Daisyworld modeling and feedback mechanisms By Mark Wittwer Environmental Engineering Project (640.476) - 1 - Abstract Watson and Lovelock first offered Daisyworld in 1983 as a response to critics that were skeptical about ‘Gaia.’ This was a theory explaining the Earth system as a single physiological being (Lovelock, 2000) where life can exert influence on the earth’s climate similarly to how climate influences life. Daisyworld was presented as a computer model where an Earth-like planet with good growth conditions was home to two organisms; black and white daisies. The model was kept simple, with no atmosphere or oceans to illustrate the daisies’ role in temperature feedback. Throughout the life of Daisyworld, solar radiation slowly increases to replicate the Sun’s influence on planet Earth. During the slow warming trend of Daisyworld, daisies begin to grow. With a low albedo, black daisies are favoured initially due to their ability to increase the local temperature. They continue to grow and cause a positive feedback to the planet’s average temperature, making it higher than if there were no daisies. Throughout time, Daisyworld becomes warmer and the two organisms compete for space and eventually the white daisies are favoured due to their positive temperature feedback and cooler local temperature, keeping Daisyworld from becoming too hot. Later, the Sun’s increasing radiation means that the planet becomes intolerably hot for life and Daisyworld dies. The original Daisyworld gave credit to the Gaia hypothesis by showing that life could maintain a prolonged temperature comfort zone despite the constantly rising insolation. In this thesis, the simple Daisyworld model was constructed, tested and later modified and extended further to include various other feedbacks that occur in the Earth’s climate system. Firstly, insolation was adjusted according to latitude and the model showed strong dependence on the heat transfer of the planet. With no atmosphere or oceans present, latitudinal heat transfer had to be approximated which yielded results that would mimic a “daisy-Earth.” Later in the model, ice albedo, water vapour and carbon dioxide feedbacks were added. Although the feedbacks coexist and conflict in the Earth’s system, the Daisyworld model and the investigations made in this project demonstrate the strength of the individual feedbacks. Evidently, these are important to maintaining stable climate in which life can exist. There were some major problems that occurred in the project. The original Daisyworld was created simple and its purpose was to highlight the albedo feedback to temperature. Adding complexity to the model proved interesting but attempting to replicate the earth’s heat - 2 - transfer and feedbacks was very difficult. This was because the earth’s climate equations did not apply to Daisyworld and approximations had to be made. Resultantly, the model only offered limited success in demonstrating the role of feedback mechanisms. - 3 - Contents Contents................................................................................................................................1 Introduction ..........................................................................................................................7 Literature Review..................................................................................................................8 1. Daisyworld................................................................................................................8 1.1. Energy balance ..................................................................................................9 1.2. Daisyworld model............................................................................................11 1.3. Existing modifications made to Daisyworld.....................................................13 1.4. Limitations to Daisyworld................................................................................15 2. Feedback mechanisms .............................................................................................16 2.1. Ice albedo feedback .........................................................................................17 2.2. Water vapour feedback ....................................................................................17 2.3. Carbon dioxide feedback .................................................................................18 Aims ...................................................................................................................................20 Methods..............................................................................................................................22 1. Assumptions............................................................................................................22 1.1. Daisyworld ......................................................................................................22 1.2. Replicating the existing modifications to Daisyworld.......................................23 1.3. Latitudinal variation addition to Daisyworld ....................................................24 1.4. Ice albedo addition to Daisyworld....................................................................26 1.5. Water vapour addition to Daisyworld...............................................................27 1.6. Carbon dioxide addition to Daisyworld............................................................28 2. Calculations.............................................................................................................29 2.1. Common base method......................................................................................29 2.2. Original Daisyworld creation...........................................................................31 2.3. Addition of existing modifications...................................................................32 2.4. Addition of latitudinal variation .......................................................................34 2.5. Addition of ice albedo feedback.......................................................................36 2.6. Addition of water vapour feedback ..................................................................36 2.7. Addition of carbon dioxide feedback................................................................38 Results ................................................................................................................................40 1. Initial model attempt results.....................................................................................40 2. Final model results ..................................................................................................43 2.1. Original Daisyworld ........................................................................................43 2.2. Existing modifications to Daisyworld ..............................................................45 2.3. Daisyworld with added latitudinal variation.....................................................48 2.4. Daisyworld with ice albedo feedback...............................................................50 2.5. Daisyworld with water vapour feedback ..........................................................52 2.6. Daisyworld with carbon dioxide feedback........................................................55 3. Sensitivities of the model parameters.......................................................................57 3.1. Iterations..........................................................................................................57 3.2. Albedo (α) .......................................................................................................59 3.3. Growth limits...................................................................................................61 3.4. Death rate ........................................................................................................63 3.5. Horizontal heat flux (q)....................................................................................63 3.6. Number of daisies (one or two)........................................................................64 4. Testing the system’s response to change..................................................................64 Discussion and analysis.......................................................................................................67 1. Original Daisyworld ................................................................................................67 2. Existing modifications.............................................................................................67 2.1. Addition of ‘cheats’ .........................................................................................68 2.2. Addition of predators and plagues....................................................................70 - 4 - 3. Addition of latitudinal variation...............................................................................71 4. Addition of ice albedo feedback...............................................................................72 5. Addition of water vapour feedback..........................................................................73 6. Addition of carbon dioxide feedback .......................................................................75 Conclusions ........................................................................................................................77 References ..........................................................................................................................81