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Title: 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 » 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.« less

Authors:
 [1]; ORCiD logo [2]
  1. Univ. of Warwick, Coventry (United Kingdom). Centre for Complexity Science
  2. 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) (SC-23); 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. doi:10.5194/npg-22-275-2015.
Rombouts, J., and Ghil, M. Thu . "Oscillations in a simple climate–vegetation model". United States. doi: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 = {2015},
month = {5}
}

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