Articles | Volume 27, issue 2
https://doi.org/10.5194/npg-27-147-2020
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the Creative Commons Attribution 4.0 License.
Special issue:
https://doi.org/10.5194/npg-27-147-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Review article
| Highlight paper
| 
03 Apr 2020
Review article | Highlight paper |
| 03 Apr 2020
| 03 Apr 2020
Baroclinic and barotropic instabilities in planetary atmospheres: energetics, equilibration and adjustment
Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford, OX1 3PU, UK
Invited contribution by Peter Read, recipient of the EGU Lewis Fry Richardson Medal 2016.
Daniel Kennedy
Max-Planck-Institut für Plasmaphysik,
Greifswald, Germany
Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford, OX1 3PU, UK
Neil Lewis
Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford, OX1 3PU, UK
Hélène Scolan
Laboratoire de Mécanique des Fluides et d'Acoustique, Université de Lyon, France
Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford, OX1 3PU, UK
Fachreddin Tabataba-Vakili
Jet Propulsion Laboratory, Pasadena, California, USA
Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford, OX1 3PU, UK
Yixiong Wang
Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford, OX1 3PU, UK
Susie Wright
Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford, OX1 3PU, UK
Roland Young
Department of Physics & National Space Science and Technology Center,
United Arab Emirates University, Al Ain, United Arab Emirates
Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford, OX1 3PU, UK
Related subject area
Subject: Bifurcation, dynamical systems, chaos, phase transition, nonlinear waves, pattern formation | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere | Techniques: Theory
Review article: Interdisciplinary perspectives on climate sciences – highlighting past and current scientific achievements
Variational techniques for a one-dimensional energy balance model
Sensitivity of the polar boundary layer to transient phenomena
High-frequency Internal Waves, High-mode Nonlinear Waves and K-H Billows on the South China Sea's Shelf Revealed by Marine Seismic Observation
Existence and influence of mixed states in a model of vegetation patterns
Rate-induced tipping in ecosystems and climate: the role of unstable states, basin boundaries and transient dynamics
Review article: Dynamical systems, algebraic topology and the climate sciences
Review article: Large fluctuations in non-equilibrium physics
Climate bifurcations in a Schwarzschild equation model of the Arctic atmosphere
Effects of rotation and topography on internal solitary waves governed by the rotating Gardner equation
Review article: Hilbert problems for the climate sciences in the 21st century – 20 years later
Anthropocene climate bifurcation
Vera Melinda Galfi, Tommaso Alberti, Lesley De Cruz, Christian L. E. Franzke, and Valerio Lembo
Nonlin. Processes Geophys., 31, 185–193, https://doi.org/10.5194/npg-31-185-2024, https://doi.org/10.5194/npg-31-185-2024, 2024
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In the online seminar series "Perspectives on climate sciences: from historical developments to future frontiers" (2020–2021), well-known and established scientists from several fields – including mathematics, physics, climate science and ecology – presented their perspectives on the evolution of climate science and on relevant scientific concepts. In this paper, we first give an overview of the content of the seminar series, and then we introduce the written contributions to this special issue.
Gianmarco Del Sarto, Jochen Bröcker, Franco Flandoli, and Tobias Kuna
Nonlin. Processes Geophys., 31, 137–150, https://doi.org/10.5194/npg-31-137-2024, https://doi.org/10.5194/npg-31-137-2024, 2024
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We consider a one-dimensional model for the Earth's temperature. We give sufficient conditions to admit three asymptotic solutions. We connect the value function (minimum value of an objective function depending on the greenhouse gas (GHG) concentration) to the global mean temperature. Then, we show that the global mean temperature is the derivative of the value function and that it is non-decreasing with respect to GHG concentration.
Amandine Kaiser, Nikki Vercauteren, and Sebastian Krumscheid
Nonlin. Processes Geophys., 31, 45–60, https://doi.org/10.5194/npg-31-45-2024, https://doi.org/10.5194/npg-31-45-2024, 2024
Short summary
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Current numerical weather prediction models encounter challenges in accurately representing regimes in the stably stratified atmospheric boundary layer (SBL) and the transitions between them. Stochastic modeling approaches are a promising framework to analyze when transient small-scale phenomena can trigger regime transitions. Therefore, we conducted a sensitivity analysis of the SBL to transient phenomena by augmenting a surface energy balance model with meaningful randomizations.
Linghan Meng, Haibin Song, Yongxian Guan, Shun Yang, Kun Zhang, and Mengli Liu
EGUsphere, https://doi.org/10.5194/egusphere-2024-92, https://doi.org/10.5194/egusphere-2024-92, 2024
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In the seismic section, high-frequency and mode-2 internal waves, along with shear instability, were identified in the ocean. Strong nonlinear high-frequency waves, believed to be from shoaling, Behind them are larger mode-2 internal solitary waves. These waves show instability, notably the second mode-2 internal waves with distinct K-H billows. Seismic data revealed that diapycnal mixing from these events in the shelf area is 3.5 times greater than than that in the slope area.
Lilian Vanderveken, Marina Martínez Montero, and Michel Crucifix
Nonlin. Processes Geophys., 30, 585–599, https://doi.org/10.5194/npg-30-585-2023, https://doi.org/10.5194/npg-30-585-2023, 2023
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In semi-arid regions, hydric stress affects plant growth. In these conditions, vegetation patterns develop and effectively allow for vegetation to persist under low water input. The formation of patterns and the transition between patterns can be studied with small models taking the form of dynamical systems. Our study produces a full map of stable and unstable solutions in a canonical vegetation model and shows how they determine the transitions between different patterns.
Ulrike Feudel
Nonlin. Processes Geophys., 30, 481–502, https://doi.org/10.5194/npg-30-481-2023, https://doi.org/10.5194/npg-30-481-2023, 2023
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Many systems in nature are characterized by the coexistence of different stable states for given environmental parameters and external forcing. Examples can be found in different fields of science, ranging from ecosystems to climate dynamics. Perturbations can lead to critical transitions (tipping) from one stable state to another. The study of these transitions requires the development of new methodological approaches that allow for modeling, analyzing and predicting them.
Michael Ghil and Denisse Sciamarella
Nonlin. Processes Geophys., 30, 399–434, https://doi.org/10.5194/npg-30-399-2023, https://doi.org/10.5194/npg-30-399-2023, 2023
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The problem of climate change is that of a chaotic system subject to time-dependent forcing, such as anthropogenic greenhouse gases and natural volcanism. To solve this problem, we describe the mathematics of dynamical systems with explicit time dependence and those of studying their behavior through topological methods. Here, we show how they are being applied to climate change and its predictability.
Giovanni Jona-Lasinio
Nonlin. Processes Geophys., 30, 253–262, https://doi.org/10.5194/npg-30-253-2023, https://doi.org/10.5194/npg-30-253-2023, 2023
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Non-equilibrium is dominant in geophysical and climate phenomena. Most of the processes that characterize energy flow occur far from equilibrium. These range from very large systems, such as weather patterns or ocean currents that remain far from equilibrium, owing to an influx of energy, to biological structures. In the last decades, progress in non-equilibrium physics has come from the study of very rare fluctuations, and this paper provides an introduction to these theoretical developments.
Kolja L. Kypke, William F. Langford, Gregory M. Lewis, and Allan R. Willms
Nonlin. Processes Geophys., 29, 219–239, https://doi.org/10.5194/npg-29-219-2022, https://doi.org/10.5194/npg-29-219-2022, 2022
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Climate change is causing rapid temperature increases in the polar regions. A fundamental question is whether these temperature increases are reversible. If we control carbon dioxide emissions, will the temperatures revert or will we have passed a tipping point beyond which return to the present state is impossible? Our mathematical model of the Arctic climate indicates that under present emissions the Arctic climate will change irreversibly to a warm climate before the end of the century.
Karl R. Helfrich and Lev Ostrovsky
Nonlin. Processes Geophys., 29, 207–218, https://doi.org/10.5194/npg-29-207-2022, https://doi.org/10.5194/npg-29-207-2022, 2022
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Internal solitons are an important class of nonlinear waves commonly observed in coastal oceans. Their propagation is affected by the Earth's rotation and the variation in the water depth. We consider an interplay of these factors using the corresponding extension of the Gardner equation. This model allows a limiting soliton amplitude and the corresponding increase in wavelength, making the effects of rotation and topography on a shoaling wave especially significant.
Michael Ghil
Nonlin. Processes Geophys., 27, 429–451, https://doi.org/10.5194/npg-27-429-2020, https://doi.org/10.5194/npg-27-429-2020, 2020
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The scientific questions posed by the climate sciences are central to socioeconomic concerns today. This paper revisits several crucial questions, starting with
What can we predict beyond 1 week, for how long, and by what methods?, and ending with
Can we achieve enlightened climate control of our planet by the end of the century?We review the progress in dealing with the nonlinearity and stochasticity of the Earth system and emphasize major strides in coupled climate–economy modeling.
Kolja Leon Kypke, William Finlay Langford, and Allan Richard Willms
Nonlin. Processes Geophys., 27, 391–409, https://doi.org/10.5194/npg-27-391-2020, https://doi.org/10.5194/npg-27-391-2020, 2020
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The climate of Earth is governed by nonlinear processes of geophysics. This paper presents energy balance models (EBMs) embracing these nonlinear processes which lead to positive feedback, amplifying the effects of anthropogenic forcing and leading to bifurcations. We define bifurcation as a change in the topological equivalence class of the system. We initiate a bifurcation analysis of EBMs of Anthropocene climate, which shows that a catastrophic climate change may occur in the next century.
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Short summary
Baroclinic and barotropic instabilities are well known as the processes responsible for the production of the most important energy-containing eddies in the atmospheres and oceans of Earth and other planets. Linear and nonlinear instability theories provide insights into when such instabilities may occur, grow to a large amplitude and saturate, with examples from the laboratory, simplified numerical models and planetary atmospheres. We conclude with a number of open issues for future research.
Baroclinic and barotropic instabilities are well known as the processes responsible for the...
