1
Atmospheric Circulations

Wind, or the motion of air with respect to the surface of the Earth, is fundamentally caused by variable solar heating of the Earth's atmosphere. It is initiated, in a more immediate sense, by differences of pressure between points of equal elevation. Such differences may be brought about by thermodynamic and mechanical phenomena that occur in the atmosphere both in time and space.

The energy required for the occurrence of these phenomena is provided by the sun in the form of radiated heat. While the sun is the original source, the source of energy most directly influential upon the atmosphere is the surface of the Earth. Indeed, the atmosphere is to a large extent transparent to the solar radiation incident upon the Earth, much in the same way as the glass roof of a greenhouse. That portion of the solar radiation that is not reflected or scattered back into space may therefore be assumed to be absorbed entirely by the Earth. The Earth, upon being heated, will emit energy in the form of terrestrial radiation, the characteristic wavelengths of which are long (in the order of 10 µ) compared to those of heat radiated by the sun. The atmosphere, which is largely transparent to solar but not to terrestrial radiation, absorbs the heat radiated by the Earth and re-emits some of it toward the ground.

1.1 Atmospheric Thermodynamics

1.1.1 Temperature of the Atmosphere

To illustrate the role of the temperature distribution in the atmosphere in the production of winds, a simplified version of model circulation will be presented. In this model the vertical variation of air temperature, of the humidity of the air, of the rotation of the Earth, and of friction are ignored, and the surface of the Earth is assumed to be uniform and smooth.

The axis of rotation of the Earth is inclined at approximately 66° 30´ to the plane of its orbit around the sun. Therefore, the average annual intensity of solar radiation and, consequently, the intensity of terrestrial radiation, is higher in the equatorial than in the polar regions. To explain the circulation pattern as a result of this temperature difference, Humphreys [1] proposed the following ideal experiment (Figure 1.1).

Figure 1.1 Circulation pattern due to temperature difference between two columns of fluid.

Source: From Ref. [1]. Copyright 1929, 1940 by W. J. Humphreys.

Assume that the tanks A and B are filled with fluid of uniform temperature up to level a, and that tubes 1 and 2 are closed. If the temperature of the fluid in A is raised while the temperature in B is maintained constant, the fluid in A will expand and reach the level b. The expansion entails no change in the total weight of the fluid contained in A. The pressure at c therefore remains unchanged, and if tube 2 were opened, there would be no flow between A and B. If tube 1 is opened, however, fluid will flow from A to B, on account of the difference of head (b - a). Consequently, at level c the pressure in A will decrease, while the pressure in B will increase. Upon opening tube 2, fluid will now flow through it from B to A. The circulation thus developed will continue as long as the temperature difference between A and B is maintained.

If tanks A and B are replaced conceptually by the column of air above the equator and above the pole, in the absence of other effects an atmospheric circulation will develop that could be represented as in Figure 1.2. In reality, the circulation of the atmosphere is vastly complicated by the factors neglected in this model. The effect of these factors will be discussed later in this chapter.

Figure 1.2 Simplified model of atmospheric circulation.

The temperature of the atmosphere is determined by the following processes:

• Solar and terrestrial radiation, as discussed previously
• Radiation in the atmosphere
• Compression or expansion of the air
• Molecular and eddy conduction
• Evaporation and condensation of water vapor.

1.1.2 Radiation in the Atmosphere

As a conceptual aid, consider the action of the following model. The heat radiated by the surface of the Earth is absorbed by the layer of air immediately above the ground (or the surface of the ocean) and reradiated by this layer in two parts, one going downward and one going upward. The latter is absorbed by the next higher layer of air and again reradiated downward and upward. The transport of heat through radiation in the atmosphere, according to this conceptual model, is represented in Figure 1.3.

Figure 1.3 Transport of heat through radiation in the atmosphere.

1.1.3 Compression and Expansion. Atmospheric Stratification

Atmospheric pressure is produced by the weight of the overlying air. A small mass (or particle) of dry air moving vertically thus experiences a change of pressure to which there corresponds a change of temperature in accordance with the Poisson dry adiabatic equation

A familiar example of the effect of pressure on the temperature is the heating of compressed air in tire pump.

If, in the atmosphere, the vertical motion of an air particle is sufficiently rapid, the heat exchange of that parcel with its environment may be considered to be negligible, that is, the process being considered is adiabatic. It then follows from Poisson's equation that since ascending air experiences a pressure decrease, its temperature will also decrease. The temperature drop of adiabatically ascending dry air is known as the dry adiabatic lapse rate and is approximately 1°C/100 m in the Earth's atmosphere.

Consider a small mass of dry air at position 1 (Figure 1.4). Its elevation and temperature are denoted by h1 and T1, respectively. If the particle moves vertically upward sufficiently rapidly, its temperature change will effectively be adiabatic, regardless of the lapse rate (temperature variation with height above ground) prevailing in the atmosphere. At position 2, while the temperature of the ambient air is T2, the temperature of the element of air mass is = T1 - (h2 - h1) ?a, where ?a is the adiabatic lapse rate. Since the pressure of the element and of the ambient air will be the same, it follows from the equation of state that to the difference - T2 there corresponds a difference of density between the element of air and the ambient air. This generates a buoyancy force that, if T2 < , acts upwards and thus moves the element farther away from its initial position (superadiabatic lapse rate, as in Figure 1.4), or, if T2 > , acts downwards, thus tending to return the particle to its initial position. The stratification of the atmosphere is said to be unstable in the first case and stable in the second. If T2 = , that is, if the lapse rate prevailing in the atmosphere is adiabatic, the stratification is said to be neutral. A simple example of the stable stratification of fluids is provided by a layer of water underlying a layer of oil, while the opposite (unstable) case would have the water above the oil.

Figure 1.4 Lapse rates.

1.1.4 Molecular and Eddy Conduction

Molecular conduction is a diffusion process that effects a transfer of heat. It is achieved through the motion of individual molecules and is negligible in atmospheric processes. Eddy heat conduction involves the transfer of heat by actual movement of air in which heat is stored.

1.1.5 Condensation of Water Vapor

In the case of unsaturated moist air, as an element of air ascends and its temperature decreases, at an elevation where the temperature is sufficiently low condensation will occur and heat of condensation will be released. This is equal to the heat originally required to change the phase of water from liquid to vapor, that is, the latent heat of vaporization stored in the vapor. The temperature drop in the saturated adiabatically ascending element is therefore slower than for dry air or moist unsaturated air.

1.2 Atmospheric Hydrodynamics

The motion of an elementary air mass is determined by forces that include a vertical buoyancy force. Depending upon the temperature difference between the air mass and the ambient air, the buoyancy force acts upwards (causing an updraft), downwards, or is zero. These three cases correspond to unstable, stable, or neutral atmospheric stratification, respectively. It is shown in Section 2.3.3 that, depending upon the absence or a presence of a stably stratified air layer above the top of the atmospheric boundary layer, called capping inversion, neutrally stratified flows can be classified into truly and conventionally neutral flows.

The horizontal motion of air is determined by the following forces:

1. The horizontal pressure gradient force per unit of mass, which is due to the spatial variation of the horizontal pressures. This force is normal to the lines of constant pressure, called isobars, that is, it is directed from high-pressure to low-pressure regions (Figure 1.5). Let the unit vector normal to the isobars be denoted by n, and...