Oscillations in a simple climate–vegetation model
Abstract
We formulate and analyze a simple dynamical systems model for climate–vegetation interaction. The planet we consider consists of a large ocean and a land surface on which vegetation can grow. The temperature affects vegetation growth on land and the amount of sea ice on the ocean. Conversely, vegetation and sea ice change the albedo of the planet, which in turn changes its energy balance and hence the temperature evolution. Our highly idealized, conceptual model is governed by two nonlinear, coupled ordinary differential equations, one for global temperature, the other for vegetation cover. The model exhibits either bistability between a vegetated and a desert state or oscillatory behavior. The oscillations arise through a Hopf bifurcation off the vegetated state, when the death rate of vegetation is low enough. These oscillations are anharmonic and exhibit a sawtooth shape that is characteristic of relaxation oscillations, as well as suggestive of the sharp deglaciations of the Quaternary. Our model's behavior can be compared, on the one hand, with the bistability of even simpler, Daisyworld-style climate–vegetation models. On the other hand, it can be integrated into the hierarchy of models trying to simulate and explain oscillatory behavior in the climate system. Rigorous mathematical results aremore »
- Authors:
-
[2]
- Univ. of Warwick, Coventry (United Kingdom). Centre for Complexity Science
- Ecole Normale Supérieure, Paris (France). Geosciences Dept. Environmental Research & Teaching Inst.; Univ. of California, Los Angeles, CA (United States). Atmospheric & Oceanic Sciences Dept. Inst. of Geophysics & Planetary Physics
- Publication Date:
- Research Org.:
- Univ. of California, Los Angeles, CA (United States); Univ. of Warwick, Coventry (United Kingdom); Ecole Normale Supérieure, Paris (France)
- Sponsoring Org.:
- USDOE Office of Science (SC), Biological and Environmental Research (BER); National Science Foundation (NSF); European Union (EU)
- OSTI Identifier:
- 1457327
- Grant/Contract Number:
- SC0006694; OCE-1243175
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Nonlinear Processes in Geophysics (Online)
- Additional Journal Information:
- Journal Name: Nonlinear Processes in Geophysics (Online); Journal Volume: 22; Journal Issue: 3; Journal ID: ISSN 1607-7946
- Publisher:
- European Geosciences Union - Copernicus
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 54 ENVIRONMENTAL SCIENCES
Citation Formats
Rombouts, J., and Ghil, M. Oscillations in a simple climate–vegetation model. United States: N. p., 2015.
Web. doi:10.5194/npg-22-275-2015.
Rombouts, J., & Ghil, M. Oscillations in a simple climate–vegetation model. United States. https://doi.org/10.5194/npg-22-275-2015
Rombouts, J., and Ghil, M. Thu .
"Oscillations in a simple climate–vegetation model". United States. https://doi.org/10.5194/npg-22-275-2015. https://www.osti.gov/servlets/purl/1457327.
@article{osti_1457327,
title = {Oscillations in a simple climate–vegetation model},
author = {Rombouts, J. and Ghil, M.},
abstractNote = {We formulate and analyze a simple dynamical systems model for climate–vegetation interaction. The planet we consider consists of a large ocean and a land surface on which vegetation can grow. The temperature affects vegetation growth on land and the amount of sea ice on the ocean. Conversely, vegetation and sea ice change the albedo of the planet, which in turn changes its energy balance and hence the temperature evolution. Our highly idealized, conceptual model is governed by two nonlinear, coupled ordinary differential equations, one for global temperature, the other for vegetation cover. The model exhibits either bistability between a vegetated and a desert state or oscillatory behavior. The oscillations arise through a Hopf bifurcation off the vegetated state, when the death rate of vegetation is low enough. These oscillations are anharmonic and exhibit a sawtooth shape that is characteristic of relaxation oscillations, as well as suggestive of the sharp deglaciations of the Quaternary. Our model's behavior can be compared, on the one hand, with the bistability of even simpler, Daisyworld-style climate–vegetation models. On the other hand, it can be integrated into the hierarchy of models trying to simulate and explain oscillatory behavior in the climate system. Rigorous mathematical results are obtained that link the nature of the feedbacks with the nature and the stability of the solutions. The relevance of model results to climate variability on various timescales is discussed.},
doi = {10.5194/npg-22-275-2015},
journal = {Nonlinear Processes in Geophysics (Online)},
number = 3,
volume = 22,
place = {United States},
year = {Thu May 07 00:00:00 EDT 2015},
month = {Thu May 07 00:00:00 EDT 2015}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 19 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Multiple equilibria on planet Dune: climate–vegetation dynamics on a sandy planet
journal, January 2013
- Cresto Aleina, Fabio; Baudena, Mara; D'Andrea, Fabio
- Tellus B: Chemical and Physical Meteorology, Vol. 65, Issue 1
The CLAW hypothesis: a review of the major developments
journal, January 2007
- Ayers, Greg P.; Cainey, Jill M.
- Environmental Chemistry, Vol. 4, Issue 6
Internal Variability of an Energy-Balance Model with Delayed Albedo Effects
journal, August 1982
- Bhattacharya, K.; Ghil, M.; Vulis, I. L.
- Journal of the Atmospheric Sciences, Vol. 39, Issue 8
The seasonal effect in one-dimensional Daisyworld
journal, December 2012
- Biton, Eli; Gildor, Hezi
- Journal of Theoretical Biology, Vol. 314
Forests and Climate Change: Forcings, Feedbacks, and the Climate Benefits of Forests
journal, June 2008
- Bonan, G. B.
- Science, Vol. 320, Issue 5882
On the stability of the atmosphere-vegetation system in the Sahara/Sahel region
journal, December 1998
- Brovkin, Victor; Claussen, Martin; Petoukhov, Vladimir
- Journal of Geophysical Research: Atmospheres, Vol. 103, Issue D24
The effect of solar radiation variations on the climate of the Earth
journal, January 1969
- Budyko, M. I.
- Tellus, Vol. 21, Issue 5
Oceanic phytoplankton, atmospheric sulphur, cloud albedo and climate
journal, April 1987
- Charlson, Robert J.; Lovelock, James E.; Andreae, Meinrat O.
- Nature, Vol. 326, Issue 6114
Dynamics of deserts and drought in the Sahel
journal, April 1975
- Charney, J. G.
- Quarterly Journal of the Royal Meteorological Society, Vol. 101, Issue 428
Drought in the Sahara: A Biogeophysical Feedback Mechanism
journal, February 1975
- Charney, J.; Stone, P. H.; Quirk, W. J.
- Science, Vol. 187, Issue 4175
On multiple solutions of the atmosphere–vegetation system in present‐day climate
journal, June 1998
- Claussen, Martin
- Global Change Biology, Vol. 4, Issue 5
Late Quaternary vegetation-climate feedbacks
journal, January 2009
- Claussen*, M.
- Climate of the Past, Vol. 5, Issue 2
Simulation of an abrupt change in Saharan vegetation in the Mid-Holocene
journal, July 1999
- Claussen, Martin; Kubatzki, Claudia; Brovkin, Victor
- Geophysical Research Letters, Vol. 26, Issue 14
Earth system models of intermediate complexity: closing the gap in the spectrum of climate system models
journal, March 2002
- M., Claussen; L., Mysak; A., Weaver
- Climate Dynamics, Vol. 18, Issue 7
Oscillators and relaxation phenomena in Pleistocene climate theory
journal, March 2012
- Crucifix, Michel
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 370, Issue 1962
Impact of vegetation changes on the dynamics of the atmosphere at the Last Glacial Maximum
journal, August 2005
- Crucifix, Michel; Hewitt, Christopher D.
- Climate Dynamics, Vol. 25, Issue 5
A delayed biophysical system for the Earth's climate
journal, September 1992
- De Gregorio, S.; Pielke, R. A.; Dalu, G. A.
- Journal of Nonlinear Science, Vol. 2, Issue 3
Coupling microscale vegetation?soil water and macroscale vegetation?precipitation feedbacks in semiarid ecosystems
journal, March 2007
- Dekker, Stefan C.; Rietkerk, Max; Bierkens, Marc F. P.
- Global Change Biology, Vol. 13, Issue 3
Characterization of the multiple equilibria regime in a global ocean model
journal, January 2007
- Dijkstra, Henk A.
- Tellus A: Dynamic Meteorology and Oceanography, Vol. 59, Issue 5
Low-frequency variability of the large-scale ocean circulation: A dynamical systems approach
journal, January 2005
- Dijkstra, Henk A.
- Reviews of Geophysics, Vol. 43, Issue 3
Role of a simplified hydrological cycle and clouds in regulating the climate-biota system of Daisyworld
journal, April 2009
- Fernando Salazar, Juan; Poveda, GermÁN
- Tellus B, Vol. 61, Issue 2
The role of orbital forcing, carbon dioxide and regolith in 100 kyr glacial cycles
journal, January 2011
- Ganopolski, A.; Calov, R.
- Climate of the Past, Vol. 7, Issue 4
Cryothermodynamics: the chaotic dynamics of paleoclimate
journal, October 1994
- Ghil, Michael
- Physica D: Nonlinear Phenomena, Vol. 77, Issue 1-3
Hilbert problems for the geosciences in the 21st century
journal, January 2001
- Ghil, M.
- Nonlinear Processes in Geophysics, Vol. 8, Issue 4/5
Topics in Geophysical Fluid Dynamics: Atmospheric Dynamics, Dynamo Theory, and Climate Dynamics
book, January 1987
- Ghil, M.; Childress, S.
- Applied Mathematical Sciences
Global Hopf Bifurcation in a Simple Climate Model
journal, October 1983
- Ghil, Michael; Tavantzis, John
- SIAM Journal on Applied Mathematics, Vol. 43, Issue 5
A delay differential model of ENSO variability: parametric instability and the distribution of extremes
journal, January 2008
- Ghil, M.; Zaliapin, I.; Thompson, S.
- Nonlinear Processes in Geophysics, Vol. 15, Issue 3
A sea ice climate switch mechanism for the 100-kyr glacial cycles
journal, May 2001
- Gildor, Hezi; Tziperman, Eli
- Journal of Geophysical Research: Oceans, Vol. 106, Issue C5
Influence of high-latitude vegetation feedbacks on late Palaeozoic glacial cycles
journal, July 2010
- Horton, Daniel E.; Poulsen, Christopher J.; Pollard, David
- Nature Geoscience, Vol. 3, Issue 8
Modeling the Climatic Response to Orbital Variations
journal, February 1980
- Imbrie, J.; Imbrie, J. Z.
- Science, Vol. 207, Issue 4434
Role of the biosphere in the mid-Holocene climate of West Africa
journal, January 2003
- Irizarry-Ortiz, Michelle M.
- Journal of Geophysical Research, Vol. 108, Issue D2
Microscale vegetation-soil feedback boosts hysteresis in a regional vegetation–climate system
journal, May 2008
- Janssen, Ruud H. H.; Meinders, Marcel B. J.; van NES, Egbert H.
- Global Change Biology, Vol. 14, Issue 5
El Nino on the Devil's Staircase: Annual Subharmonic Steps to Chaos
journal, April 1994
- Jin, F. -F.; Neelin, J. D.; Ghil, M.
- Science, Vol. 264, Issue 5155
Free Oscillations in a Climate Model with Ice-Sheet Dynamics
journal, December 1979
- Källén, E.; Crafoord, C.; Ghil, M.
- Journal of the Atmospheric Sciences, Vol. 36, Issue 12
Tipping elements in the Earth's climate system
journal, February 2008
- Lenton, T. M.; Held, H.; Kriegler, E.
- Proceedings of the National Academy of Sciences, Vol. 105, Issue 6
Deterministic Nonperiodic Flow
journal, March 1963
- Lorenz, Edward N.
- Journal of the Atmospheric Sciences, Vol. 20, Issue 2
Failure of climate regulation in a geophysiological model
journal, June 1994
- Lovelock, James E.; Kump, Lee R.
- Nature, Vol. 369, Issue 6483
The influence of terrestrial ecosystems on climate
journal, May 2006
- Meir, Patrick; Cox, Peter; Grace, John
- Trends in Ecology & Evolution, Vol. 21, Issue 5
The role of land surface dynamics in glacial inception: a study with the UVic Earth System Model
journal, December 2003
- Meissner, K. J.; Weaver, A. J.; Matthews, H. D.
- Climate Dynamics, Vol. 21, Issue 7-8
Self-sustained temperature oscillations on Daisyworld
journal, September 1999
- Nevison, C.; Gupta, V.; Klinger, L.
- Tellus B, Vol. 51, Issue 4
Energy balance climate models
journal, January 1981
- North, Gerald R.; Cahalan, Robert F.; Coakley, James A.
- Reviews of Geophysics, Vol. 19, Issue 1
Baring High-Albedo Soils by Overgrazing: A Hypothesized Desertification Mechanism
journal, November 1974
- Otterman, J.
- Science, Vol. 186, Issue 4163
Effects of Nontropical Forest Cover on Climate
journal, May 1984
- Otterman, J.; Chou, M-D.; Arking, A.
- Journal of Climate and Applied Meteorology, Vol. 23, Issue 5
Parameter estimation for energy balance models with memory
journal, September 2014
- Roques, Lionel; Chekroun, Mickaël D.; Cristofol, Michel
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 470, Issue 2169
Climate modeling
journal, January 1974
- Schneider, Stephen H.; Dickinson, Robert E.
- Reviews of Geophysics, Vol. 12, Issue 3
The lightning-biota climatic feedback: THE LIGHTNING-BIOTA CLIMATIC FEEDBACK
journal, November 2007
- Shepon, Alon; Gildor, Hezi
- Global Change Biology, Vol. 14, Issue 2
Thermohaline Convection with Two Stable Regimes of Flow
journal, January 1961
- Stommel, Henry
- Tellus, Vol. 13, Issue 2
A minimal model of interaction between climate and vegetation: qualitative approach
journal, November 1996
- Svirezhev, Yuri M.; von Bloh, Werner
- Ecological Modelling, Vol. 92, Issue 1
Climate, vegetation, and global carbon cycle: the simplest zero-dimensional model
journal, August 1997
- Svirezhev, Yuri M.; von Bloh, Werner
- Ecological Modelling, Vol. 101, Issue 1
El Nino Chaos: Overlapping of Resonances Between the Seasonal Cycle and the Pacific Ocean-Atmosphere Oscillator
journal, April 1994
- Tziperman, E.; Stone, L.; Cane, M. A.
- Science, Vol. 264, Issue 5155
Biological homeostasis of the global environment: the parable of Daisyworld
journal, September 1983
- Watson, Andrew J.; Lovelock, James E.
- Tellus B, Vol. 35B, Issue 4
The importance of timescales for the emergence of environmental self-regulation
journal, November 2012
- Weaver, Iain S.; Dyke, James G.
- Journal of Theoretical Biology, Vol. 313
Daisyworld: A review
journal, January 2008
- Wood, Andrew J.; Ackland, Graeme J.; Dyke, James G.
- Reviews of Geophysics, Vol. 46, Issue 1
Another look at climate sensitivity
journal, January 2010
- Zaliapin, I.; Ghil, M.
- Nonlinear Processes in Geophysics, Vol. 17, Issue 2
Enhancement of Interdecadal Climate Variability in the Sahel by Vegetation Interaction
journal, November 1999
- Zeng, N.
- Science, Vol. 286, Issue 5444
Earth system models of intermediate complexity: closing the gap in the spectrum of climate system models
journal, March 2002
- M., Claussen; L., Mysak; A., Weaver
- Climate Dynamics, Vol. 18, Issue 7
Cryothermodynamics: the chaotic dynamics of paleoclimate
journal, October 1994
- Ghil, Michael
- Physica D: Nonlinear Phenomena, Vol. 77, Issue 1-3
The importance of timescales for the emergence of environmental self-regulation
journal, November 2012
- Weaver, Iain S.; Dyke, James G.
- Journal of Theoretical Biology, Vol. 313
One-dimensional daisyworld: spatial interactions and pattern formation
journal, August 2003
- Adams, B.; Carr, J.; Lenton, T. M.
- Journal of Theoretical Biology, Vol. 223, Issue 4
Stability Analysis of the Climate-Vegetation System in the Northern High Latitudes
journal, March 2003
- Brovkin, Victor; Levis, Samuel; Loutre, Marie-France
- Climatic Change, Vol. 57, Issue 1/2
Holocene climate instability during the termination of the African Humid Period: TERMINATION OF THE AFRICAN HUMID PERIOD
journal, February 2003
- Renssen, H.; Brovkin, V.; Fichefet, T.
- Geophysical Research Letters, Vol. 30, Issue 4
Orbital forcing, climatic interactions, and glaciation cycles
journal, June 1983
- Le Treut, Hervé; Ghil, Michael
- Journal of Geophysical Research: Oceans, Vol. 88, Issue C9
Oceanic phytoplankton, atmospheric sulphur, cloud albedo and climate
journal, April 1987
- Charlson, Robert J.; Lovelock, James E.; Andreae, Meinrat O.
- Nature, Vol. 326, Issue 6114
Parameter estimation for energy balance models with memory
journal, September 2014
- Roques, Lionel; Chekroun, Mickaël D.; Cristofol, Michel
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 470, Issue 2169
Oscillators and relaxation phenomena in Pleistocene climate theory
journal, March 2012
- Crucifix, Michel
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 370, Issue 1962
The lightning-biota climatic feedback: THE LIGHTNING-BIOTA CLIMATIC FEEDBACK
journal, November 2007
- Shepon, Alon; Gildor, Hezi
- Global Change Biology, Vol. 14, Issue 2
Thermohaline Convection with Two Stable Regimes of Flow
journal, May 1961
- Stommel, Henry
- Tellus, Vol. 13, Issue 2
Baring High-Albedo Soils by Overgrazing: A Hypothesized Desertification Mechanism
journal, November 1974
- Otterman, J.
- Science, Vol. 186, Issue 4163
Modeling the Climatic Response to Orbital Variations
journal, February 1980
- Imbrie, J.; Imbrie, J. Z.
- Science, Vol. 207, Issue 4434
Enhancement of Interdecadal Climate Variability in the Sahel by Vegetation Interaction
journal, November 1999
- Zeng, N.
- Science, Vol. 286, Issue 5444
Global Hopf Bifurcation in a Simple Climate Model
journal, October 1983
- Ghil, Michael; Tavantzis, John
- SIAM Journal on Applied Mathematics, Vol. 43, Issue 5
The Role of Vegetation–Climate Interaction and Interannual Variability in Shaping the African Savanna
journal, August 2000
- Zeng, Ning; Neelin, J. David
- Journal of Climate, Vol. 13, Issue 15
Climate Stability for a Sellers-Type Model
journal, January 1976
- Ghil, Michael
- Journal of the Atmospheric Sciences, Vol. 33, Issue 1
Sea ice, as the glacial cycles’ climate switch, and interhemispheric thermohaline teleconnections
journal, January 2001
- Gildor, Hezi; Tziperman, Eli
- Annals of Glaciology, Vol. 33
The role of orbital forcing, carbon dioxide and regolith in 100 kyr glacial cycles
journal, July 2011
- Ganopolski, A.; Calow, R.
- Climate of the Past Discussions
A delay differential model of ENSO variability: parametric instability and the distribution of extremes
journal, January 2008
- Ghil, M.; Zaliapin, I.; Thompson, S.
- Nonlinear Processes in Geophysics, Vol. 15, Issue 3
Another look at climate sensitivity
journal, January 2010
- Zaliapin, I.; Ghil, M.
- Nonlinear Processes in Geophysics, Vol. 17, Issue 2
Hilbert problems for the geosciences in the 21st century
journal, January 2001
- Ghil, M.
- Nonlinear Processes in Geophysics, Vol. 8, Issue 4/5
Works referencing / citing this record:
A discrete dynamical system: The poor man’s magnetohydrodynamic (PMMHD) equations
journal, October 2019
- Alberti, T.; Consolini, G.; Carbone, V.
- Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 29, Issue 10
Climate bistability of Earth-like exoplanets
journal, December 2019
- Murante, Giuseppe; Provenzale, Antonello; Vladilo, Giovanni
- Monthly Notices of the Royal Astronomical Society, Vol. 492, Issue 2
Noise-induced transitions and shifts in a climate–vegetation feedback model
journal, April 2018
- Alexandrov, Dmitri V.; Bashkirtseva, Irina A.; Ryashko, Lev B.
- Royal Society Open Science, Vol. 5, Issue 4
Ocean–atmosphere interactions modulate irrigation's climate impacts
journal, January 2016
- Krakauer, Nir Y.; Puma, Michael J.; Cook, Benjamin I.
- Earth System Dynamics, Vol. 7, Issue 4
Noise-induced transitions and shifts in a climate–vegetation feedback model
journal, April 2018
- Alexandrov, Dmitri V.; Bashkirtseva, Irina A.; Ryashko, Lev B.
- Royal Society Open Science, Vol. 5, Issue 4