Entropy production in an energy balance Daisyworld model

Daisyworld is a simple mathematical model of a planetary system that exhibits self-regulation due to the nature of feedback between life and its environment. A two-box Daisyworld is developed that shares a number of features with energy balance climate models. Such climate models have been used to explore the hypothesis that non-equilibrium, dissipative systems such as planetary atmospheres are in a state of maximum entropy production with respect to the latitudinal flux of heat. When values for heat diffusion in the two-box Daisyworld are selected in order to maximize this rate of entropy production, the viability range of the daisies is maximized. Consequently planetary temperature is regulated over the widest possible range of solar forcing

Daisyworld: a review

Daisyworld is a simple planetary model designed to show the long-term effects of coupling between life and its environment. Its original form was introduced by James Lovelock as a defense against criticism that his Gaia theory of the Earth as a self-regulating homeostatic system requires teleological control rather than being an emergent property. The central premise, that living organisms can have major effects on the climate system, is no longer controversial. The Daisyworld model has attracted considerable interest from the scientific community and has now established itself as a model independent of, but still related to, the Gaia theory. Used widely as both a teaching tool and as a basis for more complex studies of feedback systems, it has also become an important paradigm for the understanding of the role of biotic components when modeling the Earth system. This paper collects the accumulated knowledge from the study of Daisyworld and provides the reader with a concise account of its important properties. We emphasize the increasing amount of exact analytic work on Daisyworld and are able to bring together and summarize these results from different systems for the first time. We conclude by suggesting what a more general model of life-environment interaction should be based on

The Daisyworld control system

The original Gaia Hypothesis proposed that life on Earth, along with the oceans, atmosphere and crust, forms a homeostatic system which reduces the effects of external perturbations, so that conditions are maintained to within the range that allows widespread life. Daisyworld is a simple mathematical model intended to demonstrate certain aspects of this planetary homeostasis. There have been a considerable number of extensions and developments to the original Daisyworld model. Some of this work has been produced in response to criticism of the Gaia Hypothesis and Daisyworld specifically and some has been produced by using Daisyworld as a testbed to explore a range of issues. This thesis examines the Daisyworld control system and in doing so explains how Daisyworld performs homeostasis. The control system is classified as a rein control system which is potentially applicable to a wide range of scenarios from physiological and environmental homeostasis to robotic control. A series of simple Daisyworld models are produced and aspects of the original Daisyworld are explained, in particular the inverse response to forcing: why temperature goes down on Daisyworld when the brightness of the star increases. The Daisyworld control system is evaluated within an evolutionary context. A key result is that environmental regulation emerges not despite of Darwinian evolution but because of it. Within an ecological context, it is found that increasing the complexity of a self-regulating ecosystem can increase its stability. An energy balance climate model is developed to assess the effects of non-equilibrium thermodynamic processes on the Daisyworld control system. Results are presented that support the hypothesis that when the system is in a state of maximum entropy production, homeostasis is maximised

The habitable zone of inhabited planets

ABSTRACT: In this paper we discuss and illustrate the hypothesis that life substantially alters the state of a planetary environment and therefore, modifies the limits of the HZ as estimated for an uninhabited planet. This hypothesis lead to the introduction of the Habitable Zone for Inhabited planets (hereafter InHZ), defined here as the region where the complex interaction between life and its abiotic environment is able to produce plausible equilibrium states with the necessary physical conditions for the existence and persistence of life itself. We support our hypothesis of an InHZ with three theoretical arguments, multiple evidences coming from observations of the Earth system, several conceptual experiments and illustrative numerical simulations. Conceptually the diference between the InHZ and the Abiotic HZ (AHZ) depends on unique and robust properties of life as an emergent physical phenomenon and not necesarily on the particular life forms bearing in the planet. Our aim here is to provide conceptual basis for the development of InHZ models incorporating consistently life-environment interactions. Although previous authors have explored the effects of life on habitability there is a gap in research developing the reasons why life should be systematically included at determining the HZ limits. We do not provide here definitive limits to the InHZ but we show through simple numerical models (as a parable of an inhabited planet) how the limits of the AHZ could be modified by including plausible interactions between biota and its environment. These examples aim also at posing the question that if limits of the HZ could be modified by the presence of life in those simple dynamical systems how will those limits change if life is included in established models of the AHZ

Life on Earth is hard to spot

This is the final version. Available on open access from SAGE Publications via the DOI in this record.  The triumph of the Gaia hypothesis was to spot the extraordinary influence of Life on the Earth. ‘Life’ is the clade including all extant living beings, as distinct from ‘life’ the class of properties common to all living beings. ‘Gaia’ is Life plus its effects on habitability. Life’s influence on the Earth was hard to spot for several reasons: biologists missed it because they focused on life not Life; climatologists missed it because Life is hard to see in the Earth’s energy balance; Earth system scientists opted instead for abiotic or human-centred approaches to the Earth system; Scientists in general were repelled by teleological arguments that Life acts to maintain habitable conditions. Instead, we reason from organisms’ metabolisms outwards, showing how Life’s coupling to its environment has led to profound effects on Earth’s habitability. Recognising Life’s impact on Earth and learning from it could be critical to understanding and successfully navigating the Anthropocene.Zentrum fur Kunst und Medien, Karlsruh

Role of the hydrological cycle in regulating the planetary climate system of a simple nonlinear dynamical model

International audienceWe present the construction of a dynamic area fraction model (DAFM), representing a new class of models for an earth-like planet. The model presented here has no spatial dimensions, but contains coupled parameterizations for all the major components of the hydrological cycle involving liquid, solid and vapor phases. We investigate the nature of feedback processes with this model in regulating Earth's climate as a highly nonlinear coupled system. The model includes solar radiation, evapotranspiration from dynamically competing trees and grasses, an ocean, an ice cap, precipitation, dynamic clouds, and a static carbon greenhouse effect. This model therefore shares some of the characteristics of an Earth System Model of Intermediate complexity. We perform two experiments with this model to determine the potential effects of positive and negative feedbacks due to a dynamic hydrological cycle, and due to the relative distribution of trees and grasses, in regulating global mean temperature. In the first experiment, we vary the intensity of insolation on the model's surface both with and without an active (fully coupled) water cycle. In the second, we test the strength of feedbacks with biota in a fully coupled model by varying the optimal growing temperature for our two plant species (trees and grasses). We find that the negative feedbacks associated with the water cycle are far more powerful than those associated with the biota, but that the biota still play a significant role in shaping the model climate. third experiment, we vary the heat and moisture transport coefficient in an attempt to represent changing atmospheric circulations

The GAIA theory: from Lovelock to Margulis. From a homeostatic to a cognitive autopoietic worldview

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