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The Role of Aerosols in Relation to Stratospheric Modelling
THE ROLE OF AEROSOLS IN RELATION TO STRATOSPHERIC MODELLING P. Chakrabarty and D . K. Chakrabarty Physical Research
Laboratory,
Navrangpura,
Ahmedabad
380009,
India
INTRODUCTION M e a s u r e m e n t s of the p o s i t i v e ion density, N , o b t a i n e d u s i n g the b l u n t p r o b e t e c h n i q u e exist a b o v e 30 k m [1] ,[2j ; b a l l o o n - b o r n e G e r d i e n c o n d e n s e r s h a v e b e e n flown to about 20 k m at v a r i o u s p l a c e s a r o u n d the g l o b e [3] - [ 6 ] . G e r d i e n c o n d e n s e r m e a s u r e m e n t s in the u p p e r s t r a t o s p h e r e , i.e. u p t o 50 km, h a v e also b e e n r e p o r t e d [7]-[9] +
In this p a p e r w e e x a m i n e a f e w o f these p r o f i l e s and their p o s s i b l e variations with changing geophysical conditions. The implications of these v a r i a t i o n s w i t h r e s p e c t to the p r o d u c t i o n and losses o f p o s i t i v e ions in this h e i g h t r a n g e are d i s c u s s e d . F i n a l l y an attempt is m a d e to e s t i m a t e the size d i s t r i b u t i o n of a e r o s o l s in the stratosphere. RESULTS AND DISCUSSION In F i g . l w e h a v e p l o t t e d a f e w p r o f i l e s o f the d a y t i m e N , for d i f f e r e n t solar a c t i v i t y c o n d i t i o n s and for summer and w i n t e r c o n d i t i o n s , for two m i d - l a t i t u d e s t a t i o n s . It is n o t i c e d , firstly, that the blunt p r o b e m e a s u r e m e n t s a r e m u c h l a r g e r than the G e r d i e n condenser measurements. S e c o n d l y , the b l u n t p r o b e m e a s u r e m e n t s r e v e a l a m a r g i n a l v a r i a t i o n of N w i t h the 10.7 cm solar flux. An e x a m i n a t i o n o f the three p r o f i l e s m e a s u r e d at A r e n o s i l l o , Spain [7] and [9] shows n o s y s t e m a t i c v a r i a t i o n w i t h the 10.7 cm flux. M e a s u r e d during l o w solar a c t i v i t y c o n d i t i o n s , the summer N profile i n c r e a s e s s h a r p l y a b o v e 35 km. At 50 km, N during the summer is about 30 times l a r g e r t h a n the w i n t e r v a l u e . In F i g . 2 a f e w p r o f i l e s o f p o s i t i v e ion d e n s i t i e s m e a s u r e d b y the blunt p r o b e t e c h n i q u e [10] at d i f f e r e n t l a t i t u d e s are shown. The low latitude m e a s u r e m e n t s w e r e m a d e d u r i n g a solar e c l i p s e w h i c h c a n b e a s s u m e d to b e e q u i v a l e n t to a n i g h t time c o n d i t i o n . It is seen that, a b o v e 40 km, the p o s i t i v e ion d e n s i t y i n c r e a s e s w i t h i n c r e a s i n g l a t i t u d e . T h e d o m i n a n t s o u r c e o f i o n i z a t i o n o v e r the a l t i t u d e r a n g e o f interest in this study is the cosmic r a y source [11] . +
+
+
+
T h e simplest p o s s i b l e m o d e l for s t r a t o s p h e r i c e l e c t r i c i t y is to c o n s i d e r the s t r a t o s p h e r e as n o t c o n t a i n i n g any a e r o s o l s . The 49
50
P. Chakrabarty and D. K. Chakrabarty
Fig.l E x p e r i m e n t a l p r o f i l e s of p o s i t i v e ion d e n s i t i e s m e a s u r e d by the blunt p r o b e as w e l l as the G e r d i e n condenser technique.
OBSERVED THEORETICAL WITH a . = 5X l6" cm 8
3
S'
THEORETICAL WITH 0!j FROM SMITH a CHURCH (1977) A - LOW LAT. ( ECLIPSE 12 N0V.I966) B - MID. LAT. (NIGHT, 6 JAN,1966) C - HIGH LAT. (NIGHT, 6 DEC, 1967)
10"
Fig.2 C o m p a r i s o n of t h e o r e t i c a l and m e a s u r e d p r o b e ) p r o f i l e s of p o s i t i v e ion density.
(blunt
-
51
The Role of Aerosols e l e c t r o n d e n s i t y b e i n g v e r y s m a l l , in this i d e a l i z e d s i t u a t i o n the loss of p o s i t i v e ions is m a i n l y by m u t u a l r e c o m b i n a t i o n w i t h negative ions. The c o n t i n u i t y e q u a t i o n of p o s i t i v e ions in the s t r a t o s p h e r e can b e w r i t t e n a s : (1) w h e r e q is the ion p r o d u c t i o n r a t e [ll] , a i s the r a t e c o e f f i c i e n t for the m u t u a l n e u t r a l i s a t i o n [12] , [ 1 3 ] , and N and N are the d e n s i t i e s of p o s i t i v e and n e g a t i v e ions r e s p e c t i v e l y . Using two v a l u e s of a ^ , as g i v e n in [12] and [13] , and a s s u m i n g steady state c o n d i t i o n s , w e h a v e c a l c u l a t e d the p o s i t i v e ion d e n s i t y p r o f i l e s from e q u a t i o n ( 1 ) . T h e s e are shown in F i g . 2 along w i t h the e x p e r i m e n t a l p r o f i l e s for the blunt p r o b e t e c h n i q u e . It is seen that the t h e o r e t i c a l N v a l u e s are m u c h larger than the o b s e r v e d v a l u e s ; similar r e s u l t s are also o b t a i n e d for the G e r d i e n condensers. T h e s e i n d i c a t e the n e e d for an a d d i t i o n a l loss p r o c e s s +
+
The loss of ions by a t t a c h m e n t to a e r o s o l s is a w e l l k n o w n p r o c e s s in s t r a t o s p h e r i c e l e c t r i c i t y and the o b v i o u s e x t e n s i o n of e q u a t i o n (1) is to i n c l u d e a loss term a c c o u n t i n g for the c o n t r i b u t i o n from this p r o c e s s . The steady state c o n d i t i o n is then: (2) w h e r e [N ](y JN_j , 3 is the a t t a c h m e n t c o e f f i c i e n t w i t h a e r o s o l s and N is the d e n s i t y of a e r o s o l s . be r e w r i t t e n a s : +
of p o s i t i v e ions E q u a t i o n (2) can
(3) The loss r a t e s of p o s i t i v e ions w i t h a e r o s o l s , 3 N , n e e d e d to r e p r o d u c e the m e a s u r e d p o s i t i v e ion d e n s i t y p r o f i l e s h a v e b e e n e s t i m a t e d for five d i f f e r e n t cases and these are shown in F i g . 3 . A c o m p a r i s o n of the three curves A, B and C shows that the loss rate of ions w i t h a e r o s o l s i n c r e a s e s w i t h l a t i t u d e . Similarly a c o m p a r i s o n of the two w i n t e r curves B and D i n d i c a t e s that 3 N by day is larger than at n i g h t . A c o m p a r i s o n of c u r v e s E and D shows l a r g e s e a s o n a l v a r i a t i o n s a b o v e 35 km. T h i s i n d i c a t e s that the loss of p o s i t i v e ions w i t h a e r o s o l s v a r i e s w i t h l a t i t u d e , season and from day to n i g h t . a
Next w e m a k e an attempt to r e t r i e v e the a e r o s o l size d i s t r i b u t i o n as a f u n c t i o n of h e i g h t h from 3 N o b t a i n e d from the o b s e r v e d p o s i t i v e ion d e n s i t y . The p r o d u c t 3 N in e q u a t i o n (3) is an a v e r a g e over the a e r o s o l size d i s t r i b u t i o n . The losses due to a t t a c h m e n t to a e r o s o l s h a v e b e e n studied by o t h e r a u t h o r s [ll], [14] A c c o r d i n g to b o t h , 3 N at a h e i g h t h can be w r i t t e n a s : a
(4) mm
w h e r e r is the r a d i u s of the a e r o s o l
S.R.—C
particles.
52
P. Chakrabarty and D. K. Chakrabarty i
1
•—
A - LOW LAT, ECLIPSE
£N (S"') a
Fig.3 P r o f i l e s o f loss r a t e of p o s i t i v e aerosols, ^ -
ions w i t h
N
a
A t t a c h m e n t c o e f f i c i e n t s in the s t r a t o s p h e r e w e r e first e s t i m a t e d by W h i p p l e [15] . IJake et a l . [11] e x t e n d e d these r e s u l t s to lower a l t i t u d e s and a w i d e r size r a n g e of p a r t i c l e s . T h e r e is a s u b s t a n tial amount o f i n f o r m a t i o n - b o t h t h e o r e t i c a l and e x p e r i m e n t a l a v a i l a b l e on c o m b i n a t i o n c o e f f i c i e n t s at ground level [11] . In the p r e s e n t w o r k , 3 ( r , h ) h a s b e e n t a k e n f r o m [11] . A l t h o u g h B r i c a r d [16] and K a w a n o et a l . [17] c o n s i d e r that the v a l u e s of [11] are u n d e r e s t i m a t e s for small r, the p r e s e n t w o r k carried out u s i n g the v a l u e o f $(r, h ) for r < 0 . 1 y m g i v e n in [17] has s h o w n that the r e s u l t s are u n a f f e c t e d . For the p a r a m e t e r N ( r , h ) , the r a d i u s d e p e n d e n t a s s u m e d to f o l l o w : a
component
is
(5) w h e r e , a c c o r d i n g to J u n g e et a l . S u b s t i t u t i n g (5) in ( 4 ) :
[18]
, v v a r i e s from 3 to 4.
(6)
K n o w i n g K, , N (r, h ) can b e c a l c u l a t e d from e q u a t i o n ( 5 ) . W e h a v e e s t i m a t e d N (r, h ) for m i d - l a t i t u d e summer and w i n t e r c o n d i t i o n s , for v a l u e s of v v a r y i n g from 0.5 to 4. In F i g . 4 , the p r o f i l e s of a e r o s o l d e n s i t i e s w i t h d i f f e r e n t r a d i i are shown for v = 3. It is seen that the c a l c u l a t e d v a l u e s a r e m u c h l a r g e r than the o b s e r v e d
53
The Role of Aerosols
10°
I0
I0
1
I0
2
3
I0
4
AEROSOL DENSITY ( c m " ) 3
aerosol densities reported
in
[ll] and
[19] .
In T a b l e 1 w e h a v e shown the v a l u e s of N (r, h ) at 20 k m for d i f f e r e n t v a l u e s o f v and r along w i t h m e a s u r e d v a l u e s for day mid-latitude winter conditions.
time
_ 3
TABLE
r\ v
1
Aerosol Densities at 20 k m
0.,5
(cm
1.0
2.0
) for D i f f e r e n t V a l u e s of v and r
3.0
4.0
(ym)\
Average observed v a l u e s [19]
0.01 *9 .65-•02
1.50+00
3..26+02 4..79+04
2,. 23+06
0.02
7. ,15-•02
8.25-01
9..81+01 7.,91+03
2..02+05
0.2
5.,29-•02
4.53-01
2,.95+01 1,.31+03
1..84+04
0.6
3.,92-•02
2.48-01
8..90+00 2..16+02
1,,67+03
8.0
2.0
2..91-•02
1.36-01
2..68+00 3,.57+01
1..51+02
(r>0.1
10.0
2..15-•02
7.48-02
8,.07-01 5.,91+00
1..37+01
* 9.65
- 0.2 = 9.65
x 10
.
100-10 (r<0.1
m)
<- 1.2 m)
54
P. Chakrabarty and D. K. Chakrabarty
It is seen that a fairly good a g r e e m e n t b e t w e e n t h e o r e t i c a l and observed v a l u e s is o b t a i n e d f o r v ^ 2 for the v a l u e s of 3 (r, h ) taken in the p r e s e n t w o r k . A l s o , m u c h smaller v a l u e s of a e r o s o l densities are o b t a i n e d at 50 km, e.g. for p a r t i c l e s of r < 0.1 y m, the d e n s i t i e s c a l c u l a t e d w i t h v = 2 are four o r d e r s of m a g n i t u d e less than those w i t h v = 4. It is c o n c l u d e d that a e r o s o l s p l a y an important r o l e in the loss of p o s i t i v e ions in the s t r a t o s p h e r e . A l s o , in the a b s e n c e of any in situ m e a s u r e m e n t s of a e r o s o l d e n s i t y for different r a d i i , m e a s u r e m e n t s of p o s i t i v e ions can be u s e d to d e t e r m i n e the a e r o s o l densities. For this one n e e d s r e l i a b l e i n f o r m a t i o n r e g a r d i n g 3(r, h ) and v .For the former m o r e l a b o r a t o r y i n v e s t i g a t i o n s n e e d to be c o n d u c t e d . For the latter m o r e s t r a t o s p h e r i c m e a s u r e m e n t s of p a r t i c l e s of d i f f e r e n t r a d i i are r e q u i r e d . REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
11. 12. 13. 14. 15. 16. 17. 18. 19.
L. C . H a l e , D . P. H o u l t and D . C . B a k e r , Space R e s e a r c h V I I I . 320 ( 1 9 6 8 ) . J. D . M i t c h e l l and L. C . H a l e , Space R e s e a r c h X I I I , 471 (1973) G. W . P a l t r i d g e , J. G e o p h y s . R e s . 7 0 , 2751 ( 1 9 6 5 ) . T . T a k e u t i , K. I s h i k a w a and A . I w a t a , J. G e o m a g n e t . G e o e l e c t . 18, 493 (1966) . Y, M o r i t a , H. I s h i k a w a and M . K a n a d a , J. G e o p h y s . R e s . 76, 3431 ( 1 9 7 1 ) . J. L. K r o e n i n g , J. G e o p h y s . R e s . 6 5 , 145 ( 1 9 6 0 ) . G. Rose and H. U. W i d d e l , R a d i o S c i e n c e 7, 81 ( 1 9 7 2 ) . J. D . M i t c h e l l , R. S. S a g a r and R. O . O l s e n , Space R e s e a r c h X V I I , 199 (1977) . H. U. W i d d e l , G. R o s e and R. B o r c h e r s , J. G e o p h y s . 4 4 , 179 (1977) . L. C. H a l e , in: C O S P A R M e t h o d s of M e a s u r e m e n t s and R e s u l t s of L o w e r I o n o s p h e r e S t r u c t u r e , A k a d e m i e - V e r l a g , B e r l i n , 19 7 4 , p. 219. R. D . H a k e , J r . , E . T . P i e r c e and W . V i e z e e , S t a n f o r d R e s e a r c h Institute Report, California, 1973. D . S m i t h , N . G. A d a m s and M . J. C h u r c h , P l a n e t . S p a c e S c i . 2 4 , 697 ( 1 9 7 6 ) . D . S m i t h and M . J. C h u r c h , P l a n e t . S p a c e S c i . 2 5 , 433 ( 1 9 7 7 ) . J. Z i k m u n d a and V . A . M o h n e n , M e t e o r o l o g i s c h e R u n d s c h a u , 2 5 , 10 (1972) . E . C . W h i p p l e , P r o b l e m s of A t m o s p h e r e and Space E l e c t r i c i t y , Elsevier, New York, 1965. J. B r i c a r d , P r o b l e m s of A t m o s p h e r e and S p a c e E l e c t r i c i t y , Elsevier, New York, 1965. M . K a w a n o , Y. Ikebe and M . S h i m o , P l a n e t a r y E l e c t r o d y n a m i c s , G o r d o n and B r e a c h , N e w Y o r k , 1 9 6 9 . C . E . J u n g e , C . W . C h a g n o n and J. E . M a n s o n , J. M e t e o r o l o g y , 1 8 , 81 (1961) . CIAP M o n o g r a p h I, C l i m a t i c Impact A s s e s s m e n t P r o g r a m , D O T - T S F - 7 5 - 5 1 , D e p a r t m e n t of T r a n s p o r t a t i o n , W a s h i n g t o n , U.S.A., 1975.
Laboratory,
Navrangpura,
Ahmedabad
380009,
India
INTRODUCTION M e a s u r e m e n t s of the p o s i t i v e ion density, N , o b t a i n e d u s i n g the b l u n t p r o b e t e c h n i q u e exist a b o v e 30 k m [1] ,[2j ; b a l l o o n - b o r n e G e r d i e n c o n d e n s e r s h a v e b e e n flown to about 20 k m at v a r i o u s p l a c e s a r o u n d the g l o b e [3] - [ 6 ] . G e r d i e n c o n d e n s e r m e a s u r e m e n t s in the u p p e r s t r a t o s p h e r e , i.e. u p t o 50 km, h a v e also b e e n r e p o r t e d [7]-[9] +
In this p a p e r w e e x a m i n e a f e w o f these p r o f i l e s and their p o s s i b l e variations with changing geophysical conditions. The implications of these v a r i a t i o n s w i t h r e s p e c t to the p r o d u c t i o n and losses o f p o s i t i v e ions in this h e i g h t r a n g e are d i s c u s s e d . F i n a l l y an attempt is m a d e to e s t i m a t e the size d i s t r i b u t i o n of a e r o s o l s in the stratosphere. RESULTS AND DISCUSSION In F i g . l w e h a v e p l o t t e d a f e w p r o f i l e s o f the d a y t i m e N , for d i f f e r e n t solar a c t i v i t y c o n d i t i o n s and for summer and w i n t e r c o n d i t i o n s , for two m i d - l a t i t u d e s t a t i o n s . It is n o t i c e d , firstly, that the blunt p r o b e m e a s u r e m e n t s a r e m u c h l a r g e r than the G e r d i e n condenser measurements. S e c o n d l y , the b l u n t p r o b e m e a s u r e m e n t s r e v e a l a m a r g i n a l v a r i a t i o n of N w i t h the 10.7 cm solar flux. An e x a m i n a t i o n o f the three p r o f i l e s m e a s u r e d at A r e n o s i l l o , Spain [7] and [9] shows n o s y s t e m a t i c v a r i a t i o n w i t h the 10.7 cm flux. M e a s u r e d during l o w solar a c t i v i t y c o n d i t i o n s , the summer N profile i n c r e a s e s s h a r p l y a b o v e 35 km. At 50 km, N during the summer is about 30 times l a r g e r t h a n the w i n t e r v a l u e . In F i g . 2 a f e w p r o f i l e s o f p o s i t i v e ion d e n s i t i e s m e a s u r e d b y the blunt p r o b e t e c h n i q u e [10] at d i f f e r e n t l a t i t u d e s are shown. The low latitude m e a s u r e m e n t s w e r e m a d e d u r i n g a solar e c l i p s e w h i c h c a n b e a s s u m e d to b e e q u i v a l e n t to a n i g h t time c o n d i t i o n . It is seen that, a b o v e 40 km, the p o s i t i v e ion d e n s i t y i n c r e a s e s w i t h i n c r e a s i n g l a t i t u d e . T h e d o m i n a n t s o u r c e o f i o n i z a t i o n o v e r the a l t i t u d e r a n g e o f interest in this study is the cosmic r a y source [11] . +
+
+
+
T h e simplest p o s s i b l e m o d e l for s t r a t o s p h e r i c e l e c t r i c i t y is to c o n s i d e r the s t r a t o s p h e r e as n o t c o n t a i n i n g any a e r o s o l s . The 49
50
P. Chakrabarty and D. K. Chakrabarty
Fig.l E x p e r i m e n t a l p r o f i l e s of p o s i t i v e ion d e n s i t i e s m e a s u r e d by the blunt p r o b e as w e l l as the G e r d i e n condenser technique.
OBSERVED THEORETICAL WITH a . = 5X l6" cm 8
3
S'
THEORETICAL WITH 0!j FROM SMITH a CHURCH (1977) A - LOW LAT. ( ECLIPSE 12 N0V.I966) B - MID. LAT. (NIGHT, 6 JAN,1966) C - HIGH LAT. (NIGHT, 6 DEC, 1967)
10"
Fig.2 C o m p a r i s o n of t h e o r e t i c a l and m e a s u r e d p r o b e ) p r o f i l e s of p o s i t i v e ion density.
(blunt
-
51
The Role of Aerosols e l e c t r o n d e n s i t y b e i n g v e r y s m a l l , in this i d e a l i z e d s i t u a t i o n the loss of p o s i t i v e ions is m a i n l y by m u t u a l r e c o m b i n a t i o n w i t h negative ions. The c o n t i n u i t y e q u a t i o n of p o s i t i v e ions in the s t r a t o s p h e r e can b e w r i t t e n a s : (1) w h e r e q is the ion p r o d u c t i o n r a t e [ll] , a i s the r a t e c o e f f i c i e n t for the m u t u a l n e u t r a l i s a t i o n [12] , [ 1 3 ] , and N and N are the d e n s i t i e s of p o s i t i v e and n e g a t i v e ions r e s p e c t i v e l y . Using two v a l u e s of a ^ , as g i v e n in [12] and [13] , and a s s u m i n g steady state c o n d i t i o n s , w e h a v e c a l c u l a t e d the p o s i t i v e ion d e n s i t y p r o f i l e s from e q u a t i o n ( 1 ) . T h e s e are shown in F i g . 2 along w i t h the e x p e r i m e n t a l p r o f i l e s for the blunt p r o b e t e c h n i q u e . It is seen that the t h e o r e t i c a l N v a l u e s are m u c h larger than the o b s e r v e d v a l u e s ; similar r e s u l t s are also o b t a i n e d for the G e r d i e n condensers. T h e s e i n d i c a t e the n e e d for an a d d i t i o n a l loss p r o c e s s +
+
The loss of ions by a t t a c h m e n t to a e r o s o l s is a w e l l k n o w n p r o c e s s in s t r a t o s p h e r i c e l e c t r i c i t y and the o b v i o u s e x t e n s i o n of e q u a t i o n (1) is to i n c l u d e a loss term a c c o u n t i n g for the c o n t r i b u t i o n from this p r o c e s s . The steady state c o n d i t i o n is then: (2) w h e r e [N ](y JN_j , 3 is the a t t a c h m e n t c o e f f i c i e n t w i t h a e r o s o l s and N is the d e n s i t y of a e r o s o l s . be r e w r i t t e n a s : +
of p o s i t i v e ions E q u a t i o n (2) can
(3) The loss r a t e s of p o s i t i v e ions w i t h a e r o s o l s , 3 N , n e e d e d to r e p r o d u c e the m e a s u r e d p o s i t i v e ion d e n s i t y p r o f i l e s h a v e b e e n e s t i m a t e d for five d i f f e r e n t cases and these are shown in F i g . 3 . A c o m p a r i s o n of the three curves A, B and C shows that the loss rate of ions w i t h a e r o s o l s i n c r e a s e s w i t h l a t i t u d e . Similarly a c o m p a r i s o n of the two w i n t e r curves B and D i n d i c a t e s that 3 N by day is larger than at n i g h t . A c o m p a r i s o n of c u r v e s E and D shows l a r g e s e a s o n a l v a r i a t i o n s a b o v e 35 km. T h i s i n d i c a t e s that the loss of p o s i t i v e ions w i t h a e r o s o l s v a r i e s w i t h l a t i t u d e , season and from day to n i g h t . a
Next w e m a k e an attempt to r e t r i e v e the a e r o s o l size d i s t r i b u t i o n as a f u n c t i o n of h e i g h t h from 3 N o b t a i n e d from the o b s e r v e d p o s i t i v e ion d e n s i t y . The p r o d u c t 3 N in e q u a t i o n (3) is an a v e r a g e over the a e r o s o l size d i s t r i b u t i o n . The losses due to a t t a c h m e n t to a e r o s o l s h a v e b e e n studied by o t h e r a u t h o r s [ll], [14] A c c o r d i n g to b o t h , 3 N at a h e i g h t h can be w r i t t e n a s : a
(4) mm
w h e r e r is the r a d i u s of the a e r o s o l
S.R.—C
particles.
52
P. Chakrabarty and D. K. Chakrabarty i
1
•—
A - LOW LAT, ECLIPSE
£N (S"') a
Fig.3 P r o f i l e s o f loss r a t e of p o s i t i v e aerosols, ^ -
ions w i t h
N
a
A t t a c h m e n t c o e f f i c i e n t s in the s t r a t o s p h e r e w e r e first e s t i m a t e d by W h i p p l e [15] . IJake et a l . [11] e x t e n d e d these r e s u l t s to lower a l t i t u d e s and a w i d e r size r a n g e of p a r t i c l e s . T h e r e is a s u b s t a n tial amount o f i n f o r m a t i o n - b o t h t h e o r e t i c a l and e x p e r i m e n t a l a v a i l a b l e on c o m b i n a t i o n c o e f f i c i e n t s at ground level [11] . In the p r e s e n t w o r k , 3 ( r , h ) h a s b e e n t a k e n f r o m [11] . A l t h o u g h B r i c a r d [16] and K a w a n o et a l . [17] c o n s i d e r that the v a l u e s of [11] are u n d e r e s t i m a t e s for small r, the p r e s e n t w o r k carried out u s i n g the v a l u e o f $(r, h ) for r < 0 . 1 y m g i v e n in [17] has s h o w n that the r e s u l t s are u n a f f e c t e d . For the p a r a m e t e r N ( r , h ) , the r a d i u s d e p e n d e n t a s s u m e d to f o l l o w : a
component
is
(5) w h e r e , a c c o r d i n g to J u n g e et a l . S u b s t i t u t i n g (5) in ( 4 ) :
[18]
, v v a r i e s from 3 to 4.
(6)
K n o w i n g K, , N (r, h ) can b e c a l c u l a t e d from e q u a t i o n ( 5 ) . W e h a v e e s t i m a t e d N (r, h ) for m i d - l a t i t u d e summer and w i n t e r c o n d i t i o n s , for v a l u e s of v v a r y i n g from 0.5 to 4. In F i g . 4 , the p r o f i l e s of a e r o s o l d e n s i t i e s w i t h d i f f e r e n t r a d i i are shown for v = 3. It is seen that the c a l c u l a t e d v a l u e s a r e m u c h l a r g e r than the o b s e r v e d
53
The Role of Aerosols
10°
I0
I0
1
I0
2
3
I0
4
AEROSOL DENSITY ( c m " ) 3
aerosol densities reported
in
[ll] and
[19] .
In T a b l e 1 w e h a v e shown the v a l u e s of N (r, h ) at 20 k m for d i f f e r e n t v a l u e s o f v and r along w i t h m e a s u r e d v a l u e s for day mid-latitude winter conditions.
time
_ 3
TABLE
r\ v
1
Aerosol Densities at 20 k m
0.,5
(cm
1.0
2.0
) for D i f f e r e n t V a l u e s of v and r
3.0
4.0
(ym)\
Average observed v a l u e s [19]
0.01 *9 .65-•02
1.50+00
3..26+02 4..79+04
2,. 23+06
0.02
7. ,15-•02
8.25-01
9..81+01 7.,91+03
2..02+05
0.2
5.,29-•02
4.53-01
2,.95+01 1,.31+03
1..84+04
0.6
3.,92-•02
2.48-01
8..90+00 2..16+02
1,,67+03
8.0
2.0
2..91-•02
1.36-01
2..68+00 3,.57+01
1..51+02
(r>0.1
10.0
2..15-•02
7.48-02
8,.07-01 5.,91+00
1..37+01
* 9.65
- 0.2 = 9.65
x 10
.
100-10 (r<0.1
m)
<- 1.2 m)
54
P. Chakrabarty and D. K. Chakrabarty
It is seen that a fairly good a g r e e m e n t b e t w e e n t h e o r e t i c a l and observed v a l u e s is o b t a i n e d f o r v ^ 2 for the v a l u e s of 3 (r, h ) taken in the p r e s e n t w o r k . A l s o , m u c h smaller v a l u e s of a e r o s o l densities are o b t a i n e d at 50 km, e.g. for p a r t i c l e s of r < 0.1 y m, the d e n s i t i e s c a l c u l a t e d w i t h v = 2 are four o r d e r s of m a g n i t u d e less than those w i t h v = 4. It is c o n c l u d e d that a e r o s o l s p l a y an important r o l e in the loss of p o s i t i v e ions in the s t r a t o s p h e r e . A l s o , in the a b s e n c e of any in situ m e a s u r e m e n t s of a e r o s o l d e n s i t y for different r a d i i , m e a s u r e m e n t s of p o s i t i v e ions can be u s e d to d e t e r m i n e the a e r o s o l densities. For this one n e e d s r e l i a b l e i n f o r m a t i o n r e g a r d i n g 3(r, h ) and v .For the former m o r e l a b o r a t o r y i n v e s t i g a t i o n s n e e d to be c o n d u c t e d . For the latter m o r e s t r a t o s p h e r i c m e a s u r e m e n t s of p a r t i c l e s of d i f f e r e n t r a d i i are r e q u i r e d . REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
11. 12. 13. 14. 15. 16. 17. 18. 19.
L. C . H a l e , D . P. H o u l t and D . C . B a k e r , Space R e s e a r c h V I I I . 320 ( 1 9 6 8 ) . J. D . M i t c h e l l and L. C . H a l e , Space R e s e a r c h X I I I , 471 (1973) G. W . P a l t r i d g e , J. G e o p h y s . R e s . 7 0 , 2751 ( 1 9 6 5 ) . T . T a k e u t i , K. I s h i k a w a and A . I w a t a , J. G e o m a g n e t . G e o e l e c t . 18, 493 (1966) . Y, M o r i t a , H. I s h i k a w a and M . K a n a d a , J. G e o p h y s . R e s . 76, 3431 ( 1 9 7 1 ) . J. L. K r o e n i n g , J. G e o p h y s . R e s . 6 5 , 145 ( 1 9 6 0 ) . G. Rose and H. U. W i d d e l , R a d i o S c i e n c e 7, 81 ( 1 9 7 2 ) . J. D . M i t c h e l l , R. S. S a g a r and R. O . O l s e n , Space R e s e a r c h X V I I , 199 (1977) . H. U. W i d d e l , G. R o s e and R. B o r c h e r s , J. G e o p h y s . 4 4 , 179 (1977) . L. C. H a l e , in: C O S P A R M e t h o d s of M e a s u r e m e n t s and R e s u l t s of L o w e r I o n o s p h e r e S t r u c t u r e , A k a d e m i e - V e r l a g , B e r l i n , 19 7 4 , p. 219. R. D . H a k e , J r . , E . T . P i e r c e and W . V i e z e e , S t a n f o r d R e s e a r c h Institute Report, California, 1973. D . S m i t h , N . G. A d a m s and M . J. C h u r c h , P l a n e t . S p a c e S c i . 2 4 , 697 ( 1 9 7 6 ) . D . S m i t h and M . J. C h u r c h , P l a n e t . S p a c e S c i . 2 5 , 433 ( 1 9 7 7 ) . J. Z i k m u n d a and V . A . M o h n e n , M e t e o r o l o g i s c h e R u n d s c h a u , 2 5 , 10 (1972) . E . C . W h i p p l e , P r o b l e m s of A t m o s p h e r e and Space E l e c t r i c i t y , Elsevier, New York, 1965. J. B r i c a r d , P r o b l e m s of A t m o s p h e r e and S p a c e E l e c t r i c i t y , Elsevier, New York, 1965. M . K a w a n o , Y. Ikebe and M . S h i m o , P l a n e t a r y E l e c t r o d y n a m i c s , G o r d o n and B r e a c h , N e w Y o r k , 1 9 6 9 . C . E . J u n g e , C . W . C h a g n o n and J. E . M a n s o n , J. M e t e o r o l o g y , 1 8 , 81 (1961) . CIAP M o n o g r a p h I, C l i m a t i c Impact A s s e s s m e n t P r o g r a m , D O T - T S F - 7 5 - 5 1 , D e p a r t m e n t of T r a n s p o r t a t i o n , W a s h i n g t o n , U.S.A., 1975.