THE EFFECT OF THE POLLUTION OF THE GROUND OF THE ATMOSPHERE ON THE ALBEDO
LAYER
JAN BEDNX~.
Institute o f Meteorology, The Charles University, Prague*)
S u m m a r y : A simple model is proposed suitable f o r studying the effect o f the ground layer o f the atmosphere, polluted by aerosol, on the albedo. This model is founded on sobbing the equation o f transfer o f radiative energy. The numerical results' are discussed, particular attention being paM to the analysis o f errors due to neglecting the multiple reflection o f solar radiation on the aerosol particles. A method which would also include the multiple reflection is proposed, and the conditions under which the presence o f the aerosol is responsible f o r an increase or decrease o f the solar radiation balance on the Earth's surface, are analysed. 1. INTRODUCTION One of the widely discussed problems in the present applied meteorology is the effect of aerosol particles, which are polluting the atmosphere in ever increasing numbers (a significant part of this being undoubtedly due to human activity), on the solar radiation balance near the Earth's surface. Of the series of papers, dealing with this topic in specialized literature in recent years, we should mention, e.g., [1--3]. The authors mostly reach the conclusion that the solar radiation balance near the Earth's surface may sometimes be decreased, at other times increased in individual local cases, depending on the physical and geographical conditions, as well as on the capability of the aerosol particles to reflect and absorb solar radiation and the local properties of the Earth's surface, specially the albedo. However, from the point of view of long-range climatic trends on a worldwide scale it is generally assumed that the increased presence of aerosols in the atmosphere will be reflected in an increase of the Earth's planetary albedo and thus in an overall decrease of the solar radiation balance with a subsequent cooling of the climate. In studying this problem a series of model studies are used, beginning with illustrative deliberation rather of a qualitative nature [1] and, so far, ending with complicated numerical models [3], the solution of which requires the use of the most sophisticated computers. This paper ties up with [4], and an idealized model of the polluted ground layer is used, founded on solving the equatiqn of transfer of radiative energy, also described in [4]. 2. DESCRIPTION OF THE MODEL USED F o r the sake of simplicity it is assumed that the Sun is always located in the zenith a n d I~ is the flux of direct solar radiation, p r o p a g a t i n g t h r o u g h the atmosphere from top to bottom. It is also assumed that the atmospheric layer, extending from the E a r t h ' s surface to height H, is polluted with aerosol particles which partly reflect a n d a b s o r b the solar radiation. Scattering o f r a d i a t i o n is n o t considered in the atmosphere above this layer. 12 represents the flux of the solar radiation, reflected upwards from the aerosol particles, on the one h a n d , a n d from the E a r t h ' s surface on the other, a s s u m i n g that radiation scattering upwards is isotropic. *) Address: Ke Karlovu 3, 121 16 Praha 2. Studia geoph, et geod. 20[19761
385
J. Bednd¢
As in [4] we are able to compute, under the conditions mentioned, the magnitudes of the radiation fluxes 11 and 12 at height z < H above the Earth's surface by solving the differential equations (1), (2)
dI,(z)/dz
=(7 +
fl)l,(z), dlz(z)/dz = -(o: + fl) qlz(z ) + ~l,(z),
where a and fl are the coefficients of reflection and absorption, respectively, in the ground layer, polluted by the aerosol, and q - 1-66 is the fictional optical mass. It can be proved [5] that in the case of radiative fluxes, dispersed isotropically, the magnitude of the flux may be substituted formally by the intensity of the ray which passes through the atmosphere so that the appropriate optical mass is close to 1'66. The coefficient of reflection is defined as the ratio of the amount of the solar radiation per unit time scattered by a unit volume of the polluted atmosphere to all directions, making an angle of more than ½n with the original ray, and the amount of radiation per unit time incident at this unit volume. Analogously, the coefficient of absorption fi represents the ratio of the amount of radiation absorbed in a unit volume per unit time and the amount of incident radiation. The signs on the r.h.s, of Eqs (1) and (2) have been chosen with regard to the fact that for the radiative flux 11 downwards dz < 0 and in (2), on the contrary, dz > 0, because the radiative flux I 2 is oriented upwards. According to [4], the solutions of Eqs (1) and (2) can be found in the form
I1(z)=C I exp If(co
(3)
(4)
12(z) = exp [ -
+
fl)dz],
fq(:~ + fl)dz] f~ I~(z)exp [fq(c~ + fi)dz] dz,
where C 1 is an integration constant which can be determined from condition
I,(H) = I o ,
(S)
I o representing the magnitude of the flux of the direct solar radiation entering the polluted layer at height z = H. If we assume that c~ and /3 are independent of the vertical co-ordinate z for z < H, (3) and (4) can be adjusted to read
la(z) = C a exp [(c~ +
(6) (7)
f2(z)
=
~
/3) z ] ,
Cl[(c~ + /3)(I + q)]-I exp [(c~ + /3) z] + GI exp [ - q ( e + /3) z ] .
The integration constant G, in (7) is then determined from the boundary condition for the Earth's surface (z = 0), (8)
12(0) = A I,(0),
where A is the albedo of the Earth's surface. 386
Studia g e o p h , at geod, 20 [1976]
The Effect o f the Pollution... 3. N U M E R I C A L R E S U L T S We have assumed a polluted ground layer, 200 m thick (i.e. H .... 200 m) at which the flux of the direct solar radiation I I ( H ) = - I o ~ 1.400 cal cm - 2 min -1 , is incident perpendicularly. (The flux of the solar radiation, entering the Earth's atmosphere, has therefore, been decreased above the considered polluted ground layer about 30~o of its original value). The values of the coefficients of reflection e a n d absorption p were adopted to make c~ -t- / / = 1 0 - 5 c m - ~ always, and the absorption of the solar radiation by the gaseous components of the atmosphere ( H 2 0 , CO 2) was neglected. After substituting the given values into (5) and (6) we arrive at the following value for the flux of the solar radiation incident at the Earth's surface I1(0) -- 1-15 cal cm - z r a i n - 4, i.e. 0"25 cal c m - 2 m i n - 1 was absorbed by the aerosol particles, or reflected by them upwards. Using Eqs (7) and (8) we also computed the radiative flux 12(H) which escapes from the polluted ground layer upwards, in turn for the values of the coefficient of reflection c~ = 1 0 - 6k c m - 1, where k = 0, 1 , . . . , 9, 10(coefficient /? always being taken to make e q - f l = = 1 0 - 5 c m - 1 ) and for the following values of the albedo of the Earth's surface A = 0, 0"10, 0.20, 0.30 and 0.70. The case with ~ = 0 corresponds to idealized aerosol particles which do not reflect solar radiation, whereas in the other extreme case, /~ = 0, the aerosol particles only reflect the solar radiation, but do not absorb it. As regards the values of A, A = 0 represents a fictional case of an absolutely black Earth, A = 0"10, 0"20 and 0"30 correspond to real cases of various types of soils and vegetation cover, and finally A = 0.70 roughly simulates the Earth's surface covered with ice or
snow.
Table 1. A (10 - 6 c m - 1) .
.
.
.
.
.
.
.
.
.
.
0 I
2 3 4 5 6 7 8 9 10
0 .
.
.
.
.
.
.
.
0-10 .
0-000 0"021 0"043 0"066 0-087 0"109 0"130 0"150 0"173 0"195 0'216
.
.
.
.
.
.
.
.
.
0 20 .
0-083 0"104 0-126 0"148 0-169 0-191 0"213 0-234 0"256 0"278 0'299
.
.
.
.
.
.
.
.
0"30 .
0"166 0-186 0'208 0"231 0"252 0"274 0"295 0-316 0"339 0"361 0"382
.
.
.
.
.
.
.
.
I .
0"248 0'269 0"291 ~0"314 0'335 0"355 0"378 0-399 0'421 0"443 0"464
0-70 . . . . . . .
0-579 0-600 0-622 0'644 0-665 0-687 O'709 O-730 0-752 0-774 0"795
Table 1 gives the computed values (in cal cm - 2 m i n - 1 ) of the flux of the reflected solar radiation i z ( H ) which escapes from the polluted ground layer of the atmosphere upwards under the given values of the coefficient of reflection e and of the albedo of the Earth's surface A. The ratio A* =- I 2 ( H ) / I I ( H ) then represents the total albedo related to the system formed by the Earth's surface and the polluted ground layer and not just the Earth's surface itself: The values of A*, again computed for all given values of e and A, are in Tab. 2. , ~ , , ~ geovh, et geod. z0 [~976]
387
J. Bednd? However, the results in Tabs 1 and 2 arc subject to a certain error, because multiple reflection of solar radiation takes place on the aerosol particles. Besides the radiation fluxes 12 and 12, for example, there also exists the radiation flux 13 of the solar radiation which has been reflected once on the aerosol particles or Earth's surface upwards and then again downwards. We can also consider the radiation flux I 4 upwards after one reflection downwards and two upwards. Clearly, in general we can consider I n radiation fluxes. The odd n refer to radiation fluxes propagating downwards after ½(n -- 1) reflections upwards and the same n u m b e r of reflections downwards towards the Earth's surface. If n is even, the radiation flux propagates upwards after ½ n - 1 reflection downwards and ½n reflections upwards• If we assume that all the reflected radiative fluxes are scattered isotropically, according to [4] we are able to determine the dependence of I n on the vertical co-ordinate z for n ";: 3 inside the polluted ground layer by solving the differential equation (9)
dln(z)/d z = ( _ 1)n+ 1 q(o: -[- ,8) In(z ) 4- (-- 1)" c~qln _ l ( z ) ,
which for n = 3, 4 and assuming c~and ,8 to be independent of z, yields (I0)
13(z) = ~2Clq( 1 + q ) - I (q . - 1 ) - 1 ( ~ + ,8)-2 exp [(~ 4- fl) z] ~4- ½~GI(~ 4- f l ) - I exp [--q(~ @ ,8) z] 4- G 2 exp [q(0c 4- fl) z],
(1 l)
14(z ) = 0c3q2C1(1 + q ) - 2 ( q _
1)-1 (¢~ @ ,8)-3 exp [(~ @ ,8)z] @
4- ½~2qGl(0, _~_ f l ) - i z exp [--q(~-~- ,8)z]-~- ½~G2(~ @ ,8)-I exp [q(~-+- fl)z] @ + G3 e x p [ - q (
~ fl) z ] ,
where G 2 and G 3 are other integration constants which can be determined from the boundary conditions (12), (13)
/ 3 ( H ) =~ 0 ,
14(0) = A 13(0) .
Should we want to increase the accuracy of the results given in Tabs l and 2, it would be necessary to carry out all the computation including Eqs (10) and (1t). Table 1 would then show I2(H) + I,,(H) instead of 12(H) and Tab. 2 would show A* = [12(H) %- I 4 ( H ) ] / I I ( H ). The procedure is similar if radiation fluxes I n for n > 4 are being considered. We shall now attempt to estimate the accuracy of the results in Tabs 1 and 2, which were computed using the first approximations only, i.e. only the radiation fluxes 11 and I 2, whereas the fluxes of the radiation reflected multiply were neglected. Clearly, the larger the capability of the aerosol particles to reflect the solar radiation, the larger the error due to neglecting the multiply reflected radiation. For a given value of the albedo of the Earth's surface A, therefore, the results in the last lines of Tabs 1 and 2 will be subject to the largest error, and these are the results which we shall now analyse. We computed the values of the radiation flux 13(0) at the level of the Earth's surface according to Eqs (I0) and (t2) for c~ ..... 1 0 - 5 c m - 1 and ,8 = 0 and A .... 0, 0"10, 0-20, 0"30 with the following results: 1 3 ( 0 ) = 0-029, 0'057, 0"085, 0 ' ] 1 2 c a l c m - 2 rain -1. If one considers that the Earth's surface will absorb [12(0) + 13(0) ] (1 -- A) solar radiation and that after a simple reflection upwards the radiative flux 12(H) escapes from the polluted ground layer, the residue in favour of the neglected fluxes of the multiply reflected radiation -/I a =:- I t ( H ) - 1 2 ( H ) - (l --- A)• • [/j(0) 4- I3(0)], which yields 0"005, 0-015, 0"034 and 0-050 cal cm - 2 rain - I in turn for A ~ 0, 0"10, 0.20 and 0"30. The latter values represent the upper limit of the estimate of the possible error in Tab. 1 by neglecting the multiple reflection of the solar radiation (the real error wilt be smaller, because a part of the multiply reflected radiation is absorbed in the ground layer and by
388
~tudia geoph, et geod. 20 [1976]
The Effect of the Pollution... the Earth's surface). If we now execute ~a = AA/II(H), for A = 0, 0"10, 0'20 and 0"30 we in turn arrive at d~A .......0, 0"0t, 0-02, 0-04 which represents the upper limit of the estimate of the error to which the results in Tab. 2 are subject. F r o m the above it can be seen that we are able to neglect the multiple reflection o f solar radiation without substantial detriment to accuracy at least for tentative computations in the presented model of the polluted ground layer when the atbedo o f the Earth's surface is taken to be A < 0"30. Table 2. A (10 - 6 cm - 1 )
0"10
0"20
0"30
0"70
I
0"06
0"12
0"18
0'41
I
0"07 0"09
(Y'I3 0"15
0"19 0"21
0"43 0"44
t
0
0"00
1 2
0-01 0-03
3 4
0-05 0"06
0"11 0"12
0"16 0"18
0"22 0'24
0"46 0"47
5 6 7
0"08 0"09 0"11
0"14 0q5 0"17
0"20 0'21 0"23
0"25 0"27 0"28
0'49 0'51 0"52
8 9 10
0"12 0"14 0'15
0"18 0"20 0"21
0'24 0"26 0"27
0"30 0"32 0"33
0"54 0"55 0"57
i A
The situation is, however, different if A = 0"70 (the last column in Tabs 1 and 2). If the estimate o f the upper limit of the possible error is carried out in the same way, we arrive at/3(0) = 0"223 cal cm - 2 rain - a , AA = 0.193 c a l c m - 2 rain - 1 , 6a = 0.14 and the error in computing the overall albedo A*, which could come close to 0i14, must be considered quite significant. In our model we computed tentatively 14(H) for ~ = 10 - 5 cm - 1 , f l = 0 and A = 0'70, which yielded I4(H) = 0"144 cal c m - 2 m i n - 1 . If we now analyse the accuracy again, we have AA = I I ( H ) - I 2 ( H ) - I 4 ( H ) ( 1 - - A ) [ 1 1 ( 0 ) + / 3 ( 0 ) ] = 0"049calcm - 2 r a i n - 1 and ~ a = = Aa/I~(H)= 0.03. This means that if the second approximation is applied, in which case we are considering radiative fluxes reflected 3 times at the most, we shall incur an error o f less than 0"03 in computing the albedo A*, which represents an accuracy roughly the same as that achieved when the first approximation was used with values of the albedo of the Earth's surface A :Z 0-30. The m a i n purpose of this paper was to illustrate the conditions under which the presence of the aerosol particles in the ground layer of the atmosphere is reflected in a decrease or increase of the solar radiation balance at the Earth's surface. It is evident that the first case will occur if A* > A and the second if A* < A. The bold line in Tab. 2 divides the values of c~ and A, under which the aerosol decreases the solar radiation balance at the level of the Earth's surface (the region below this line) from the values under which the presence of the aerosol particles has the opposite effect. Since the average real albedo of the Earth's surface is estimated by most authors to be close to 0-1 [3], drawing on the results in Tab. 2 we are able to conclude that the pollution o f t h e a t m o sphere by aerosol particles will in most cases cause an increase in the overall albedo and, therefore, a decrease of the solar radiation balance at the Earth's surface. This would, of course, studia geoph, et geod. 20119761
389
J. Bedndi: The Effect of the Pollution... result in a lower degree of heating of the ground layer of the atmosphere during daytime and, consequently, in reduction the convection and an overall stabilization of the Jower atmosphere. These results do not agree apparently with the numerical results published in [6], which indicate that the polluted ground layer becomes unstable under solar radiation. However, this disagreement is only apparent, because the radiation model, proposed in [6], has so far only been used to study idealized aerosol particles which only absorb and do not reflect solar radiation. The results, published in [6], therefore, can only be compared with results given here in the first lines of Tabs 1 and 2 which also indicate an increased solar radiation balance in the neighbourhood o f the Earth's surface. In geographic areas covered by ice and snow for most of the year, however, the presence of atmosphere aerosol may, on the contrary, cause an increase in the solar radiation balance. Consider that the estimate of the overall atbedo A* (last column in Tab. 2) in our model for A = 0.70 could not have been underestimated by more t h a n 0"14. This shows that the presence of the aerosol practically always causes a decrease of the overall albedo for the described model of the polluted ground layer of the atmos sphere and for albedo of the Earth's surface A -- 0-70. Drawing o n the above results we may conclude that the albedo of the Earth's surface A is a very important quantity in assessing the effect of the pollution of the atmosphere by aerosols on the balance of the solar radiation. In [2] it was shown that there exists a critical value of the albedo of the Earth's surface Acrit for each degree of pollution. If at a given degree of pollution the actual local value A is smaller than Acrit , the presence of the aerosol will be reflected in a decrease of the solar radiation balance at the Earth's surface, however, if A > .Acrlt , the aerosol has the opposite effect. The same conclusion can be drawn from our results.
Reviewer: J. Lukd6
Received 5. 9. 1975
References [1] J. M. M i t c h e l l : The Effect of Atmospheric Aerosols on Climate with Special Reference to Temperature Near the Earth's Surface. J. Appl. Meteorol., 10 (1972), 703. [2] L. S h o t k i n , H. L u d e w i g , J. T h o m p s o n : J. Appl. Meteorol., 14 (1975), 189.
Calculated Effects of Aerosols on Sunlight.
[3] W. W a n g , G. D o m o t o : The Radiative Effect of Aerosols in the Earth's Atmosphere. J. Appl. Meteorol., 13 (1974), 521. [4] J. Bedn~i[': ~;i~eni slune6ni a tepeln6 radiace v aerosolov,jch vrstv~ich atmosf6ry. Meteorol. zpr., 27 (1974), 116. [5] K. Yl. K o r ~ p a T t , eB: JIy,~I,ICTb1~ Tensloo6Men r) aTMoc~epe. FH~lpoMereorla21ar, 5Ieumwpa~ 1956. [6] J. Bedn~if: Model of Radiation Processes in Atmospheric Layers Polluted by Aerosol Particles. Studia geoph, et geod., 19 (1975), 167.
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Studia geoph, at good. 20 [1976]
