Modelling climate change: the role of unresolved processes
BY PAUL D. WILLIAMS
Department of Meteorology, Centre for Global Atmospheric Modelling,
University of Reading, PO Box 243, Earley Gate, Reading RG6 6BB, UK
Our understanding of the climate system has been revolutionized recently, by the development of sophisticated computer models.
The predictions of such models are used to formulate international protocols, intended to mitigate the severity of global warming
and its impacts. Yet, these models are not perfect representations of reality, because they remove from explicit consideration
many physical processes which are known to be key aspects of the climate system, but which are too small or fast
to be modelled.
The purpose of this paper is to give a personal perspective of the current state of knowledge regarding
the problem of unresolved scales in climate models. A recent novel solution to the problem is discussed, in which it is proposed,
somewhat counter-intuitively, that the performance of models may be improved by adding random noise to represent
the unresolved processes.
It is difficult to think of a more complicated physical system than Earth’s climate. Governed by a combination of the laws
of fluid dynamics, thermodynamics, radiative energy transfer and chemistry, the climate system is composed of the
atmosphere, the oceans, ice sheets and land.
Each of these four subsystems is coupled to each of the other three,
through the exchange of immense quantities of energy, momentum and matter (Peixo´to & Oort 1984). Nonlinear
interactions occur on a dizzying range of spatial and temporal scales, both within and between the subsystems,
leading to an intricate and delicate network of feedback loops
. But climate modellers must not be dismayed by the
enormity of the challenge facing them, for, though it is difficult to think of a more complicated physical system,
it is equally difficult to think of one that has a greater impact on all the people of the world.
A general review of the problem of unresolved scales in climate models has been presented. Important unresolved
features include ocean eddies, gravity waves, atmospheric convection, clouds and small-scale turbulence, all of which
are known to be key aspects of the climate system and yet are too small to be explicitly modelled.
The law of large
numbers and an analogy with the microscale and macroscale in fluids have served to demonstrate the inadequacy
of conventional approaches to unresolved scales. The alternative stochastic approach, proposed relatively recently,
holds that a noise-based solution may be more appropriate.
Examples have been given of stochastic studies of midlatitude weather systems, El Nin˜o events and the ocean THC.
Noise-induced transitions between different stable states (§3a,c) are poorly understood at present, but they may play
a crucial role in meteorology, oceanography and climate. Indeed, one of the most important metrics with which
to assess the reliability of climate models must surely be their ability to predict the probabilities of such rapid transitions
accurately, since these are arguably the climatological phenomena that threaten us most.
are known to depend sensitively on noise levels, and yet we have seen that the sub-grid-scale noise is filtered out
of climate models as a necessity.
Given that the full spectrum of spatial and temporal scales exhibited by the climate system will not be resolvable
by models for decades, if ever, stochastic techniques offer an immediate, convenient and computationally cheap
solution. Yet much is still unknown about the potential of stochastic physics to improve climate models
even though it is 30 years since Hasselmann (1976) first raised this possibility. So strong is the evidence that weather
forecasts are improved by random noise that it is now routinely added at the European Centre for Medium-range
Weather Forecasts (Buizza et al. 1999). Furthermore, a team at the UK Met Office is currently testing various
stochastic physics schemes in their weather forecasting model (Glenn Shutts 2005, personal communication).
But, if you look at the contents of any climate journal, you will find that almost none of the modelling studies