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Active Climate Control


J. Warrington

Master thesis written in 2007-8 at Cambridge University, UK, supervised by Prof Malcolm Smith.

Climatologists have reached virtual unanimity in judging humans responsible for a severe and growing threat to the stability of the earth's climate. The mechanisms by which anthropogenic greenhouse gas (GHG) emissions bring about detrimental consequences such as temperature increases and ocean acidification are now well-understood, and the solutions to these problems represent arguably mankind's greatest challenge. These solutions can be of two kinds. Firstly diplomatic agreements can be made with the aim of reducing GHG emissions markedly over the course of this century. Although some progress is being made on this front, many argue that an investment of a second kind - in an active climate control (ACC) scheme - will be necessary in order to prevent catastrophe. Virtually everyone agrees that the cost of a 'business-as-usual' scenario would be far higher than that of taking positive action to counteract climate change. Many predictions of warming over the next 100 to 200 years, based on complex threedimensional circulation models of the climate, have been made and publicised. Despite the apparent detail in these models, there is often conflict between the predictions. The motivation for this project has therefore been that of any engineer: to reduce an extremely complex system down to a well-chosen approximate model in order to extract the basic characteristics of the system adequately but efficiently. With that achieved, the aim is not to use control theory to judge how best to control the climate in the face of the changes described above; this is something that has not been applied before to simplified climate models. A box model of the climate system has been developed. It is divided into four boxes (reservoirs) for the thermal cycle, with flows between them representing the major geophysical heat transfers, and four boxes for the carbon cycle, with carbon flows between these. The thermal cycle model is based on a paper by Harvey and Schneider; the carbon cycle model is based on a review of several papers and books. The flows between reservoirs in both cycles are coupled so that heat transfers may also be functions of carbon reservoir levels, and vice versa. The model described above is encapsulated in a matrix equation, the lines of which represent conservation laws for the flows between reservoirs. This equation can include as inputs any anthropogenic effects we wish to study: fossil fuel burning (FFB), solar dimming, deforestation, carbon sequestration etc. The nonlinear functions controlling the flow rates between the reservoirs are linearised about the equilibrium state, which was taken to be the state of the pre-industrial climate, even though technically the climate has never been in equilibrium for any sustained period of time. This gives a linear time-invariant model of the familiar type x' = Ax + Bu. This linearised model has been validated by comparing its forcing responses to those from literature. Those responses of the model that are tested are found to behave similarly to the reference sources, which suggests the 'engineering' reduction made has largely been a successful one. The model has been developed such that ACC schemes can be simulated and their consequences discussed. Many Active Climate Control schemes have been proposed since the global warming problem became apparent. These proposals include carbon sequestration; seeding the ocean surface with nutrients in order to soak up carbon by promoting biological growth; pumping nutrient-rich deep seawater to the surface for the same effect; placing a large shield, or cloud of small shields, in space to block part of the earth's sunlight; or encouraging cloud formation by spraying particles into the air to act as nucleation sites. The solar dimming (space shield) option has been studied in most detail here. Two feedback control schemes are presented. In the first, the dimming input is uniquely determined by setting the time derivative of atmospheric temperature to zero at all times. Although this holds temperature constant for any rate of solar dimming, it cannot compensate for an initial temperature offset. Also, if there is any error in the model then temperature error accumulates over time. In the second scheme, a linear quadratic regulator (LQR) is implemented. It is shown that if there is no FFB input then temperatures can be regulated to pre-industrial conditions in reasonable time. In the presence of continued FFB input, it is shown that the scheme fails but that integral feedback can be used to regulate the atmospheric temperature to its pre-industrial value. Parameters for the LQ regulator and the integral feedback are chosen so that the scheme remains practical while delivering cooling in reasonable time. Both control schemes show that a steady-state dimming of about 1.5% of incident solar radiation is required to offset emissions of 5 Gt/yr. This compares well with similar predictions in literature. The second scheme suggests that blocking a little more than 2% in the short term would be beneficial until the cooling effect has permeated the oceans. However, the major drawback of solar dimming is that it has almost no effect on the carbon cycle, as confirmed by these simulations. Therefore, dimming does nothing to prevent effects such as ocean acidification. Other control schemes have been investigated briefly, suggesting that either seeding the ocean with nutrients or carbon sequestration would be successful in limiting warming.


Type of Publication:

(12)Diploma/Master Thesis

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% Autogenerated BibTeX entry
@PhdThesis { Xxx:2008:IFA_3752
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