Air Pressure and Winds

Air Pressure: the weight of the air about us. Weight is the force exerted by gravity on a unit mass.

The average pressure at the sea level is about 1.0 kg cm-2 (1000 mb), which can be calculated in the knowledge of MA: total mass of the atmosphere (5.26x1018 kg), g0: gravitational acceleration (9.8 m s-2), and RE: mean radius of the earth (6.37x106 m)

The average sea-level air pressure reading is 1013.25 mb (29.92 inch of mercury). The usual worldwide range in sea level air pressure is about 970 to 1040 mb (28.64 to 30.71 inch of mercury).

The lowest sea level air pressure ever recorded was 870 mb (25.69 in.) in the eye of Typhoon (Tip) over the Pacific Ocean, whereas the highest sea level air pressure ever recorded was 1084 mb (32.01 in.) at Siberia associated with an extremely cold air mass. In the US, the lowest observed pressure was 882 mb during Hurricane Wilma (2005), while the highest observed pressure was 1064 mb in Miles City, Montana

Figure 8.4, page #203 (Ahrens)

Pressure balance: At any specified point within the atmosphere, air pressure has the same magnitude in all directions.

Air density: Mass of air molecules per unit volume of air. Air density has its maximum at the Earth's surface where air molecules are most closely spaced. The number of air molecules per unit volume decreases with altitude rapidly such that air density at 16 km (~10 mile) altitude is only about 10% of its average sea level value.

The decrease of air density with altitude is accompanied by a decline in air pressure. Florin Perier (French, 1658) was the first who observed the drop of air pressure with altitude. Because of the compressibility of air, air pressure and air density decrease rapidly with altitude in the lower troposphere and become more gradual aloft.

Figure 1.8, page #11 (Ahrens)

The Earth's atmosphere is thinner with altitude. Half of the atmosphere's mass lies between the Earth's surface and an altitude of about 5.5 km (18,000 ft). About 99% of the atmosphere's mass is below 32 km (20 mile). In terms of air pressure, at an altitude of only 32 km, air pressure is less than 1% of its average sea level value. air pressure at Denver "mile-high" city, 1584 m (5280 ft), is about 83% of the air pressure at Boston (about sea level).

The atmosphere has no clearly defined upper boundary. Rather, the Earth's atmosphere gradually merges with the highly rarefied interplanetary gases, hydrogen and helium, at about 1000 km (620 mile). If the Earth's atmosphere had a uniform density throughout and if air temperature were equal to the average value at sea level (15C, 59F), the top of the atmosphere would be at only 8 km (5 mile) altitude.

Pressure gradient: the change in pressure with distance. Horizontal variations in air pressure is much less than the vertical one. In fact, the same pressure change observed in the lowest 30 m (98 ft) of the troposphere may not be equaled over a horizontal distance of 200 km (124 mile) at sea level.

Ideal (perfect) gas: the one which follows kinetic molecular theory precisely. Although the atmosphere is a mixture of many gases, it behaves much as if it were a single ideal gas.

Charles's law: i) At constant pressure, the absolute temperature and density of an ideal gas are inversely proportional. T a (1/ r) ii) At constant density, the pressure and absolute temperature of an ideal gas are directly proportional. T a P

Boyle's law: At constant temperature, the pressure and density of an ideal gas are directly proportional. P a r

The combined Charles's and Boyle's laws give ideal gas law, that is: P a r T The constant of proportionality, R, varies depending on the specific gas.

Equation of state: the one describes approximately the behavior of dry air. P = rRT, where R = 287 J/kg-K

Virtual temperature (Tv): the temperature of dry air having same pressure and density as moist air. Tv = T(1+0.61q), where q refers to specific humidity, which is the ratio of the mass of water vapor to the mass of humid air, expressed as grs of water vapor per kg of humid air. The equation of state for humid air then becomes P = rRTv

Temperature effect: Temperature is a measure of the average kinetic energy of individual air molecules. If air is heated within a closed container, air pressure inside the container will rise following Charles's 2nd law. The air density remains constant without adding/removing air in/from the container.

However, the atmosphere is not confined by walls (except the Earth's surface), so the air is free to expand and contract. Air density is variable within the atmosphere. Therefore, when the air is heated, air pressure decreases as a result of reduction in air density. Warm air is lighter (less dense) and consequently exerts less pressure. Cold air, on the other hand, is heavier (more dense) exerting higher pressure.

Water vapor effect: Humid air is lighter (less dense) exerting less pressure than dry air at the same temperature. This is because molecular weight of water is less than average molecular weight of dry air.

Cold, dry air produce higher surface pressure than do warm, humid air. Warm, dry air produces higher surface pressure than equally warm, but more humid air.

Pressure tendency: the change in pressure with time. Pressure changes at a given location at the Earth's surface as a result of i) air mass advection, ii) local effects.

Barometer: the instrument used to monitor changes in air pressure. There are two basic types of barometer: i) mercury, and ii) aneroid. Mercury barometer invented by Torricelli (1643) is more accurate, but less portable than aneroid (non-liquid) barometer.

Mercury barometer consists of a glass tube and an open container of mercury. The tube, filled with mercury, is inverted into the container. The height of the mercury column is a measure of the air pressure. The average air pressure at sea level supports the mercury column in the tube to a height of 760 mm.

Figure 8.5, page #203 (Ahrens)

Figure 8.6, page #204 (Ahrens)

Barograph: an instrument which records the continuous trace of air pressure with time. It has an aneroid cell which is tighly sealed. Before it was sealed, the air is partially removed, so small changes in air pressure cause the cell to contract or expand.

Figure 8.7, page #205 (Ahrens)

Figure 8.8, page #205 (Ahrens)

Altimetry: the determination of altitude above mean sea level based on air pressure. An altimeter typically does not give the true altitude. The altimeter reading is the true altitude only when air temperature and pressure matches the standard atmosphere. The discrepancy between the altimeter reading and the true altitude can pose series problems, especially during the takeoff and landing phases of flight.

Air pressure drops more rapidly with altitude in a column of cold (dense) air than in a column of warm (less dense) air. Therefore, air pressure has a certain value (i.e. 500 mb) at a lower altitude over the cold (dense) air than over warm (less dense) air. When an aircraft flies into colder air than specified by the standard atmosphere, altimeter reading will be higher than the true altitude.

Figures 2,3, page #210 (Ahrens)

Radio altimeter: the instrument that determines the altitude using radio waves.

Reduction of station pressure (Pst) to sea level pressure (Psl):

Psl = Pst exp(g h / R <T>)

where: h is the height of the station, g is an approximate to gravitational acceleration (g0), R is the gas constant, and T is the average absolute temperature in the layer, K.

<T> = (T + T-12h)/2.

Figure 8.9, page #205 (Ahrens)

Pressure on a weather map is given in millibar (mb) unit in three digits with one decimal point, for example, 102 represents 1010.2 mb, 943 represents 994.3 mb etc. Pressure change in last 3 hours is also given in mb with one of the following pressure tendency symbols: / increase, \ decrease, and - no change.

Isobars: lines of constant pressure. Isobars are plotted with 4 mb interval on the weather map, for example, 1000 mb, 1004 mb etc.

Wind: an air motion relative to the Earth's surface. It results from the interaction of several forces in the atmosphere. It can be considered as a continuous stream of air composed of discrete air parcel. The movement of an air parcel in the atmosphere follows two principles of motion, formulated by Isaac Newton (1642-1727):

i) An object at rest will remain at rest and an object in motion with remain in motion (and travel at a constant velocity along a straight line) as long as no force is exerted on the object.

ii) The force exerted on an object equals its mass times the acceleration produced. When the mass of an object is constant, the force acting on the object is directly related to the acceleration produced.

Wind is a vector quantity, that is, has both direction and magnitude. Hence, an acceleration in wind may consists of a change in speed or direction or both.

The forces that affect horizontal and vertical air motions in the atmosphere are i) pressure gradient force, ii) centripetal force, iii) coriolis force, iv) friction, and v) gravity.

Pressure gradient force: the resulting force based on the difference in pressure over a given distance. It arises from spatial variations in air temperature and, to a lesser extent, water vapor concentration. The greater the pressure difference, the stronger the pressure gradient, hence the stronger the pressure gradient force.

Figure 8.18, page #211 (Ahrens)

Figure 8.19, page #212 (Ahrens)

Pressure gradient force is responsible for triggering the initial movement of air, which in turn leads to the development of wind. It is directed from higher to lower pressure at right angles to the equal pressure surfaces, isobars. The closely spaced isobars in a weather chart indicate steep pressure gradients, strong forces, and high winds, while widely spaced isobars indicate gentle pressure gradients, weak forces, and light winds.

Figure 8.20, page #212 (Ahrens)

Centripetal force: an inward-directed force on an parcel moving in a curve path. It is not itself an independent force; it results from an imbalance of other forces operating in the atmosphere. The centripetal force is responsible for a change in direction of the wind and not a change in speed.

Figure 8.21, page #213 (Ahrens)

Coriolis force: a deflective force arising from the rotation of the earth on its axis. It deflects the wind to the right of its initial direction in the Northern Hemisphere and to the left in the Southern Hemisphere. Coriolis force is zero at the equator and increases with latitude to a maximum at the poles. The deflection also increases with increasing wind speed. The coriolis effect is important only in large-scale circulation systems.

Figure 8.22, page #213 (Ahrens)

Friction: the resistance that an object (e.g. air parcel) encounters as it comes into contact with other object. The friction of fluid flow, known as viscosity, is of two types, molecular and eddy. The molecular viscosity arises from the random motion of molecules composing a liquid or gas. The eddy viscosity arises from the random motion of eddies within a fluid such as air or water.

Friction slows winds within about 1 km (0.62 mi.) of the Earth's surface by breaking into turbulent eddies. Turbulence is the flow field that is characterized by eddy motion. Turbulent motion of eddies is either mechanical or thermal in origin. The atmospheric zone subjected to the friction is named as atmospheric boundary layer.

Gravity: the force that holds an object (e.g. air parcel) on the Earth's surface. It accelerates a unit mass of any object at a rate 9.8 m/sec each second as the combination of gravitational and much weaker centripetal force. The gravity force always acts downward and perpendicular to the Earth's surface. Therefore, it does not modify horizontal winds.

Hydrostatic equilibrium: the balance between the vertical pressure gradient force (directed upward) and the force of gravity (directed downward). When forces are in balance, no acceleration occurs, that is, there is no change in velocity such that an upward-moving air parcels continue upward at constant speed and vice versa.

Geostrophic wind: an un-accelerated, large-scale, and frictionless horizontal wind which results from a balance between the horizontal pressure gradient force and the coriolis force. It blow along a straight path, parallel to the isobars with the lowest pressure left to the air motion in the Northern Hemisphere above the friction layer.

Figure 8.24, page #215 (Ahrens)

Figure 8.25, page #217 (Ahrens)

Gradient wind: an un-accelerated, large-scale, and frictionless wind which results from the horizontal pressure gradient force, the coriolis force and the centripetal force.

In around a high pressure center, anticyclone, horizontal pressure gradient force is directed outward away from the center, while the coriolis force is directed inward. The coriolis force is slightly greater than the pressure gradient force with the difference giving rise to the inward-directed centripetal force. In the Northern Hemisphere, gradient wind will then blow clockwise and parallel to curved isobars around the high pressure center.

In around a low pressure center, cyclone, horizontal pressure gradient force is directed toward the center, while the coriolis force is directed outward toward the center. The pressure gradient force is slightly greater than the coriolis force with the difference giving rise to the inward-directed centripetal force. In the Northern Hemisphere, gradient wind will then blow counter-clockwise and parallel to curved isobars around the low pressure center.

Figure 8.27, page #218 (Ahrens)

Surface winds: result from a balance between the coriolis force, the horizontal pressure gradient force, and the force of friction. They blow opposite direction to the force of friction and perpendicular and to the left of the coriolis force. Surface winds cross isobars with angles that vary from about 10 over relatively smooth surfaces, where friction is low, to almost 45 over rough terrain, where friction is greater.

Horizontal winds strengthen with altitude as the influence of friction decreases and becomes negligibly small at the top of the boundary layer. At the same time, the angle between the wind direction and isobars decreases with altitude and becomes zero at the top of the boundary layer.

Figure 8.29, page #220 (Ahrens)

Friction slows cyclonic and anticyclonic winds. Together with the coriolis force, it shifts the winds that then cross the isobars. Therefore, surface winds blow clockwise and outward around a anticyclone and counter-clockwise and inward around a cyclone in the Northern Hemisphere and vice versa in the Southern Hemisphere.

Figure 8.30, page #220 (Ahrens)

Thermal wind: a component of geostrophic wind that arises from a horizontal temperature gradient. It blows parallel to isotherms with cold air to the left of the direction of air motion. The thermal wind adds to the low-level geostrophic (or gradient) wind so that the wind speed usually continues to rise with altitude above the friction layer and up to the tropopause.

In the Northern Hemisphere, surface winds around an anticyclone spiral clockwise and outward. Therefore, they diverge away from the high pressure center resulting descending air. Surface winds around a cyclone, on the other hand, spiral counter-clockwise and inward in the Northern Hemisphere. Therefore, they converge toward the low pressure center resulting ascending air. Anticyclones are associated with fair weather system, while cyclones are typically stormy weather systems.

Figure 8.34, page #223 (Ahrens)

When the horizontal wind blows from a rough surface (i.e. land) to relatively smooth surface (i.e. sea), it accelerates and diverges (stretches), inducing the downward motion. When the horizontal wind blows from a smooth to a rough surface, it slows and converges (piles up), inducing the upward motion. This is why a cumulus cloud tend to develop along a coastline with an onshore wind and tend to dissipate with an offshore wind.

Wind gusts: the small-scale winds that are caused by eddies. They result from turbulent motion within the boundary layer. Surface winds are less gusty in the stable atmosphere while relatively energetic and gusty winds could be present in unstable air.

Wind shear: the change in wind speed (or direction) with distance. Wind shear in vertical characterizes the friction layer. When the air unstable, eddy transport reduces the wind shear, while vertical wind shear could be quite strong in the absence of eddy transport in stable air.

Figure 9.3, page #232 (Ahrens)

The atmospheric circulation may be classified depending on its spatial scale and its life expectancy. In addition, the vertical winds may be comparable in magnitude to the horizontal winds in micro- and meso-scale circulation, but not in planetary- and synoptic-scale circulation. The Coriolis force, on the other hand, is very important in synoptic- and planetary-scale motions, but is usually negligible in micro- and meso-scale motions.

Figure 9.2, page #231 (Ahrens)

Wind pressure: the pressure produced by the wind on an object in its path. It is proportional to the square of the wind speed. It is an important factor for construction industry.

Wind vane: an instrument used to monitor wind direction by always pointing into the wind. Wind direction is always designated as the direction from which the wind blows. Measured clockwise from the true north, an easterly wind is designated as 90, a southerly wind as 180, a westerly wind as 270, and a northerly wind as 360. The wind recorded as 0 is only at calm conditions.

Figure 9.47, page #258 (Ahrens)

Wind rose: reprsents the percent of time the wind blew from different direction at a given site based on a month or longer time scale.

Figure 9.46, page #256 (Ahrens)

Aerovane (skyvane): an instrument that measures both wind speed and direction. It consists of a bladed propeller that rotates at a rate proportional to the wind. The blades face to the wind. If it is attached to a recorder, a continuous record of wind speed and direction can be obtained.

Figure 9.48, page #258 (Ahrens)

Pilot balloon: measures wind speed and direction above the Earth's surface and is used in radiosondes. It is filled with Helium and rises at a known rate. The balloon drifts freely with the wind. It is manually tracked with a small telescope, known as theodolite . Its vertical and horizontal angle are measured every minute or so. The wind speed and direction is then calculated at specific intervals, usually every 300 meters.

Wind sock: a large, conical, open bag designed to indicate wind direction and relative speed. It is usually used at small airports.

Anemometer: the instrument used to monitor changes in wind speed. There are two basic types of anemometer: i) cup anemometer, and ii) hotwire anemometer. Both anemometers accurately monitor the wind speed, but hotwire anemometer is more sensitive than the cup anemometer.

Figure 9.47, page #258 (Ahrens)

Wind speed can be estimated by observing the wind's effect on lake or ocean surfaces or on flexible objects such as trees. Such observations are on the basis of Beaufort scale, which ranges from 0 (calm conditions) to 12 (hurricane-strength winds)

Appendix C, page #A-7 (Ahrens)