29/01/2014 10:44 GMT | Updated 30/03/2014 06:59 BST

Opening the Black Box: The Invisible Science of Climate Models

(Co-authored by John Norbury, Oxford University)

While the residents of the Somerset Levels languish in the miserable conditions brought by incessant deluges, the Energy and Climate Change Committee is today holding its first evidence session into the Intergovernmental Panel on Climate Change 5th Assessment Review.

The climate debate is now fuelled, not only by controversial policies such as carbon tax, but by a sense of urgency: from Somerset to Saskatchewan and from Adelaide to Atlanta, weather has been hitting us hard. One of the topics up for debate by the Commons Select Committee is the enduring problem concerning the reliability of climate models: results differ, perhaps even contradict each other, and don't agree with observations - ergo the models are flawed.

This puts us in an invidious position. Just what can we learn from this science?

One of the real problems with the climate debate is the way in which climate science is not explained but is 'refereed' in the public domain.

In 1637 the French philosopher René Descartes expounded his ideas about what constitutes good scientific method, insisting on two particular points: 1) to divide difficult problems into small parts, and to solve the problem by attacking these parts; and 2) to always proceed from simple ideas to more complex ones.

The vast majority of papers on climate science adhere to these principles, and indeed many papers devote the majority of their content to describing the hypotheses and methods used to tackle the particular problem being studied. However, the arguments that get bandied about in blogs and debates invariably focus solely on the predicted impacts of climate change, without any discussion of the caveats and assumptions that lie behind the models. Little surprise that climate scientists are often perceived as making unjustified claims, or peddling bogus theories and giving untrustworthy advice.

Global climate models, or GCMs, are hugely complicated mathematical models that describe the atmosphere, the oceans, the biosphere and the cryosphere. The maths is not difficult in the way that particle physics or Einstein's theory of relativity are perceived as difficult: that is, based on some rather perplexing ideas. Indeed, much of the basic physics that lies at the heart of these models is taught during the first two years of a university degree course. But by many measures we know far more about black holes than we know about the "black box" that constitutes a GCM.

The point is that the component parts of the Earth system can interact in incredibly complicated ways, and this makes explicit mathematical analysis of the entire problem impossible. So we adopt Descartes' principles and study the constituents of the problem, and break these parts into pieces that often prove much more tractable. For example, a so-called "radiative transfer scheme" in a GCM describes the absorption, emission and scattering of the Sun's radiation. Very often this problem is studied using a "single column model": that is, a mathematical model of the transfer processes that occur in a single, hypothetical column throughout the depth of the atmosphere, without any account being taken of the winds that blow clouds, for instance, from one place to another. The strengths and weaknesses of this part of the model can then be studied in detail, and the implications for incorporating the latest advances in modelling radiative transfer in a GCM can be assessed.

The reductionist approach of Descartes is vital: if we use a sophisticated mathematical model to understand climate change, we have to understand the anatomy of the model itself. Confining our attention to the output of GCMs is insufficient.

Considerable advances are being made in understanding many parts of the natural environment - from aerosols and ice floes to flora and fauna. The links and feedbacks between different parts of the Earth system are subtle and delicate, and we must understand the uncertainties associated with modelling each component in order to assess the big picture. So we should ask the physicists, the chemists, the biologists, the ecologists, the meteorologists, the oceanographers, and the mathematicians for their views. If the debate continues without this expert opinion, we have to question whether it is a meaningful debate at all.

Reliable forecasts of the recent freak weather have affirmed the value of mathematical modelling. One reporter in The Daily Telegraph commented after their recent visit to the operations centre of the UK Met Office "the scene resembled the set of a James Bond movie", referring to all the computers, graphics, and real-time imagery from satellites. They went on to conclude "nobody does it better", in terms of monitoring and predicting what Mother Nature will do next. Quite an accolade for the scientists, and rightly deserved too. These same scientists are exploiting this success to advance our understanding of future climate. We should listen to them.

Ian Roulstone and John Norbury are authors of Invisible in the Storm: the role of mathematics in understanding weather. Princeton University Press, 2013.