## Atmospheric pressure

Atmospheric transport that is central to climate of the first kind and the atmospheric branch of the hydrologic cycle is accomplished by the response of the Earth's atmosphere to pressure distributions. The dynamically changing distribution of atmospheric pressure is in response to the principles of energy, mass, and momentum conservation underlying the vertical and horizontal pressure gradients that set the atmosphere in motion. Measuring atmospheric pressure at the surface is essential for defining horizontal pressure patterns and related atmospheric circulation features accounting for atmospheric moisture transport.

Atmospheric pressure is the force exerted by the atmosphere on a unit area of the underlying surface. The force associated with atmospheric pressure is due to the mass of the air molecules, the kinetic activity of the gas molecules, and the pull of gravity on the gas molecules. Since weight is the gravitational force acting on a unit mass, atmospheric pressure at a given location on the Earth's surface is the weight per unit area of air above that site. Atmospheric pressure is measured in units of pascals (Pa), but the accepted practice for meteorological applications is to use the unit hectopascal (hPa) which is equal to 100 Pa (WMO, 1996). Standard sea-level pressure is 1013.25 hPa.

### 3.5.1 The gas law

Atmospheric pressure is one of the three variables that define the thermodynamic state of the atmosphere through the equation of state for a mixture of gases or the ideal gas law. Thermodynamics plays a central role in quantitative understanding of atmospheric phenomena and especially processes related to the general circulation of the atmosphere. The ideal gas law is a combination of Boyle's law and Charles' law expressing the relationship of pressure, volume, and temperature of a gas. The Earth's atmosphere is practically an ideal gas, and the ideal gas law is a basic starting point for understanding atmospheric dynamics. The ideal gas law for dry air is expressed as

where P is pressure of dry air in Pa, p is the density of dry air (1.29 kg m"3), R is the gas constant for dry air (287J kg"1 K"1), and T is ambient air temperature in K.

Equation 3.2 shows that atmospheric pressure can vary in response to changes in either atmospheric density or temperature. Consequently, atmospheric pressure variations must be expected to occur both vertically and horizontally as changes in density and temperature are realized in both dimensions. The attraction of gravity compresses the atmosphere so that the maximum air density is at the Earth's surface. In addition, air temperature decreases vertically in the lower atmosphere with increasing distance above the Earth's surface, which is the major source for heating the atmosphere.

The vertical forces of gravity and atmospheric pressure acting on the atmosphere are almost always in balance. The result is atmospheric pressure decreases exponentially with height, and atmospheric pressure at any selected height is equal to the weight of the atmosphere above that height. The hydrostatic equation relates changes in pressure to changes in height in the atmosphere in full derivative form as dp -"P (3.3)

where p is pressure (hPa), z is geometric height (m), g is acceleration due to gravity (9.81ms"2), and p is defined above (Andrews, 2000). The negative sign indicates that pressure decreases with height.

The atmospheric pressure profile (Fig. 3.3) shows that pressure is about 700 hPa at 3000 m, 500 hPa at 5500 m, and 300 hPa at 10 000 m. These pressure values indicate that an increasingly small proportion of the atmosphere is contained in the atmospheric column above a specified level above the surface. Near the surface a change in elevation of 100 m is associated with a pressure

1 100 200 300 400 500 600 700 800 9001000 Pressure (hPa)

Fig. 3.3. Atmospheric pressure profile from the Earth's surface to the upper atmosphere.

1 100 200 300 400 500 600 700 800 9001000 Pressure (hPa)

Fig. 3.3. Atmospheric pressure profile from the Earth's surface to the upper atmosphere.

decrease of 10 hPa. Horizontal pressure differences are commonly less than 10 hPa over a distance of 1000 km.

### 3.5.2 The barometer

A barometer is the instrument used to measure atmospheric pressure. The most common mercurial barometer is a cistern-type instrument that has a glass column closed at one end with the other end submerged in a mercury-filled reservoir. Mercury in the tube adjusts until the weight of the mercury column balances the atmospheric force exerted on the reservoir. The mercurial barometer is very accurate, but it is cumbersome and requires special care in handling and reading the values. The glass tube is attached to a wooden mounting for stability. The mercurial barometer requires adjustments for expansion and contraction of mercury with temperature changes and variations in gravity and latitude (Guyot, 1998).

Aneroid barometers are less accurate but more portable and more easily automated than mercurial barometers. The aneroid barometer is a fully or partially evacuated small, flexible metal box called an aneroid cell. The cell expands and contracts in response to small changes in external atmospheric pressure (DeFelice, 1998). A series of mechanical levers and linkages are attached to a pointer that is calibrated to indicate pressure. The cell can move plates of a capacitor in an electric circuit for automated transmission.

Piezoresistive barometers are increasingly common for both surface and upper air applications. The piezoresistive sensor uses very thin silicon membranes chemically etched on a small wafer. Two electrical resistance elements are deposited along the grain of the crystal, and two other elements are aligned across the grain. This configuration provides opposite resistance changes as the membrane stretches in response to pressure changes, and it alters the balance of an active Wheatstone bridge. Balancing the bridge accomplishes an accurate pressure determination (WMO, 1996).