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Mathematics and Statistics

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Dr Paul Ritchie

Postdoctoral Research Fellow

 Paul.Ritchie@exeter.ac.uk


Overview

I'm currently a postdoc on the ECCLES project led by Prof. Peter Cox studying connections between emergent constraints and early-warning signals used to detect the approach of a tipping point. A system is often described to pass a tipping point when gradual changes made to input levels or rates cause the output to suddenly change state. Whilst Emergent Constraints are a method for reducing uncertainties in climate change projections. Other current work involves studying the possibility of briefly overshooting tipping thresholds, and the stability of methane hydrates in the sediment beneath the ocean floor.  

In my previous postdoc position, supervised by Prof. Tim Lenton and Dr. Anna Harper, I studied potential tipping points in UK ecosystem services from future land-use and climate change projections. This project involved used the Joint UK Land Environment Simulator (JULES) a land-surface model to look for tipping events in carbon stocks, greenhouse gas emissions and frehwater fluxes.

During my PhD (also here at Exeter) I studied the underlying dynamics behind tipping points, supervised by Prof. Jan Sieber and Prof. Peter Cox. In particular my work studied a more recent concept of tipping known as rate-induced tipping. For classical tipping events such as a slow passage through a fold bifurcation, so-called early-warning indicators (increase in autocorrelation and variance) have been developed to detect the approach of a tipping point. However, for rate-induced tipping the dynamics are different and thus it is unclear if these early-warning indicators can still be used for rate-induced tipping events. However, we were able to show that there exists both a delay in the time of tipping from when one would expect to see tipping and in the early-warning indicators. Furthermore, these delays are consistent such that we conclude that early-warning indicators can be used for rate-induced tipping events.

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Publications

Copyright Notice: Any articles made available for download are for personal use only. Any other use requires prior permission of the author and the copyright holder.

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Further information

Conferences and Presentations

Challenges of Predicting Critical Transitions in Natural Systems, Exeter, December 2023

NADCOM23, Non-autonomous Dynamics in Complex Systems: Theory and Applications to Critical Transitions, Dresden, Germany, October 2023 

SIAM Conference on Applied Dynamical Systems, Portland, USA, May 2023

EGU General Assembly, Lead convener, Vienna, Austria, April 2023

EGU General Assembly, Vienna, Austria, April 2023

Invited One World Mathematics of Climate seminar, Online, April 2023

Joint TiPES/CriticalEarth Conference, Munich, Germany, February 2023

OptimESM kick-off meeting, Online, February 2023

TiPES Conference, Dartington Hall, September 2022

GAMM Conference, Aachen, Germany, August 2022 

SIAM Mathematics of Planet Earth, Online, July 2022

Tipping Points Reading Group, March 2022

Sky news appearance for Nature paper, April 2021

Invited Applied Mathematics Seminar to Universiry College Cork, Online, February 2021

Emergent Constraints & Tipping Points workshop, Online, November 2020

TiPES Webinar, Online, July 2020

EGU2020: Sharing Geoscience Online, Online, May 2020

CMIP6 Analysis Workshop, Online, April 2020

XCS Seminar, February 2020

Tipping Points Reading Group, January 2020

Valuing Nature Conference, London, October 2019

European Climate Change Adaptation (ECCA) Conference, Lisbon, Portugal, May 2019

CRITICS Summer Meeting, Cork, Ireland, August 2018

JULES users Reading Group, March 2018

LWEC Conference, January 2018, Poster

Met Office visit, December 2017

Valuing Nature Conference, Edinburgh, October 2017, Poster

Tipping Points Reading Group, September 2017

CRITICS Summer meeting, Valladolid, Spain, September 2017

Dynamics Days Europe, Szeged, Hungary, June 2017

SIAM Conference on Applications of Dynamical Systems, Snowbird , USA, May 2017

Tipping Points Reading Group, August 2016

Climate Tipping Points Workshop, Dartington Hall, April 2016

Dynamical Systems Reading Group, November 2015

Dynamics Days Conference, Exeter, September 2015, Poster

Equadiff Conference, Lyon, France, July 2015

SIAM Conference on Applications of Dynamical Systems, Snowbird, USA, May 2015

Dynamical Systems Reading Group, May 2014

ICMS Tipping Points Worshop, September 2013, Poster

Emergent Constraints & Tipping Points workshop

In November 2020 we hosted an online collaborative workshop to bring together Climate Scientists, Mathematicians and Ecologists to answer key questions around the relationships between the variability and sensitivity of the Earth System and its subcomponents. The first part of the workshop discussed proposed emergent constraints on future projections, many of which are based-on assumed relationships between sensitivity and variability. The second part of the workshop examined potential climate tipping points, in both observational data and climate model projections. The programme is given below and recordings of the presentations can be found using the links attached to the talk titles:

Emergent Constraints Presentations

Monday 23rd November

16:00 – 16:15: Peter Cox & Mark Williamson: Welcome and introduction to the workshop

16:15 – 16:45: Manuel Schlund: Emergent constraints on ECS and carbon cycle feedbacks in CMIP6

16:45 – 17:00: James Annan: What can we learn about climate sensitivity from interannual variability?

17:00 – 17:15: Rebecca Varney: A spatial emergent constraint on the sensitivity of soil carbon turnover to global warming

17:15 – 17:30: Nick Watkins: On Generalized Langevin Dynamics and the Modelling of Global Mean Temperature

17:30 – 18:00: Break

18:00 – 18:30: Peter Caldwell: Evaluating and combining emergent constraints for climate sensitivity

18:30 – 18:45: Benjamin Sanderson: Addressing structural errors in emergent constraints

18:45 – 19:00: Aurélien Ribes: Making climate projections conditional on historical observations

Tuesday 24th November

16:00 – 16:30: Femke Nijsse: Emergent constraints on transient climate response and equilibrium climate sensitivity from historical warming in CMIP5 and CMIP6 models

16:30 – 16:45: Tim Palmer: Very short-range prediction skill as an emergent constraint

16:45 – 17:00: Kasia Tokarska: Observational and emergent constraints on future warming in CMIP6 models

17:00 – 17:15: Richard Wood: Does recent warming constrain long term climate sensitivity?

17:15 – 17:30: Ryan Padrón: Controls of land carbon sink projections from CMIP6 models

17:30 – 18:00: Break

18:00 – 18:15: Jens Terhaar: Emergent constraints on the Southern Ocean anthropogenic carbon uptake

18:15 – 18:45: Chad Thackeray: Assessing prior emergent constraints on surface albedo feedback in CMIP6

18:45 – 19:00: Nicholas Lutsko: Do Low Cloud-Based Emergent Constraints Fail in CMIP6?

Tipping Points Presentations

Wednesday 25th November

14:00 – 14:30: Marten Scheffer: Lost Attraction: tipping humans

14:30 – 14:45: Joe Clarke: The Compost Bomb in the Continuum Limit

14:45 – 15:00: Eoin O’Sullivan: Non-Obvious Thresholds in the Compost Bomb Model

15:00 – 15:15: Niklas Boers: Precursor signals for abrupt transitions in Earth system dynamics

15:15 – 15:45: Break

15:45 – 16:15: Ulrike Feudel: How to study tipping phenomena in highly multistable systems?

16:15 – 16:45: Ricarda Winkelmann: Beyond gradual change: Tipping points in Antarctica

16:45 – 17:00: Paul Ritchie: Overshooting Tipping Point Thresholds in A Changing Climate

Thursday 26th November

14:00 – 14:30: Peter Ditlevsen: What we learn about tipping points from past climate and models

14:30 – 14:45: Frank Kwasniok: Data-driven modelling and prediction of Atlantic Meridional Overturning Circulation collapse

14:45 – 15:00: Johannes Lohmann: Risk of tipping the overturning circulation due to increasing rates of ice melt

15:00 – 15:15: Hassan Alkhayuon: Phase-sensitive tipping: cyclic ecosystems subject to contemporary climate

15:15 – 15:30: Cris Hasan: Spatiotemporal stability of travelling waves in a Rock-Paper-Scissors model

15:30 – 16:00: Break

16:00 – 16:30: Tim Lenton: Tipping positive change

16:30 – 16:45: Nico Wunderling: Network dynamics of drought-induced tipping cascades in the Amazon rainforest

16:45 – 17:00: Concluding Remarks (Peter Cox)

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