Wind. Pressure Gradient Force

Winds are the balance of three forces acting simultaneously: the pressure gradient force, the Coriolis force, and friction. The pressure gradient force is the primary cause of air movement. If the pressure gradient force were the only force acting on air, winds would always flow directly from high to low pressure. However, the Coriolis force, which is the apparent motion caused by Earth’s rotation, deflects air as it moves and causes wind to flow parallel to isobars in the absence of friction from the surface. Near the surface, frictional drag slows wind speed and deflects the direction of motion. Surface winds do not flow parallel to the isobars but rather cross them moving from high to low pressure.

Pressure Gradient Force. Winds are created by horizontal gradients in air pressure. For example, a column of air with a surface pressure of 1020 hPa has a mass of 10,400 kg m^-2. Suppose a nearby column of air, separated by a distance of 100 km, has a lower surface pressure of 1012 hPa (10,320 kg m^-2). The difference in mass between the two columns is 80 kg m^-2, which creates a pressure gradient of 8 hPa per 100 km. The resulting pressure gradient force causes air to flow from high to low pressure. This force is directed from high to low pressure at right angle to lines of equal pressure, or isobars. Closely spaced isobars indicate steep pressure gradients, strong forces, and strong winds; widely spaced isobars indicate weak pressure gradients and weak winds.

Differences in air temperature can create horizontal pressure gradients that initiate air movement. Molecules in warm air move fast and spread apart; the air becomes less dense and the column expands vertically. Conversely, molecules in a column of cold air move slowly and become dense; the column shrinks. That warm air is less dense than cold air is evident from the ideal gas law, from Eq. (3.10). If pressure remains constant, any increase in temperature must result in a corresponding decrease in density. A decrease in temperature results in an increase in density. In other words, a short column of cold, dense air exerts the same surface pressure as a tall column of warm air.

The result is that the mass of air, or air pressure, decreases more rapidly with height in a column of cold air than in a column of warm air. Consider the two columns of air in Figure 5.1. Both have a total mass of 10,400 kg m^–2 and a surface pressure of 1020 hPa. However, because cold air is denser than warm air, more air molecules are closer to the ground in the cold column than in the warm column. For example, air molecules below height A in the cold column have a combined mass of 2000 kg m^-2 . In the warm column, where air molecules spread farther apart, the mass is only 1500 kg m^-2. Both columns of air have the same total mass, and therefore the number of molecules (i.e., mass) above height A is less in the cold air (8400 kg m^-2) than in the warm air (8900 kg m^-2); and because there is less mass above height A in the cold column, air pressure (i.e., the mass of air above height A) is lower than in the warm air column. This is true at other heights.

Fig. 5.1. Pressure gradient resulting from temperature differences. In this fi gure, each dot depicts many air molecules with a combined mass per unit area of 100 kg m^-2. the atmosphere is depicted uniformly with height. In fact, mass and pressure decrease rapidly with height. This is omitted from the fi gure for simplicity and does not invalidate the general conclusions. Shown are mass and pressure at several heights for a column of cold air (left) and a column of warm air (right). Mass at the surface and at heights A, B, and C are the mass of air above each height. Pressure is the corresponding air pressure

For any given height above the surface, a column of cold air has fewer air molecules, less mass, and lower air pressure than a column of warm air. Hence, warm air is associated with high air pressure aloft and cold air is associated with low air pressure aloft. Differences in temperature, by creating a horizontal pressure gradient, initiate wind flow aloft from high pressure (warm air) to low pressure (cold air). As air aloft leaves the warm column, the mass of air in the column decreases and surface pressure decreases. Conversely, the addition of air to the cold column increases its mass and surface pressure. As a result, high surface pressure develops under the cold column and low surface pressure develops under the warm column. Surface wind flows from high pressure (cold air) to low pressure (warm air), closing the atmospheric circulation.

This simple model of thermally driven atmospheric circulation begins to explain the geographic redistribution of heat by atmospheric winds. Tropical regions, because they gain radiation, are hot and develop high pressure aloft. Polar regions, because they lose radiation, are cold and develop low pressure aloft. In response to this pressure gradient force, warm tropical air flows towards the poles aloft. A broad band of surface low pressure develops in the tropics, while the poles, where air converges aloft, develop high surface pressure. In response to this surface pressure gradient, cold polar air flows over the surface towards the equator and completes the atmospheric circulation.