Objectives: This workshop (September, 2013) brings together mathematicians and statisticians, whose research expertise is relevant to investigating threshold behaviour in complex environmental systems, with the climate scientists and ecologists who exploit mathematical modelling in their research on tipping phenomena.
The participants have identified a number of topics, problems and questions, to be discussed during the workshop activities, which are listed below. Discussion groups were formed around some of them -- these are the topics that are followed by a number inside parentheses, representing the number participants within the corresponding discussion group.
- Difference between physical data (which have clear underlying physical laws/eqns) and e.g. financial data (without underlying equations).
- Robust/generic indicators to tipping in complex systems. (10)
- Mechanisms beyond saddle-nodes, and >1-d, for tipping. (15)
- Connection between the predictions of models and real world systems. How much predictability is there? (8)
- Definition of skill of prediction methods.
- Appropriate complexity for each question.
- Estimating radius of basin of attraction. (4)
- Non-smooth phenomena in the climate system. (5)
- Testing for multi-stability in systems: dynamic hysteresis vs static hysteresis. (5)
- How to exploit multiple time-series/representations of the same phenomenon and different responses of different proxies.
- Data collection: passive vs. perturbed-with-intent.
- Exploiting natural variance and natural forcing of system.
- Improving internet/video collaboration and lectures.
- How to facilitate collaboration between conceptual model(er)s and large climate model(er)s.
Based on these discussions, the participants have identified a number of research directions, which they discussed in focus groups:
- Spatial versus temporal data analysis.
- Non-smooth mathematical models for climate.
- Multiple time series.
- Noise and attraction in random dynamical systems.
Summaries of discussions:
Summary from the group exploring "Hysteresis and multiple stability in numerical simulation"
Summary from the group exploring "Robust/generic indicators of tipping points"
Summary from the group exploring "Non-smooth phenomena in the climate system"
Summary from the group exploring "Spatial versus temporal data analysis"
Summary from the group exploring "Noise and attraction in random dynamical systems"
Summary from the group exploring “Tipping Points Beyond Saddle-Node Bifurcations”
Summary from the group exploring “Non-smooth phenomena"
Blog post by Kaitlin Hill, September 16, 2013
Blog post by Karna Gowda, September 23, 2013
Overview Talk 1: Who, or what, will tip the big climate models?, Christopher K.R.T. Jones
Overview Talk 2: Complex networks: a useful tool to detect climate transitions?, Henk Dijkstra
Estimating Climate System Sensitivities from Temporal Variability, Peter Cox
On the use of Extreme Value Theory for detecting global stability thresholds in multi-stable systems: the case of transitional plane Couette flow, Valerio Lucarini
Overview Talk 3: Intermittent criticality in financial markets high frequency trading to large-scale bubbles and crashes, Didier Sornette
Overview Talk 4: Multiple stable points, tipping points, and warning signs in ecological systems, Alan Hastings
A study on early warning signals for desertification, Anna Maria Cherubini
Overview Talk 5: Dynamical transitions in stochastic models, Rachel Kuske
Overview Talk 6: Bayesian Uncertainty Analysis for complex physical systems modelled by computer simulators, with application to tipping points, Michael Goldstein
Tipping points and power cuts, Chris Budd
A statistical approach to the forecasting of tipping points, Peter Challenor
A Coarse Grained Stochastic Interacting Particle System for Tropical Convection, Boualem Khouider
Tipping points and bifurcations - some examples and questions, Peter Ashwin
To tip or not to tip: billiard in stability regions of patterns, Jens Rademacher
Detecting Tipping points in the climate system and inferring their predictability from observations, Peter Ditlevsen
Slides of workshop presentations:
Peter Ashwin, titled "Tipping points and bifurcations - some examples and questions"
Claudie Beaulieu, titled "Early warning signals before critical transitions: sense, sensitivity and specificity"
Chris Budd (and Jon Wilson), titled "Power Cuts and Tipping Points"
Chris Budd, titled "Why do things sometimes change so fast? Tipping Points in Life and Nature"
Anna Cherubini, titled "A study on early warning signals for desertification"
Peter Cox, titled "Estimating Climate System Sensitivities from Temporal Variability"
Cees Diks (with Cars Hommes and Juanxi Wang), titled "Early Warning Signals for Critical Transitions in Finance"
Peter Ditlevsen, titled "Detecting Tipping points in the climate system and inferring their predictability from observations"
Barbara Gentz (and Niels Beglund), titled "Noise-induced passage through an unstable periodic orbit"
Michael Goldstein (and Camila Caiado), titled "Bayesian Uncertainty Analysis for complex physical systems modelled by computer simulators, with application to tipping points"
Alan Hastings, titled "Multiple stable points, tipping points, and warning signs in ecological systems"
Christopher K.R.T. Jones, titled "Who, or what, will tip the big climate models?"
Boualem Khouider, titled "A Coarse Grained Stochastic Interacting Particle System for Tropical Convection"
Christian Kuehn, titled "Some Frontiers in Mathematical Tipping Point Theory"
Rachel Kuske, titled "Dynamical transitions in stochastic models"
Frank Kwasniok, titled "Modelling and predicting critical transitions from time series"
Valerio Lucarini, titled "Breakdown of turbulence in a plane Couette flow: Extreme fluctuations and critical transitions"
R.S. MacKay, titled "Tipping Points and nudges in complex systems"
Jens Rademacher, titled "To tip or not to tip: billiard in stability regions of patterns"
Didier Sornette, titled "Intermittent criticality in financial markets"
Jesse Berwald and Marian Gidea, titled "What is the Shape of Noise Near a Tipping Point?"
Chris A. Boulton, Peter Good and Timothy M. Lenton, titled "Early warning signals of simulated Amazon rainforest dieback"
Karna Gowda, Hermann Riecke and Mary Silber, titled "Transitions between patterned states in vegetation models"
Kaitlin Hill, Dorian S. Abbot, and Mary Silber, titled "An Arctic Sea Ice Model: Analysis in the Discontinuous Albedo Limit"
Tatiana Kiseleva et al., titled "Small Noise Asymptotics, Path-dependence and Thresholds in Presence of Tipping Points"
Clare Perryman and Sebastian Wieczorek, titled "Rate Induced Tipping"
David Plotkin, Jonathan Weare and Dorian Abbot, titled "Characterizing the Kuroshio: A Random Walk to Bimodality"
Paul Ritchie and Jan Sieber, titled "Escape Rates for Tipping"
Ivan A. Sudakov, Sergey A. Vakulenko, Kenneth M. Golden, titled "Geometry of Arctic Melt Ponds: from Circles to Fractals"
Zoë Thomas et al., titled "Abrupt Transitions in the East Asian Summer Monsoon: Early warnings and missed alarms"
Jan Viebahn and Henk Dijkstra, titled "Critical transition analysis of the wind-driven ocean circulation - a new network approach"
- Marian Gidea (Yeshiva University)
- Jan Sieber (University of Exeter)
- Mary Silber (Northwestern University)
- Sebastian Wieczorek (University of Exeter)
Cite this work
Researchers should cite this work as follows:
2013 9 9
Mathematics of Climate Tipping Points (2010-2015)
This resource belongs to the Mathematics of Climate Tipping Points (2010-2015) group.