climate models Climate models are an attempt to simulate and predict changes to the climate system. The climate system consists of five components, each of which is a system in itself. The components are the atmosphere, the hydrosphere (all liquid water), the cryosphere (all frozen water), the biosphere (living things) and the lithosphere. In essence the climate is driven by the balance between the incoming solar (short-wave) radiation and the outgoing terrestrial (thermal and infrared) radiation. The amount of solar radiation received at the tropics is far more than at the poles. This results in a temperature imbalance. Atmospheric and oceanic circulations consequently work to redistribute heat from the Equator to the poles. These circulations interact with the other components of the climate system through processes which transfer energy, mass, and momentum and this then determines the Earth's climate.

The climate is in dynamic equilibrium, that is, over a sufficient period of time the incoming and outgoing radiation are in global balance. Should there be changes (forcings) in either the amount of incoming or outgoing radiation, then the climate system will respond to that change by moving to a new equilibrium position. The climate will not move instantaneously to the new equilibrium climate; there will be a transition period during which there is a transient climate. The forcings which cause changes can be external to the system, such as changes in the amount of solar radiation reaching the Earth due to changes in the orbital configuration, or they can be internal. These internal forcings result from feedback within the climate system. Climate models show that increased carbon dioxide from human activity will result in a temperature increase, often referred to as global warming. This increase in temperature will lead to more water vapour in the atmosphere, and, as water vapour is also a greenhouse gas, there will be a further increase in temperature. As this reinforces the original change it is called a positive feedback. There are many examples of this type of feedback within the climate system. Negative feedback, which will counteract the original change, is less common.

Each component of the climate system takes a different amount of time to respond to a change in the radiation regime. The atmosphere takes only a few days to respond, but the surface layers of the ocean take weeks to months, and the deep circulation takes centuries. Temporal scales are as important to climate modelling as spatial scales, for they will determine which components and which processes need to be considered in a climate model. An example of this point is the lithosphere, which through processes such as mountain building can alter the climate. The processes occur, however, on such long timescales that, except for studies concerned with geological climate change, the lithosphere can be regarded as constant.

Analogue models

The term ‘climate model’ is most often used to describe computer-based models of the climate. However, past climates can be used as analogue models of future climates. These have been used to predict the consequence of global warming. There is strong evidence that during several periods in the geological past carbon dioxide levels in the atmosphere were far greater than they are now. By using data derived from geological sources it is possible to reconstruct temperature and precipitation at those times and hence build up a picture of the climate. These models can then be used as analogues for a climate perturbed by anthropogenically increased greenhouse gases. The mid-Holocene optimum (5–6 thousand years BP), The Last Interglacial (125–30 thousand years BP), and the Pliocene (3–4 million years BP), have been used as analogues for 2000, 2025, and 2050 respectively. The chief criticism of analogue models is that the forcing mechanisms in the past may not mimic those of the future. Other criticisms are that relatively local geological data are being used to represent a large area, and that the proxy data are imprecisely dated; there can also be disagreement over the reconstructed climate.

Computer-based models

Computer-based climate models attempt to predict the climate from basic physical principles. These models can be used to examine present, past, and future climates. The difference between the present-day climate simulated by the model and the climate produced by some change in the forcing is the simulated climate change. The simplest of computer-based climate models are energy balance models. These models divide the Earth into latitude zones. As latitude is the only dimension used, these are one-dimensional models. For each latitude zone the model computes the incoming and outgoing energy. The equations that govern the model are then all written in terms of the variable to be predicted, usually surface air temperature. Energy balance models of this type came to prominence in the late 1960s, when they were used to assess the sensitivity of the climate to a change in the amount of incoming solar radiation. The models predicted that a relatively small decrease in the amount of radiation reaching the Earth could lead to total glaciation. At the time when these results were published, temperatures in the northern hemisphere were on a downward trend. This led to speculation that the Earth could be heading for a new ‘ice age’. The extreme sensitivity turned out, however, to be due to the simple way in which the model represented the climate and did not present a true picture of the climate response. Energy-balance models have since increased in sophistication and are still in use today, mostly to study climates in the geological past.

The first type of model to be used, the three-dimensional atmospheric general circulation model (AGCM), is the most complex. Models of this type emerged from numerical weather-prediction models which were developed in the years after the Second World War. In the 1960s, oceanic general circulation models were developed. Since then many other components of the climate system, such as sea ice and the biosphere, have been modelled. All these models have to be coupled together in order to simulate the climate. Until the mid 1990s most large-scale climate change experiments were restricted to AGCMs, and the following discussion reflects that fact. As the name suggests, AGCMs attempt to predict the general circulation of the atmosphere from first principles. The basic laws of physics that govern the motion of the atmosphere are embodied in what are called the fundamental equations. They are the conservation of momentum (Newton's second law of motion), the conservation of mass (the continuity equation), the conservation of energy (the first law of thermodynamics), the equation of state (the ideal gas law); there is also a fundamental equation for moisture. This group of equations relates the basic variables (pressure, wind velocity, temperature, and humidity) in both space and time. Given a set of values for the variables at some starting time (the initial conditions), it should be possible to solve the equations for some future time and obtain new values for the variables. The equations are, however, extremely complex, and in order to solve them approximations have to be derived. This can be achieved in two ways, leading to two types of GCM. One is called a Cartesian grid GCM; the other a spectral GCM. The former works on a grid akin to the latitude-longitude grid which appears on maps of the Earth. The latter is much more difficult to visualize, for it represents the fundamental equations as wave forms. Both types of models typically have a horizontal grid spacing of between 250 to 800 km in both latitude and longitude. The third dimension, the vertical, usually has 10 to 20 levels to describe it. It might be thought that a sensible choice for the vertical coordinate would be pressure. This, however, leads to some interesting problems; grid points could change height and could even appear inside a mountain. To avoid these problems a method was devised called the sigma coordinate system. In this system the actual pressure at a point is divided by the surface pressure at the point vertically below it. The lowest sigma level follows the contours of the Earth's surface exactly.

Although the fundamental equations can predict the dynamics of the atmosphere, there are other physical processes that also have to be modelled, such as radiation, clouds, and surface exchanges. These processes occur on spatial scales far smaller than the grid spacing of the climate model and they are not predictable from first principles. Instead they are parameterized; that is, the equations to predict these processes are simplified and formulated as functions of the variables from the fundamental equations. There are good reasons for parameterization. First, it would be impossible computationally to predict everything from first principle. Secondly, we often do not know in enough detail the underlying principles of the processes, and so the equations have to be simplified in some way. Most parameterizations are based on sound empirical evidence or are approximations of more complex functions. An example of the latter is the parameterization of the incoming and outgoing radiation streams. For both Cartesian grid models and spectral models the calculation of these parameterizations is completed on a Cartesian grid. Spectral models therefore have to transform from one grid type to the other.

To a large extent oceanic general circulation models (OGCMs) are based on the same fundamental equations as for the atmosphere, as both are fluids. There are, however, some important differences. The atmosphere responds much more quickly to changes in the energy balance than the ocean; OGCMs therefore need to consider far longer time-scales than AGCMs. In contrast, the spatial scales of OGCMs need to be much smaller than AGCMs, for important motion occurs at lower spatial scales. The radiation treatment is less complex than for the atmosphere. The ocean is affected far more by the ocean bottom than the atmosphere is by the Earth's surface. Sea ice, by its very nature, is very different from the atmosphere and the ocean, and consequently so are the models. To a large extent sea-ice models concentrate on predicting whether sea ice exists or not at a particular location and time, rather than determining its properties as in the atmospheric models.

Once a climate model has been constructed, it needs to be validated. This is achieved by comparing the simulated present-day climate with observed data. Validation studies have revealed that general circulation models can predict on a global scale the features of the present-day climate. It should, however, be borne in mind that in the earlier studies sea-surface temperatures and sea ice were often constrained to have realistic values only. Predictions of regional-scale features are widely recognized as being poor. These large-scale climate models have been extensively used to investigate global warming. The studies suggest a 2–5 °C temperature rise in the global average. Such equilibrium studies are rather false, as the climate will reach equilibrium only long after the amount of carbon dioxide has reached some constant level. Initially most of the studies were equilibrium studies based on an instantaneous doubling of carbon dioxide. They are, however, computationally efficient, for they do not require the deep circulation of the ocean to be considered. Furthermore, the results from different climate models can easily be compared. Nevertheless atmospheric and oceanic general circulation models, as well as sea-ice models, are increasingly being coupled to predict transient climate changes. These studies allow for gradually increasing levels of carbon dioxide as well as deep ocean circulation. It should be mentioned that GCMs are not without their critics, who argue that the sensitivity of the climate to changes in carbon dioxide is overestimated.

In an effort to understand more about the regional changes that might occur with global warming, the results from large-scale climate model studies, such as those discussed above, are being used as initial conditions for regional-scale model studies. Also, as the need for policy decisions related to global warming increases, models are being formulated which include a climate model together with various socio-economic models in an effort to model future emissions of greenhouse gases and the consequent climate change.

Frances Drake

Bibliography

Houghton, J. T. (1994) Global warming: the complete briefing. Lion Publishing.

climate modelling The construction of mathematical descriptions of the general circulation of the global atmosphere for the purpose of predicting future climates. Because of their complexity, such models can be made and manipulated only with the largest, fastest, and most powerful computers and, even then, certain phenomena (e.g. cloud formation and precipitation, which occur on scales smaller than the models can accommodate, and the relationship between oceanic heat transport and the atmosphere, which is not well understood) must be greatly simplified or described by simple assumptions. See global warming and ‘greenhouse effect’.