## The theory of climate and climate modeling

The influence of atmospheric composition (and other factors) on climate can be studied by determining physical principles governing the climate and by constructing appopriate mathematical equations on the basis of these principles. As we have seen, the climate (radiation balance, temperature, circulation, etc.) is determined by the interaction of several processes. The parameters controlling these processes can be included in statistical or physico-mathematical equation systems which are called climate models. The solutions of these model equations provide the so-called climate theories. With the aid of these models, if they are formulated correctly, we can calculate theoretically the consequence of a given change in the parameters (e.g. an increase of C02 level). Furthermore, it is also possible to include the effects of human activity in the models as supplementary mathematical relations.

More precisely, climate modeling consists in the simulation of large-scale atmospheric processes by applying the basic physical principles and the correct initial conditions in a consistent way (Smagorinsky, 1974). An important part of climate modeling is the consideration of the interaction of macro-processes with phenomena taking place on the micro-scale (radiative transfer, turbulence, and processes of cloud physics and air chemistry). In the equations, the horizontal scale of variations is at least 100 km, while the vertical scale lies between 10 m and 100 km. The volume of air taken into account is a measure of the resolution of the calculation. Phenomena of smaller scale can be included in the model by appropriate statistical methods. This procedure is termed the parameterization.

If surface effects and extraterrestrial factors (e.g. the intensity of incoming solar radiation) are assumed to be known, then atmospheric processes are described by the following laws (SMIC, 1971):

(1) Newton's second law concerning the conservation of momentum;

(2) the principle of conservation of mass;

(3) the first law of thermodynamics relating the work done by the system and its temperature to the heat received or emitted;

(4) the laws of radiative transfer, relating heat emission and absorption to the molecular structure and composition of the atmosphere;

(5) the principles of diffusion and the thermodynamics of water vapour.

The mathematical formulation of these principles gives a closed system of equations governing the model. Without going into detail we have to mention that, in accordance of our foregoing discussion, small scale processes also have to be included in the model. In the governing equations the following parameters can be found: horizontal and vertical components of the wind (also the random turbulent components after parameterization), the atmospheric pressure, temperature and density as well as the mass fraction of different chemical substances.

Climate models can be diveded in four categories:

(1) Global-average models, in which the parameters determining the climate are independent of location and are averages for the whole of the atmosphere (Earth).

(2) "Statistical" models, in which the variables depend only on geographical latitude and time. In these models large scale atmospheric motions are taken into account statistically.

(3) Semiempirical climate models, in which partially empirical relations are included on the basis of atmospheric observations.

(4) Large-scale dynamic models, in which large-scale atmospheric processes are taken into account in an explicit way and all important physical effects can be modelled in a parameterized form.

The discussion of the details of these models is not within the scope of this book. We mention here only the following. It is evident that models of the first type are the simplest one, while large-scale dynamic models simulate reality most closely. However, the differential equations in these complicated models pan only be integrated numerically which involves serious computer problems. Furthermore, in simulating climate (minimum time scale is one week) the interaction of atmosphere and ocean also has to be considered. That is, the model must contain equations which relate changes in the state of the ocean to atmospheric parameters. Unfortunately the variations of the state of the ocean as a function of time are not well understood; as a result the parameterization of the effect of the ocean is particularly difficult.

Finally, in this section some words must be said about feedback mechanisms, which complicate considerably the simulation of atmospheric phenomena. Modifications in atmospheric composition can produce deviations from the present radiation balance. These changes in radiation balance bring about further effects which can accentuate (positive feedback) or suppress (negative feedback) initial variations.

One of the best-known feedback mechanisms is the radiation-temperature coupling. The principle of this coupling is as follows. If the radiant heat received by a body is increased then the temperature of the body increases. Since higher temperature involves the emission of more energy, the increased radiation emission of the body limits the temperature changes. This is the classical example of the negative feedback.

An obvious positive feedback mechanism is provided by the interrelation between the temperature of the atmosphere and the extent of polar ice. When the temperature decreases, the extent of the ice cover increases. Since the albedo of ice is much higher than that of other surfaces, this change leads to a further temperature drop; that is, the process is accentuated. In the case of temperature increase the inverse phenomenon is produced. Thus, positive feedback mechanisms are particularly serious from the point of view of climate variation, since small initial effects can lead to significant irreversible changes.

Unfortunately, the incorporation of feedback mechanisms into climate models is not easily done. Thus, we are sure that changes of the radiation balance (due e.g. to the rise of C02 level) produce modifications in the atmospheric circulation, but we do not know the nature of these modifications. We have also no doubt that variations in cloud cover (due, e.g., to anthropogenic alteration of the aerosol burden) can substantially influence the radiation balance, but we are not able to predict the direction of this effect in a reliable way sinceclouds control the transfer of incoming shortwave radiation as well as of outgoing infrared radiation.

It is obvious from this discussion that much work remains to be done to construct acceptable climate models. This work seems to be indispensable, however, to understand the relation between human activity and the atmospheric environment.

### 6.4 Present climatic variations

In the following, the word "present" refers to the last hundred years during which industrial activity has considerably increased and the scale of human activity has become large enough that an impact on climate is credible. For this time period we have fairly satisfactory data obtained by routine meterological observations, which means that a description of climatic variation during that period is an easy task. It must be emphasized that, while the climatic impact of man is most striking in large cities, these local effects will not be discussed here. Our aim is to evaluate only global modification caused by large-scale atmospheric pollution.

During the last hundred years the temperature of the Earth s atmosphere has varied significantly. The most important feature of this variation is the nearly steady temperature increase from the eighties of the last century until about 1945. The mean annual temperature increase was 0.008 C. From 1945 the temperature