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| Titel |
Pattern formation through spatial interactions in a modified Daisyworld model |
| VerfasserIn |
Tommaso Alberti, Leonardo Primavera, Fabio Lepreti, Antonio Vecchio, Vincenzo Carbone |
| Konferenz |
EGU General Assembly 2015
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 17 (2015) |
| Datensatznummer |
250101497
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| Publikation (Nr.) |
 EGU/EGU2015-654.pdf |
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| Zusammenfassung |
| The Daisyworld model is based on a hypothetical planet, like the Earth, which receives the
radiant energy coming from a Sun-like star, and populated by two kinds of identical plants
differing by their colour: white daisies reflecting light and black daisies absorbing light.
The interactions and feedbacks between the collective biota of the planet and the
incoming radiation form a self-regulating system where the conditions for life are
maintained. We investigate a modified version of the Daisyworld model where a spatial
dependency on latitude is introduced, and both a variable heat diffusivity along
latitude and a simple greenhouse model are included. We show that the spatial
interactions between the variables of the system can generate some equilibrium
patterns which can locally stabilize the coexistence of the two vegetation types.
The feedback on albedo is able to generate new equilibrium solutions which can
efficiently self-regulate the planet climate, even for values of the solar luminosity
relatively far from the current Earth conditions. The extension to spatial Daisyworld
gives room to the possibility of inhomogeneous solar forcing in a curved planet,
with explicit differences between poles and equator and the direct use of the heat
diffusion equation. As a first approach, to describe a spherical planet, we consider the
temperature T(θ,t) and the surface coverage as depending only on time and on latitude θ
(-90° ≈¤ θ ≈¤ 90°). A second step is the introduction of the greenhouse effect in
the model, the process by which outgoing infrared radiation is partly screened by
greenhouse gases. This effect can be described by relaxing the black-body radiation
hypothesis and by introducing a grayness function g(T) in the heat equation. As a third
step, we consider a latitude dependence of the Earth’s conductivity, Ï = Ï(θ).
Considering these terms, using spherical coordinates and symmetry with respect
to θ, the modified Daisyworld equations reduce to the following set of equations
/α/wt = αw [(1- αw - αb)β(T)- γ] (1)
/αb= α [(1- α - α )β (T )- γ] (2)
/T 1 /t b Ïă w b 1 / [ /T]
/t-= Ïcp [1 - A(θ,t)]R(θ)- Ïcpg(T)T4 + r2E-cosθ/θ κ(θ)cosθ/θ (3)
where αw,b are the daisy coverages of each species, β(T) and γ are the growth rate and the
death rate per unit of time of daisies respectively, A(θ,t) is the albedo of the Earth, R(θ)
describes the incident radiation, Ï is mass density of the atmosphere, cP is the heat capacity,
κ = Ï/ÏcP, rE ≈ă 6.37 x 108 cm is the Earth’s radius and in which we use the expression of
the Laplace operator in spherical coordinates. We found that, at variance with previous
results, the system is able to self-regulate even in presence of values of the incident
luminosity which are far from the current Sun-Earth conditions. In particular, the mutual
exclusion of the two vegetation types, observed in previous models, is never observed in our
case. Of course the model can be further enriched by considering, for example, more
realistic conditions, e.g. the dependence of cp and κ on temperature, more realistic
greenhouse effect and different initial conditions of daisies, which are currently under
investigation. |
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