Articles | Volume 30, issue 4
https://doi.org/10.5194/npg-30-585-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/npg-30-585-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
11 Dec 2023
Research article |
| 11 Dec 2023
| 11 Dec 2023
Existence and influence of mixed states in a model of vegetation patterns
Lilian Vanderveken
CORRESPONDING AUTHOR
Earth and Life Institute, UCLouvain, Louvain-la-Neuve, Belgium
Marina Martínez Montero
Earth and Life Institute, UCLouvain, Louvain-la-Neuve, Belgium
Michel Crucifix
Earth and Life Institute, UCLouvain, Louvain-la-Neuve, Belgium
Related authors
Lilian Vanderveken and Michel Crucifix
EGUsphere, https://doi.org/10.5194/egusphere-2024-2830, https://doi.org/10.5194/egusphere-2024-2830, 2024
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Vegetation patterns in semi-arid regions arise from interactions between plants and environmental factors. This study uses a numerical model to explore how vegetation responds to changes in rainfall and random disturbances. We identify key timescales that influence resilience, showing that ecosystems rely on both stable and transitional states to adapt. These findings offer insights into the resilience mechanisms that help ecosystems maintain stability under environmental stress.
Takahito Mitsui, Peter Ditlevsen, Niklas Boers, and Michel Crucifix
Earth Syst. Dynam. Discuss., https://doi.org/10.5194/esd-2024-39, https://doi.org/10.5194/esd-2024-39, 2024
Preprint under review for ESD
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The late Pleistocene glacial cycles are dominated by a 100-kyr periodicity, rather than other major astronomical periods like 19, 23, 41, or 400 kyr. Various models propose distinct mechanisms to explain this, but their diversity may obscure the key factor behind the 100-kyr periodicity. We propose a time-scale matching hypothesis, suggesting that the ice-sheet climate system responds to astronomical forcing at ~100 kyr because its intrinsic timescale is closer to 100 kyr than to other periods.
Lilian Vanderveken and Michel Crucifix
EGUsphere, https://doi.org/10.5194/egusphere-2024-2830, https://doi.org/10.5194/egusphere-2024-2830, 2024
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Vegetation patterns in semi-arid regions arise from interactions between plants and environmental factors. This study uses a numerical model to explore how vegetation responds to changes in rainfall and random disturbances. We identify key timescales that influence resilience, showing that ecosystems rely on both stable and transitional states to adapt. These findings offer insights into the resilience mechanisms that help ecosystems maintain stability under environmental stress.
Victor Couplet, Marina Martínez Montero, and Michel Crucifix
EGUsphere, https://doi.org/10.5194/egusphere-2024-2279, https://doi.org/10.5194/egusphere-2024-2279, 2024
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We present SURFER v3.0, a simple climate model designed to estimate the impact of CO2 and CH4 emissions on global temperatures, sea levels, and ocean pH. We added new carbon cycle processes and calibrated the model to observations and results from more complex models, enabling use over time scales ranging from decades to millions of years. SURFER v3.0 is fast, transparent, and easy to use, making it an ideal tool for policy assessments and suitable for educational purposes.
Justin Gérard, Loïc Sablon, Jarno J. C. Huygh, Anne-Christine Da Silva, Alexandre Pohl, Christian Vérard, and Michel Crucifix
EGUsphere, https://doi.org/10.5194/egusphere-2024-1983, https://doi.org/10.5194/egusphere-2024-1983, 2024
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We used cGENIE, a climate model, to explore how changes in continental configuration, CO2 levels, and orbital configuration affect ocean oxygen levels during the Devonian period (419–359 million years ago). Key factors contributing to ocean anoxia were identified, highlighting the influence of continental configurations, atmospheric conditions, and orbital changes. Our findings offer new insights into the causes and prolonged durations of Devonian ocean anoxic events.
Justin Gérard and Michel Crucifix
Earth Syst. Dynam., 15, 293–306, https://doi.org/10.5194/esd-15-293-2024, https://doi.org/10.5194/esd-15-293-2024, 2024
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We used cGENIE, a climate model, to investigate the Atlantic Meridional Overturning Circulation (AMOC) slowdown under a warming scenario. We apply a diagnostic that was used in a previous study (Levang and Schmitt, 2020) to separate the temperature from salinity contribution to this slowdown. We find that, in our model, the initial slowdown of the AMOC was driven by temperature and that salinity takes the lead for the termination of the circulation.
Jonas Van Breedam, Philippe Huybrechts, and Michel Crucifix
Clim. Past, 19, 2551–2568, https://doi.org/10.5194/cp-19-2551-2023, https://doi.org/10.5194/cp-19-2551-2023, 2023
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We investigated the different boundary conditions to allow ice sheet growth and ice sheet decline of the Antarctic ice sheet when it appeared ∼38–34 Myr ago. The thresholds for ice sheet growth and decline differ because of the different climatological conditions above an ice sheet (higher elevation and higher albedo) compared to a bare topography. We found that the ice–albedo feedback and the isostasy feedback respectively ease and delay the transition from a deglacial to glacial state.
Mikhail Y. Verbitsky and Michel Crucifix
Clim. Past, 19, 1793–1803, https://doi.org/10.5194/cp-19-1793-2023, https://doi.org/10.5194/cp-19-1793-2023, 2023
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Are phenomenological dynamical paleoclimate models physically similar to Nature? We demonstrated that though they may be very accurate in reproducing empirical time series, this is not sufficient to claim physical similarity with Nature until similarity parameters are considered. We suggest that the diagnostics of physical similarity should become a standard procedure before a phenomenological model can be utilized for interpretations of historical records or future predictions.
Marina Martínez Montero, Michel Crucifix, Victor Couplet, Nuria Brede, and Nicola Botta
Geosci. Model Dev., 15, 8059–8084, https://doi.org/10.5194/gmd-15-8059-2022, https://doi.org/10.5194/gmd-15-8059-2022, 2022
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We present SURFER, a lightweight model that links CO2 emissions and geoengineering to ocean acidification and sea level rise from glaciers, ocean thermal expansion and Greenland and Antarctic ice sheets. The ice sheet module adequately describes the tipping points of both Greenland and Antarctica. SURFER is understandable, fast, accurate up to several thousands of years, capable of emulating results obtained by state of the art models and well suited for policy analyses.
Jonas Van Breedam, Philippe Huybrechts, and Michel Crucifix
Geosci. Model Dev., 14, 6373–6401, https://doi.org/10.5194/gmd-14-6373-2021, https://doi.org/10.5194/gmd-14-6373-2021, 2021
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Ice sheets are an important component of the climate system and interact with the atmosphere through albedo variations and changes in the surface height. On very long timescales, it is impossible to directly couple ice sheet models with climate models and other techniques have to be used. Here we present a novel coupling method between ice sheets and the atmosphere by making use of an emulator to simulate ice sheet–climate interactions for several million years.
Mikhail Y. Verbitsky and Michel Crucifix
Earth Syst. Dynam., 12, 63–67, https://doi.org/10.5194/esd-12-63-2021, https://doi.org/10.5194/esd-12-63-2021, 2021
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We demonstrate here that a single physical phenomenon, specifically, a naturally changing balance between intensities of temperature advection and diffusion in the viscous ice media, may influence the entire spectrum of the Pleistocene variability from orbital to millennial timescales.
Mikhail Y. Verbitsky and Michel Crucifix
Earth Syst. Dynam., 11, 281–289, https://doi.org/10.5194/esd-11-281-2020, https://doi.org/10.5194/esd-11-281-2020, 2020
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Using the central theorem of dimensional analysis, the π theorem, we show that the relationship between the amplitude and duration of glacial cycles is governed by a property of scale invariance that does not depend on the physical nature of the underlying positive and negative feedbacks incorporated by the system. It thus turns out to be one of the most fundamental properties of the Pleistocene climate.
Mikhail Y. Verbitsky, Michel Crucifix, and Dmitry M. Volobuev
Earth Syst. Dynam., 10, 257–260, https://doi.org/10.5194/esd-10-257-2019, https://doi.org/10.5194/esd-10-257-2019, 2019
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We demonstrate here that nonlinear character of ice sheet dynamics, which was derived naturally from the conservation laws, is an effective means for propagating high-frequency forcing upscale.
Mikhail Y. Verbitsky, Michel Crucifix, and Dmitry M. Volobuev
Earth Syst. Dynam., 9, 1025–1043, https://doi.org/10.5194/esd-9-1025-2018, https://doi.org/10.5194/esd-9-1025-2018, 2018
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Using a dynamical climate model purely reduced from the conservation laws of ice-moving media, we show that ice-sheet physics coupled with a linear climate temperature feedback conceal enough dynamics to satisfactorily explain the system response over the full Pleistocene. There is no need, a priori, to call for a nonlinear response of, for example, the carbon cycle.
Masa Kageyama, Pascale Braconnot, Sandy P. Harrison, Alan M. Haywood, Johann H. Jungclaus, Bette L. Otto-Bliesner, Jean-Yves Peterschmitt, Ayako Abe-Ouchi, Samuel Albani, Patrick J. Bartlein, Chris Brierley, Michel Crucifix, Aisling Dolan, Laura Fernandez-Donado, Hubertus Fischer, Peter O. Hopcroft, Ruza F. Ivanovic, Fabrice Lambert, Daniel J. Lunt, Natalie M. Mahowald, W. Richard Peltier, Steven J. Phipps, Didier M. Roche, Gavin A. Schmidt, Lev Tarasov, Paul J. Valdes, Qiong Zhang, and Tianjun Zhou
Geosci. Model Dev., 11, 1033–1057, https://doi.org/10.5194/gmd-11-1033-2018, https://doi.org/10.5194/gmd-11-1033-2018, 2018
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The Paleoclimate Modelling Intercomparison Project (PMIP) takes advantage of the existence of past climate states radically different from the recent past to test climate models used for climate projections and to better understand these climates. This paper describes the PMIP contribution to CMIP6 (Coupled Model Intercomparison Project, 6th phase) and possible analyses based on PMIP results, as well as on other CMIP6 projects.
Guillaume Lenoir and Michel Crucifix
Nonlin. Processes Geophys., 25, 145–173, https://doi.org/10.5194/npg-25-145-2018, https://doi.org/10.5194/npg-25-145-2018, 2018
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We develop a general framework for the frequency analysis of irregularly sampled time series. We also design a test of significance against a general background noise which encompasses the Gaussian white or red noise. Our results generalize and unify methods developed in the fields of geosciences, engineering, astronomy and astrophysics. All the analysis tools presented in this paper are available to the reader in the Python package WAVEPAL.
Guillaume Lenoir and Michel Crucifix
Nonlin. Processes Geophys., 25, 175–200, https://doi.org/10.5194/npg-25-175-2018, https://doi.org/10.5194/npg-25-175-2018, 2018
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There is so far no general framework for handling the continuous wavelet transform when the time sampling is irregular. Here we provide such a framework with the Morlet wavelet, based on the results of part I of this study. We also design a test of significance against a general background noise which encompasses the Gaussian white or red noise. All the analysis tools presented in this article are available to the reader in the Python package WAVEPAL.
Natalie S. Lord, Michel Crucifix, Dan J. Lunt, Mike C. Thorne, Nabila Bounceur, Harry Dowsett, Charlotte L. O'Brien, and Andy Ridgwell
Clim. Past, 13, 1539–1571, https://doi.org/10.5194/cp-13-1539-2017, https://doi.org/10.5194/cp-13-1539-2017, 2017
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We present projections of long-term changes in climate, produced using a statistical emulator based on climate data from a state-of-the-art climate model. We use the emulator to model changes in temperature and precipitation over the late Pliocene (3.3–2.8 million years before present) and the next 200 thousand years. The impact of the Earth's orbit and the atmospheric carbon dioxide concentration on climate is assessed, and the data for the late Pliocene are compared to proxy temperature data.
Paul J. Valdes, Edward Armstrong, Marcus P. S. Badger, Catherine D. Bradshaw, Fran Bragg, Michel Crucifix, Taraka Davies-Barnard, Jonathan J. Day, Alex Farnsworth, Chris Gordon, Peter O. Hopcroft, Alan T. Kennedy, Natalie S. Lord, Dan J. Lunt, Alice Marzocchi, Louise M. Parry, Vicky Pope, William H. G. Roberts, Emma J. Stone, Gregory J. L. Tourte, and Jonny H. T. Williams
Geosci. Model Dev., 10, 3715–3743, https://doi.org/10.5194/gmd-10-3715-2017, https://doi.org/10.5194/gmd-10-3715-2017, 2017
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In this paper we describe the family of climate models used by the BRIDGE research group at the University of Bristol as well as by various other institutions. These models are based on the UK Met Office HadCM3 models and here we describe the various modifications which have been made as well as the key features of a number of configurations in use.
N. Bounceur, M. Crucifix, and R. D. Wilkinson
Earth Syst. Dynam., 6, 205–224, https://doi.org/10.5194/esd-6-205-2015, https://doi.org/10.5194/esd-6-205-2015, 2015
P. A. Araya-Melo, M. Crucifix, and N. Bounceur
Clim. Past, 11, 45–61, https://doi.org/10.5194/cp-11-45-2015, https://doi.org/10.5194/cp-11-45-2015, 2015
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By using a statistical tool termed emulator, we study the sensitivity of the Indian monsoon during the the Pleistocene. The originality of the present work is to consider, as inputs, several elements of the climate forcing that have varied in the past, and then use the emulator as a method to quantify the link between forcing variability and climate variability. The methodology described here may naturally be applied to other regions of interest.
Q. Z. Yin, U. K. Singh, A. Berger, Z. T. Guo, and M. Crucifix
Clim. Past, 10, 1645–1657, https://doi.org/10.5194/cp-10-1645-2014, https://doi.org/10.5194/cp-10-1645-2014, 2014
M. N. A. Maris, B. de Boer, S. R. M. Ligtenberg, M. Crucifix, W. J. van de Berg, and J. Oerlemans
The Cryosphere, 8, 1347–1360, https://doi.org/10.5194/tc-8-1347-2014, https://doi.org/10.5194/tc-8-1347-2014, 2014
M. Crucifix
Clim. Past, 9, 2253–2267, https://doi.org/10.5194/cp-9-2253-2013, https://doi.org/10.5194/cp-9-2253-2013, 2013
Related subject area
Subject: Bifurcation, dynamical systems, chaos, phase transition, nonlinear waves, pattern formation | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere | Techniques: Theory
Dynamically optimal models of atmospheric motion
Energy transfer from internal solitary waves to turbulence via high-frequency internal waves: seismic observations in the northern South China Sea
Solving a North-type energy balance model using boundary integral methods
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
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
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Anthropocene climate bifurcation
Baroclinic and barotropic instabilities in planetary atmospheres: energetics, equilibration and adjustment
Alexander G. Voronovich
Nonlin. Processes Geophys., 31, 559–569, https://doi.org/10.5194/npg-31-559-2024, https://doi.org/10.5194/npg-31-559-2024, 2024
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A derivation of discrete dynamical equations for the dry atmosphere without dissipative processes based on the least action principle is presented. For a given set of generally irregularly spaced grid points and a given mode of interpolation, through the minimization of action, the algorithm ensures maximal closeness of the evolution of the discrete system to the motion of the continuous atmosphere. The spatial resolution can be adjusted while executing calculations.
Linghan Meng, Haibin Song, Yongxian Guan, Shun Yang, Kun Zhang, and Mengli Liu
Nonlin. Processes Geophys., 31, 477–495, https://doi.org/10.5194/npg-31-477-2024, https://doi.org/10.5194/npg-31-477-2024, 2024
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With seismic data, we observed high-frequency internal waves (HIWs) with amplitudes of around 10 m. A shoaling thermocline and gentle slope suggest that HIWs result from fission. Remote sensing data support this. Strong shear caused Ri below 0.25 over 20–30 km, indicating instability. HIWs enhance mixing, averaging 10-4 m2s-1, revealing a new energy cascade from shoaling waves to turbulence, and enhancing our understanding of energy dissipation and mixing in the northern South China Sea.
Aksel Samuelsberg and Per Kristen Jakobsen
Nonlin. Processes Geophys. Discuss., https://doi.org/10.5194/npg-2024-11, https://doi.org/10.5194/npg-2024-11, 2024
Revised manuscript accepted for NPG
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We explored a simplified climate model based on Earth's energy budget. One advantage of such models is that they are easier to study mathematically. Using a mathematical technique known as boundary integral methods, we have found a new way to solve these climate models. This method is particularly useful for modeling climates very different from Earth's current state, such as those on other planets or during past ice ages.
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
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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.
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.
Peter Read, Daniel Kennedy, Neil Lewis, Hélène Scolan, Fachreddin Tabataba-Vakili, Yixiong Wang, Susie Wright, and Roland Young
Nonlin. Processes Geophys., 27, 147–173, https://doi.org/10.5194/npg-27-147-2020, https://doi.org/10.5194/npg-27-147-2020, 2020
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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.
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Short summary
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.
In semi-arid regions, hydric stress affects plant growth. In these conditions, vegetation...
