Complexity in nature: new calculational tools and theoretical approaches in astronomy, meteorology, seismology, evolution, What have we learnt about complex systems; what are the prospects and limits of our description.
Chair: Hartmut Grassl Executive Director,
Session co-ordinator: Hartmut Grassl Executive
Director, WCRP; Switzerland
The predictability of climate
Tim N. Palmer
Our climate is a complex dynamical system, with variability on scales ranging 1from the individual cloud to global circulations in the atmosphere and oceans. Climate scientists interact with society through the latter's demands for accurate and detailed environmental forecasts: of weather, of El Nino and its impact on global rainfall patterns, and of man's effect on climate. The complexity of our climate system implies that quantitative predictions can only be made with comprehensive numerical models which encode the relevant laws of dynamics, thermodynamics and chemistry for a multi- constituent multi-phase fluid. Typically such models comprise some millions of scalar equations, describing the interaction of circulations on scales ranging from tens of kilometres to tens of thousands of kilometres; from the ocean depth to the upper stratosphere. These equations can only be solved on the world's largest supercomputers.
However, a fundamental question that needs to be addressed, both by producers and users of such forecasts, is the extent to which weather and climate are predictable; after all, much of chaos theory developed from an attempt to demonstrate the limited predictability of atmospheric variations. In practice, estimates of predictability are made from multiple forecasts (so-called ensemble forecasts) of comprehensive climate models. The individual forecasts differ by small perturbations to quantities that are not well known. For example, the predictability of weather is largely determined by uncertainty in a forecast's starting conditions, whilst the predictability of climate variations is also influenced by uncertainty in representing computationally the equations that govern climate (for example, how to represent clouds in a model that cannot resolve an individual cloud). Chaos theory implies that all such environmental forecasts must be expressed probabilistically; the laws of physics dictate that society cannot expect arbitrarily accurate weather and climate forecasts. The duty of the climate scientist is to strive to estimate reliable probabilities; not to disseminate forecasts with a precision that cannot be justified scientifically. Examples will be shown that, in practice, the economic value of a reliable probability forecast (produced from an ensemble prediction system) exceeds the value of a single deterministic forecast with uncertain accuracy.
However, producing reliable probability forecasts from ensembles of climate model integrations puts enormous demands on computer resources. As more is understood about the complexity of climate and the need to forecast uncertainty in our predictions of climate, the more the demand for computer power exceeds availability, notwithstanding the unrelenting advance in computer technology. It is possible that, in the future, climate scientists around the world will need to rationalise their resources in much the same way that experimental particle physicists already have.Disturbed carbon cycle
Berrien Moore III
Chair, IGBP; University of New Hampshire, USA
Modeling of policy-making and policy-implementation
The social world seems to compete well with the natural world in terms of complexity. Understanding human behaviour or the operation of social systems poses as intriguing challenges to science as that of understanding the dynamics of nature. The inherent complexity and reflexivity of the subject matter make most social scientists reluctant even to engage in formal or numerical modelling exercises comparable to those of their natural science colleagues. Yet, some aspects of human behaviour most notably, the logic of choice are more amenable to modelling than others (e.g. processes of learning or interpretation). Moreover, certain ideal type constructs the perfect market being one example are more easily analysed than their impure real-world counterparts. It is in these areas that the boldest claims can be made. The study of social systems cannot, however, be confined to these aspects and constructs. Many social scientists therefore find themselves caught at the horns of a dilemma between realism and relevance on the one hand and manageability, precision and rigour on the other.
In this presentation I will show how political scientists struggle with this dilemma in the analysis of policy making and implementation processes. One major challenge is to predict and explain what comes out of such processes. Most simply, the task can be described as one of feeding alternative options into a particular system and predicting what will come out of the political process that is thereby generated (see figure).
More specifically, I will deal with four principal challenges: (1) describing options, in terms of the criteria by which they are evaluated; (2) analysing political systems, in terms of institutional setting, configuration of preferences, and distribution of power; (3) capturing the dynamics of decision-making processes; and (4) deriving predictions about outcomes. Throughout, I will refer to the case of the global climate change negotiations for purposes of illustration.
Towards an integrative biology
and GaiaList 21:
It is said that the biosphere makes up only about one part in ten billions of the earth's mass. Yet, as a result of evolution for almost four billion years, the biosphere is presumably consisted of hundreds of millions of species, all of which are more or less related phylogenetically as well as ecologically. It is also said that each single adult is consisted of sixty trillions of cells, all of which derived from a single cell, a fertilized egg. Yet all these cells cooperatively keep the integrity of an individual.
Two new programs are being developed to understand such complexity of living organisms; "Towards An Integrative Biology" by the International Union of Biological Sciences, and "GaiaList 21" by the Zoological Society of Japan. TAIB programme emphasizes and enhances the integrative nature of the biological sciences, while GaiaList 21 proposes to prepare a list of comprehensive biological information of various living beings present on the earth and to store their genome DNA, gametes and other cells.
Uncertainty and complexity:
Uncertainty and randomness are more than a century old concepts in Science. It can be traced back to Maxwell, Boltzmann, Poincare- One way to formalize uncertainty is the idea of "sensibility of a system with respect to initial conditions". A system here means a transformation in a space of events: From a initial event, the system (process) generates another one, in a unit of time; in some cases, the process is continuous. Such systems are called "dynamical", discrete or continuous, expressing the idea of successive repetition of the process in a discrete or continuous way. Population growth and weather prediction are typical important examples to which dynamical systems have been applied, to try to foresee their future behavior. So, we want to apply the system many, many times, and we would like to describe how it tends to behave in the long future (horizon). Sensitivity with respect to initial conditions is very relevant here: The long term result may vary substantially when we vary very little the initial conditions, that is the initial event. This is clearly the case in weather prediction, since it is impossible to provide all the exact numbers for temperature, pressure, amount of rain, winds and so on, as pointed out by Lorenz in his remarkable 1963 work. Such systems are called chaotic. The concept became so much in evidence in the last two decades or so, that a controversy arose about to whom we should attribute the original idea: To one of those great mathematicians/physicists mentioned before or to Steve Smale, one of the great dynamicists of the sixties, who lead the construction of the so called hyperbolic theory in dynamics? To avoid such a discussion, perhaps we can honour Edgar Alan Poe, who prior to all of them, wrote the following remarkable paragraph:
"For, in respect to the latter branch of the supposition, it should be considered that the most trifling variation in the facts of the two cases might give rise to the most important miscalculations, by diverting thoroughly the two courses of events; very much as, in arithmetic, an error which, in its own individuality, may be inappreciable, produces, at length, by dint of multiplication at all points, a result enormously at variance with truth".
The mystery of Marie Rogér
Our present view is that most systems either provides a definite single answer in the future (possibility that was well appreciated in the sixties) or else they are chaotic or have multiple answers (much more appreciated nowadays), WHEN we disregard (throughway) a very small number of initial events or, equivalently, a small portion of the space of events. Moreover, the behavior of such systems in the horizon is concentrated in a finite number of pieces of the space of events (attractors), which can be just simple points (non-chaotical behavior) or bigger pieces (chaotic behavior) as above: Our beautiful task is to describe such attractors, whose diameter measures the degree of uncertainty of the model! This new present scenario grew up from models posed by non-dynamicists in the seventies like Lorenz, Ruelle (and Takens, a dynamicist), Henon, May, Feigenbaum, Coullet-Tresser, that in a sense challenged previous models and indeed the very objectives of dynamics.
The concept of a complex system is much more recent and still not very well posed. We know approximately what we would like to describe, like the behaviour of the neuron-networks (brain), and some properties of the dynamical system, like being non-linear, adaptive, that is, in constant evolution, having some random characteristics, multiple attractors, fractal structure and so on. Also, a complex system should not be chaotic, but very near being so (on the boundary of chaotic systems). In particular, we should not see "exponential" sensitivity with respect to initial conditions.
To mathematicians, it is a great challenge at this very moment. to interact with physicists, biologists, chemists, and perhaps even social scientists, to built up a good theory for complex systems.