Funded Grants

Climate: Complex system, simple behavior

That climate is an almost hopelessly complex system is normally taken to imply that it is therefore also very diffcult to understand and predict. Indeed, predicting the next season's total precipitation, which is especially critical to populations in arid and semi-arid regions, is still an elusive objective. Similarly, although El Niño affects weather, societies and economies worldwide, we still cannot predict its next occurrence suffciently in advance, nor are we certain about the response of the North Atlantic Ocean, which affects Europe's climate, to global climate change. Yet, we have learned over the past 15 years, that in some important ways climate behavior is, in fact, very simple.

This simplicity is expressed in the fact that the major qualitative features of natural climate variability phenomena such as El Niño may be attributed to simple mechanisms and may be represented by quite simple models. We know now, for example, that the El Niño warming events in the equatorial Pacifc ocean owe their characteristics to the slow back and forth oscillation of large scale, deep ocean waves between the west and east margins of the equatorial Pacifc Ocean. This led to a simple and very useful "delayed oscillator" paradigm for El Niño. We also understand quite a bit now about the thermohaline ocean circulation (THC) which transports warm water to the North Atlantic. This circulation may become unstable under certain circumstances such as glacial climate or global warming, with possible influences on Europe's climate. Much of our present knowledge of the THC, which is based on complex three dimensional global general circulation models, was anticipated as early as 1961 by Stommel, using an ingenuously simple model in which the ocean is represented by merely two boxes.

Earth's climate undergoes variability due to different phenomena with time scales from one year to hundreds of millions of years. El Niño induces droughts in Africa and floods in south America every 2 to 7 years; changes to the THC can create anomalously cold or warm climate over the North Atlantic that can last from several decades to a couple of hundred years. Such a change to the THC is one explanation for the "little ice age" which resulted in the near abandonment of the Viking settlements in Greenland. Ice ages have occurred every 100,000 years, etc.

While each of these climate variability phenomena has been investigated in much detail, the question of why is it that these systems are characterized by simple behavior did not arise so far, nor has it been answered yet. We suggest here that the key is that each of the climate phenomena (El Niño, THC, etc) is (weakly) coupled to the others via mutual feedbacks. Moreover, each slow time scale climate sub-system, both controls the variability of a faster one such as to keep its behavior simple, and is also affected by the faster system. These feedbacks and mutual control between different time scales have hardly been explored so far, and will be our focus in this project.

Feedback control between different sub-systems is ubiquitous in designed engineering systems. The fundamental purpose of control in such systems is to enhance robustness and reduce sensitivity to uncertainties or disturbances. E.g., the outside weather may be quite complex and variable, yet the temperature of an air-conditioned room controlled by a thermostat is much simpler and more robust. Now, the rich set of tools that are in use in control engineering to design such feedback systems, can signifcantly enhance the understanding of feedbacks between different climate phenomena. Note that this project is about understanding climate using control tools, and not about controlling climate, which we feel is inappropriate given our still very modest understanding of the inner workings of climate. In order to carry out this research we will build and analyze a hierarchy of models, from detailed and realistic three dimensional models of the ocean and atmosphere and the observations that they require, to idealized conceptual models.

Earth's Climate has been very robust over millions of years now, and in particular, the past 10,000 years during which human evolution was exceptionally rapid, were also characterized by an exceptionally stable climate. It is now understood that designed systems (in Engineering) or evolved systems (in the natural world) which are robust to certain expected perturbations, are often very fragile with respect to unexpected perturbations. We are clearly now facing an unexpected perturbation to the climate system: the atmospheric CO2 levels in 100 years will be the highest they have been during the past thirty million (!) years. Having reformulated the climate feedbacks and interactions in the language of control theory, we will thus examine the robustness of coupled climate phenomena to expected perturbation (natural climate variability), versus a possible fragility with respect to unexpected perturbations such as global warming.

I have been working on the different climate variability phenomena mentioned above for some 15 years, and have always been fascinated by this apparent simple behavior of such a highly complex system. I have been talking to numerous people from different disciplines about this problem, in search for some appropriate methodology. My Caltech collaborator and I are very excited about the potential opportunity opened by the application of tools from control theory and engineering to the climate system. Part of this project will involve the organization of a frst joint workshop of control scientists and engineers with climate dynamics scientists, in order to explore possible interactions of these two communities.

Engineers and scientists have inherently different view points, and often don't see things eye to eye. However, Control engineers such as my Caltech collaborator are used to communicating and helping specialists from other disciplines. The climate issues to be studied in this project are clearly highly relevant to people's life, and have important societal and economical implications. Doug and I are therefore looking forward to working together toward a better understanding of what controls the behavior of these natural climate systems, their robustness, and perhaps most importantly, their potential fragility with respect to human actions.