The aim of this chapter is to introduce the basic physical laws which govern the circulation of the atmosphere and to express them in convenient mathematical forms. No attempt is made at either completeness or rigour beyond the requirements of the later chapters. Those who wish for a more detailed discussion are referred to one of the many excellent texts on dynamical meteorology which are now available. Those by Holton (1992) and by Gill (1982) are particularly recommended.

The first law of thermodynamics

The first law may be stated simply in its qualitative form: heat is a form of energy. The transformation of heat energy into various forms of mechanical energy is the process which drives the global circulation of the atmosphere and which is responsible for the formation of the weather systems whose cumulative effects define the climate of a particular region. These transformations will be discussed in more detail in Chapter 3. In this section, the first law will be expressed in mathematical terms. But, first, it will be necessary to consider the thermodynamic properties of the air which makes up the atmosphere.

The ‘thermodynamic state’ of a parcel of air is defined by specifying its composition, pressure, density, temperature, and so on. In fact, these properties are not independent of one another, but are related through the ‘equation of state’ of the air.