Abstract
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 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.
Highlights
1.1 BackgroundClimate has an important effect on vegetation
There is a slow expansion of sea ice and rapid melting, which resembles the behavior of land ice volume during glacial–interglacial cycles. This highly nonlinear oscillation in our model indicates that it might be of interest to include vegetation in “ice age oscillators”, possibly combining it with a simple carbon cycle
We described a simple dynamical systems model for climate–vegetation interaction
Summary
1.1 BackgroundClimate has an important effect on vegetation. Plant growth is affected by temperature, carbon dioxide (CO2) levels and nutrient availability. The space available for growth matters as well: ice-covered parts of land are not suitable for it. Many different effects are at play, with the albedo being one of the most important ones: vegetation is darker than bare ground or ice and absorbs more solar radiation and warms the planet. This vegetation–albedo feedback appears to be important in semi-arid regions (Otterman, 1974), where it interacts with the hydrological cycle. The vegetation–albedo feedback matters in certain high-latitude regions (Otterman et al, 1984), where boreal forests mask snow in winter, causing an effective warming of the surface (Brovkin et al, 2003; Bonan, 2008)
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