CHAPTER XIV
Having thus briefly examined the composition and certain gaseous properties of free air, both dry and moist, we may now study the atmosphere as a whole. We wish particularly to know of its distribution of temperature and pressure; of its general and permanent circulation; of its great periodic currents; of its vertical movements, and its minor local winds with their pulsations of velocity and direction. Fortunately much information is available, due both to governmental and private research, though this was collected more for purposes of meteorology than of aërial locomotion. Of late, however, attention has been given to the aëronautic study of the atmosphere, which will, it is hoped, prove valuable to the aërial navigator.
The movements of the atmosphere are due mainly to the sun’s heat and to the rotation of the earth. The earth’s internal heat and the moon’s attraction are other minor agencies, but these may be neglected by comparison. The earth’s rotation also would be ineffectual in modifying the aërial movements, except for the coöperation of the sun. Without his influence the atmosphere, always stagnant, would simply rotate with the globe, at constant angular velocity and uniformly graded density at various levels. This evenness of density for any level is broken by the solar radiation increasing the temperature and moisture, otherwise the air would remain practically at a standstill.
Though the moisture by its lesser density causes some lightening of the air at fixed temperature, this at most is hardly one per cent, as already shown, and on the average is much less. Its effect, therefore, is equivalent to less than that caused by a rise of temperature of three degrees. But if precipitation occurs, an enormous amount of stored sunshine, or latent heat, is liberated and applied to warming the associated air. Thus each pound of vapor condensed may, by the release of its thermal store, heat more than a ton of air one degree in temperature, or more than half a ton of air two degrees, etc. The actual number of pounds of air at constant pressure, raised one degree Centigrade by the condensation of one pound of vapor at various temperatures, is given in the following table:
TABLE IV
| Temperature of condensation | 0° | 25° | 50° |
| Pounds of air heated one degree | 2550 | 2480 | 2407 |
The sun then is father of the wind. By uneven heating of the atmosphere it disturbs the uniform density gradation that would otherwise exist. Thus abnormal pressures are generated which disturb the repose of the aërial sea, causing the fluid to flow from regions of excessive to regions of defective pressure. Hence the study of insolation[59] and temperature distribution is fundamental to the science of the winds.
Without detailed study, we may note the aggregate insolation received by the earth, at various latitudes, and its general effect on terrestrial temperature. The sun emits a nearly constant stream of radiation, from year to year, which plays continuously upon the earth as a whole, with an intensity which varies but slightly from month to month, due to the slightly varying distances of the earth from the sun. Owing to the sun’s seasonal wandering across the equator, the insolation at any latitude varies considerably month by month, and the polar regions receive much more light than if no such wandering occurred. The total yearly insolation for every 5° of latitude is shown in the following table from Hann, in which the unit is the amount that the earth would receive in one day at the time of the equinox, if the sun were at its mean distance from the earth:
TABLE V
Annual Amounts of Insolation
| Latitude. | Thermal Days. | Difference. |
|---|---|---|
| 0° | 350.3 | |
| 5° | 349.1 | 1.2 |
| 10° | 345.5 | 3.6 |
| 15° | 339.4 | 6.1 |
| 20° | 331.2 | 8.2 |
| 25° | 320.5 | 10.7 |
| 30° | 307.9 | 12.6 |
| 35° | 293.2 | 14.7 |
| 40° | 276.8 | 16.4 |
| 45° | 258.7 | 18.1 |
| 50° | 239.6 | 19.1 |
| 55° | 219.4 | 20.2 |
| 60° | 199.2 | 20.2 |
| 65° | 180.2 | 19.0 |
| 70° | 166.2 | 14.0 |
| 75° | 156.5 | 9.7 |
| 80° | 150.2 | 6.3 |
| 85° | 146.5 | 3.7 |
| 90° | 145.4 | 1.1 |
From this it appears that the equator receives nearly 2.5 times as much heat yearly as the poles. Since, moreover, the equator enjoys nearly constant insolation, while the polar regions suffer great variations of heat, with the varying altitude of the sun, the equatorial atmosphere is both much hotter and more equable than the poles, and high latitudes generally. Thus at the equator the frost level stands constantly at 18,000 feet, while in the middle latitudes it varies greatly in height from season to season. If, for example, a circle be drawn to represent the earth, and above it a line to indicate the mean altitude of the frost level in July, the frost line starting at the equator at an elevation of 18,000 feet will decline north and south, finally touching the earth well toward the frigid zones. The levels for other temperatures, above and below freezing, are similarly inclined downward from the equator to north and south. Obviously these isothermal levels vary with the varying season, and at any fixed time differ on different longitudes. On the plane of any given latitude the frost line varies much less in altitude, and so for the other isothermals. This is particularly true at the poles and equator, and everywhere at considerable altitude. If one voyaged around the earth at the equator at an elevation of 5,000 feet, he should find the average temperature about 65° F. In the temperate zone, following a line of latitude at the same height, he should have a lower temperature, but still comparatively equable. The average annual temperature of the earth’s entire surface is about 60° F.
In practical meteorology the temperature is observed at many points simultaneously over a wide stretch of the earth’s surface. These are then plotted on a weather chart, and through all points of like temperature are drawn lines known as isothermals. These lines not only map the earth’s surface into regions of equal temperature, but they also show the direction of fall or rise of temperature, and its space rate of change. This rate is called the “temperature gradient,” and when estimated straight across from isothermal to isothermal, that is in the direction of liveliest change of temperature, it is the maximum gradient. Such a map is very useful in forecasting the weather. It is but a particular instance of the more general map conceived by the physicist, exhibiting the thermal condition of the entire atmosphere by means of a series of equal temperature surfaces one above the other. Here, of course, the temperature gradient at any point is the space rate of change of temperature in any direction, being zero along the isothermal surface and greatest normal to it.
The vertical temperature gradient is of particular interest, since it determines the condition of fluid equilibrium at any point in the atmosphere when the level surfaces are isothermal. If, for example, a balanced balloon or portion of air, on starting upward from any level, cools faster than the environing stagnant air, it will become more dense, and cease to ascend, in which case the atmospheric equilibrium is stable. Again, if the ascending gas or air cools more slowly than the surrounding medium, it will become less dense, and so continue to ascend, in which case the atmospheric equilibrium at the point is unstable. Thirdly, if the rate of cooling be identical for the ascending gas and its surrounding medium, the equilibrium is neutral, and the motion will be stopped by friction but unaffected by change of buoyancy, since no such change can occur. Of these three states of equilibrium, the stable is dominant above the cirrus level, while below that level each state may be found, at various times, prevailing at random in all parts of the world, but more generally the stable and neutral states. When the unstable condition occurs at any locality and any level, it is usually followed ere long by a commotion or upheaval in the atmosphere, until the temperature gradient alters to the neutral or stable.
Many observations have been made to determine the variation of temperature along the verticle in various places and in different seasons. From the temperature records obtained in 722 balloon ascensions near Paris, France, the mean fall of temperature per 1000 feet up to 20,000 feet was found to be 2°.4 in winter, 2°.8 in spring, 2°.6 in summer, 2°.5 in autumn and 2°.6 for the year. Near Berlin 3°.1 for the year was found from 75 balloon ascensions, the rate being nearly the same for the halves of the year. Fig. 44 gives the average of 52 winter and 65 summer temperature gradients, taken at about 8 a.m. by means of sounding balloons sent up at Munich, Strassburg, Trappe and Uccle. It will be noted that in both summer and winter the temperature falls rapidly with increase of elevation, up to ten or eleven kilometers, but above twelve remains nearly constant for all altitudes. The difference in temperature summer and winter is interesting, also in its gradual diminution with altitude. Another striking feature is the inversion of gradient shown at twelve kilometers elevation, where the temperature ceases to diminish, and may even increase with altitude. This region is known as the upper inversion level of the atmosphere, as distinguished from other levels at or below three kilometers height, known as lower inversions, where the temperature gradient is sometimes reversed, though not so illustrated in the diagram.
Thus the atmosphere divides into three marked layers. The lower layer, three kilometers deep, is the region of turbulence and storm, the home of heavy rain clouds, lightning, wind gusts and irregular temperatures. The middle layer, some seven kilometers thick, bounded top and bottom by the upper and lower inversion levels, is a clear region of steady-falling temperature, for the most part frigid—a region of far reaching and rapid winds, sweeping eastwardly, except near the equator, and bearing on their backs the frosty cirrus clouds. The upper layer reaching from the cirri to the cosmic void, is always cloudless and very frigid, with temperature nearly constant, or maybe slightly increasing with elevation.
Fig. 44.—Summer and Winter Average Vertical Temperature Gradients.
A striking peculiarity of these three regions is that the lower and middle layers may freely intermingle with each other, but never with the upper, or isothermal layer. Owing to its constant temperature, the upper layer floats on its neighbor like oil on water.[60] If a mass of dry air were forced up into it from below, with the natural cooling due to adiabatic expansion, such mass would be denser than the surrounding medium, and hence would promptly sink back to its initial position. Thus whatever turmoil may vex the middle or lower region, it can at most upheave the floor of the isothermal layer, leaving inviolate the crystal depths of the empyrean.
We may now turn to the distribution of barometric pressure in the atmosphere and the effect of its variation. In general, the distribution is not very uniform, but it can be graphically pictured by drawing a series of surfaces connecting all points of equal pressure. These are called isobaric surfaces. In a stagnant uniformly heated atmosphere, for example, these surfaces would lie one above the other parallel to the ocean face; but where turmoil exists, and irregular temperature distribution, the isobaric surfaces are bent into hills and hollows of varied form. These surfaces not only map the aërial sea into regions of equal pressure, but they also show the direction of fall or rise of pressure, and its space rate of change. This rate is called the “pressure gradient.” When estimated straight across from surface to surface, that is, in the direction of the liveliest change of pressure, it is the maximum pressure gradient. Along this normal direction the air tends to flow with an acceleration proportional to the gradient. The velocity thus acquired by any portion of air in being pushed along the line of falling pressure, combined with its velocity due to other causes, gives its true velocity. A most important consideration, therefore, in a scientific study of the wind is the pressure distribution.
In practical meteorology, observations of the barometric pressure are made simultaneously at many points on the earth’s surface, and the readings then plotted on a map, after “reduction to sea level.” This reduction is made by adding to each barometric reading the weight of a column of air between the barometer level and the sea level, according to tables prepared for this purpose. Lines called “isobars”[61] are then drawn, at regular intervals, through all points of like sea-level pressure, the indicated change of pressure between consecutive isobars on the U. S. weather map being usually one-tenth of an inch of mercury. These exhibit at once, over the entire field of observation, the horizontal pressure gradient reduced to sea level, and commonly called the “barometric gradient.” In meteorology, the pressure normal to the isobar is called the gradient, and is expressed in millimeters of mercury per degree of a great circle. On the same weather chart are mapped the isothermal lines and wind directions for all the stations of the weather service. From these data and the reported moisture conditions, the meteorologist forecasts the probable weather some hours or days in advance.
No perfectly comprehensive formula can be given for the barometric pressure at any place and altitude, but certain general laws may be observed. Where, for example, the speed of the air is increased along any level of an air stream, the pressure is lessened, and conversely. Thus, if the wind blows squarely against the front of an isolated house, the speed will be greatly checked at the center front, and accelerated at both sides and over the roof, thereby increasing the apparent barometric pressure on the front, and lessening it on the sides and over the top. A similar effect may be observed when the air flows round the hull and framing of air craft.
Again, if the atmosphere over any locality is heated appreciably more than its environment, the heated column tends to expand upward and overflow aloft in all directions toward the cooler neighborhood, thus lessening the pressure throughout the heated column, and increasing the pressure throughout the environing atmosphere laterally. When this effect is marked the plotted isobars often form a series of closed curves about the heated region, manifesting a pressure gradient at the lower levels in all directions toward the heated area. This grouping of the isobars exhibits the familiar low pressure area of the weather map. On the other hand, if any locality be cooled appreciably more than its environment, the cooled column sinks, so that the surrounding warmer air aloft flows in over it, thereby increasing the pressure over the cooled area, and diminishing it throughout the environment. The isobars may then form a series of closed curves about the cooled region, with a pressure gradient along the higher levels in all directions away from the cooled area. Of course, if heat were the only agency disturbing the earth’s barometric pressure, there should be a parallelism between the heat and pressure gradients; but, as already noted, the speed or momentum of the aërial currents is also a substantial agency in modifying the pressure lines.
It is well to remember that, while the base of a warm column of air may, due to the overflow aloft, have less pressure than the base of the cool environing column which receives the overflow, the high part of the column may have greater pressure than the equally high part of the cool. For if the columns be initially of the same temperature and pressure, heating one of them uplifts its levels of given pressure above those of its neighbor. When the overflow begins, a partial equalization of pressure levels occurs, but not a complete one so long as the flow has any head.
An interesting hygrometric feature of these highs and lows may here be observed in passing. As already explained, when a column of air ascends it cools by expansion, and tends to precipitate its water content as cloud or rain; and conversely, when the air sinks it heats by compression, thus acquiring greater moisture capacity and tending to clarify. As a consequence, the areas of low pressure and a rising atmosphere are usually marked by clouds and rainfall, while the areas of high pressure and falling atmosphere are marked by clear, or clearing weather. In the low, damp areas, then, the air feels heavy while it is really light; in the high and dry area the air feels light, while it is really dense, and most favorable to air men for carrying heavy loads in their balloons or flyers. Similarly when air flows over a mountain range the ascending stream precipitates moisture, due to cooling by expansion, while the descending stream, on the other side, comes down hot and dry, due to compression.
A characteristic mechanical feature of the high and low pressure areas is the closed circulation between them, involving practically the whole atmosphere below the isothermal layer. If we conceive the entire globe spotted with high and low areas, we may picture the air surging upward in the lows, flowing outward under the isothermal layer, descending in the highs, then flowing outward along the earth’s surface toward the lows in a continuous cycle. Thus, chiefly is maintained the vast and multifold circulation of the atmosphere over the entire world.
In general the motion is of a vortical nature, by which is meant that the masses of air as they flow along stream suffer more or less change of orientation in space, the rotation at times being so slight as to be undetectable, and again so marked as to excite wonder, as in the whirlwind. Many of these atmospheric vortices, even though varying in diameter from a few yards to hundreds of miles, resemble in their behavior the gyrating column of water in a common circular basin emptying through an orifice at its bottom. If the water is very still when the drain opens, the column descends with imperceptible, if any, rotation; but if the column has an initial whirl, or angular velocity, this is magnified as the water approaches the axis of the vortex, the tendency of the mass being to preserve its angular momentum, or fly wheel property. A like action obtains in the great atmospheric vortices, though here the motion far from the axis may seem like a straight-blowing wind, rather than part of a vast whirl covering thousands of square miles.
But even if all the air started directly for the axis of the ascending column, like still water in a basin, it would promptly acquire vortex motion, because it flows on the surface of a rotating sphere. The deflection so produced is evidently greatest at the poles, and for other places equals the polar value multiplied by the sine of the latitude. The effect is similar to what occurs when a basin, rotating about a vertical axis and carrying water with the same angular velocity, is opened at the bottom. In this case the water at once begins to gyrate within the basin, as the particles move toward its axis.
With these preliminary generalities we may proceed to study the more prominent movements in the atmosphere.