1896 Arrhenius (1119300), страница 5
Текст из файла (страница 5)
2, and for the heat in theair that contained in a column of 1 cm. 2 cross-section andthe height of the atmosphere. The heat that is reflectedfrom the ground is not appreciably ~tbsorbed by the air(see p. 252), for it has previously traversed great quantitiesof water-vapour and carbonic acid~ but a part of it may bereturned to the ground by means of diffuse re flexion. Letthis part not be included in the albedo (l--v).
7, A, v, M, N,and a are to be considered as constants, f~ as the independent~and 0 and T as the dependent variables.Then we find for the column of air~,ye,=~,y,,(T,-e,)+o,A+~. . . .(1)The first member of this equation represents the heat* Langley, ~Prot Papers,' No. 15, p. 1'22. "The Temperature of ~he~Ioon," p. '206.T2256Prof. S. Arrhenius on tl~e Tnfluence of Carbonic A d dradiated from the air (emission-coefficient/~, temperature 0)to space (temperature 0). The second one gives the heatradiated from the soil (1 cm?, temperature T, aIbedo 1 - v ) tothe air; the third and fourth give the amount of the sun'sradiation absorbed by the air, and the quantity of heat obtained by conduction (air-currents) fi'om other parts of theair or from the ground. In the same manner we find for theearth's surface/~/v(T4--~)-F (.l--/~),'/v'i~: (l--o0yA +INT.(2)The first and second members represent the radiated quantities of heat that go to the air and to space respectively,(1--a)vA is the part of the sun's radiation absorbed, and Nthe heat conducted to the point considered from other partsof the soil or from the air by means of water- or air-currents.Combining both these equations for the elimination of 0~which has no considerable interest, we find for T 4T,=aA+~+(!--a)A(l+v)+N(l+l/v)~,(I +v--i$v)K-- l + v ( l - - f l ) "(3)For the earth's solid crust we may, without sensible error,put v equal to 1~ if' we except the snowfields, for which weassume v--0"5.
For the water-covered parts of the earth .[have calculated the mean value of v to be 0"925 by aid of thefigures of Zenker*. We have, als% in the following to makeuse of the albedo of the clouds. I do not know if this hasever been measured, but it probably does not differ very muchfrom that of fresh fallen snow, which ZSllner has determinedto be 0"78, i. e. r=0"22. For old snow the albedo is muchless or v much greater; therefore we have assumed 0"5 as amean vahle.The last formula shows that the temperature of the earthaugments with fl, and the more rapidly the greater v is.
Foran increase of 1° if v-= 1 we find the following increases forthe values of v=0"925~ 0"5~ and 0"2"2 respectively : - ft.v=O'92&v=0"5,v= 0"22.0"650"9440"5750"2750"750"9400~5560'2610"850"93405350"2450"950"9280"5120"2281"000"9250"5000"220This reasoning holds good if the part of the earth's surface* Zenker, Die Yertheilu~q der Wiirme auf der Erdober3Ci~ehe, p. 54(Berlin, 1888).in the Air upon the Temperature of the Ground.257considered does not alter its albedo as a consequence of thealtered temperature.
In that case entirely different circumstances enter. :If, for instance~ an element of the surface whichis not now snow-covered, in consequence of falling temperaturebecomes clothed with snow~ we must in the last formula notonly alter f~ but also v. In this case we nmst remember thata is very small compared to/3. For a we will choose thevalue 0"40 in accordance with Langley's* estimate.
Certainly a great part of this value depends upon the diffuselyreflected part of the sun's heat~ which is absorbed by theearth's atmosphere, and therefore should not be included in a,as we have defined it above. On the other hand, the sunmay in general stand a little lower than in Langley's measurements, which were executed with a relatively high sun, andin consequence of this a may be a little greater~ so that thesecircumstances may compensate each other.
F o r /3 we willchoose the value 0"70, which corresponds when K----1 andW = 0 ' 3 (a little below the freezing-point)with the factor 1"66(see p. 253). In this case we find the relation between T(uncovered) and T1 (snow-covered surface) to beT4:T4=A(I+I-0"40)+M__7(1 + 1 --0"70): A(I+0"50--0"20)÷M~/(1 + 0"50-- 0"35)1"60 +~b1"30+ ~---- 1'30: 1"15 'if M--~bA. W e have to bear in mind that the mean M forthe whole earth is zero, for the equatorial regions negativeand for the polar regions positive. :For a mean latitudeM = 0 , and in this case TI becomes 267"3 if T - - 2 7 3 , that isthe temperature decreases in consequence of the snow-covering by 5°'7 C.~ The decrease of temperature from this causer--~illbevalid until ~b~-l, i. e.
till the heat dehvered by convection to the air exceeds the whole radiation of the sun.This can only occur in the winter and in polar regions.But this is a secondary phenomenon. The chief effect thatwe examine is the direct influence of an alteration of B uponthe temperature T of the earth's surface.
I f we start from avalue T = 2 7 3 and B = 0 " 7 0 , we find the alteration (t) in the* Langley, "Temperature of the Moon~" p. 189. On p. 197 he estimatesa to be only 0"33.t According to the correction introduced in the sequel for the differentheights of the absorbin~ and radiatin~ layers of the atmosphere, thenumber 5°'7 is reduced t"o 4°'0. But a-s about half the sky is cloudcovered, the effect will be only half as gn'eat as for cloudless sky, i. e. themean effect will be a lowering of about 2 ° C,258Prof.
S. Arrhenius on the Influence o f Carbonic Acidtemperatm'e which is caused by the variation of /3 to thefollowing values to be/3=0'600"800"901"005 ° C.+ 5"6+11"7+18'6.t=--These values are calculated for v----1, i. e. for the solid crustof the earth's surface, except the snowfields. F o r surfaceswith another value of v, as for instance the ocean or thesnowfields, we have to multiply this value t by a fractiongiven above.W e have now shortly to consider the influence of theclouds. A great part of the earth's surfaco receives no heatdirectly fl'om the sun, because the sun's rays are stopped byclouds.
How great a part of the earth's surface is coveredby clouds we may find from Teisserenc de Bort's work* onNebulosity. From tab. 17 of this publication I have determined the mean nebulosity for different latitudes, and found : Latitude.. 60.45. 30.15. O. --15.--30. --45. --60.Nebulosity. 0"603 0"48 0'402 0"511 0"581 0'463 0'53 0'701For the part of the earth between 60 ° S.
and 60 ° N. wefind the mean value 0"525~ i. e. 52"5 per cent. of the sky isclouded. The heat-effect of these clouds may be estimated inthe following manner. Suppose a cloud lies over a part ofthe earth s surface and that no connexion exists between thisshadowed part and the neighbouring parts, then a thermalequilibrium will exist between the temperature of the cloudand of the underlying ground. They will radiate to eachother and the cloud also to the upper air and to space, andthe radiation between cloud and earth may, on account of theslight difference of temperature, be taken as proportional to thisdifference. Other exchanges of heat by means of air-currentsare also, as a first approximation, proportional to this difference.
I f we therefore suppose the temperature of thecloud to alter (other circmnstances, as its height and composition, remaining unchanged), the temperature of the groundunder it must also alter in the same manner if the same supplyof heat to both subsists--if there were no supply to theground from neighbouring parts, the cloud and the groundwould finally assume the same mean temperature. If, therefore,the temperature of the clouds varies in a determined manner* Teisserenc de Bort, "Distribution moyenne de la ngbulosit6," Ann.du bureau central znet~orologique de JFrancG Anuge 1884, t.
iv. 2d°pattie,p. 27.in the Ate upon t/~e Temperature of the Ground.259(without alteration of their other proper Lies, as height, compactness, &c.), the ground will undergo the same variations oftemperature. Now it will be shown in the sequel thai avariation of the carbonic acid of the atmosphere in the sameproportion produces nearly the same thermal effect independently of its absolute magnitude (see p. 265). Therefore wemay calculate the temperature-variation in this case as if theclouds covered the ground with a thin film of the albedo 0"78(v=0"22, see p. 256). As now on the average K = I andW = 1 nearly, and in this case fi is about 0"79, the effect on theclouded part will be only 0"25 of the effect on parts that havev = l . . I f a like correction is introduced for the ocean(v=0"925) on the supposition that the unclouded part of theearth consists of as much water as of solid ground (which isapproximately true, for the clouds are by preference storedup over the ocean), we find a mean effect" of, in round numbers, 60 p.
c. of that which would exist if the whole earth'ssurface had v = 1. The snow-covered parts are not considered~for, on the one hand, these parts are mostly clouded toabout ~5 p. e. ; further, they constitute only a very smallpart of the earth (for the whole year on the average onlyabout 4 p. c.), so that ~he correction for this case would notexceed 0"5 p. c. in the last number 60.
And further, on theborder countries between snowfields and free soil secondaryeffects come into play (see p. 257) which compensate, andperhaps overcome, the moderating effect of the snow.In the foregoing we have supposed that the air is to be regarded as an envelope of perfectly uniform temperature. Thisis of course not true, and we now proceed to an examinationof the probable corrections that must be introduced for eliminating the errors caused by this inexactness. I t is evidentthat the parts of the air which radiate to space are chieflythe external ones, and on the other hand the layers of airwhich absorb the greatest part of the earth's radiation do notlie very high.
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
