How Deep is the Ocean, How High is the Sky?

Dimensions and data on the earth, ocean and atmosphere


Contents

  1. Introduction
  2. The Earth
    Size, Shape and Motions
    Gravity
    Heat and Radiation
    Geomagnetism
    Permafrost
  3. The Ocean
    Size and Composition
    Temperature and Radiation
    Propagation of Sound
    Currents
    The Tides
    The Ocean Bottom
    Hydrocarbons
  4. The Atmosphere
    Pressure, Temperature and Composition
    Lapse Rate and Stability
    Propagation of Sound, Light and Radio Waves
    Winds
    Highs, Lows, Air Masses, Fronts and Weather
    Clouds
    Hurricanes
  5. References

Introduction

This article is intended to help the reader comprehend the size and nature of the surface of the earth, and the many natural processes that occur in it. The oceans and the atmosphere are fluid sheets of great extent and remarkable thinness, so that they are essentially two-dimensional, interacting at their interface. The ocean covers most of the earth's surface and controls its climate in cooperation with the atmosphere, which manages surface heat transfer between radiational processes and the mobile heat reservoir of the sea. The sea is 370 times more massive than the atmosphere, and responds with corresponding slowness, but controls all long-term conditions. The solid earth is not treated in much detail in this article, but it is the stage on which everything else happens, so its major dimensions are given. The structure and history of the earth are left to other pages. For some years now, we have been able to see the earth as a globe in space in satellite photographs. The one at the right was taken on 30 March 2003, showing a large clear area over the western United States, depressions in the North Atlantic, and scattered clouds over the Amazon. The sharpness of the edge shows how thin the atmosphere is, and it is easy to appreciate that it and the oceans are, on this scale, smooth and two-dimensional. The GEOS-E IR image of the earth is from the Dundee University Satellite Receiving Facility.

Accounts of interesting processes will also be included, such as the propagation of sound and electromagnetic radiation in the ocean and in the atmosphere, the geomagnetic field, permafrost, ocean currents and sediments, continental shelf petroleum, vertical structure of the atmosphere, the ionosphere and atmospheric electricity, lapse rate, global circulation, winds and weather. Where these subjects are covered in depth in other pages, links will be provided. Internet resources will also be noted, such as the sources of good weather maps. Brief treatments may be expanded in later editions, or extended treatments may be separated as individual articles.

This article is now approaching maturity, and most of the topics that I want to include have been included. Although I have used the best information available to me, there may be errors that will be corrected as soon as they come to my attention. Of course, there will be mistypings that are so hard for a author to detect.

The Earth

Size, Shape and Motions

To a good approximation, the earth is a sphere of radius 6400 km (4000 mi) in radius (more exactly, the mean radius is 6371 km). The circumference of the earth is 40,000 km (25,000 mi). Its surface area is 5.15 x 108 km2 (2 x 108 mi2), of which 70% is ocean and 30% is dry land. Its volume is 1.1 x 1012 km3 (2.7 x 1011 mi3). Since the average density of the earth is 5.5 g/cc, its mass is 6.0 x 1024 kg. Acting as if concentrated at the centre, this creates a gravitational attraction GM/r2 = 9.8 m/s2 at the surface.

The earth rotates about its polar axis once in 23h 56m 4.0989s, and revolves about the sun once in 365d 6h 9m 10s. The mean distance to the sun is 1.5 x 108 km (94 x 106 mi). The axis of the earth is inclined to the plane of its orbit (the ecliptic) at an angle of 23° 26' 21.448", or about 23.5°. The earth's orbit is nearly circular, with an eccentricity of 0.0167. Perihelion currently occurs when the N pole of the axis is pointing away from the sun, in January. The axis precesses about the pole of the ecliptic once in about 25,900 years. It requires about 8.3 min for light to travel from the sun to the earth. It is 272,500 times farther to the nearest star, Proxima Centauri, 4.3 light-years away. Human "space travel" today means circling a few hundred miles above the earth. Astronauts never come close to any astros, by a very, very long way. Space is utterly hostile to terrestrial life, and at the end of a journey there is no "there" there. The earth is quite isolated in space, especially in view of humans' delicacy, short life span and requirements for warmth, air and food.

The rotation of the earth causes a centrifugal force (in a frame of reference in which the earth does not rotate) that distorts the sphere so that its surface is a gravitational equipotential, called the geoid, which is very closely an spheroid, the figure of an ellipse rotated about its minor axis. Although the earth has flowed into this equilibrium position over time, in its resistance to deformation over a short time it is more rigid than steel. The equatorial radius of the earth is 6378.140 km and the polar radius is 6356.752 km, making the flattening f = 1/298.257, which would be too small to perceive by eye. If the earth were uniform, f would be 1/233, but the lesser flattening is evidence of a heavy core. These are actually the dimensions of the geodetic reference ellipsoid, but are close to those of the actual earth. The rotation also causes gravitational acceleration to increase toward the poles, according to g = 980.621 - 0.02593 cos 2φ + 3x10-5 cos 4φ cm/s2. The actual figure of the earth varies slightly from the ellipsoid because of the uneven distribution of crustal mass, but this departure can be detected only with very careful measurements. It does, nevertheless, affect the orbits of earth satellites. The equatorial section of the earth is actually approximated by an ellipsoid, with a major axis 165 m longer than the minor axis, at 38° E latitude, as determined by Heiskanen in 1929. Other bumps have been described since then, mainly by observing satellite orbits, but this geophrenology does not alter the conclusion that the earth is very closely a spheroid, and almost a sphere.

The moon, with a radius of 1738 km and mean density 3.3 (mass 7.3 x 1022 kg), revolves around the earth at a mean distance of 3.8 x 105 km (237,500 mi, 60 earth radii) once in 27.321661 days. The orbital eccentricity is 0.055, and the inclination to the ecliptic is 5.1454°, making its inclination to the earth's equator vary from 18° to 28°. The nodes and perigee precess rapidly. At their mean distances, the angular diameters of the sun and moon are 32' and 31', respectively. The earth-moon barycentre (centre of gravity) is 4671 km from the centre of the earth, about 73% of the radius. The rocks of the moon do not appear to be different from similar rocks of the earth. The moon is probably a sphere of olivine, lacking a heavy core, and radially unsorted.

There have been some popular recent theories of the moon's orgin, but the sceptical note that this was a unique event, and evidence one way or the other is not available, and will probably never be available. The small eccentricity of the earth's orbit, and the low inclination of the moon's orbit, are not concordant with the idea of a collision with an external body. Lots of things could have happened, many fewer probably did happen. Any such theories make no contribution whatever to effective knowledge and understanding, and are only fables of the unknowable, so attractive these days in place of real progress. It is dynamically impossible for the earth to have "captured" a satellite as large as the moon without assistance. The two bodies almost certainly condensed out of the same material at about the same time, but why there are two and not one is a mystery. There is a link to an explanation of the collision theory of the moon's origin in the References. This theory was originated around 1975 by Hartmann and Davis. Anyway, the moon is a pleasant thing to have around to look at.

Gravity

The observation that objects are attracted vertically downward is surely a very remarkable thing. Like the atmosphere, gravity is something we live with every day, and is scarcely noticed, though its effects, like those of the atmosphere, are essential to life. The gravitational force on a body is proportional to its mass, so a body falls with a constant acceleration vertically downward in the absence of resistance. This acceleration has been carefully measured at Potsdam, latitude 52° 23' N, elevation 100 metres above m.s.l., with the result 981.274 cm/s2 or gal. One gal (for Galileo) is 1 m/s2, a thousandth of which is the milligal, mgal. The acceleration of gravity is a constant at any station, depending on the distribution of mass in the earth. Gravitation is a phenomenon that should always excite wonder.

Mixed with the gravitational attraction is the centripetal acceleration ω2R cos φ due to the rotation of the earth, which is a maximum at the equator and zero at the poles. Because of this, and because the earth is not spherical, the acceleration of gravity is less at the equator and greater at the poles, the difference being 5.2 gal. The ratio of the centrifugal force to the gravitational force is about 1/288 at the equator. Measured gravity is compared with the gravity of an ideal ellipsoidal earth, which can be accurately specified and mathematically described. One such formula is g = ge(1 - 0.00530 sin2φ), which assumes that the flattening of the earth is f = 1/297 and the ratio of the maximum centrifugal force to the average acceleration of gravity is 1/288. It gives the value of gravity at the surface of the gravitational ellipsoid, which is a gravitational equipotential surface. This ellipsoid is close to, but not identical with, the ellipsoid used in geodetic surveying. If we use the Potsdam value, ge = 978.049 gal. We have adjusted the Potsdam value slightly by a method to be described below. The polar value of g then turns out to be 983.236 gal. Another formula is g = 980.621 - 2.593 cos 2φ + 0.003 cos 4φ, based on a different ellipsoid, but giving closely similar results. We assume here that the mountains are air, and the oceans are rock, but remember that these two features are very thin, comparatively.

The difference between the observed gravity at a point and the value calculated by the formula is called the anomaly. A positive anomaly means that gravity is greater than would be predicted by the formula. This implies that there is some concentration of mass beneath the point in addition to that assumed in the gravitational ellipsoid. Anomalies are not unexpected, since the distribution of mass in the earth is not uniform, or even accurately known. What is remarkable is that anomalies are, in general, small, and formulas based on assumed gravitational ellipsoids are a good approximation to observed gravities. If you are interested only in the gross value of the acceleration, then these formulas are all you ever desired. However, finer details are quite necessary for predicting satellite orbits, and even more necessary if gravitational surveys are to be used for geophysical purposes, to determine the actual distribution of mass in the earth.

Gravity is not usually measured at the surface of the gravitational ellipsoid, and the observing station is in the midst of topography, which obviously pulls this way and that, and has little to do with the variations in gravity that are of interest. Therefore, the value predicted by a formula is corrected for these disturbances before the anomaly is calculated. This is a very intricate subject, so I shall only present the broadest principles so that at least the terms have some significance to the reader. First of all, gravity decreases with altitude above the ellipsoid even if there is only air there. This decrease is described approximately by gA = g(1 - 2h/R), where h is the height above the ellipsoid and R an average value of the radius of the earth (6371 km). The difference is called the free air correction, and can be applied to reduce any gravity measurement to the ellipsoid under this assumption. The free air correction was applied to the Potsdam value above, and amounted to 30.8 mgal. All gravity measurements should at least be adjusted in this way to remove, to some degree, the effect of different altitudes.

There is, of course, more than free air between Potsdam and the ellipsoid. The 100 m of rock exerts a downward attraction, which really should also be considered. Doing this accurately on a bumpy spheroidal earth is a horrible problem, and the ingenious Pierre Bouguer (pronounced "Boo-gher," 1698-1758) found an approximate way to do it that is really easy. It gives good results only for the vicinity of the station to which it is applied, but this is perfectly satisfactory in most cases. Bouguer simply replaces whatever is actually there by an infinite horizontal slab of density δ. By analogy with electrostatics, a sheet of mass of thickness h produces a uniform field 2πGδh on either side. G can be found in terms of the average density of the earth, ρ, by Newton's Law of Gravitation to be G = 3g/4πRρ. The acceleration due to the slab is then (3/2)(δ/ρ)(g/R)h. For these calculations, we take ρ = 5.5, and δ = 2.67 for surface rocks, and 1.03 for sea water. Taking δ/ρ = 0.5, the free air and Bouguer corrections can be combined in the simple formula gB = g(1 - 5h/4R). This correction is usually enough to smooth out variations due to elevation and terrain and reveal the gravitational anomalies due to the subsurface.

Bouguer anomalies are good enough for finding relatively shallow structures over limited areas, but for geophysical investigations, something better is required. The upper layers of the earth's crust seem to float on a weak layer deep in the earth, usually taken as about 113 km. The total mass in any column of the same area is the same. Mountains that rise far above sea level have roots that penetrate deep into the earth. This property is called isostasy, and is pretty well satisfied in most areas, but not all. Isostatic correction of gravity values takes into account not only the observed topography, but the subsurface condtions necessary to support it. Hayford compensation is one method of doing this. Hayford anomalies allow us to study the completeness of isostatic compensation and deep structures over large areas.

Colorado Springs, at about 2000 m elevation, and the top of Pike's Peak, at over 4000 m elevation, are only 13 miles apart, so they form a good test of gravity reduction methods. The free-air correction gives about a zero anomaly for Colorado Springs, and a +200 mgal anomaly for Pike's Peak. The Bouguer anomaly in both cases is about -200 mgal, which not only shows that the effect of the great difference in altitude has been removed, but that the resulting negative anomaly is consistent with the deep roots of the rockies, where light rock (granitic) gives a mass deficit. Bouguer anomalies of mountain stations typically show this effect. Note that the uncorrected free-air anomalies give an erroneous impression of the deep structure, if anything. In a similar way, the Bouguer anomalies of ocean stations are typically positive, because of the heavy rocks of the ocean floor. With Hayford compensation, the anomalies are all reduced to fairly small values around zero for both mountain and ocean stations. Large anomalies are exceptional cases; the anomalies of ordinary low-lying stations are usually small.

Heat and Radiation

The earth receives electromagnetic radiation from the sun at an intensity of about 1.95 cal/g/cm2 above the atmosphere. The spectrum is continuous, peaking at about 500 nm and extending from short-wave UV to long infrared. The average planetary albedo (fraction of radiation reflected) is 37%, and the surface albedo is about 14%. The ocean has a low albedo, except when covered with ice, when it can rise to 55%. At low and mid latitudes, it varies from 4% to 10%, with a maximum of 19%. Grasslands and forests have an albedo of around 15%, deserts 20% to 30%, and snow cover 35% to 82% depending on age. The earth radiates energy from the surface and from infrared-active ("greenhouse") gases in the atmosphere at an equivalent temperature of around 300K. A negligible amount of heat arrives at the surface from within the earth, where crustal radioactivity is responsible for about 80%, and heat flow from the mantle, 20%. The ultraviolet part of the incident radiation has important photochemical effects in the upper atmosphere, where it is largely absorbed, either in producing the ozone layer around 50 km altitude, or by the ozone so produced. This absorption of energy raises the temperature of the upper atmosphere.

The energy absorbed on the sunlit side of the earth is about 1.1 x 1017 W. In equilibrium, the same energy must be radiated from the whole area of the earth, as from a black body at some temperature T. This is not a bad assumption, except that T corresponds to an average of T4. Stefan's Law then gives T = 248K, or -25°C. This is a reasonable estimate of the temperature at the effective altitude for radiation in the atmosphere. The surface is maintained at a comfortable temperature by water vapor in the atmosphere, which hinders the upward flow of radiant energy from the surface, as mentioned in the preceding paragraph.

The earth also receives the solar wind, consisting mostly of protons, which interacts with the geomagnetic field in complicated ways. A typical solar wind might travel at 508 km/s, and contain 4.16 protons per cc (values from SOHO; see References). Electrons are also included to make the solar wind a weak plasma. These charged particles are responsible for the aurora borealis and australis, the ionosphere with its effect on radio waves, and the short-term magnetic variations called magnetic storms. Cosmic rays are received from outside the solar system. These are largely protons of very high energy that cause cascades of other particles by collisons in the atmosphere. Some of this background radiation reaches the surface, but it increases significantly with altitude.

Geomagnetism

The earth has a magnetic field which is approximately that of a dipole at the centre of the earth, aligned so that its south magnetic pole is on a line that cuts the surface of the earth near the north geographical pole. This means that the north magnetic pole of a compass needle will point roughly in the direction of north. The angle of this magnetic north at any point to the east or west of true north is the declination. In some parts of the earth the declination is so large and varies so rapidly with position that the magnetic compass is nearly useless. These are usually regions near the magnetic poles. Unlike gravity, the magnetic field varies with time in a complicated way. The calculation of magnetic anomalies for subsurface exploration is not as simple as the calculation of gravity anomalies. For details on the geomagnetic field, see Geomagnetism. The effects of the solar wind of charged particles on the magnetic field is treated in Magnetic Storms. The cause of geomagnetism is certainly electric currents in the interior of the earth, but the theory is sketchy and imperfect, and of no predictive value at the current time.

Permafrost

Nearly all the land north of the Arctic Circle, and all of Antarctica, is covered with permafrost. This is land where the ground water is permanently frozen from a few metres beneath the surface, to a considerable depth, where the normal increase of temperature with depth causes the temperature to rise above 0°C. The top layer freezes in the winter and thaws in the summer, supporting trees, mosses, and a layer of peat. In Siberia, the evergreen forests of this area are called taiga. Permafrost covers a wide area of Siberia (nearly all of the Republic of Yakutia). There is sporadic permafrost over much of the Canadian North, which becomes more and more discontinuous as one moves south, until it is restricted to the higher mountains. While frozen, permafrost is a good foundation, but melted permafrost can lack any strength whatsoever. When building in permafrost areas, its properties must be kept in mind.

The Ocean

Size and Composition

As has been mentioned above, the sea occupies about 70% of the surface area of the earth. The mean elevation of the land above sea level is 840m, while the mean depth of the sea is 3800m. If the area of the sea is represented by the area of a sheet of typing paper, the thickness of the paper (0.003" or 0.08 mm) is about twice the proportional depth of the sea. The sea is a thin, two-dimensional region between the atmosphere and the crust of the earth. It is the home of most of the life on earth, and controls its climate. The volume of the sea is about 2 x 109 km3, and so its mass is 2 x 1021 kg. Note that this is only 1 part in 3000 of the total mass of the earth. Most of the hydrogen that remains on the earth is in the water of the sea; the rest has escaped to space. Sea levels at present are lower than average, and much of the continental shelf is exposed.

Sea water is salt, about 3.5% solids, or 35‰, as the salinity is usually expressed, which is g per kg of sea water. The salinity is somewhat greater where evaporation is high, and lower where precipitation is high, but remains rather constant. It is lower in bodies of water connected with the sea, but which receive fresh waters, such as the Baltic and the Black Sea. Salinity in the Gulf of Bothnia is 5‰, while in the Red Sea it is over 40‰. The density of sea water is about 1.026 g/cc, ranging from 1.022 to 1.028, or 63.86 pounds per cubic foot. It increases about linearly with the salinity, according to d = 1.0 + 7.4 x 10-4s. Of the salinity, Cl- is about 55%, Na+ 30.6%, the major constituents. SO4-- is 7.7%, Mg++ is 3.7%, Ca++ is 1.1%, K+ is 0.4%, HCO3- and CO3++ is 0.2%, and Br- is 0.1%. Boric acid, silicic acid, strontium and fluorine are also present amounts greater than 1 ppm. Sea water, then, is effectively a solution of NaCl, MgSO4 (Epsom salt), MgCl2, and CaHCO3. So far, magnesium is the only metal that can economically be obtained from sea water. Sea water is about pH 8, or slightly alkaline, because of the bicarbonate and carbonate it contains.

The concentration of the ions in sea water is determined by the solubility of the corresponding salts. Very insoluble salts are not represented, because they are easily precipitated out. The sea is not becoming saltier, as was once thought, but each ion has a characteristic residence time in seawater. Na and Cl have the longest residence times, on the order of 200 million years, which is defined as the amount present divided by the amount added per year. Calcium, by contrast, has a residence time of only 1 million years, and silicate only 40,000 years. River water, that flows into the ocean, is rich in calcium bicarbonate and silicic acid, but poor in salt and magnesium. Water that evaporates from the ocean to fall as precipitation is, of course, pure except for the CO2 that it picks up from the atmosphere. The amount of carbon dioxide in the ocean is 60 times the amount in the atmosphere.

The vapor pressure of sea water is less than that of pure water. For a salinity of S ‰, e = eo(1 - 0.00053S). Sea water freezes at -0.17S °C. Since it is not a pure substance, freezing is a more complicated process in which the ice is less saline than the remaining liquid. Sea ice can show wet briny patches even at very low temperatures. The maximum density of pure water occurs at 4°C. For sea water, this temperature decreases until at -2°C the temperature of maxiumum density equals the freezing temperature for S = 24.70‰. The density of pure ice is 0.92, but the density of sea ice is from 0.88 to 0.93, depending on impurities and air content (dissolved air is also rejected when water freezes).

Sea ice occurs as fast ice, solid and strong, in fjords and inlets where freezing is facilitated, as drift ice in small floes carried by currents, and as pack ice where drift ice has been compressed into a rough and chaotic mass. Icebergs are not sea ice, but are the products of glaciers made of pure water containing rocks, air and other impurities. North Atlantic icebergs come mostly from Greenland, and are carried south on the Labrador current in the spring and early summer. Antarctic icebergs are larger and flatter, made of floating ice that has broken away from ice shelves.

Temperature and Radiation

Although water appears as a clear, transparent liquid to us, it is a strong absorber of electromagnetic radiation from 1 GHz up through X-rays, except for a deep, narrow window exactly coinciding with the spectral sensitivity of our eyes. This is no accident, since our eyes evolved in the ocean. Sea water, because it is electrically conducting, also absorbs radiation of lower frequencies, and only very low frequencies can penetrate more than a few metres. Infrared is absorbed in a few millimetres, far infrared even more rapidly. Only 10% of the incident energy reaches a depth of 10 m. If the water has much suspended matter in it (such as plankton), the penetration is even less. This means that the sea absorbs practically all the radiation that falls on it, 90% or more, except for that reflected by the impedance mismatch at the surface. Only 8% of the diffuse radiation from sky and clouds is reflected, and only 2% of solar radiation with the sun's elevation at 60° or above. The sun's heat is absorbed principally at the ocean's surface, and heats this thin layer accordingly. The ocean re-radiates infrared with a black-body spectrum characteristic of its temperature, about 280K. To a clear sky, the ocean's net radiation is about 200 to 250 cal/cm2 per day. The ocean surface heats or cools the air that is in contact with it by turbulent diffusion. The land surface acts in the same way, but its smaller area and higher albedo means that it is not as important in the global energy balance.

The surface layer of the ocean is disturbed by winds, and is heated and cooled by solar radiation and the air. Its surface temperature differs with location and the season, from about 10°C at polar boundaries to 30°C in the tropics. The range is from -2°C to 31°C. Visible light penetrates to about 100m, depending on the turbidity of the water, defining the photic zone in which photosynthesis can take place. This zone is a thin vegetable soup of diatoms and coccolithophores, which manage the energy input and productivity of the ocean. The ocean is as productive as tropical rain forest, by far the most important "green thing" on the earth. Life activities deplete this layer of carbon dioxide, silica and phosphorus, and the intensity of life depends on the supply of these nutrients from below. The oxygen content of surface water is also critical to life. Although carbon dioxide is quite soluble in water, oxygen is not. The normal content is 4 to 7 cc per litre of water. Cold water dissolves more oxygen than warm. In the Black Sea, brackish warm surface water overlies salty cool deep water, and there is very little mixing. Lacking a source, oxygen is depleted in the lower layer, which has become anaerobic. Anaerobic bacteria extract oxygen from SO4 and CO3, leaving sulphur (or H2S) and carbon, usually as hydrocarbons or methane, which has been the source of fossil fuels.

Deep waters are very cold, about 4°C, the temperature of maximum density of water. Colder water would rise and be heated; warmer water would also rise. The upper boundary of the cold water is at a depth of around 1000m. The region where the temperature decreases from the surface value is called the thermocline, and the gradient is rather gentle. In a lake, the thermocline has a large gradient, 1°C per meter or so, but this is not the case in the ocean. This temperature distribution shows that the ocean is very stable, and stratification can be expected, for example on the basis of salinity.

Air at the surface of the oceans is usually around 80% relative humidity and is kept at the sea surface temperature by turbulent mixing. In the trade wind zone, this layer of humid air may be relatively thin (below 800 mb), and above it is very dry air. At the interface, there is usually a strong temperature inversion that acts as a "lid" on convection from below. The typical "trade wind cumulus" clouds extend from the condensation level up to the trade wind inversion, giving the clouds a blocky shape, all with bases and tops at the same levels. "Chimney clouds" may poke through this inversion, bringing moist air to the very unstable air (large lapse rate) above the inversion. Rapid evaporation from warm seas supplies the energy for tropical depressions, tropical storms, and hurricanes.

Propagation of Sound

The speed of sound in the ocean depends on the temperature, pressure and salinity. A formula gives c = 1449 + 4.2t - 0.0366t2 + 1.137s, where t is the temperature in °C and s is the salinity in ‰. To estimate the effect of pressure, we use the general formula c = (κρ)-1/2, where κ is the compressibility (1/V)(dV/dp) and ρ is the density. At 0°C the compressibility of water is 50.4 x 10-6 bar-1 and the density is 1 g/cc, giving 1432 m/s at 1 atm, which does not disagree too badly with the formula for s = 0. The table in the Handbook of Chemistry and Physics gives compressibilities at 25°C for 1 atm and 1000 atm as 45.7 and 34.8, respectively. The density at 1000 atm can be found using an average compressibility of 40.25, giving dV/V = 0.04025, and so ρ = 1.04025. Then, the speed of sound at 1 atm is 1479 m/s, and at 1000 atm 1662 m/s, or an increase of 0.183 m/s per atmosphere. At 3000m depth, the pressure is about 290 atm, so the speed of sound is about 53 m/s faster than at shallow depths. The speed of sound decreases from about 1558 m/s at the surface (20°C) to 1492 m/s at 1000m, and then increases thereafter. This makes a sound duct in which sound can propagate for large distances with only 1/r spreading. For most purposes, the speed of sound in the ocean can be taken as 1500 m/s.

Currents

Surface ocean currents have been known since ancient times, and have always been important for navigation. They have been scientifically studied since the 18th century, and their surface expression well described since the mid-19th century. There are also deep currents of great importance to the composition of the oceans and the climate of the earth, but these are much less well understood even at the present time.

Surface ocean currents are primarily wind-driven. At the fastest, they run at 2 m/s, 5 mph or 4 knots. The great anticyclonic gyres in the north and south Atlantic and Pacific oceans are driven by the temperate westerlies and the tropic easterlies (trade winds). Currents in the Indian Ocean are more complex, in part driven by the seasonal monsoon winds and reverse during the year. There is a strong West Wind Drift encircling Antarctica, driven by the Roaring 40's, that is the only current mixing water in all the oceans of the earth. These large currents are only partly determined by the winds; to some degree they and the winds have the same cause, in unequal heating at different latitudes and the Coriolis force, and are cooperative, rather than being cause and effect. The surface currents interact with the deeper currents, and are much more massive than the fickle winds.

Deep currents are called thermohaline, reflecting their dependence on temperature and salinity distributions. They resemble the gradient winds of the atmosphere, flowing in response to small differences in pressure caused by mass distributions, with the pressure force balancing the Coriolis force.

In the North Atlantic, the trade winds drive warm water towards the Caribbean and the Gulf of Mexico. This water finds its way through the Strait of Florida to move as a narrow stream of blue, salty water, about 50 miles wide northeastwards along the North American coast. It does not touch the coast, but is separated from it by a cold southerly current. This is the famous Gulf Stream, moving at 2.7 to 3.8 mph, widening as it moves northward. To its east is the Sargasso Sea, named from the floating brown alga Sargassum. The Gulf Stream is about 2000 ft deep, while the abyssal depths beneath the Sargasso Sea descend to 12,000 feet.

Southeast of Newfoundland, near the Grand Banks, the Gulf Stream meets the southward-flowing Labrador current from Baffin Bay, part of a polar cyclonic gyre encouraged by the permanent Icelandic Low in the vicinity. This is a cold current, rich in nutrients for plankton. In winter, it carries drift ice as far south as 42° and makes copious fog. The meeting of the currents forms a perfect environment for the blooming of sea life. The Grand Banks have been a great fishing resource, but over-exploitation has led to its destruction and exhaustion. The combined currents move across the ocean as the North Atlantic Drift at about 4 to 5 miles per day. As it approaches Europe, the Drift splits into three tongues. The southerly one bends southward to the Azores, continuing the gyre. The central tongue warms Spain, France and England, moderating the weather most agreeably. As it is cooled, the salty water sinks to the depths and joins the deep circulation. The northern tongue slips by Norway, keeping its ocean approaches and its northern coast free of ice. Even Spitsbergen is free of drift ice in the summer, and vessels have reached as far as 82°N in this region. The last of the warmth is spent above Murmansk, and in the approaches to Novaya Zemlya in the Arctic Ocean.

The South Pacific gyre transports cold water north by the Peru Current, then sends it westward into the equatorial Pacific. This cold water overturns the stability of warm surface waters on the western coast of South America, causing upwelling that brings nutrients up from the depths. Similar effects occur on each of the other great gyres as they move from polar regions to the tropics, in North America (California Current), Northwest Africa (Canary Current), and southwest Africa (Benguela Current), all (at least formerly) rich fisheries. The Indian ocean coasts of the Horn of Africa and Arabia also benefit from upwelling caused by the cold current coming up from Madagascar. The Labrador Current comes down between Greenland and Labrador to the Grand Banks. When the Peru current is abnormally warm, which occurs every few years, this upwelling does not happen, and fishing is poor. The warm water also evaporates more readily, providing moisture for Mexico and the southwestern United States. This phenomenon is famous as El Niño, since it happens near Christmas, in the southern summer.

The trade winds blow warm water toward the Phillipines, which turns northward as part of the North Pacific gyre. The Kuroshio is the Pacific equivalent to the Gulf Stream, which begins near Taiwan, moves northwards along the Ryukyu Islands, and then northeastwards along Japan. As in the Atlantic, a narrow southerly cold current separates it from the Japanese islands. Kuroshio moves at about 4 mph, slightly faster than the Gulf Stream, but it is also salty and warm. Southeast of Kamchakta, it meets the cold, southward flowing Oyashio, the Pacific analogue to the Labrador current. Oyashio originates in the Bering Sea. Like the Labrador current, it is cold and rich in nutrients, and is part of a polar cyclonic gyre. Their meeting creates a great fishery, which has not been as ruinously exploited as the Grand Banks have. The united currents then drift eastward across the Pacific, warming the Aleutians and bringing continual fog. Off the coast of North America, the cold California Current replaces the final traces of Kuroshio.

The trade winds, both north and south of the equator, blow constantly and pile up water on the western boundaries of the Atlantic and Pacific Oceans. Since the equatorial region is one of calm, there is no wind to maintain the elevation, and a current flows "downhill" to the east. These equatorial counter currents are found in both oceans. The Atlantic one flows into the Gulf of Guinea of Africa, while the Pacific one is important in the El Niño phenomenon.

Less visible are the deep ocean currents. The most important of these is the downwelling of cold, saline water east of Greenland that flows down the length of the Atlantic (North Atlantic Deep Water, NADW), to join the West Wind Drift encircling Antarctica. This current channels cold Antarctic Bottom Water (AABW) into the Pacific and Indian oceans. Like the winds, these currents are affected by the Coriolis force, and may be called geostrophic; they also follow bottom contours, and are also called contour currents. They are important in the CO2 balance of the ocean, as well as for their indirect effect on the climate. It is interesting to note that before the present Ice Ages (which we are still in) there was deep communication between the oceans around the equator. As the Ice Ages began, these gates closed, and a new route around Antarctica was opened as the continents moved north.

The Tides

Everyone who lives by the sea is familiar with its restless periodic changes in level, called the tide, a word that, in fact, means "time." The tidal movements are related to the position of the moon, occurring about 50 minutes 28 seconds later every day, to match the eastward motion of the moon relative to the sun. Usually there are two high tides and two low tides each day. When the sun and moon are aligned, at new and full moon, the tides are larger and are called "spring" tides, while at first and third quarters, the lesser tides are called "neap" tides. This general behavior is by no means the same in all locations, and successive tides may not be of the same magnitude. For more information on tides, see Tides.

The tide is the result of the attractions of the moon and the sun on the waters of the ocean. Similar attractions act on all bodies of water, large and small, and even on the solid matter of the earth, as well as on the atmosphere. These attractions act to exite modes of oscillation, which only in the ocean reach easily observable amplitudes. Atmospheric tides produce ionospheric effects. Tides in smaller bodies of water, and in the earth, can be detected, but are of tiny amplitudes. Meteorological effects can be stronger in smaller bodies of water, producing the oscillations known as seiches, similar to the sloshing of water in a bathtub. There are only small tides on the Mediterranean, and they are negligible on the Great Lakes. Tidal theory is very complicated, and there is a very large literature on it. It is by no means a complete theory, and the tides are, mainly, studied empirically.

The gravitational forces exerted by the sun and moon on the oceans have an effect proportional to the differences in gravitational attraction. Since the gravitational attraction is inverse-square, the differences are inverse-cube. Because of this, the solar tides are less than the lunar tides by the ratio of the cubes of their distances, which makes the lunar tides predominate. If the gravitational attraction were uniform, there would be no differential forces. Subtracting the average effect, the oceans are pulled both toward and away from the moon on opposite sides of the earth, giving the usual double tides. The most effective forces on the ocean are those at about 90° to the moon, perpendicular to the large gravitational attraction of the earth.

If the moon moved in the equatorial plane, and the oceans were more than 21 km deep, the tides could be described quite simply. The combination of the attractions of the earth and moon, added to the centrifugal forces of their mutual revolution, results in a gravitational potential of A + B cos 2φ at any point P on the surface of the earth. The forces producing the tides are a result of the differences in gravitational attraction; orbital motions have no effects. The equipotential surface of the tidal forces would be very close to an ellipse with its major axis pointing toward the moon. The ocean surface would conform to the equipotential surface, so that there would by two semi-diurnal tides a day. This tide would be about 30 cm in amplitude. The sun, also in the equatorial plane, would cause a similar semi-diurnal tide, but its amplitude would be only about 10 cm. Through the month, these two tides would superimpose, making spring tides of 40 cm amplitude, and neap tides of 20 cm amplitude. The tides at many locations are quite similar to this simple case, but usually of larger amplitudes. The spring and neap tides lag the phases of the moon by an amount called the age of the tide, which may be as much as 60 hours.

The moon and sun are not in the equatorial plane, however, their declinations varying continuously through the month and year. The out-of-plane stimulation causes a diurnal tide, with a period of one day, and an annual tide with period one year. The diurnal tide can be as large as 30 cm amplitude in open sea, and the annual variation may cause higher tides near the equinoxes, when the moon and sun are in line. These variations, superimposed on the dominant semidiurnal tides, can result in a very complex, but periodic, variation. Where the semidiurnal tide is small, there may be only one tide a day due to the diurnal tide, usually of small amplitude. The Gulf of Mexico and the Caribbean show diurnal tides prominently, as do tides on the west coast of the United States. Tidal currents, which should be distinguished from the tides, flow in and out near land. Slack water occurs when the currents are reversing. In addition, the oceans are not deep enough for the tidal wave to move fast enough to follow the apparent motion of the moon as the earth rotates. Because of this, the tide lags behind the moon. The interval between the meridian passage of the moon and high tide is the lunitidal interval for the location, and can be as much as six hours. In addition, the shape of the ocean bottom as land is approached can funnel or spread the tidal wave, and resonances can cause its amplitude to increase. The greatest tides are in the Bay of Fundy, where the amplitude is over 30 metres. Resonance in the Bristol Channel cause higher tides at the mouth of the Severn, producing the Severn Bore in the high equinoctial tides.

Tides are not the only influence on the height of the sea. Tsunami, or tidal waves, are produced by underwater earthquakes, slumps and volcanic eruptions (this Japanese word does not form a plural with "s"). They are of low amplitude in the open ocean, but "break" as they approach shallow water, causing what appear to be sudden and high tides, which is responsible for the name. Meteorological effects can also be important, such as the storm surge of a hurricane. All of these effects are superimposed on the tides, so that a storm surge at a time of high tide can be very destructive should a tsunami arrive. The tsunami of 26 December 2004 in the Indian Ocean, where tsunami rarely occur, was notably destructive. It originated at a magnitude 9.0 earthquake at a plate boundary off northwestern Sumatra, where a section of the plate suddenly sunk. The decrease of the earth's moment of inertia was noticeable in the rotation of the earth. It was reported that animals retreated to higher ground as the tsunami approached; very few, if any, dead animals were found. This is probably just a coincidence, but a curious one.

The tidal range can be used as a source of energy. A basin is drained to the level of low water. On the next high tide, it is filled by water entering through turbines. When the tide goes out, it is emptied, again passing through turbines to extract its gravitational potential energy. The turbines must be designed to operate with a low head, and the intermittent nature of the output is annoying. Although one tidal power station 0f 240 MW exists on R. Rance in northwestern France, it would seem that the capital costs of the considerable construction necessary would outweigh the revenue from the electricity. A tidal power station has long been proposed for Passamaquoddy Bay on the Bay of Fundy.

Trials are now in progress of tidal current turbines, that are very much like wind turbines, but are under water. One 11-m turbine, with two blades, is now testing a mile off Lynmouth, Devon on the south side of the Bristol Channel. This turbine develops 340 kW, and can be raised and lowered into the water. The cost for such turbines is much less than for large tidal storage basins. Tidal currents are regular, so are much more reliable than the wind. However, the currents reverse twice a day in the Bristol Channel, so there are intervals in which power cannot be produced.

Tidal prediction consists of summing the effects of the many harmonic components active at a certain site. Although the frequencies can be determined from theory, the amplitudes and phases must be measured for any port. Once this is done, tides can be predicted with good reliability for very long intervals, up to 50 years. Computers can now do this easily, but once analog computers called tidal predictors were used that mechanically added the contributions of the different frequencies. Tides are, of course, of great interest to navigators who want to know when there will be enough water to cross the bar at the entrance to a port.

The tide exerts a drag on the rotation of the earth that tends to make the day equal to the month. When this finally happens, the moon will hang over a favored spot on earth, becoming a full moon except when eclipsed, and the tides will cease to flow. Do not expect this any time soon, but the earth has already made the moon's day equal to the month.

Mean sea level is found by averaging hourly observations of sea level by a tide gauge for a year (8,760 of them). The result will be consistent within a centimeter or so with other years.

An excellent source of tidal information can be found at UK Hydrographic Office. The scope is worldwide, and predictions are made for up to a week ahead. The site is easy to use, and includes tide graphs that are very informative. The largest tides I found were at Hopewell Cape, Canada, which is on the arm of the Bay of Fundy that leads up to Moncton. In June 2003, they were about 13 m or 40 ft in amplitude. At Halifax, on the Atlantic side of Nova Scotia, the tidal amplitude was only 2 m. One can observe the relative amplitudes of semidiurnal and diurnal tides. At Plymouth, England the tide is almost purely semidiurnal, as it is at Chittagong, Bangladesh, while at ports on the Gulf of Mexico, such as Galveston or Tampico, the tide is predominately diurnal. At Los Angeles Harbor and Basra,Iraq diurnal and semidiurnal components are comparable in magnitue, diurnal predominating. The same is true at København, at the western end of the Baltic, but the amplitude is only 10 cm, but the relative phases of the components is unusual. Mediterranean tides are small, but semidiurnal. The amplitude at Messina is about 20 cm, while at the eastern end at Sidon it is about 40 cm. I could find no ports listed in Hudson Bay, or in the eastern Baltic, but tides are probably negligible. If you are interested in tidal patterns, this site will fascinate you.

If you have a favorite port, studying tide patterns, both by themselves and in reference to the moon and sun can show a lot. I followed the tides at Plymouth and Exmouth Dock, locations about 40 miles apart on the south coast of Devon, England, on the northern side of the entrance to the English Channel. Times of high tide were compared at both places. High tide at Exmouth was about 53 minutes later than at Plymouth, showing that the tidal wave was running up the Channel at about 45 mph, though the moon's motion was in the opposite direction. High tide at Plymouth occurred about 5 hours after meridian passage of the moon, which would be the lunitidal interval. Tides were about 50 minutes later on successive days, as generally expected, but there were considerable variations. On 14th June, the moon was crossing the meridian a full hour later each day, instead of the usual 50 minutes later. The reason was that the moon was at perigee on the 12th, and the inequality of orbital velocity caused this variation. In a few days, the moon was back to crossing the meridian 50 minutes later each day as usual. The tidal period did not change much during this time, showing that the tides are a resonance phenomenon depending on average perturbations. Tides in the English Channel are a complex phenomenon.

The tide at Sharpness Dock, England, at the upper end of the Bristol Channel can be watched to predict when the Severn Bore will occur. The tidal range becomes much larger near the equinoxes, and this is when noticeable bores happen. This would be a good place to watch the difference between spring and neap tides, as well as the equinoctial effects. There is a resonance in the Bristol Channel that magnifies the tides in this area, which are unusually high. The highest seem to be at Port of Bristol (Avonmouth), and there is a large range between spring and neap tides. The tide takes about two hours to run from Ilfracombe, in North Devon, to Sharpness Dock. Note that this is not the speed of the tidal current that fills and empties the channel, and drives the turbine at Lynmouth.

The Ocean Bottom

The margin between the continents and the oceans is usually a gentle slope. It begins on the landward side as the continental shelf, which is an extension of the coastal plains of the continent. The continental shelf may be narrow or wide, and extends to a depth of 100-400m, where the slope increases slightly to the continental slope. At some poorly-defined point, where the depth is 1500-3500m, the slope decreases at the start of the continental rise, which gradually joins the abyssal zone at 3000-5000m. This is typical at a passive boundary where a plate is not being subducted. At a subduction zone or trench there is a sharp break at the descent into the hadal zone, down to 10,000m or more. These trenches were discovered in the western Pacific by the Challenger expedition of 1863-1867, and have been objects of wonder ever since. They were thought to be subduction features for many years, and now even American geologists believe this.

The ocean floor is by no means a smooth and featureless plain, except where sediment has smoothed out irregularities, but features spreading zones, transform faults, trenches, and volcanic activity of wide variety. Under the thin sediment, it is all young basaltic rock, only 5 to 10 km thick, riding on the mantle rocks below, which drag it from the spreading zones to the trenches and recycle it there, together with whatever it has accumulated in the meantime. Ocean sediments are thin away from the continents, and consist of red clay and biogenic oozes. Red clay is an inorganic sediment colored by ferric iron and containing anything that is not something else. Something else is siliceous ooze or carbonate ooze. Siliceous ooze consists of diatom frustules and radiolarian shells. Carbonate ooze consists of coccoliths and foraminifer shells. Diatoms and coccolithophores are members of the phytoplankton, microscopic floating plants, while radiolarians and foraminifers, mostly globerigina, are members of the zooplankton, microscopic floating animals. Microscopic plankton dominates life in the ocean, and works very efficiently.

Red clay can occur anywhere, but it accumulates so slowly that it is usually dominated if there is any other kind of sediment. There is a constant rain of carbonaceous residues, but at some depth, called the Carbonate Compensation Depth (CCD), the rate of dissolving equals the rate of deposition, and below this depth carbonates disappear. Siliceous residues dissolve in warm upper waters, and unless they survive this, do not persist to form sediment. Diatom ooze is found mainly in cool waters, but this does not imply that diatoms live only in cool waters, simply that their fossils are preserved there. The fossil record in the oceans is short, but has the excellent characteristic that it is more or less continuous, not interrupted as the terrestrial fossil record is. In recent years, this record has led to intensive study of Ice Age climates and other relatively recent geological events, poorly recorded on dry ground.

Hydrocarbons

The continental margins consist of thick wedges of sediment derived from the land, and are also very productive of life. Where conditions are anaerobic, organic residues rich in hydrocarbons form black shales interlayered with sands and, in exceptional cases, with evaporites such as salt, gypsum and anhydrite. When deep burial increases temperatures and pressures, hydrocarbons leave the black shales and collect in the sandy, porous and permeable strata where they may be trapped against impermeable salt or anhydrite, by salt domes or faulting, or in domed structures with no outlet. Present-day continental margins are often rich in hydrocarbons, such as in the Gulf Coast, California and the North Sea. Modern exploration and drilling techniques have made these resources available. However, the accumulation of petroleum is exceptional, and the Atlantic coast of North America is relatively poor in hydrocarbons.

Natural gas often seeps from the rocks underwater. This gas is usually lost, or may be lighted to create the eternal flames of Iran. It is also possible for the gas to form a clathrate with water, in which a methane molecule is surrounded by a dodecahedron of water molecules, imprisoned securely but not chemically combined. Clathrates can form above 0°C, and look like ice. They release the methane on heating, sometimes explosively, since the clathrate stores the gas very compactly.

No oceanic hydrocarbons, like all petroleum of whatever source, show any indication of abiogenic origin--all occurrences are consistent with microbial action on organic materials. There are no hydrocarbons on the ocean bottom, only on continental margins.

The Atmosphere

Pressure, Temperature and Composition

The atmospheric pressure at the surface is 1.01325 bar (1 bar = 106 dyne/cm2) or about 14.7 psi. Since we know the area of the earth, we can find that the total weight of the atmosphere is 5.4 x 1018 kg, 1/370 the mass of the ocean. Meteorologists like to measure atmospheric pressure in millibars, while chemists and physicists prefer the length of a mercury column (d = 13.56) exerting the same pressure. The standard atmospheric pressure is then 760 mmHg (or torr; 1 torr = 1 mmHg). This is 29.92 inHg; 30 inHg was the original British standard atmosphere, which corresponds to 33.9 ftH2O. These days you also find hectopascals, hPa, which are exactly the same as millibars, but with a stupid name.

The atmosphere has a remarkably constant composition below about 90 km altitude. By volume (or mole fraction) in dry air it is 78.088% N2 and 20.949% O2. 78% and 21% are close enough for government work, and easier to remember. The molecular weight is 28.966, and the round figure 29 is almost right. At 20°C, the vapor pressure of water is 17.535 mmHg. At 50% relative humidity, the vapor pressure of water is 8.77 mmHg. In a total pressure of 760 mmHg, we have 586.6 mmHg of N2, 157.4 mmHg of O2, and 8.8 mmHg of H2O, which makes this moist air 77.2% N2, 20.7% O2 and 1.2% H2O. The amount of water vapor is variable, but in the lower atmosphere it is the third most abundant component of air. The ideal gas law is adequate in almost all cases for dealing with the atmophere, even with water vapor, since the pressure is low, and the gas mixture is also ideal.

The humidity of air may be stated as the absolute humidity, the actual weight of water per unit volume, or the relative humidity, the actual partial pressure of water vapor divided by the saturation vapor pressure at that temperature, usually expressed as a percentage. The mixing ratio is the ratio of the mass of water vapor to the mass of dry air in the same volume, w = (Mwater/Mair)[e/(p - e)] = 0.6214e/(p - e), where e is the water vapor pressue and p the total pressure. The dew point of a sample of moist air is the temperature at which the saturation vapor pressure equals the actual pressure of water vapor. When the sample is cooled to this point, water will begin to condense, or a fog will form.

The odd 1% in dry air is largely argon, 0.93%. For practical purposes, it can be lumped with the nitrogen to make 79% by volume of dry air. Most of this argon probably came from the radioactive decay of K40, since it is heavy enough (M = 39.9) not to have been lost, and is 99.6% A40. Next in abundance is the heavy gas CO2 (M = 44), about 0.03%, the object of a great deal of current worry. Helium is about 10 times more abundant than hydrogen, but both are very scarce, since they are easily lost gravitationally. The helium comes from the alpha particles emitted in radioactivity. A cubic metre of air contains only 5.24 cc of He. It is easier to get it from natural gas that has collected He from nearby granite over millions of years, where it can be present up to 6%. Neon is actually about twice as abundant as helium. Krypton is present at 1.14 ppm, and xenon at 0.86 ppb. Methane is at 1.4 ppm, slightly more abundant than krypton, while nitrous oxide is 0.5 ppm. Ne, Kr and Xe are probably original ingredients, while methane and nitrous oxide are unreactive enough to have permanent residence.

The "greenhouse" gases are those that absorb and emit infrared radiation, either in vibration or rotation or both. These are, in order of amount: water vapor, carbon dioxide, methane and nitrous oxide. Nitrogen, oxygen and hydrogen do not absorb in the infrared (but do in the ultraviolet), while the noble gases have no internal degrees of freedom. The "greenhouse gases" allow the atmosphere to be transparent to visible radiation which heats the earth and sea, while making it much less able to transmit the infrared which is emitted by earth and sea to space to establish an energy balance. The earth and sea must, therefore, become warmer to get rid of the same amount of energy that they receive. Without this effect, the temperature at the surface of the earth would be about 217K (-56°C). Actually, this would freeze all the water and increase the albedo of the earth, so things might not be so bad, just about -30°C, say. At any rate, life would be impossible. The primary actor in this play is water vapor, not the bit actor carbon dioxide, which has only a small (but real) influence.

The atmosphere behaves, as the sea does, according to the hydrostatic equation dp/dz = -ρg, where p is the pressure, z the altitude, ρ the density and g the acceleration of gravity. In U.S. engineering units, ρg is the weight density in, say, pounds per square foot. Water is nearly incompressible, as has been noted, so its density depends mainly on the temperature and salinity. Hence, warm water floats on cold water, and fresh water floats on salt, giving convective stability. Air is quite different, since it insists that p = mRT/MV, where m is the mass of air with molecular weight M (= 29), V is the volume, T the absolute temperature, and R is the universal gas constant. If m is in grams, V in m3 and T in K, then R = 8314 J/gmolK and p is in N/m2 (Pa). The compressibility of air is -(1/V)dV/dp = 1/p, about 1 bar-1 at atmospheric pressure, about 200,000 times larger than the compressibility of water. The density now varies rapidly with temperature and pressure, so the ocean of air is very different from the ocean of water. The standard temperature profile of the atmosphere is shown at the right, with the usual names of the different regions. This is only an average profile; actual conditions may differ somewhat, but the general behavior is shown. The temperature in the thermosphere is the kinetic temperature of the particles, not the equilibrium temperature with a macroscopic body. Above about 50 km, a macroscopic body will radiate energy faster than it can be conducted from the surrounding air, and will chill to a very low temperature (unless the sun is shining on it!).

Combining the hydrostatic and ideal gas equations, we have the barometric equation dp/dz = -(Mg/RT)p. If we know the temperature profile T(z), we can find the pressure at any altitude. For constant T or linear gradients, the equation can be integrated in closed form. For practical work, it is easily integrated numerically. The quantity H = RT/Mg is called the scale height, and is really just another way to express the temperature T. At 0°C, H = 7992m, or close to 8 km. If H is constant, the barometric equation integrates to ln p = z/H + const., or p = p' exp(-z/H). The scale height is then the difference in altitude for which the pressure decreases by a factor 1/e = 0.368. Since MgH = RT = pMV/m, or ρgH = p, H is also the height of an atmosphere of constant density equal to that at the surface, and is sometimes called the "height of the homogeneous atmosphere." However, an outstanding feature of the atmosphere is that it is not homogeneous, but that the pressure and density decrease rapidly with height.

Centred on 30 km altitude is the region where short-wave ultraviolet radiation dissociates O2 → 2O, and then the atomic oxygen rapidly forms ozone, O3. The ozone concentration can exceed 10 ppm in this region. Above this ozone later, the absorption of ultraviolet in photochemical processes heats the thin air, and the temperature begins increasing again at about 25 km, to reach a maximum at around 50 km nearly as high as the surface temperature, typically 283K. Above this level, the temperature again decreases steadily, reaching 166K at 80 km. The temperature remains nearly constant to 90 km, after which it begins a steady increase continuing into the region of free molecular motion. At 90 km, the pressure is down to 1 μmHg, a fairly good laboratory vacuum, and the mean free path is about 3 cm. Beyond this is the region of the ionosphere, where the atmosphere is a thin plasma. In fact, the D region of the ionosphere, its lowest layer, is centred at 90 km. It forms during the day when ionization by the ultraviolet is active, then disappears at night as the ions and electrons recombine. This is also the region where meteors burn up from friction with the air. These regions of the atmosphere are indicated on the temperature profile above.

Lapse Rate and Stability

Suppose for a moment that we have an isothermal atmosphere. Then the density decreases rapidly with height, so that light air is on heavy air, a very stable state of affairs. Such an atmosphere would be expected to be strongly stratified, as is the sea. We naturally expect, however, that as we ascend and approach the cold of space, that the atmosphere would become cooler. That is, there would be a lapse rate of so many degrees per kilometer. This was exactly what was suggested by the temperatures at mountain tops and confirmed by balloon ascensions. It was also noted that the atmosphere was rather well mixed, by winds and convection. If we take a small parcel of air (imagine it surrounded by an imaginary very flexible envelope) and suddenly carry it to a higher altitude, it expands because of the lower pressure until its pressure is equal to that of its surroundings. In doing so, it must push out its boundary, doing work on its surroundings at the same time, which must come from its store of internal energy, so it must become cooler than it was in its original place. If it is now cooler than its surroundings (which it would be in an isothermal atmosphere) it is denser, and so sinks back toward its original level. If we carry the parcel to a lower altitude, the increased pressure makes it smaller, and does work on it, making it also hotter. Then, since it will be less dense than its surroundings, it will rise back toward its original position. There is convective stability in an isothermal atmosphere.

If there is a lapse rate, then the surroundings are also cooler at greater altitudes and warmer at lower. Should the lapse rate exactly match the temperature change of our parcel, the parcel will be content wherever we put it, and we will have neutral stability. Of course, there will be some heat conduction when there are temperature differences, but the rate of heat conduction is small enough that coming to equilibrium will require considerable time. In fact, more heat is spread by turbulent mixing than by conduction anyway. If there is no heat flow to our parcel, then the pressure and volume change according to pVγ = constant, where γ is the ratio of the specific heat at constant pressure to the specific heat at constant volume. For air, it is close to 1.4. Such a process is called adiabatic. This relation can be combined with the ideal gas law to find how the temperature varies as a function of pressure as well. Since entropy change in a reversible process is dQ/T, where dQ is the heat transfer, and dQ = 0 in this case, this process is also called isentropic. If the air is thoroughly mixed, it will be in neutral equilibrium with a lapse rate characteristic of an adiabatic process, the dry adiabatic lapse rate. A linear lapse rate at 9.77°C per km is the result. This is a very rapid decrease of temperature with height, but it will still permit dry air to remain stable. Well-mixed dry air will usually give a lapse rate close to 10°C per km, inviting convection and turbulence.

If the lapse rate is still greater than this, then a rising parcel of air will find itself warmer and lighter than its surroundings, which will encourage it to rise further. Should the parcel sink, it will become warmer, but not as warm as the air around it, so it will be heavier and will be encouraged to sink further. Therefore, any small motion of an air parcel will be amplified by buoyancy effects, and turbulence will break out. The air is now unstable, and will naturally become turbulent. For dry air, a greater lapse rate than 9.77°C per km will result in turbulence and mixing, while a smaller lapse rate will result in stability and stratification.

On the other hand, if the parcel of air contains water vapor, the adiabatic cooling may bring it to saturation, and any further attempt to cool it will result in the condensation of water. This level is quite obvious on a sunny day as the base of cumulus clouds formed by the upward motion of moist air. The condensation of water releases considerable heat, which will make the parcel even more eager to rise. The temperature does not decrease with altitude as rapidly as it does for dry air, so a smaller lapse rate is required for stability. The temperature decrease is not linear as it is for the dry adabatic process. At 20°C and 1000 mb, the saturated pseudoadiabatic lapse rate is 4.3°C per km. At 0°C and 700 mb, it is 5.8°C/km. These figures give some idea of its usual value, which is much less than the dry adiabatic lapse rate. It is easy to see the change from stability as moist air rises to the condensation level, and then boils with instability above it, as we see from the cumulus cloud that results from the condensation.

The standard lapse rate is 6.5°C per km, from 288.16K at 0 km altitude, to 216.66K at 11 km. This is between the dry and wet adiabatic lapse rates, and is only an average or characteristic value. Any lapse rate comfortably less than the value for stability is called an inversion (though strictly this term should be used for negative lapse rates, when the temperature actually increases with altitude). The air will then be stable and stratified, hot air above cold air, with little mixing. This is very easy to arrange when the air is very dry and the ground cools rapidly. In the desert, the sun heats the earth during the day, creating a strong lapse rate encouraging turbulence and dust devils from the strong convection. In the evening, the earth cools more rapidly than the air, and an inversion is created, with layers of dusty or misty air. Convection and turbulence cannot easily be seen near the ground, unless emphasized by dust and wind, but it is always there when bright sunshine makes a strong lapse rate, and the ground is covered with a pattern of ascending and descending currents, the tops of which are seen in the cloud bases, where the temperature has declined to the dew point of the air mass.

The region of moderate lapse rate is the troposphere, which ends at the tropopause, above which the temperature is roughly constant, giving high stability, the result of which is expressed in the name, stratosphere. The pressure at the tropopause is about 200 mb, and the scale height in the stratosphere is about 6400m. The tropopause is at an altitude of roughly 10 km in polar regions, and 16 km in equatorial regions. The change is rather abrupt, occurring between 40° and 60° latitude where the strong westward winds called the jet stream occur. The jet stream is at the polar front, the boundary between cold polar and warm tropical air. Jet stream winds typically have speeds of 100-200 kt (5-10 m/s) at the core.

Propagation of Sound, Light and Radio Waves

The existence of the ionosphere was discovered in the 1920's because of its effect in reflecting radio signals of about 30 MHz and lower in frequency, making long-distance radio communication possible. However, that there was a temperature maximum above 25 km was not suspected until anomalous sound propagation over long distances was attributed to this cause. For details, see The Guns of Barisal. Until sounding rockets became available after World War II, balloons were the only way of sounding the upper atmosphere, and a balloon can only reach altitudes of about 30 km.

The speed of sound in air can be obtained from the general formula for the speed of dilational waves by using the adiabatic compressibility κ/γ = 1/γp. This gives c = √(γp/ρ) = √(γRT/M). At 0°C, 273.15K, c = 331 m/s. The speed of sound is independent of the pressure, but depends strongly on the temperature. Since moist air has a slightly smaller molecular weight than dry air, the speed of sound is slightly greater. For the air at 20°C with 50% relative humidity mentioned above, the speed of sound is 343.97 m/s, while for dry air at the same temperature it is 343.22 m/s. Generally, we can neglect the effect of moisture on the speed of sound.

Along a sound ray in a horizontally-stratified medium, the ratio cos θ/c = constant, where θ is the inclination of the ray to the horizontal, and c is the speed of sound. This is just a restatement of Snell's Law of refraction for this case. If c decreases, then θ must increase to maintain the ratio constant. Let's suppose the speed of sound at the surface is 331 m/s, corresponding to 273K, and we launch a sound wave horizontally. At an altitude of 1000m, the temperature is 266.5K if the lapse rate is the standard one, and the velocity is 327 m/s. Then cos θ = (327/331)(1.0), or θ = 8.9°. The ray is curved upwards, and will pass 1 km above the head of an observer about 13 km distant (assume the average inclination is half of 8.9°). For this reason, we do not normally hear sounds created at a distance, and the zone of audibility is a restricted one. To understand this clearly, think of a vertical wavefront that is moving at 331 m/s down here, and 327 m/s 1 km above; it will soon be tilted and will propagate at an increasing angle.

Such a ray will be curved upwards, almost as an arc of a circle, then will travel straight through the constant-temperature stratosphere, and then will bend over when the temperature increases upwards, becoming horizontal again when the temperature again reaches 273K, which it will do at around 44 km altitude, on the average. The the ray will bend downwards, retracing a path symmetrical to the ascending route, until it again reaches the surface at a distance about 120 km from the source. The sound (if loud enough) will again be heard at a large distance from the source, and delayed relative a direct path because of the detour through the stratosphere; it will seem to come from the horizon. This is called anomalous sound propagation, and has often been observed.

The propagation of light in the atmosphere is a large and interesting subject. The characteristics of light rays in the atmosphere, and the observed effects, including the mirage, is discussed in Mirages. The green flash is introduced in Green Flash, where links are given to further information. A further interesting field is that of refraction and diffraction in water droplets and ice crystals in the atmosphere, giving rainbow and halo phenomena. There is not yet an article on these phenomena in this website.

Winds

Global wind patterns are reasonably stable, and are determined mainly by solar heating of the earth's surface, where heat transfer occurs. The winds are driven largely by the temperature difference between equatorial and polar regions and tend to equalize temperatures over the earth. The sea, however, probably exerts the major influence on heat distribution, but is characterized by slow response, while the response of the atmosphere is rapid. Moist, warm air rises in equatorial regions where it cools and condenses on its movement away from the equator at upper levels. The air descends again at latitudes of around 30°, the horse latitudes, as dry, warm air, and then returns towards the equator as the easterly trade winds, steady and strong. The wind directions are the same in both northern and southern hemispheres. The zone where the trade winds meet is called the doldrums, from the general lack of wind. The horse latitudes are so named from the floating dead horses found there, jettisoned by becalmed ships that ran low on water.

Winds from the horse latitudes blow northwestwards at the surface to form the temperate westerlies, normally dry except when they pick up moisture from the warm sea surface and carry it north. These currents then rise at the polar front and return southward to arrive in the horse latitudes cooler than when they left, counterbalancing the heat arriving from the equator. Warm air rising at the polar front then moves northward to the pole, where it sinks to the surface, returning as cold, moist polar easterlies. This general circulation is modified by the seasons and local conditions, and especially by interaction with the ocean surface.

In India, the surface winds blow from the northeast from October to April, across the dry steppes of Tibet, but from the southwest from April to October, over the warm Indian ocean, where they pick up moisture. A seasonal pattern such as this is called a monsoon, from the Arabic for "season." These winds drive corresponding currents in the Indian ocean, that reverse with the seasons. India would normally be in the zone of easterly trade winds. The monsoon rains are essential to agriculture in the region. In Denver, the winds are southwesterly in the summer, which can bring in moisture from the Gulf of California that is not wrung out as thoroughly as the usual westerly winds. In the winter, northeasterly winds bring in polar cold and snow. This pattern is often called a "monsoon" locally.

Surface winds blow from high pressure to low pressure, but the matter is not as simple as this. The atmosphere between 1000 mb (surface) and 200 mb (tropopause) is, as we noted for the sea, a two-dimensional system when seen in the large, of great exension but negligible thickness. A surface high pressure region, or "high," is a region where air is sinking to the surface, and from which it flows out in all directions. The air is subject to very little friction and restraint, so it responds to the slightest force that acts generally on it. One such force is the Coriolis force, a force that we must consider acting if the earth is considered as at rest. An explanation of this force can be found in Dynes and Slugs. In the northern hemisphere, it is a force tending to deflect motion to the right, while in the southern hemisphere, the deflection is to the left. It is proportional to the speed of the motion. It is not mysterious, merely the result of inertia in moving to a point a different distance from the axis of rotation. More information on winds can be found at The Winds.

Highs, Lows, Air Masses, Fronts and Weather

Air moving out of a high, therefore, is deflected to the right, or in a clockwise direction around the high, in the northern hemisphere. The pressure force is directed radially outward from the high, while the Coriolis force is directly inwards when the air is moving along an isobar, a contour of constant pressure. Therefore, the forces balance when the air is moving clockwise around the high, and the wind is called geostrophic. Actually, some wind does actually have to blow somewhat outwards, but the geostrophic wind is a good approximation. At a low, air is rising, so it must come in from the periphery. Again, the wind flows almost along the isobars, but now in the opposite direction, anticlockwise, since the pressure force is inward toward the low. In the southern hemisphere, the circulation around a low is clockwise, and anticlockwise around a high. This is seen on weather maps, and is pleasant to notice, as evidence that everything works out as expected. It is easy to see why highs, lows and isobars are so important in weather forecasting, because they indicate the direction and strength of the winds. When the isobars are closer together, the wind must blow more strongly (faster) to make the Coriolis force balance the greater pressure force.

There are permanent lows in the North Pacific and North Atlantic, where cool moist air converges and rises above the cold ocean in the global circulation, and permanent highs in the horse latitudes, where cooler air sinks to the hot surface and diverges. These highs and lows play a constant role offstage in North American weather. When I looked recently, the Pacific low was off the Aleutians, at 972 mb, while the Atlantic low was east of Greenland at 971 mb, both surrounded by closely-spaced isobars meaning strong winds. A high at 1026 mb was off California, with gentle winds. Lows and highs spun off over continental areas can be labelled for discussion by their central pressures. Lows tend to fill or merge, highs to empty, and have a finite life as they move eastwards.

Air masses acquire their natures from the surfaces over which they lie. Maritime air forms over the ocean, and is moist and often unstable (high lapse rate). Air called maritime polar (mP) forms over the north Atlantic and the bay of Alaska, and is cold, while maritime tropical (mT) forms over the equatorial Pacific and the Gulf of Mexico, and is hot. In what follows, I will describe what is important in North America, but the same principles apply to other temperate zones in both hemispheres. Continental air is dry, and stable. Continental polar (cP) air is made over Canada (and Siberia); it is very cold, quite dry, and stable. Continental tropical (cT) air is very dry, and hot. It forms over the American southwest, for example. Air masses retain their characteristics as they are carried by the global winds, and when they meet form distinct boundaries, called fronts. Recall that the atmosphere is essentially two-dimensional, and the line contacts of air masses affect the properties of the masses very little. The weather in the temperate zone between latitudes of 30° and 60° is a story of the battle between polar and tropical air masses in contact along the jet stream, which writhes back and forth across this area, driving the weather from west to east.

Cross-sections of frontal systems are shown in the figure at the right. When a cold air mass (say, cP) moves into a warm air mass (say, mT), a cold front forms, and the warm air rises along a steep slope (all the slopes are greatly exaggerated in the diagrams). Condensation may produce a squall line of storms like the usual convective thunderstorms of summer. When a warm air mass moves into a cool air mass, it rides up a gentle slope. The general lifting may cause widespread, persistent precipitation. As we shall see, a cold front may move more rapidly than a warm front, and catch up with it, lifting the warm air completely off the surface. This is called an occlusion, and there are two types, as shown, depending on which mass of cold air is the colder. In each case, the front is moving in the direction shown by the arrow. The air masses involved mix only slowly, usually by turbulent motions. A fifth type of front is the stationary front, in which the two air masses are in contact along a line, but not moving rapidly. Cold and warm front characteristics can alternate along the stationary front, shown by placing the triangles and semicircles identifying cold and hot front alternately, triangles on one side and semicircles on the other. At an occluded front, the alternating symbols are all on the same side of the line.

There is often a chain of lows and highs along the general path of the jet stream, a stationary front, joined by alternating cold and warm fronts, when the jet stream is blowing to the northeast, which carries the lows in the same general direction. The low, or cyclone, is accompanied by anticlockwise winds that blow warm air northwards in front of the low, and cold air southwards behind it. The situation shown in the diagram is greatly oversimplified, but it shows the principles of what often takes place. On the approach of a low, the barometer falls, and the southerly winds are warm. When the low passes, cold winds blow from the north, and the squall line may produce rain. The barometer rises, and the winds change from northerly to southerly as the high passes, setting the stage for the next low. Highs generally bring clear, fine weather because the air is generally descending and warming as it does so, while lows are associated with storms because they are areas of rising, cooling air. Although the details are always different, the correlation of weather with barometric pressure is so evident that barometers are often labeled with the expected weather. What has just been described is typical of the temperate zone, but is of little help in either polar or tropical regions, whose weather is dominated by other causes.

The behavior of the winds when typical cold and warm fronts pass is shown at the right. Note the inclination of the winds to the isobars, and the angles made by the isobars at the fronts. Both the anticlockwise rotational motion, and the inward motion or convergence towards the low are illustrated. Only one isobar is shown, but higher pressures are farther from the cyclone, and lower ones toward it. The feathers on the wind diagrams point into the wind, and the wind speed is indicated by the barbs. A long barb corresponds roughly to 10 mph (or knots), a half-barb to 5 mph. The exact definitions can be found in the references. A solid triangle instead of a line corresponds to 50 mph. Concentric circles (like a hole reinforcement) mean calm winds. The change in the wind direction on frontal passage is clockwise (or "sunwise") in both cases, and is called veering. The reverse motion is called backing, and is less common. Here in Denver, gentle, warm southwesterly winds, often Chinook winds in the winter, are succeeded by cold north winds when a cold front passes. The passage of a warm front is much less dramatic, and seldom noted.

The weather map, or synoptic chart, shows isobars, highs and lows, fronts, temperature, winds and precipitation (a dot is rain, an asterisk is snow) by a complicated symbolism. A great deal of information is included, and the general course of the weather is easily deduced from it. American newspapers, and even TV reports, used to give weather maps, but the almost total inability of the public to make anything of them has led to their degeneration. My daily paper has only a useless map, with only temperatures and precipitation indicated. TV weather reports sometimes show lows and highs, and a front or two, but I sometimes doubt if the presenter can make much of it. The weather now comes already predicted by the Weather Bureau, and all you have to do is read it off for your location. This is rather unfortunate, since regular study of weather maps can make one a good weatherman.

If you search for "weather map" on the Internet, you will get millions of targets, most of which are useless. A better search is "weather map isobars," in which what we desire is more concentrated. The subject seems to be taught in schools and colleges, mostly in geography courses, and many of the targets are instructional material, of generally little use even if you are allowed to access it. The US Weather Bureau has sites, but their information appears to be distributed largely for the benefit of commercial activities, and much of what you find is very bad and uninformative, with dark, muddy backgrounds. While searching, you can have porno pushed on you, and flashy ads for this and that. Excellent maps are available at the Canadian Weather Office (see References for the link). Look for Surface Analysis Charts, MSLP. Head and shoulders above the shameful mess at the US Weather Bureau are the Canadian Weather Office, the Met Office in Britain and the Bureau of Meteorology (BoM) in Australia. Even New Zealand has an excellent site, though they depend a lot on Australian weather (New Zealand is the size and population of the State of Colorado, which has no weather bureau at all). Some links are given in the References. An Australian weather map, from the BoM, is shown above for illustration (it suffered when reduced to fit). The weather is moving from west to east, as in the northern hemisphere, but the rotation around the cyclones and anticyclones is reversed. Note in particular the cold front running north from low 992. More information on weather maps can be found in Weather Maps.

It would be interesting to investigate tropical (+30° to -30°) and polar (>60°) weather, which should be much different from temperate weather. The tropics are probably boring, with seasonal wind patterns of predictable nature. Mexico is a good example, with its rainy and dry seasons that occur regularly. Polar weather is probably constant minor storms and chaos, dominated by seasonal freezing and thawing. Alaska (Anchorage has a good site), Iceland or Scandinavia might have weather services to investigate for polar weather. For tropical weather, Mexico, Colombia, India, the Phillipines and Indonesia might be good choices. This occupation could keep one busy, like cloud-watching.

Clouds

Clouds are aerosols of water droplets that form when moist air cools to its dew point. Clouds are beautiful to watch, allow us to see the movements of the atmosphere, and bring rain and snow. The water droplets condense on cloud condensation nuclei (CCN) of many kinds, which are always present in large numbers. It is very difficult to get a droplet started spontaneously, though it will happen if the supersaturation is large. Condensation on a small droplet is more difficult than on a large one, because the surface energy is relatively larger due to the large area to volume ratio of colloidal drops. Condensation on hygroscopic nuclei (like salt particles) can occur before the relative humidity reaches 100%. CCN may be electrically charged (it helps in attracting the polar water molecule), and the small droplets may collect negative ions, so the droplets are charged with the same sign of charge, which keeps them apart, stabilizing the aerosol. CCN are typically less than 1μm in diameter, while cloud droplets are typically from 10μm to 50μm in diameter. A particle of diameter 10μm falls at about 0.3 cm/s, so cloud droplets easily remain suspended.

Droplets of this size scatter light very effectively without wavelength dependence, so clouds are white (or shades of grey as interpreted by our visible sense). Smaller droplets, in the range 0.1 to 0.3 μm, scatter proportionally to λ-4, the Rayleigh law, so red light is more effectively scattered than blue. Such droplets cause the familiar blue haze that lends visual perspective. The blue of the sky is caused by scattering from density fluctuations in the thinner air of high altitudes, above the tropopause. The oranges and blues of atmospheric light, especially at twilight, is a result of atmospheric scattering by all small scatterers, and is pleasing to the sensitive observer.

When droplets condense, the remaining air is less humid, and the droplets stop growing when their vapor pressure is in equilibrium with the water vapor pressure in the air. The aerosol is stablized by droplet charges, and the cloud appears to be permanent. The cloud is transported by local air movements, and disrupted by turbulence, but often a cloud forms in a wave in the wind. As the wind blows through the wave, the cloud first condenses, and then evaporates at the trailing edge. Such clouds are not carried by the wind, but form in the wave. Although clouds seem fairly permanent, close observation will reveal that they are usually changing rapidly in size and shape, forming and dissipating, and are very dynamic objects.

It is remarkable that clouds do not always rain; in fact, this seldom happens except under special (but fortunately frequent) conditions. The formation of ice crystals is one such condtion. When formed at high altitudes, they grow to larger sizes than water droplets would, and fall. They sweep up water droplets as they descend more and more rapidly, melt, and fall as rain. If the water content is high enough, the aerosol may destablize by droplet growth or charge neutralization, and the droplets coalesce or the larger ones grow at the expense of the smaller, and again fall as rain. The precise mechanism of raindrop formation is disputed, but these explanations may be approximately correct. Near a high, or anticyclone, the sinking air discourages cloud formation, so highs are associated with fine weather and clear skies.

Clouds formed in a convective, unstable atmosphere are typically boiling heaps, called cumulus (Cu). Clouds formed in a stable, stratified atmosphere, often as a result of general lifting of the moist air in a cyclonic system or over a warm front, are typically more or less uniform sheets, bounded above and below. These clouds are called stratus (St). [The letters in brackets are the usual abbrevations for the cloud types.] These two conditions are so frequently encountered that most clouds can be classified as one or the other, and a quick glance at them suffices to learn the state of the atmosphere. Wave clouds have distinctive shapes, and are given various names, such as orographic clouds when the wave is caused by surface topography, or billow clouds produced in the waves at the interface of wind velocity layers. Orographic clouds are often lenticularis, lens-shaped clouds with feather edges that are often iridescent.

Clouds are also classifed by the height at which they form. The temperature at 6-7 km and above is low enough that ice crystals are formed instead of water droplets. They fall more rapidly, either because they are larger or the air is thinner, and trail below the cloud top, where they are blown by the wind into the feathery mares' tails of cirrus (Ci) (Latin: curl of hair) clouds. Sometimes the aerosol is stable, and the ice-crystal clouds form a thin, high veil (cirrostratus, Cs) sometimes kilometers thick. The tops of cirrus clouds is as often as not within about 1 km of the tropopause. They display the humidity and winds in the upper troposphere to a casual view from the ground. The ice crystals in cirrostratus clouds create the fascinating halo phenomena around the sun and moon. The jet stream is located at these altitudes, and its influence can often be seen in cirrus clouds.

The names of clouds at altitudes from 3 to 7 km are prefixed with "alto-" to indicate that they are at a high level. The pressures at these levels are from 400 to 700 mb, and what is going on at these levels can be determined with synoptic charts drawn for these pressures. There tends to be considerable variation in the winds with altitude, as can often be clearly seen in the relative motions between these clouds and the cirrus above them. Billow clouds and other wave phenomena are also often seen. Altocumulus is common at this level, which can even rain ice like a cirrus, or if there is instability can form altocumulus castellanus, with small turrets and castles. At lower levels, stratocumulus may form in the evening at the level of the bases of the cumulus clouds of earlier in the day. A generally lifted air mass can exhibit all three layers of stratus clouds, at three distinct levels.

Near the surface, the sun's heat act first on the ground, and is only slowly communicated to the cool air just above, so bubbles of warm, moist air ascend in invisibility ("thermals") until they reach the lifting condensation level (LCL) at perhaps a kilometer altitude. Then their moisture condenses, heating the bubble so that it boils up into a cottony cumulus humilis (Cu) until equilibrium obtains. The water content is about 1-3 g/m3. The cloud neither goes high enough for ice to form, nor is saturated enough to disturb the aerosol, so there is no precipitation. The name fair weather cumulus is well-deserved, since it happens when the weather is otherwise sunny and warm, and merely represents the transfer of a little water from the moist earth to the air. If a steady wind is blowing, successive bubbles may produce a line of clouds called a cloud street.

If there is more moisture available in the air, and bubbles arrive from the ground to set off convection, the rising currents tend to attract more moist air from the sides and send it up into the heights to condense and fuel further convection. The boiling cloud is now higher than it is wide, and enters the "alto" region. Such a cloud is a cumulus congestus, the seed of a large convective storm. The water content is 2-7 g/m3. When the top of the cloud reaches above 7 km, it begins to glaciate. Its outline turns fuzzy, and it forms a cirrus cloud. We cannot see the ice falling from it, however, until it emerges as heavy rain below the cloud, which can extend for 10 km vertically, and poke through the tropopause. When it does this, the high stability of the stratosphere puts a lid on it, and it spreads out horizontally, making the characteristic anvil. The cloud is now a cumulonimbus (Cb), a thunderstorm, with all its interesting accompaniments. A cumulonimbus can have a water content of 2.5 to 20 g/m3. When you see a cumulonimbus from the distance, you see the whole extent of the troposphere. They are so large that they can sink beneath the horizon like a distant ship. Nearly all the rain in Denver comes from such storms. When the storm dissipates, sometimes the remnant of the anvil is left as a cirrus cloud, called cirrus spissatus, "thickened cirrus."

Special features that appear now and then in connection with the cumulonimbus include the mammae that appear under the anvil when air cooled by falling ice sinks in warmer air just below it. This mammatocumulus can be a menacing feature, but occurs when the main show is over, and the cloud is dissipating. There are the pileus clouds forming a cap-like, domed detached cloud sheet that develops above a rapidly ascending convective top of a cloud ("pileus" is Latin for a cap of this shape). Sometimes rain leaving the base of a cloud evaporates before reaching the surface (this always happens with the ice showers of cirrus and altostratus). These showers should be called virgae (Latin: brooms), but are usually called virga under the erroneous impression that this is a neuter plural. "Mamma" can suffer the same indignity.

After the sun sets, the top of the cloud can be cooled by infrared radiation from its water vapor, maintaining a temperature difference between base and top that supports convection long into the night. This is the reason for night thunderstorms that can be so impressive in the dark. It is now known that there are lightning discharges of special kinds between the tops of thunderstorms and the ionosphere. There are always several thousand thunderstorms going on around the earth at any one time, creating continuous radio noise ("static"). The subject of lightning and thunder is an interesting one, but there is no room here for it.

The suffix "-nimbus" refers to a cloud that is raining or snowing. A cirrus cloud is snowing, of course, but it is not called a cirronimbus. A raining stratus cloud is not a stratonimbus, but a nimbostratus (Ns). The small bits of stratus torn off by the wind are called "scud" or fractostratus (Fs). Similar bits from cumulus are fractocumulus (Fc). Any of the field guides in the References will give a detailed descriptive taxonomy of clouds, with many photographs. All the names are fun, but their informational content is low, and it is more useful to think of general principles. Weather watching is an interesting hobby, frequently (and not very successfully) used to interest children in science. Perhaps the reason is that the scientists try to get the kids to do what they do, which, these days, is usually intensely boring. A motto of the Discovery Channel might show what is wrong: "So much fun, you'll never realize it's Science!"

Clouds are mostly a feature of the troposphere. High clouds, above the tropopause, are always ice-crystal clouds. Cirrus clouds are sometimes seen up to a few kilometers above the tropopause, but above this the stratosphere is cloudless, mostly because of a lack of water. The curious noctilucent clouds are very much higher, and appear like thin, fibrous cirrus. They are called noctilucent because they can only be seen when the sun is below the horizon, for otherwise the sky is too bright. They remain illuminated while the sun is above -16°, but disappear when the sun goes lower. They are seen in summer, May to August, in high latitudes, 50° to 70°. Therefore, they are usually seen from Scandinavia, Scotland, Iceland and Northern Canada. They occur near the upper temperature minimum of about 166K at 80-90 km altitude. Some have supposed that they are dust clouds, but it is just as hard to get dust at that altitude as water. The vapor pressure of ice is 1.5 x 10-5 mmHg at -98°C (this is as far as the table goes). The total pressure at that height is about 7.5 x 10-3 mmHg, so a mixing ratio of no greater than 2 x 10-6 would be enough to cause ice to form. If any water gets up that high, it will condense to form clouds, so ice is at least as likely as dust.

Hurricanes

Tropical storms are relatives of the frontal lows of temperate latitudes, both having cyclonic circulation, but driven by a different mechanism. While frontal lows are driven by the gravitational instability of air masses of different temperature in contact, tropical storms are driven by the latent heat of moist air. When the sea surface temperature exceeds 25°C, the moist sea air rises in the strong lapse rate and condenses, fuelling the creation of what is essentially a large cumulonimbus. The strong upward flow brings air in from the sides, and the Coriolis force gives it a twist, creating vorticity. Such rotating storms are also seen at temperate latitudes in the summer, spawning tornadoes. The flow patterns of neighboring vortices interact to cause the vortices to coalesce and strengthen. This can be seen in the frontal lows of the temperate zone, which tend to do the same thing. The difference in the tropical storm is that much more moist air is available, constantly spawning new convective systems.

The cyclonic flow creates a strengthening region of low pressure as the storm organizes, and a circular wind pattern becomes dominant. With a frontal low, the warm sector winds up and lifts, which eliminates the forces driving the low and causes the low to fill and dissipate. In a tropical storm, this does not happen as long as further moist air is fed to it near the surface. Winds, strongest at the centre, continue to increase as angular momentum is brought in from the sides and must be represented by the rotating air. Finally, an eye is created surrounded by a wall cloud in which centrifugal force is balanced by pressure force, and the tropical storm becomes a hurricane. A tropical cyclone or tropical depression has maximum winds of less than 40 mph (17 m/s, Force 8), a tropical storm 40 to 75 mph (17-33 m/s), and a hurricane 75 mph (33 m/s, Force 12) and above, according to the customary nomenclature. Hurricane winds can be as high as 155 mph (70 m/s). A storm is generally named when it reaches the tropical storm stage, when its low is surrounded by several closed isobars.

A hurricane can be 1000 km in diameter and extend from the surface to 15 km, the tropical tropopause. A satellite photograph of Hurricane Andrew (24-26 August 1992) from the Dundee Satellite Receiving Station is shown at the right. Its outer parts are lines of cumulonimbus separated by clear lanes, called the spiral rain bands, twisted into a spiral by the peripheral winds that increase towards the centre, and drifting inward to form a disk of thick cloud. At the centre is a remarkable circular disc of relatively clear air, the eye, in which the winds may be 25 mph (Force 6), and the sea is disturbed by waves. The air in the eye is slowly sinking, and is warmer than would be expected. The eye is surrounded by the wall cloud, in which moist air spirals upwards, and under which the rainfall is heavy. The air flow is inwards in the lowest 3 km, then up the wall, and spreading out at the top in a cap of cirrus cloud to complete the circulation. Condensation releases latent heat that drives hot air upwards, and creates the copious rainfall. The slightly less warm air in the interior sinks slowly as the eye of the storm. As much as 250 mm of rain can fall on the passage of the eye and its wall clouds. Low pressure in the eye causes the sea to rise in the storm surge. Air in the centre of the eye is slowly falling, keeping the air clear as it warms, except perhaps for some cumulus due to incidental convection. The dynamics of the eye do not appear to be well understood. The size of the eye and the central pressure depend on the development of the storm. I believe I saw in a book the isobars for the Galveston hurricane of 1901, in which the central pressure was 900 mb.

To understand hurricanes, it is a help to analyze the rectilinear vortex in an incompressible fluid. See The Vortex for an explanation. Of course, the analogy is not close except on the largest scale, since heat effects and radial and axial motions are not included. However, the reason for the existence of an eye, the region of vorticity, and the irrotational region are illustrated. The velocities are tangential, increasing proportionally to the distance in the rotational region (wall cloud), and decreasing inversely proportional to the distance in the peripheral irrotational region. The monotonic decrease of pressure from the periphery to the centre is also represented.

Hurricanes are born at latitudes of 10° to 30°, in the zones of the trade winds. They happen in the North Atlantic, in the Pacific on both sides of the equator, and in the Indian Ocean. For some reason, they do not occur in the South Atlantic, possibly because the sea is not warm enough. In the western Pacific, they are called typhoons, and in the Indian Ocean, cyclones. For North America, hurricanes originating in the Caribbean, and in the Pacific off Central America, are the most important. The hurricane season here extends from June to November, peaking in August to October. We'll discuss the characteristics of Caribbean hurricanes here, but they all behave similarly. The ocean becomes warm enough at the end of May for storms to form, usually in the westward drift from Africa to the Caribbean, and continues until November. There are about six full hurricanes in a season, mostly in August and September. The path of a hurricane is guided mainly by the upper winds, but predicting the exact path of a hurricane is quite difficult. When a hurricane moves over land or cold seas, its source of energy is gone, and it must live on the moist air that it has brought with it. The central low begins to fill, and the winds decrease. Then the eye is lost, and the storm retraces the stages of its growth in reverse. A typical North Atlantic mid-season hurrican begins off Cape Verde in late August, moves straight across the Atlantic toward the Gulf of Mexico on the trade winds, hooks to the north after passing Cuba, then moves northeast by north until it dissipates in the cold waters after the Gulf Stream veers eastward.

The most devastating hurricane in the U.S. occurred on the afternoon of 8 September 1900 on Galveston Island, Texas. This storm had been observed in mid-Atlantic gathering strength on 27 August. Accompanied by a large amount of rain, it entered the Caribbean, then moved west and northwest across Cuba, entering the Gulf and becoming a category 4 hurricane near Key West. On the 6th, a hurricane warning was issued for New Orleans, extended the next day to the Texas coast. On the 7th, Galveston enjoyed clear skies and a light, warm breeze. At 4 am on the 8th, driving rain began, and by 9 am the water was rising. The highest elevation on Galveston Island is 8.7 ft. By mid-afternoon, the winds reached 84 mph, and there was 5 ft of water. A steamship broke loose from its moorings behind the city, and destroyed all three bridges to the mainland as it was driven west by the wind. About 8.30 pm the eye of the storm passed over, causing a storm surge of 15.7 ft. The maximum winds were officially 115 mph, but 130 to 140 mph is more probable. The minimum pressure was variously said to be 27.64 inHg (933 mb) and 28.55 in Hg (953 mb). By midnight, the winds and waters had subsided as the storm moved inland. More than 6000 people were killed in the city of 37,000, and a large number of horses, which created a terrible problem when the water went down and the late summer heat returned. There had been 4 days' warning of the storm, but the storm surge had been overlooked.

The storm remained a hurricane deep into Texas, to the vicinity of Waco. It then moved northward, reaching Des Moines on the 11th, and turned northeastwards over Chicago, Michigan and Ontario, finally reaching the Atlantic at Gander, Newfoundland, while still a major depression. In Canada, it was responsible for at least 68 deaths. It is said that the storm crossed the Atlantic and finally expired in Siberia, its career lasting nearly a month. At the time, Galveston and Houston were struggling for supremacy, and the storm gave the advantage to Houston, which was further strengthened by the discovery of petroleum at Spindletop, near Beaumont, on 10 Jan 1901. The Canadian Meteorological Service has a good section on hurricanes on its website (see References).

The smallest-scale vortex storms are dust devils and tornadoes. Dust devils are made by convection over a hot surface, so usually condensation is not present, and the vortex is made visible only by the dust it kicks up. Snow devils kick up snow instead of dust at high altitudes, and steam devils occur in cold air over warm water (as near a geyser). These vortices are only from 100 to 500 m high, have winds seldom exceeding 50 mph or 22 m/s, and blow for only a hour or so. Of course, there are all sizes. They can form complete vortex rings, like a smoke ring, and steam devils are particularly susceptible to this. "Whirlwinds" are small dust devils, showing the persistence of vorticity in the air.

The core of a tornado is of a small diameter, often only a few hundred yards. The winds are correspondingly strong, and the central pressure correspondingly low. The rotation is almost always cyclonic, though anticyclonic tornadoes have been observed. They extend from the ground to the cloud base, and the circulation is similar to that of a hurricane, but on a smaller scale. There is condensation in what corresponds to the eye wall of a hurricane, but it is not a major energy source for the tornado. It feeds on vorticity brought in at its base, and deposits air in the cloud overhead. The winds in a tornado can be up to 250 mph (110 m/s). It does its damage by exploding a building in its low pressure, and then blowing away the fragments. Only a small band is subject to this destruction. Tornadoes can be seen coming, and are easily escaped by going beneath ground. They cause fewer fatalities than lightning (60 compared to 100 annually).

Larger tornadoes consist of several vortex tubes in the same general area up to a mile or so in diameter (the individual tubes are not persistent, and are constantly forming and dissipating). These are generally the supercell tornadoes from a mesocyclone, a rotating cumulonimbus association rich in vorticity. Most ordinary tornadoes have winds up to about 150 mph, and live for about 15 minutes, often not touching ground. A cloud that is receiving vorticity from below in convective bubbles may develop protuberances that show the condensation at the upper parts of these accretions. These funnels may develop into tornadoes by touching the ground. Usually, incipient tornadoes are not seen because of heavy rain in the area. The Great Plains of North America host about 75% of the world's tornadoes. From the Rocky Mountains westward, tornadoes are extremely rare, as they are in the Appalachian Mountains. Tornadoes move with the surface winds, usually southwest to northeast, at speeds of around 35 mph. Of course, there is much variation in this. If you observe a tornado moving to the right or left, it will not hit you; begin worrying if it appears to be standing still. Flying debris is the principal hazard when a tornado is about. A waterspout is a tornado over water; these form more easily and are less violent than the usual land tornado.

Tornadoes are classified according to maximum wind velocity in the Fujita-Pearson Scale from F0 (weak) to F5 (violent). The classes are: F0, 0-72 mph; F1, 72-112 mph; F2, 112-158 mph; F3, 158-206 mph; F4, 206-260 mph; F5, 260 and up. Most tornadoes (62%) are F0 or F1. Because of great public interest, a lot of material can be found on tornadoes.

References

E. Seibold and W. H. Berger, The Sea Floor 3rd ed. (Berlin: Springer, 1996). English edition of Das Meeresboden.

C. F. Campen, Jr., et. al., editors, Handbook of Geophysics, revised edition (New York: The Macmillan Company, 1960). Mostly atmospheric information.

S. L. Hess, Introduction to Theoretical Meteorology (New York: Henry Holt & Co., 1959).

V. J. Schaefer and J. A. Day, Peterson Field Guides: Atmosphere (Boston: Houghton Mifflin, 1981)

D. M. Ludlum, The Audubon Society Field Guide to North American Weather (New York: A. A. Knopf, 1991). This and the preceding work are excellent guides to clouds and the weather, though nontechnical.

L. Page, Introduction to Theoretical Physics, 3rd ed. (New York: D. Van Nostrand, 1952). The irrotational vortex, Art. 69, pp. 251-257.

G. Bomford, Geodesy (Oxford: The Clarendon Press, 1952). An excellent text on classical geodesy, including gravity.

E. I. Butikov, A dynamical picture of the oceanic tides, Am. J. Phys. 70, 1001-1011 (2002). An excellent account of the physical basis for the tides.

The Solar and Heliospheric Observatory (SOHO) website is at SOHO. Space weather is reported on this website. There are also solar images.

The Dundee University Satellite Receiving Station is at Dundee University Satellites, where many fascinating images of the earth can be seen.

See Planetary Science Institute for the collision theory of the moon's origin.

Weather internet links where synoptic charts can be found: Canadian Weather Office; Met Office; Australia; New Zealand; NOAA; Michigan. The University of Central Michigan site has many links, including webcams. Many of the commercial external links are cookiepushers with intrusive, vulgar, crass advertising, so beware. The surface weather map from Intellicast is much better than the poor, muddy map from The Weather Channel. Both are much inferior to the Canadian analysis charts.


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Composed by J. B. Calvert
Created 28 February 2003
Last revised 31 December 2004