Climate is the average weather of a place as determined by temperature and various meteorological conditions such as precipitation, wind, glaciations and also by the frequency of extreme events such as typhoons, hurricanes, etc. The most important attribute of climate change is however the variations in temperature.
The evidences gathered by climatologists such as historical documents, tree rings, change in sea level, etc., have shown that our planet has maintained an average temperature within a limited range, but seem to be changing continuously.
Thus, to predict the future impacts of anthropogenic activities on the global climate and consequently on the key environmental parameters, a mathematical model needs to be developed that explains the past.
If various parameters affecting climatic change are considered, the mathematical model will become complex. Therefore a simple zero- dimensional-model, which calculates only the single parameter, temperature as the main attribute of climate change, is proposed.
In order to avoid further complexity in the mathematical model the various factors of temperature such as altitude, longitude, latitude as well as time is ignored.
In such models, the solar energy absorbed by the earth is equated with the energy that the earth radiates back to space. Radiation from the sun arrives just outside the earth's atmosphere with an average annual intensity, called solar constant S, equal to 1370 W/m2.
A simple way to calculate the total rate at which energy hits the earth is to note that all of the flux passing through a 'hoop' having radius equal to that of the earth, are placed normal to the incoming radiation that strikes the earth's surface.
Some of the incoming solar energy which hits the earth is reflected back into space. Such reflected energy is not absorbed by the earth or its atmosphere and thus does not contribute to their heating.
The fraction of incoming solar radiation that is reflected is called Albedo and for the earth, the global annual mean value is estimated to be 31 per cent. The radiation which is not reflected is absorbed.
Now, we will estimate the rate at which the earth sends energy back into space. Since, heat transfer from earth cannot occur by conduction or convection; the only way in which the earth gets rid of energy is via radiation.
In this model, the earth is considered to be a black body (emissivity = 100 per cent). Again we assume that it is isothermal, temperature is same everywhere in the planet. The energy radiated from this black body (earth) with surface area 4nR2 is given by the 'Stefan-Boltzman' equation as
The factor that makes the model differ so much from reality is that it does not account for interactions between the atmosphere and the radiation that is emitted from the earth's surface. That is, it does not include the greenhouse effect.