Correlation Between Pressure and Temperature
Height km.
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o
i
2
3
4
5
u
7
8
9
10
u
12
13
Jan.-March
02
54
82
79
86
85
84
87
91
81
35
-32
38
37
April-June
14
28
49
79
89
89
92
87
81
45
20
12
-24
-OI
July-Sept.
02
31
56
72
75
81
83
87
87
88
43
-08
-. 4 I
-19
Oct.-Dec.
33
56
76
77
83
87
85
85
86
78
29
-24
-34
-.50
Means
ii
42
66
77
84
85
86
86
86
72
32
-19
-.36
-28
is reached at about 1820 kilometres. The temperature from about 2 to 8 or 9 km. falls, and from 10 to 20 km. it rises. The height at which the lapse rate ceases, the limit of the troposphere falls. These statements are based on the very high correlation coefficients that are found to exist between pressure and temperature. It will be seen from the accompanying table (which gives the correlation coefficients) that close to the surface the correlation is low, but it is very high from 4 km. to 8 kilometres. In calculating these values the observational errors have not been allowed for, the correct values are most likely well over -90. There are probably two reasons for this. The surface temperature is governed by many considerations the tim'e of day, the state of the sky, the strength and direction of the wind ; higher up these disturbances do not apply, for, as has been already stated, the diurnal variation is very shallow and the correla- tion between the components of the wind and the temperature is surprisingly small above a few km. height. Secondly it may well be that the chief item in determining the temperature is the recent vertical motion of the air, and a systematic vertical flow of air either up or down is plainly impossible quite close to the surface. The rise and fall of the tropopause (H c ) and the regularity with which it occurs is shown by the high correlation, -84, between it and the pres- sure at 9 km. height. There is hardly a single instance of observa- tions made in Europe at a time of really low barometer in which H has not been found well below its average value. The dependence of the temperature of the stratosphere on the barometric conditions is not so close, the correlation being only -50; but based on some hundreds of observations as these correlation coefficients are, -50 is amply significant. Still the importance of a correlation in general depends upon its square rather than upon itself, and the significance of -50 is very different to that of -90 or -85.
One noticeable result of this high correlation between pressure and temperature is that the density is not subject to much variation save close to the surface, for a high pressure and a high temperature act upon the density in opposite ways and since they occur together the density remains comparatively unchanged.
The Vertical Flux of Heat in the Atmosphere. A much clearer and more definite view of the passage of heat upwards and down- wards in the atmosphere has been secured, and in no direction excepting perhaps that of our knowledge of the upper air has the advance of meteorological knowledge been greater. This desir-- able result is largely due to a paper by Major G. T. Taylor (Phil. Trans., A., vol. ccxv., pp. 1-26), which formed the starting- point, and has been followed by other papers on the same sub- ject by himself, by Mr. L. F. Richardson, by Dr. W. Schmidt (Vienna), and by others.
There are seemingly four methods by which an appreciable vertical flux of heat energy is produced in the atmosphere. (l) Convection, which carries heat upwards from the earth's surface; its action does not extend beyond the first few kilometres. (2) The latent heat set free by the condensation of aqueous vapour which carries upwards to the regions where clouds are formed the solar heat which has evaporated the water from the sea or wet land surface; this acts in just the same region as convection. (3) Radiation, which mostly carries heat upwards from a lower to a higher stratum. These three methods present no difficulty but it must be pointed out that " con- vection," as is usual in meteorological literature, means local con- vection, i.e. heat carried by an ascending current that is produced by local warmth, not heat carried by an air current or by eddy motion due to the general circulation.
The fourth method, which invariably brings heat downwards, is not so easy to understand but is no less genuine than the others. It has been given various names, " mixing," " stirring," ' turbu- lence," and (from the German) " mass-interchange." Taylor seems to have been the first to attempt its numerical measurement. The treatment of the subject has been mostly mathematical, but a rough explanation can be given without resort to mathematical symbols. The amount of heat possessed by a gramme of air is proportional to its potential temperature as defined long since by von Bezold and, save in the comparatively rare cases where the lapse rate is adiabatic, in which case heat is almost certainly being carried upwards by con- vection, the higher potential temperature is found at the higher level. The interchange, therefore, of two grammes of air between different levels (and it is obvious that if one gramme is carried up another must come down somewhere else to take its place) produces in general a flow of heat downwards, since the downward-coming gramme carries with it more heat than the upward-going gramme
carries back. W. Schmidt has estimated the amount of heat carried downwards across the 2-km. level in Europe by this cause as 50 gramme-calories per sq. cm. per day. The necessary interchange of mass between the strata is produced by wind, for even the lightest wind seems capable of mixing the air in a vertical direction. The mixing produced by convection will have the same effect and if the return convection currents are in a region where the lapse rate is not adiabatic the total result of the convection in carrying heat upwards may be very small.
Two important conclusions follow. Since all four causes save radiation convey heat to the lower strata, say o up to 4 km., those strata must be losing heat by radiation. Also, since above the region of the formation of heavy clouds neither convection nor the supply of latent heat by condensation is efficacious, the actual lapse rate there must represent the balance of two opposing tendencies, one radiation, tending towards an isothermal condition, and the other, mixing, tending to an adiabatic lapse rate.
Radiation. -Considerable progress has been made in the sub- ject of radiation, solar and atmospheric, both from the obser- vational and theoretical sides. Abbot and Fowle's valuable work has been continued, and each issue of the Monthly Weather Review contains an article by Kimball giving the results of observations at Washington and other stations. The value of the solar constant, 1-93 g.c. per sq. cm. per minute, has not been appreciably altered by the later observations, but the instru- mental outfit has reached a greater stage of precision, and it appears that the radiant heat given out by the sun varies from week to week within small limits.
Dr. Anders Angstrom (Upsala), Prof. Boutaric (Dijon), and others have contributed much useful information on the net radiation between the earth and atmosphere. Dr. Emden has contributed an important paper (" Radiation Equilibrium and Atmospheric Radia- tion," Sitz. Ber. Ak. Wien, 1913, p. 55) dealing with the radiation between layers of the atmosphere. With regard to the net radiation from the earth to the sky on clear nights there seems to be a fairly general agreement that the value is from 200 to 300 g.c. per sq. cm. per day. These values have been obtained in widely different lati- tudes and seasons. The return radiation from the sky, excluding all solar radiations, is largely dependent on the prevailing tempera- ture at the time; the average in England for all days, cloudy as well as clear, is about 600 gramme-calories.
Weather Forecasts. During the World War, and since, large sums of money and much time have been spent on preparing forecasts. Of long-range forecasts it must be said that the position is not hopeful; in general a forecast of the weather a month ahead is a pure guess and nothing more. The British Meteorological Office has extended the period to a few days, and now mostly gives on Thursday a forecast for the week-end, with satisfactory results. With regard to the daily forecasts covering a period of 30 hours there has been a decided improvement. The extension of the area of the weather chart to cover Iceland, and the information obtained by wireless from the Atlantic have helped.
Forecasting has been and still is more or less a rule of thumb, but it depends upon the rules which govern the motions of cyclones and anticyclones, and if we could discover those rules and fully understand the causes which produce them an improve- ment iA forecasting should follow. By the extensive use of pilot balloons a very large amount of information is now available with regard to the direction and velocity of the wind at various heights at the times when telegraphic reports are sent in to the head offices so that there is ample material showing the relation of the wind to the barometric gradient, but at present very little of this has been worked up. Much theoretical work has also been done on the gradual change from the surface wind to the gradient wind that generally lies above it. Sir Napier Shaw has con- tributed two useful papers (" Principia Atmospherica," Trans. Royal Society of Edinburgh, Dec. 1913, and " Upper Air Cal- culus," /. Scott. Met. Soc., vol. xvi., 1913) of which a summary
