Yamamoto  Giichi

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Yamamoto, Giichi

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Effect of Radiative Transfer on the Vertical Distribution of Temperature in the Troposphere

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Effect of Radiative Transfer on the VerticalDistribution of Temperature in the Troposphere著者 Yamamoto  Giichi雑誌名 Science reports of the Tohoku University. Ser.5, Geophysics巻 4号 2ページ 64-70発行年 1952-10URL http://hdl.handle.net/10097/44482 Effrct of Radiative Transfer on the Vertical Distribution                    of  Temperature in the Troposphere                               By Giichi YAMAMOTO  institute of Geophysics,  Faculty of Science,  TOloku University                                     (Received September 9 1952)      1. Introduction where  T =  the temperature of the air at level  z         Until some time ago the effect of radiative P  =the density of the air at level z       transfer on the vertical distribution of tem-  1C-----the eddy diffusivity       perature in the tropospherewas much under-                                               Jr—thedry adiabaticlapse-rate                                              1  estimated by the meteorologists than it ought= the time       to be. For instance,  according to BRUNT  (1)If we consider, in addition to the eddy flux,                                              the radiativefluxes due to infra-rad radiationthe transfer of heat by infra-red radiation was                                              and solar radiation, the equation of heat      estimated tobe1/10-1/100 of the turbulent  :       transfer and accordingly was considered to betransfer  will become as  follows       negligible. It was also disregarded in discuss-  aT a0T  Pcp={Kt)cp( az  + I.)}       ing the transfer of heat near the ground. at      However, recently the  role of the radiation on aFi a F2      the problems of the tropospheric temperature  az az(2)       changes was emphasized by DEACON (23 and where  cp is the specific heat of air at constant       ROBINSON  (6). It was also noticed by pressure,  Fl is the infra-red net flux which is       ELSASSER  (3) that the radiative cooling of the directed upwards and F2 is the mean effective      troposphere will act as the stabilizing factor in solar radiation per day which is directed down-      the troposphere. In this paper it is shown wards. In the case of steady state, we have       that the actual lapse-rate of temperature in      cleara) +Fi— F2  = const. (3)       dry adiabatic  Iapse-rate is the consequence of                                              Equation (3) means that thetroposphere is       the balance of the eddy transfer and the                                               neither in convective nor in radiative equili-       radiative transfer. It is also shown that near       the ground the temperature changes due tobrium, but in, so to  say, radiato-convctive       radiation are sufficiently large to account forequilibrium. If we designate the surface values       the observed temperature  changes,of the variable quantities in (3) by adding                                              suffix 0 to the variables then we have       2. The Effect of Radiation on the Lapse-Rate        of  Temperature in the Troposphere Kp  cp  +  1') K,A)cp {(  8,7") + rt.  dz•UZ)         It was shown by BRUNT  (1) that the  +  [F1— (F1)0}--[F2—(F.)0]. (4)       vertical transfer of heat by turbulence is given                                            Bythe recent works of LONDON  (4),  YAW-     by                                          MOTO (83 and YAMAMOTO and ONISHI  (93,           aT a 1Twe can see thatft— (Fi)o).i[F2--(F2)0}  P  at—1K°r)P(1)takes positive values throughout the tropo-         EFFECT OF  RADIATIVE TRANSFER ON THE VERTICAL DISTRIBUTION OF  ••.  a sphere, and  KoPocp  t(aT  /0  z)o  +  r} is also model atmospheres in clear skies, assuming positive in general case. Hence from equation that Ko =  1O  cm'  sec' at each case. Also (4) it will be said that the normal lapse-rate the Austausch  coefficient A (=  PcpK) was  corn-in clear skies which is generally smaller than puted. The results of computation were shown the dry adiabatic lapse-rate is due to the in  table 1 and fig. 1 and 2. Fig. 1 shows that radiato-convective equilibrium of the tropo- the computed values of K generally increase  sphere. Regrettably the values of the eddy with height at each latitude belt. In the lower diffusivity K are not so  well known with regard troposphere below 3 km K increases linearly to height as to be able to infer the normal with height, and in the middle troposphere the values of the lapse-rate in the troposphere rate of increase of K with height becomes which satisfy equation (4). rapid, until K reaches maximum in the upper    However, if we assume the validity of troposphere, and in the uppermost layer  im-equation (4), we can inversely use the equa- mediately below tropopause K tends to de-tion to compute the vertical distribution of K crease at each latitude belt. The vertical for tropospheric conditions in which the values distribution of A  (fig• 2) also shows similar of F1, F2 and  8770z are known. The values tendency as K . However, in this case the of F1 and F2 were most fully investigated by decrease of A with height begins at lower LONDON (4) for model atmospheres during altitude than that of K , and it is more marked March, northern hemisphere, so that the  corn- in the upper troposphere than in the case  putation of K was carried out on LONDON's of K.           Table 1. Vertical distribution of eddy diffusivity K and Austausch coefficient A,                       during March, northern hemisphere, in clear skies.  2: km,  a  TI'az+r:  -C.  cm-1,  Ft  -  (  .1i1  )c,and  F2-(F2)0: cal.  cm.-2  min,-1                           K:  cm.2  sec,-I A: cal.  cm.-1 sec.-1  `C-1     0-10' N 10-20' N      aT1'a- +r Fi---(F1)0 F2-(1072)0KA Ia T/1E32-1-1.Fl- (Fl)U 12.--(14)0K 2-     x10-5  x10-1 x10-2  x105 x10-5  x10-1  x10-2  x105A  - 0 4.96 0 0  1.00 27.9 0 4.56 0 0 1.00 28.6  1 5.11 0.25 1.33 1.21 30.8 1 4.56 0.31 1.26 1.36 35.4  2 5.11 0.49 2.45 1.52 35.0 2  4  51 0.56 2.43 1.75 40.7  3 4.66 0.68 3.43 2.19  45.21 3 4.26 0.79 3.52 2.28 47.6  4 4.21 0.88 4.31. 2.70 50.6 4 4.16 1.01 4.41 2.82 54.2  5 4.21 1.07 5.13 3.22 54.8 5 4.26 1.25 5.10  3.44 59.5  6 3.86 1.27  5.85 4.19 65.4 6 3.56 1.49 5.72 5.12 79.8  7 3.31 1.45 6.48 5.80 82.0 7 2.96 1.69 6.26 7.46 104  8 3.26 1.63 7.02 7.06 89.9 8 2.96 1.87 6.70 8.93 111  9 3.16  1.80 7.49 8.80 99.2 9 2.96 2.01 7.05 10.4 118 10 2.16 1.95 7.88 14.9 153.5 10 2.56 2.13 7.32 14.1 142 11 1.26 2.07 8.21 31.0 275 11 2.26 2.22 7.53 18.7 166 12 1.31 2.19 8.46 34.9 277 12 2.41 2.30 7.69 20.2 159 13 2.31 2.28 8.85  29.2 204 13 3.31 2.36 7.79 17.1 119 14 321 2.35 8.74 19.9 118 14 4.36 2.40 7.86 15.9 92  15 3.26 2.42 8.81 24.0 121 15 4.36 2.45 7.91 20.5 93 16  J 3.36 2.46 8.85 27.6 132 16 4.36 2.45  7.95 19.4 93  66 G. YAMAMOTO    --- .--.......--...--..--.--....           20-30' N 11 30-40° N  a  2  7az+1-  F1-0700  F2-(F2)0 K  A  1 a 17az -L r F1-(FI)o F2 - (F2A                                          )0 KA z x 10-5 x  10-1 x 10-2 x  105I x 10-5 x  10-1 x10-x  105      0 4.06 0 0 1.00 28.8  1 0 5.86 0 0 1.00 29.8        1 3.86 0.30 1.27 1.44 37.7  ' 1 5.56 0.23 0.81 1.33 35.8        2 3.96 0.58 2.35 1.89 43.0  ,1 2 4.86  0.46 1.56  . 1.91 46.3        3 4.21 0.84 3.19  2  29 48.3  II 3 4.51 0.66 2.33 2.52 54.4        4 4.16 1.03 3.89 2.83 53.7  1 4 4.16 0.85 2.88 3.28 64.6        5 4.21 1.20 4.52 3.28 57.5 5 3.41 1.04 3.35 4.89 85.6        6 3.56 1.38 5.06  4.74 73.9 6 2.56 1.22 3.84 7.51 123        7 2.76 1.56 5.52 7.28 103 I 7 2.06 1.37 4.25 11.6 162       8 2.61 1.73 5.89 9.41 117 8  2.26 1.50 4.53 12.3 154       9 2.46 1.88 6.19 11.8 132  1 9 3.11 1.59 4.71 10.5 116      10 2.91 2.00 6.41 12.8 129  I 10 4.56 1.65 4.83 8.2 81       11 3.46  2.08 6.56 11.5 102 11 5.61 1.70 4.91 8.2 67      12 3.36 2.13 6.68 13.9 107 12 6.26 1.72 4.97 8.4 60      13 4.81 2.16 6.75 10.9 76 13 6.91 1.74 5.03 8.2 55      14 6.31 2.19 6.79 9.7 58       15 6.16 2.22 6.84 12.0 61      16 6.47 2.25 6.88 12.2 60  40-50- N  1  50-60° N      0 6.86 0 0 1.00 30.7 0 7.36 0 0 1.00 31.6        1 6.36 0.19 0 56 1.35 34.6 1 6.96 0.16 0.45 1.28 362       2 5.51 0.37 1.14 1.88 46.0 2 5.96 0.32 0.86 1.81 46.7        3 4.36 0.58 1.79 2.94 63.5 3 4.51 0.49 1.26 2.98 65.1        4 3.21 0.79 2.34 4.76 94.8 4  , 3.56 0.68 1.62 4.50 89.6  5 2.86 0.99 2.76  6.48 115 5 3.76 0.83 1.90 5.08  90.2  6 2.86 1.12 3.10 7.51 121 6 4.06 0.94 2.11 5.51 87.2        7 2.96 1.23 3.36 8.57 121  , 7 4.46 1.02 2.26 5.79 82.0        8 3.61 1.32 3.53 8.25 103 8 4.86 1.10 2.37 6.20 77.4  91 3.91 1.39 3.63 8.85 98  1 9 4.96 1.14 2.45 6.98 76.4       10 6.11 1.42 3.70 6.25 63 10 7.66 1.17 2.52 5.26 50.5       11 8.71 1.45 3.76 5.33 45  1         60-70' NII      0 7.16 0 0 1.00 32.8        1 7.01 0.12 0.24 1.23 35.8        2 6.71 0.25 0.49 1.56 402       3 5.36 0.42 0.73 2.40 54.7        4 4.51 0.54 0.94 3.45 68.7        5 5.26 0.64 1.08 3.42 61.5        6 5.86 0.70 1.19 3.52 56.6        7 6.21 0.75 127 3.99 54.5       8 6.41 0.80 1.35 4.41 54.0  .        9 6.46 0.83 1.41 5.12 54.1        10 8.51 0.86 1.46 4.45 41.6 - -         & The Radiative Temperature Change near strated that the night cooling of air can be         the Ground fully explained by the radiative cooling. RO-           DEACON and ROBINSON have emphasized BINSON's computations were carried out on        the importance of the radiative temperature three examples at midday, evening and early        change near the ground. DEACON's corn- night. According to his computations the         putations of the radiative flux were carried out radiative heating at midday or the radiative         on an example at night, which has demon- cooling at night far exceeds the observed rate EFFECT OF  RADIATIVE  TRANSFER ON THE VERTICAL DISTRIBUTION  OF  ••• 67             Fig.  1 Vertical distribution of eddy diffusivity K.  - 20  30°  3040°  0  -  le          40-50°                                                    0--i0   10-            50.1.10,10   60- O1p 5 fiff 00 S10 15  K                     20 253035X  105           Fig. 2 Vertical distribution of Austausch  coefficient A.  }um   15-  2030°  30-10'  40-50°  1°'  10-0-10'              4410                5060°           60 70°        5 -   1/41001      50  100 150  200 250 300                 A 68. G.  YANL--  MOTO of temperature change, so that it may be to measure, it has been shown by ROBINSON likely that the radiative heating at midday or  Cfl that the radiative temperature of ground the cooling at night is almost balanced by covered by short grass is indicated by a spirit convection. Then, convection or turbulent thermometer lying on the ground with the transfer will to cool the air near the ground following degree of  approximation  :at midday when the earth is heated by solar  T1.=  T3  + 0.25 ± 0.6°C at night and at radiation and to heat the air at night when daytime with weak insolation the earth surface is cooling. This conclusion  Tr =  T,- 0.5 ± 1.2°C at daytime with seems to be somewhat curious. To investigate strong insolation more fully the role of radiative transfer near where TT is the radiative surface temperature the ground, it is necessary to carry out corn- and  T8 is the reading of the surface  therm°. putations of the radiative flux near the ground meter. on more numerous examples. PASQUILL's observations extend up to 2 m    Now to be able to compute the radiative high, so that data of temperature and humidity flux near the ground, the complete knowledge at higher level are desirable to carry out of the vertical distributions of temperature and reliable computations of the radiative flux. humidity including the surface values are Thus the values of temperature and humidity necessary. Although many observations have at 10  m high were assumed by extrapolating been carried out on the  vertical distributions his observations. Also surface values of the of temperature and humidity, such complete absolute humidity which were lacking in his observations are rare. Recent observations of observations were assumed. The complete PASQUILL C5  D are one of these few, in which data thus supplemented were obtained on No. the surface temperature was measured by a 6-10, and 15-19 of table 2 of PASQULL's paper spirit thermometer lying on the ground. Al- and were shown in table 2. though the true surface temperature is  difficult                Table 2. Vertical distributionof  ternpertaure and reduced path  z T  u  z T u  (ctu.)  ('K) (g  cm_") (cm)  (`K) (g  cm-`-')  -  0  ._288.9600 280.71 0        25 285,04 0.000168 25 283.47 0.000156 No. 6No.9       50 284.67 0.00033150 283.94 0.000309  101,331u100 100 284.35 0.000647100 284.46 0.000609        5.20 0.000956 150 284.72 0.000905         200 284.10 0.001261  t 200 284.88 0.001198        1000  • 283.66 0.005946 1000 285.94 0.005813  0 290.56 0 0 279.11 0        25 285.53 0.000170 25 28L68 0.000197 No. 7No.10        50 286.13 0.00033450 281.94 0.000393        100 285.77 0.000649100 282.23 0.000781 121'30111191,30n,        150 285.60 0.000955150 282.38 0.001167        200 285.49 0.001256 200 282.49 0.001551        1000  284,94 0.005816 1000 283.16 0.007641      0 286.60 0  ,  ,  0. 287.06 0  No. 8          25 286.58 0.000163No.1525 282.65 0.000137        50 .59 0.00032450 282.43 0.000267            100 286.60 0.000638  15h3oui091,38",1 0 282.17 0.000517        150 286.60 0.000945 150 282.11 0.000757        200 286.60 0.001249 200 281.99 0.000992  1000 286.60 0.006049 1000 281.49 0.004562 EFFECT OF RADIATIVE TRANSFER ON THE VERTICAL  DISTRIBUTION OF  - 69   z T u  i  z T  it  I       (cm)  (a) (g  cm-2) (cm)  (°K) (g cm-2)   ., I  .  0 290.66  0  .  1 0 284.83 0        25 285.35 0.000157 25 284.83 0.000141 No. 16.No18        50 285.04 0.00030750  284  83 0.000277   1111.301,1           100 284.66 0.000591'i16h3Oin100 284.83 0.000540             '        150 284.52 0.000865 150 284.83 0.000796        200 284.38 0.001135 200 284.83 0.001048        1000 283.61 0.005235 1000 284.83 0.004908     0 288.96 0 0 277.21 0   No. 17         25 286.74 0.000151No. 1925 279.35 0.000119        50 .47 0.00029650 279.64 0.000236 141130m1811301,1        00 286.24 0.000570100 279.99 0.000466        5 .10 0.000832 150 280.22 0.000692        200 285.99 0.001090 200 280.38 0.000916        1000 285.41 0.005020 1000 281.33 0.004416    Now the differences of net flux at each are nearly equal and the effect of  CO2 will 50 cm interval from the ground up to 2 m be cancelled in taking flux divergence. The high were computed using the radiation chart obtained flux divergences were expressed by developed by the author  C8). In this corn- the temperature change per hour and were  putation the CO2 correction was neglected, shown in table 3. In table 3 are also shown because CO2 contents in each 50 cm interval the observed temperature changes per hour.                  Tabel 3 Computed radiative temperature change and observed  temperature change as functions of height.    ---- --- - -- - - - -   A B A B               Mean observed Mean radiative Mean observed Mean radiative  Z temperature temperature A-B  Z temperature temperature A-B        change change change change     (cm) W A  ) obs( T }rad (cm)(AT )At                                 obsrad    At\AtAT                          ()  (°C  hour  -1)  (  °C  hour-1) (,C hour-1)  (V  hour-1)        0- 50 0.76 3.19  -2.43  0- 50 1.56 3.54 -1.98  No. 6-7 50-100 0.72 2.95 -2.23 No.  15  16  50  100 1.36 3.10 -1.65        100-150 0.68 2.50 -1.82 100 150 1.31 2.49 -1.18        150-200 0.66 1.89  -1.23 150 200 1.28 1.97  -0 69        0- 50  -0,28 1.58 -1.86 0 50 0.12 2.62 -2.50  No. 7-8 50-100 +0.22 1.53 -1.31  No.  16-17 50-100 0.50 2.38 -1.88        100-150 +0.31 1.33 -1.02 100-150 0.53 1.96 -1.43        150-200 +0.35 0.98 -0.63 150-200 0.53 1.49 -0.96         0- 50 -1.96 -0.80 1.16 0- 50 -1.28 0.78 -2.06  No. 8-9  50--100 -1.20 -0.96 -0.24  No.  17-18 50-100 -0.77 0.70 -1.47         100-150 -1.01  -0.89  -0.12'  .  100  -150 0.68 0.52 -1.20        150-200 -0.90 -0.70 0.20k 150-200 -0.61 0.39 -1.00         0- 50 -0.87 -1.74  +0.87  j 0 50  -3.09 -0.61  -2.48  No. 9-10 50-100  -1.06 -1.78  +0.72  No.  18-19 50 100 -2.51 -0.59 -1.92         100-150 -1.15 -1.47  +0.32 100-150 - 2.37 -0.54 -1.38        150 200  1.19 -1.18 -0.01 150 200 -2.27 -0.53 -1.74 0^1^^^•^=•^•^   •••^111^1           No. 6  :  1011331)1 No. 15  : 91138n1           No. 7  :  1211301., No. 16  :  11113011          No. 8  :  1511300, No. 17  :  14h3011           No. 9  :  171,3011' No. 18 :  161'301.^           No. 10 :  19h301,, No.  19  1811301h 70 G.  YAMAIVIOTO It will be seen from the table that the is one way of thinking to escape from this radiative heating at midday far exceeds the curious conclusion. As the wind was blowing observed temperature change at corresponding with 2-3  m/sec during the observations, the time. On the other hand the radiative cooling observed temperature change represents that at night is not necessarily so, that is, at No.9- of the average of considerable quantity of air, 10, the radiative cooling is larger than the while the computed radiative temperature  actual temperature change, while at No. 18-19 change depends mostly upon the surface tern-the contrary is the case. And at evening the perature of a spot. If we assume that the radiative tempefature change is zero. In the mean surface temperature of some area around table are also shown the difference of the the spot is smaller than the surface  tem-observed temperature change and the radiation perature of the spot at midday, then the temperature change, which will correspond to radiative heating will be diminished and there the turbulent temperature change. Table 3 may be a possibility that the above conclusion shows that the turbulent temperature change will be remedied. is negative at midday, that is, it means cooling.  Finally, from table 3 we can see that the The curious conclusion of ROBINSON was thus radiative heating at midday and the radiative not removed by the present computation. There cooling at night both decrease with height.                                           References (1)  BRUNT,  D., 1939 : Physical and  Dynamical Me- (5)  PA.s(11,-u,T,, F.,  1949: Proc. Roy.  AS'oc., A, 198, 116           teorology, 2nd ed., London, Cambridge (6)  RoBncsoN, G. D., 1950: Cent., Proc. Roy. Met.     Univ., Press. Soc., 26 (2) DEACON, E.  L., 1950: Australian  I.  Sci. Res., A, (7) ROBINSON, G. D., 1950:  Quart. J. Roy. Met.  Soc.,  3,  274 76, 37 (3)  ELsAssErty W. M., 1942: Harvard Meteorological (8)  YAmAmoTo, G., 1952 : Sci. Rep. Tohoku Univ.      Stvdics, No. 6 Ser. 5, Geophysics 4, 9 (4)  LONDON)  3., 1950 :  U. S. Air Force Cambridge (9)  YAmAmoTo,G. and G.  Osrsui, 1951: Jap. Jour.          Res. Lab. Progress  Rep  ,  131.02 & 131.03 Met., 29, 103 (in Japanese)  1951  : ibid, 131.05

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Effect of Radiative Transfer on the Vertical Distribution of Temperature in the Troposphere

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