially in the midlatitudes in both hemispheres, with some regions experiencing several hundred per cent more turbulence. The busiest international airspace experiences the largest increases, with the volume of severe CAT approximately doubling over North America, the North Pacific, and Europe. Over the North Atlantic, severe CAT in future becomes as common as moderate CAT historically. These results highlight the increasing need to improve operational CAT forecasts and to use them effectively in flight planning, to limit discomfort and injuries amongst passengers and crew.

#### Joe Wallwork, Imperial College London

**Title: Multi-scale numerical simulation of a tsunami using mesh-adaptive methods**

**Abstract:**

Since the millennium two particular tsunamis, impacting the Indian Ocean rim in 2004 and Japan in 2011, caused enormous destruction and claimed very many lives. How can numerical modelling of tsunamis be made more efficient in order to provide better early warning systems, using which governments could mitigate the damage caused by such events?

One possible approach is to make use of *adaptive meshes* for use in numerical solution of the shallow water equations. Through adaptivity we can focus computational power where it is needed, accurately resolving the tsunami waves and especially those at important coastal locations, using a fine mesh. Using a coarser mesh elsewhere, we can keep the overall computational cost of the algorithm low. Adaptivity has been shown to be effective in solving tsunami-type problems by [Behrens et al., 14] and [Davis and LeVeque, 16], some of the results of the latter of which I have been able to reproduce during my MRes project.

Mesh adaptive approaches are traditionally categorised as either *h-adaptive*, whereby mesh entities, such as vertices and edges, (corresponding to degrees of freedom) can be inserted into and removed from the mesh, and *r-adaptive*, whereby the topology of the mesh remains constant, with the entities only moving geometrically. There are advantages and disadvantages of both of these approaches, motivating the development of a hybrid *(hr) *method. One possibility is provided by *anisotropic mesh adaptivity*, which seeks to allow both *h-* and *r-* adaptive capabilities, and it is this type of adaptivity which I consider in detail in my MRes project.

My preliminary experimentation in solving the shallow water equations over various model domains has been so far successful. Over the past months I have developed a standalone shallow water code using *Firedrake*, an automated system for solving partial differential equations using the finite element method. Outputs from the code so far illustrate the enormous potential of a mesh adaptive approach to solving fluid dynamics problems.

I have also considered the realistic ocean domain surrounding Fukushima and have made some first attempts at emulating the 2011 tsunami. The end goal of my project is to be able to accurately and efficiently hindcast the dynamics of this particular case study using anisotropic mesh adaptivity.