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bY
S. M. Radicelia
D. W. Stowe
July 15, 1970
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A E R O N O M Y R E P O R T
N O . 3 8
D-REGION I O N CHEMISTRY
bY
S. M. Radice l la
D. W. Stowe
J u l y 15, 1970
Supported by National Aeronautics and Space Administration Grant NGW3T3 Na/A-/.ct'- d d g - 6 / 2
Aeronomy Laboratory Department of Electrical Engineering
Universi ty o f I l l i n o i s Urbana, I l l i n o i s
UILU-ENG-70-261
iii
ABSTRACT
The n e u t r a l composition of t h e mesosphere i s reviewed with emphasis on
n i t rogen oxides and oxygen a l lo t ropes . Then ion iza t ion sources i n t h e D
region are s tud ied inc luding the effects of recent experimental r e s u l t s .
F ina l ly , t h e nega t ive ion chemistry i s discussed including the ca l cu la t ion
On the b a s i s of t h e experimental 'eff' of an "e f f ec t ive attachment f a c t o r ,
a new f a s t b inary attachment process is considered. 'eff'
In t h e appendix, r e l evan t experimental da t a i s tabula ted , and t h e d iu rna l
va r i a t ion of atomic oxygen and ozone concentrat ions i s presented, based on
recent values f o r t h e r e l evan t ra te c o e f f i c i e n t s .
V
TABLE OF CONTENTS
Page iii ABSTRACT
LIST OF' FIGURES vi
viii LIST OF TABLES
1. D-REGIOTJ NEGATIVE-ION CHEMISTRY 1
1 1.1 Introduction
2. NEUTRAL COMPOSITION OF THE MESOSPHERE 3
3 4 18 22 25
2.1 Introduction 2.2 Odd Allotropes of Oxygen 2.3 Nitrogen Oxides 2.4 Hydrogenous Compounds 2.5 Carbon Dioxide
3. RATES OF IONIZATION 26
26 26 28 31 31 38
3.1 Introduction 3.2 Ionization by Solar Lyman-Alpha 3.3 Ionization by X-Rays 3.4 3.5 Ionization by Precipitated Electrons 3.6 Ionization by Cosmic'Rays
Ionization of Metastable Molecular Oxygen
4. NEGATIVE-ION CHEMISTRY IN THE D REGION 39
4.1 4.2
Laboratory Measurements of Negative-Ion Reaction Rates General Schemes of D-Region Negative-Ion Chemistry
39 43
55 APPENDIX I
1. SOURCES OF DATA 55
1.1 Introduction 1.2 Neutral Atmosphere Parameters [Oz], [MI 1.3 Initial Values f o r the Oxygen Atmosphere 1.4 Time-Dependent Oxygen Atmosphere
55 55 61 61
122 2. COMPUTATIONAL CONSIDERATIONS
REFERENCES 135
v i
LIST OF FIGURES
Figure Page
1 Molecular oxygen concentrat ion a t 45" l a t i t u d e derived from 5 U.S. Standard Atmosphere Supplement 1966. Fu l l l i n e ind ica t e s summer condi t ions; broken l i n e ind ica t e s win ter condi t ions .
2 Experimental p r o f i l e s of atomic oxygen and ozone concent ra t ions . 6 1. Daytime ozone concentrat ion by Johnson, e t a l . (1954); 2 . Daytime ozone concentrat ion by Rawcliffe, e t a l . (1963); 3. Nighttime ozone concentrat ion by Carver, e t a l . (1966); 4. Nighttime ozone concentrat ion by Reed (1968); 5. Nighttime ozone concentrat ion by Mikirov (1965) and 6 . Atomic oxygen night t ime concentrat ion by Fedynskii , e t a l . (1967).
-- -- --
-- 3a
3b
4
5
6
7
8
9
10
02 absorpt ion cross sec t ions as a func t ion of r a d i a t i o n wave- length (see Appendix f o r r e fe rences ) .
Ozone absorpt ion c ross sec t ions as a func t ion of r a d i a t i o n wavelength ( s e e Appendix f o r re ferences) . Solar f l u x r a d i a t i o n as a func t ion of wavelength (see Appendix f o r r e fe rences ) .
Theore t ica l p r o f i l e s of noon atomic oxygen and ozone concen- t r a t i o n a t 45' N. l i n e ind ica t e s win ter p r o f i l e s . f o r oxygen alone atmosphere.
Fu l l l i n e ind ica t e s summer p r o f i l e s ; broken These values were computed
Theore t ica l p r o f i l e s of midnight atomic oxygen and ozone concentrat ion a t 45" N . broken l i n e ind ica t e s win ter p r o f i l e s . computed f o r oxygen alone atmosphere.
F u l l l i n e ind ica t e s summer p r o f i l e s ; These values were
Theore t ica l values of d iu rna l l a t i t u d i n a l and seasonal v a r i a t i o n of atomic oxygen and ozone f o r an oxygen alone atmosphere (70 km).
Theoret ical values of d iu rna l l a t i t u d i n a l and seasonal v a r i a t i o n of atomic oxygen and ozone f o r an oxygen alone atmosphere (80 km).
Theore t ica l values of d iu rna l l a t i t u d i n a l and seasonal v a r i a t i o n of atomic oxygen and ozone f o r an oxygen alone atmosphere (90 km).
Nitr ic oxide concentrat ion as a func t ion of he ight by Mitra (1968) and Pearce (1968).
8
8
9
1 2
13
15
16
17
19
Figure
11
1 2
13
14
15
16
17
18
19
20
2 1
Absorption coe f f i c i en t of molecular oxygen i n the far u l t r a - v i o l e t (Watanabe, -- e t a l . , 1953).
Daytime D-region rates of ion iza t ion due t o d i f f e r e n t sources. 1 i s t h e ion-pa i r production by La r ad ia t ion on NO concentra- t i o n given by Mitra (1968). 2 i s ion iza t ion of NO with Pearce (1968) d i s t r i b u t i o n , 3 i s x-ray ion-pair production from Ohshio, e t a l . (1966) and Hinterreger, -- e t a l . (1965). 4 and 5 are rates of ion iza t ion o f 02(lAg) given by Hunten and McElroy (1968).
--
Solar x-ray emission f o r various s o l a r conditions. The curves drawn are based on measurements i n th ree wavelength bands, as ind ica ted by t h e heavy ba r segments. The s lopes of t h e ba r segments a re t h e s lopes of t h e assumed x-ray emission funct ions used t o reduce t h e photometer responses t o t h e p lo t t ed energy f luxes. The energy f luxes refer t o values observed a t t he e a r t h ' s d i s tance above the atmosphere (from H. Friedman, 1963).
The concentrations of 02(lAg) above 70 km, from t h e dayglow measurement of Evans, e t a l . (1968). The smooth vers ion shown dashed was used f o r t h e ca lcu la t ions i n t h i s paper.
--
Flux measurements of pyec ip i ta t ing energe t ic p a r t i c l e s .
1 Rate of ion iza t ion computed from O'Brien, -- e t a l . (1965) measured e l ec t ron f luxes and estimated spectrum. Tulinov, -- e t a l . (1968) r a t e of ion iza t ion from p rec ip i t a t ed e lec t rons .
2
Comparison of experimental and theo re t i ca l e lec t ron dens i t i e s i n the nighttime D region.
Comparison of daytime e l ec t ron dens i t i e s . Experimental by Mechtly and Smith (1968b); t h e o r e t i c a l from Equations (58) and (66) and NO concentration by Pearce (1968).
Comparison of daytime e l ec t ron dens i t i e s . Experimental by Mechtly and Smith (1968b) ; t h e o r e t i c a l from Equations (58) and (69) and NO concentration by Pearce (1968).
Comparison of daytime e lec t ron dens i t i e s . Experimental by Mechtly and Smith (1968b) ; t h e o r e t i c a l from Equations (58) and (71) and NO concentration by Pearce (1968).
Comparison of e f f e c t i v e attachment values. Computed from experimental d a t a of Mechtly and Smith (1968b) and Pearce (1968) and from Equations (69) and (71).
v i i
Page
27
29
30
32
35
36
37
49
50
52
53
viii
LIST OF TABLES
Tab le Page
1 Reaction rate coefficients f o r oxygen including Kaufman's 10 adopted values
2 Reaction rate coefficients for the oxides of nitrogen 21
3 Reaction rate coefficients for hydrogen and hydrogeneous 24 compounds
4 Absorption and ionization coefficients for 0 2 and N2 33 in the X-ray region
1
1. D-REGION NEGATIVE-ION CHEMISTRY
1.1 Introduct ion
Electron-densi ty d i s t r i b u t i o n is, a t t h i s t ime, t h e b e s t known parameter
i n t h e D region.
be deduced (Mechtly and Smith 1968a,b; Mechtly and Shirke 1968). Unlike t h e
upper ion ized regions, D-region s t r u c t u r e i s charac te r ized by t h e attachment
From recent work, a general p i c t u r e of t h i s parameter can
of e l ec t rons t o n e u t r a l molecules t o form, through complex chemistry, a l a rge
number of negat ive ions of va r i ab le d i s t r i b u t i o n and mass.
is the re fo re s t rong ly con t ro l l ed by t h e negat ive- ion chemistry. This , i n
t u rn , i s determined by t h e rates of r eac t ions t h a t produce o r e l imina te d i f -
Electron dens i ty
f e r e n t spec ies of nega t ive ions .
f i c i e n t s now q u i t e well e s t ab l i shed by labora tory measurements (Fehsenfeld
I- e t a l , 1967; Fehsenfeld and Fergiison, 1968) and upon t h e concentrat ion of
n e u t r a l spec ies such as O , O and NO.
odd a l l o t r o p e s of oxygen is very l imi ted , and t h e o r e t i c a l computations depend
upon seve ra l f a c t o r s s t i l l doubtful . Recent d i r e c t estimates of NO concen-
t r a t i o n (Barth 1966; Pearce 1968) show much l a r g e r values than those obtained
with i n d i r e c t ionospheric methods based upon e lec t ron-dens i ty da t a and ion-
Reaction rates depend upon t h e r a t e coef-
The experimental knowledge about t h e 3
reac t ion schemes widely accepted at t h i s time.
da t a f o r t h e NO concentrat ion w i l l fo rce a re-evaluat ion of t h e negat ive- ion
chemistry, i n a search f o r missing r eac t ions , i n order t o r e c o n c i l i a t e those
da t a and d i r e c t measurements of e l e c t r o n dens i ty .
To accept t h e experimental
The first chapter o f t h i s repor t w i l l review t h e n e u t r a l composition
of t h e mesosphere, where D-region ion ized spec ies are very minor cons t i t uen t s .
Nitrogen oxides and oxygen a l lo t ropes d i s t r i b u t i o n s w i l l b e discussed i n
more d e t a i l .
2
The second chapter w i l l be devoted t o a review of t h e sources of i o n i -
za t ion i n t h e undisturbed D region f o r both daytime and night t ime.
impact of high values of NO concentrat ions (Pearce, 1968) i n r e l a t i o n t o t h e
ion iza t ion of n i t r i c oxide by Lyman-alpha r ad ia t ion w i l l be descr ibed.
importance of p r e c i p i t a t i o n of e l ec t rons , as a source of i on iza t ion during
night t ime w i l l be considered.
The
The
I n t h e t h i r d chapter , t h e negat ive- ion chemistry w i l l be discussed. An
is defined, t h i s being t h e only term i n 'eff "ef fec t ive at t achment fact or"
t h e con t inu i ty equation f o r e l ec t rons and ions t h a t depends upon t h e negat ive-
ion schemes.
mental e lec t ron-dens i ty p r o f i l e s , ca l cu la t ed rate of i on iza t ion and labora tory
de ioniza t ion da ta .
w i l l become evident during t h e d iscuss ion . I t w i l l b e shown t h a t i n order
t o obta in t h e o r e t i c a l l y t h e experimental B e f f a new fast b inary attachment process
should be pos tu l a t ed when NO concentrat ion measurements are used.
Assuming s teady state condi t ions, Beff i s computed from experi-
The problem introduced by d i f f e r e n t values of NO concentrat ion
3
2. NEUTRAL COMPOSITION OF THE MESOSPHERE
2 . 1 In t roduct ion
The atmospheric region between roughly 50 and 90 km, c a l l e d t h e meso-
sphere, i s chemically very ac t ive . Photodissociat ion produces atomic spec ies
t h a t , i n a r e l a t i v e l y dense medium, can r eac t r ap id ly with o the r cons t i t uen t s
forming a la rge number of more o r l e s s s t a b l e minor spec ie s .
o f s o l a r u l t r a v i o l e t r ad ia t ion by ozone a t wavelengths of 2100-3000 i s a
s t rong source of hea t ing . The e f f e c t of t h i s is t h e l a rge temperature observed
around 50 km.
80-90 km.
of the mesosphere because many r eac t ion r a t e c o e f f i c i e n t s a re s t rong ly tem-
pera ture dependent.
The absorpt ion
A decrease i n temperature i s observed above t h a t he ight up t o
This a l t i t u d e gradient of temperature i s important t o t h e chemistry
In t h e region of 50 t o 90 km t h e r e a re a number of three-body reac t ions
among both n e u t r a l and i o n i c spec ie s . The passive t h i r d body is represented
i n most cases by t h e general atmospheric molecule, i . e . , t h e concentrat ion
of t he t h i r d body involved i s t h e atmospheric number dens i ty i t s e l f .
Both t h e COSPAR In te rna t iona l Reference Atmosphere (1965) and t h e U.S.
Standard Atmosphere Supplement (1966) give experimental models of t h e n e u t r a l
gas d e n s i t i e s , temperature, and o the r parameters as a funct ion of he ight ,
season and l a t i t u d e . Below approximately 80 km a constant mean molecular mass
o r , what is equiva len t , a constant mixing r a t i o can be assumed for t h e major
cons t i t uen t s .
l e a s t known experimentally, and cons t i tuent d i s t r i b u t i o n is s t i l l uncer ta in .
Variat ions of 0 d i s t r i b u t i o n a r e very important because d i s soc ia t ion of
molecular oxygen cont ro ls t h e chemistry of t h e odd a l lo t ropes of oxygen and
The n e u t r a l atmospheric region between 80 and 120 km is t h e
2
4
a l so some aspects of t h e ion chemistry. Figure 1 shows t h e concentration
o f 0
t h e U. S. Standard Atmosphere Supplement (1966) . from winter and summer a t 45' l a t i t u d e and low s o l a r a c t i v i t y from 2
A s a product of t h e chemical a c t i v i t y o f t h e mesosphere, numerous neu t r a l
species a re present i n t h a t region.
by severa l orders of magnitude of O2 o r N
cons t i tuents . Photodissociation of 02,
t he formation o f :
Most of them have concentrations smaller
Such species a re c a l l e d minor
H 0 and CH is t h e first s t e p i n
2'
N2' 2 4
0 , 0 3 , NO, NOZ, N 0 , H, OH, HO H 0, e t c . Other minor 2 2 ' 2
cons t i tuents i n the mesosphere could be c l u s t e r s of neu t r a l
(H20).N0 could be produced i n t h e region of low temperature
Also chemically important i s C02.
A t t h i s t ime, a l l t h e species mentioned above, t h e odd
molecules l i k e
around 80 km.
a l lo t ropes of oxygen
and the oxides of n i t rogen are considered t h e most important ones t o t h e
negative-ion chemistry. Hydrogenous compounds appear t o be o f i n d i r e c t importance
because they represent only per turba t ions introduced i n t h e chemistry o f oxygen.
The r o l e played by n e u t r a l c l u s t e r s is unknown.
2 . 2 Odd Allotropes of Oxygen
The experimental knowledge about 0 and 0 d i s t r i b u t i o n at D-region a l t i t u d e s 3
is very l imi ted . Only one nighttime preliminary p r o f i l e o f mesospheric
oxygen concentration has been published (Fedynskii -- e t a l , 1967) . ozone measurements have been ca r r i ed out by Johnson e t a l , (1954) and by
Rawcliffe -- e t a l , (1963). Nighttime p r o f i l e s have been obtained by Carver
-- e t a l . (1966), Mikirov (1965) and Reed (1968). Figure 2 summarizes these
experimental r e s u l t s .
Daytime
-e
Theoret ical computations o f 0 and O3 d i s t r i b u t i o n a re based upon t h e
knowledge about: f luxes of t he s o l a r rad ia t ion capable o f photodissociat ing
5
ti
dw
Q
Ta
t
-w
z
x
e I
I 1
I I
I I
I I
I I
0
-
0
-
0
CU _D
-
__I
6
n
h
L'
7
O2 and 03, d i s soc ia t ion cross sec t ions as a function of t h e r ad ia t ion wave-
length, and r a t e s o f t h e chemical reac t ions involved. The l a t t e r represents
t h e l e s s known f a c t o r .
The b a s i c photochemical reac t ions of atmospheric oxygen are :
(1) j 2 0 + hv + 0 + 0 (1375 < A < 2424i) 2
j 3 O3 + hv -t 0 + O2 (1375 < A < 7500)
kg O + O + M + 0 2 + M
O + 0 2 + M -f k4 0 3 + M
% 0 + 0 3 + O 2 4. O2
(4)
(5)
Cross sec t ions and f luxes of r ad ia t ion involved i n reac t ions (1) and (2)
a re shown i n Figures 3 and 4.
The d i v e r s i t y o f published laboratory values f o r t h e r a t e coe f f i c i en t s
of (3), (4) and (5) i s very wide. I t r e f l e c t s t h e complications introduced
i n the experimental determinations by t h e e f f e c t o f hydrogenous and n i t r o -
genous t r a c e impur i t ies and the formation of metastable species (Schofield,
1967).
A recent discussion of experimental s tud ies of reac t ions (3) , (4) and
(5) has been given by Kaufman (1967). This author adopts f o r t h e range - - (2.6 - + 0.4) -33 T
(XRi) between 190 and 400°K, t h e value of k3 = 3.0 x 10
obtained by combining severa l da t a when M E N 2 . Also k5 = (1.4 - + 0.3) x - (3.0 + 0.4)
exp RT is adopted by t h e same author . I t m u s t be noted
t h a t some discrepancies among d i f f e r e n t experimental s tud ie s of t hese reac t ions
s t i l l e x i s t s . Table 1 shows t h e individual r e s u l t s o f some o f t hese s tud ie s
8
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L L =0
EjN’ u “p: --
c)
0 t 5 -I
0 3
?J,
WRVELENGTH IRNGSTROMSJ I X I O 1 I
I I I I
Figure 3a. O2 absorption cross sections as a function of radiation wavelength (see Appendix for references).
Figure 3b. Ozone absorption cross sections as a function of radiation wavelength (see Appendix for references).
9
0 0
Figure 4. Solar flux radiation as a function of wavelength (see Appendix for references) .
10
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11
f o r t h e range of atmospheric temperatures, t oge the r with t h e da t a adopted by
Kaufman (1967).
Theore t ica l models of 0 and 0 have been ca lcu la ted by seve ra l au thors .
Some of them considered a photochemical reac t ion scheme based upon an oxygen
alone atmosphere as represented by reac t ions (1) and (5) , (Craig, 1950; Hunt,
1966a; London, 1967; Maeda and Aikin, 1968). However, some of t hese authors
a re mainly concerned with s t r a t o s p h e r i c ozone.
r a t e c o e f f i c i e n t s used i n the above-mentioned s t u d i e s a re notably d i f f e r e n t
from the values adopted by Kaufman (1967) using a l l experimental da ta ava i l -
able a t t h i s t i m e .
3
It must be noted t h a t t h e
Models of 0 and 0 t h a t take i n t o account reac t ions of hydrogenous com- 3
pounds i n t h e chemical scheme have been published by Hampson (1965) and
Hunt (1966b). However, they have used reac t ion r a t e coe f f i c i en t s t h a t d i f f e r
sens ib ly from t h e ones t h a t a re considered co r rec t a t t h i s t ime. O f p a r t i -
c u l a r importance, besides t h e b a s i c oxygen reac t ions r a t e s a l ready discussed,
i s t h e r a t e c o e f f i c i e n t of r eac t ion :
- 1 2 3 -1 Hunt (1966a) assumed a value of k6 - 10 (cm s e c ) . A more r e a l i s t i c
one appears t o be : k = 5 x 10-l ' as deduced from McGrath and McGarvey (1967). 6
A more soph i s t i ca t ed approach is t o consider an oxygen-hydrogen atmo-
sphere including a l s o t h e dynamics terms. Konashenok (1967) and Hess tvedt
(1968) introduced v e r t i c a l eddy t r anspor t i n t h e i r ca lcu la t ions e From t h e
work of t hese authors it is c l e a r t h a t t h e dynamical terms can change t h e
v e r t i c a l and geographic d i s t r i b u t i o n of atomic oxygen and ozone. I t must be
12
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noted however t h a t t h e r eac t ion r a t e c o e f f i c i e n t s of r eac t ions (3) and (5) adopted
i n a l l t h e s t u d i e s mentioned above, d i f f e r notably from t h e Kaufman (1967)
values which, at t h i s time, should be considered more r ep resen ta t ive .
I t is convenient t o compute t h e temporal and s p a t i a l v a r i a t i o n s of 0
and O 3 based on t h e Kaufman r a t e c o e f f i c i e n t s f o r t h e reac t ions (3) and
(5) and a l s o on recent values of s o l a r f luxes.
model and a function of time and l a t i t u d e is obtained.
a second s t e p , by in t roducing hydrogenous compound reac t ions and dynamical terms.
Time v a r i a t i o n s as a function of he igh t , l a t i t u d e and season a re computed
by so lv ing t h e con t inu i ty equations i n t h e d i f f e r e n t i a l forms:
In t h i s way a b a s i c photochemical
I t can be changed as
The computer programs used and t h e input values of cross sec t ions , s o l a r
r a d i a t i o n f luxes , atmospheric temperature, and d e n s i t i e s adopted i n t h e
ca l cu la t ions a re given i n t h e Appendix.
da t a (atomic oxygen and ozone concentrations) a r e a l s o given t h e r e . Figures
5 and 6 show t h e computed 0 and 0
and winter, and noon and midnight. Figures 7, 8 and 9 show t h e l a t i t u d i n a l
v a r i a t i o n of atomic oxygen and ozone concentrations a t 70, 80 and 90 km. A
f u l l discussion o f t h e s e d a t a w i l l be given elsewhere.
Detailed t abu la t ion of t h e output
p r o f i l e s f o r 45' of l a t i t u d e no r th , summer 3
15
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18
2.3 Nitrogen Oxides
Minor cons i tu t en t s o f grea t importance t o t h e chemical aeronomy and,
i n p a r t i c u l a r , t o t h e D-region ion iza t ion are n i t r i c oxide and, i n a minor
s c a l e , n i t rogen dioxide.
region as considered by Nicolet and Aikin (1960). Thei r paper represents one of
t h e f irst attempts t o expla in t h e o r e t i c a l l y what was known a t t h e end o f t h e
f i f t i e s about t h e D region.
t he b a s i c process of formation during low s o l a r a c t i v i t y was t h e ion iza t ion
of NO by Lyman-alpha s o l a r r ad ia t ion with a production peak between 75 and
80 km. Un t i l 1964 no d i r e c t experimental da t a on t h e n i t r i c oxide d i s t r i -
but ion were published.
t h e i n d i r e c t ionospheric estimates as t h e ones obtained by Mitra (1966) and
Wagner (1966) f o r D-region he igh t s . A f i n a l model deduced using t h e same
methods has been published r ecen t ly by Mitra (1968).
NO i s t h e re levant spec ie t o t h e chemistry of t h e D
These authors introduced t h e hypothesis t h a t
The only methods used t o der ive NO concentrat ion were
H i s NO d i s t r i b u t i o n is
expressed by:
[NO] = 4 x
Figure 10 shows Mitra's
Direct photometric
(1968) d i s t r i b u t i o n of NO.
measurements of t h e NO airglow were made by Barth
(1964, 1966) from Wallops I s land during low s o l a r a c t i v i t y . The d a t a obtained
from a rocket f l i g h t i n November 1963 shows an NO concentrat ion of 6.2 x 10 7
-3 7 cm a t 75 km and 6.0 x 10 a t 95 km. These values are much h igher than t h e
ones deduced by i n d i r e c t ionospheric methods. For some time t h e Barth (1966)
values were considered doubtful , bu t a recent rocke t photometric experiment
by Pearce (1968) again shows very high values o f n i t r i c oxide concentrat ion
a t a l l he igh t s i n t h e mesosphere. H i s values are a l s o p l o t t e d i n Figure 10.
19
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The more comprehensive t h e o r e t i c a l s tudy o f t h e NO d i s t r i b u t i o n has
been publ ished by Nicole t (1965a,b). This author shows t h e importance
of atomic oxygen and ozone as r eac t an t s i n t h e chemistry of t h e oxides of
n i t rogen i n t h e atmosphere. He shows a l s o t h a t i n order t o c o n c i l i a t e t h e
values given by Barth (1964) it was necessary t o introduce i o n i c r eac t ions
i n the chemical scheme.
Nitrogen dioxide d i s t r i b u t i o n i n t h e atmosphere have not been determined
experimentally. However i t s chemistry i s s t rongly r e l a t e d t o t h a t o f n i t r i c
oxide.
The b a s i c r eac t ion scheme o f t h e oxides of n i t rogen appears t o be
(Nicolet , 1965a,b) as follows :
1 N, + hv -+ N2(a ng) (1200 < A < 1250) L
N + O3
N + O + M
N + O2
NO + hv
N + NO
NO + O3
NO + hv
ql' NO + O2
-+ N O + M k12
NO i- 0
j 15 -+ O + N 2
Rate c o e f f i c i e n t s f o r t hese reac t ions are given i n Table 2 .
21
TABLE 2
Reaction ra te coef f ic ien ts f o r the oxides of ni t rogen
Re ac t ion Reaction Rate Coeff ic ient Source
kll N + O3 -+ NO + O2
5 2 N + O + M - + N O + M
N + O2 :l3 NO + 0
k15 N + N O + O + N 2
k16 NO + O3 -+ NO2 + O2
5.7 1 0 - l ~
- 0.5 + 0.2 -33 T - 1.1 x 10 (m)
(1.4 + 0.2) x -
1 7100 +- 400 eq - ( RT
(2.2 + 0.6) x -
1 2450 2 150 9.5 1 0 - ~ ~ ~ ~ ~ - ( RT
Ph i l l i p s and Schiff (1962)
Kaufman (1968)
Clyne and Thrush (1961)
Ph i l l i p s and Schiff (1962)
Clyne e t a l . (1964) --
R = 1.987 K cal ( O K mole)
22
Mesospheric d i s t r i b u t i o n of NO obtained by using t h e above-mentioned
r ad ia t ion scheme give values much lower than t h e experimental da t a obtained
by Barth (1966) and Pearce (1968). A poss ib l e way o f explaining high values
of NO concentrat ion around 80 km is by tak ing i n t o account v e r t i c a l downward
motions of NO from t h e lower thermosphere as discussed recent ly by Geisler
and Dickinson (1968). Large amounts of n i t r i c oxide can be produced below
120 km by t h e ion-molecule reac t ion :
:l8 NO+ + NO + O 2 + N2
as shown by Ryan (1968).
2.4 Hydrogenous Compounds
The b a s i c hydrogenous compound i n t h e atmosphere below 90 km is water
vapor. The only experimental d a t a ava i l ab le on t h e concentrat ion of water
vapor a re t h e da t a by Fedynskii -c e t a l . (1967) which show very l a rge values
i n t h e mesosphere up t o an a l t i t u d e of approximat.ely 85 km.
d i s soc ia t ed by s o l a r r a d i a t i o n of wavelength less than 2400i:
Water vapor is
j 19 H O + h v + O H + H 2
Both atomic hydrogen and hydroxyl a re chemically very a c t i v e and are capable
of undergoing a very complex series of r eac t ions with atomic oxygen and ozone.
The problem o f t h e presence and d i s t r i b u t i o n of hydrogenous compounds i n t h e
mesosphere and s t r a tosphe re has been s tud ied i n d e t a i l by ~Hess tvedt (1964, 1965,
1968). The chemistry of water vapor i s c lose ly r e l a t e d t o t h e chemistry of
oxygen. For example, t h e r eac t ion :
23
H + O3 t 2 0 OH + o2
is capable of reducing t h e concentrat ion of ozone i n t h e mesosphere as
ind ica ted o r i g i n a l l y by Nicolet (1964) and shown by Hunt (1966b).
Other b a s i c r eac t ions of hydrogen and hydrogenous compounds are:
O H + O + k2 1 H + 0 2
H + O + M + k2 2 H 0 2 + M 2
H02 + 0 q2' OH + O 2
HO + hv t24 OH + 0 2
k25 H02 + 0 -f OH + 2 o2 3 (25)
Table 3 gives t h e rate c o e f f i c i e n t s of t h e s e r eac t ions . Hydrogen peroxide
i s an add i t iona l compound t h a t could be present i n t h e mesosphere but i n very
small concentrat ion. I t s presence gives r ise t o a l a rge number of secondary
r eac t ions .
Hesstvedt (1968). I n t h e same paper, t h e o r e t i c a l models of hydrogen and hydro-
A very d e t a i l e d chemical scheme has been given r ecen t ly by
genous compounds, d i s t r i b u t i o n s a r e shown. A s a comment t o these models , i t
should be noted t h a t when dynamical v e r t i c a l t r anspor t i s taken i n t o account,
the dominant hydrogenous cons t i t uen t i s water vapor up t o a he igh t o f about
85 km. This fact i n d i c a t e s t h a t H and OH (both very a c t i v e and important
f o r t h e oxygen chemistry) are less abundant than expected, reducing t h e i r
e f f e c t on t h e d i s t r i b u t i o n of o the r spec ie s .
24
TABLE 3
Reaction ra te c o e f f i c i e n t s f o r hydrogen and hydrogeneous compounds
R e act i on
k20 H + O3 -f OH + O2
O H + O t 2 1 H + 0 2
Reaction Rate Coeff ic ien t Source
(2.6 i 0.5) x -
(5 - + 2) x 10-l1
-32 273 1 .3 3 x 1 0 (+ k22 H + 0 + M + H02 + ' M 2
k 2 3 H02 + 0 + OH + O2
k25 H02 + 0 -+ OH + 202 3
- > 10-11
% 1 0 - l ~ (est imate)
P h i l l i p s and S c h i f f (1962)
Kaufman (1968)
Schofield (1967)
Kaufman (1964)
25
2 . 5 Carbon Dioxide
The importance of carbon dioxide i n t h e hea t balance of t h e region below
90 km has been recognized f o r a long time
study of t h e photochemistry of t h e atmospheric C02, Bates and Witherspoon
(1952) deduced t h a t carbon dioxide should be i n constant mixing r a t i o up t o
(Gowan 1947a,b). I n t h e i r
100 km, approximately.
sphere has been given by Craig (1965).
have been made o f t h e d i s t r i b u t i o n v a r i a t i o n s t h a t can be expected. Also,
no d i r e c t measurements of t h i s cons t i t uen t above t h e troposphere are ava i l -
ab le a t t h i s time.
A recent discussion of t h e r o l e of C02 i n t h e meso-
However, no d e t a i l e d ca l cu la t ions
The photochemistry of CO can be expressed b a s i c a l l y by t h e r eac t ions : 2
c02 + hv 127 CO + 0 (X<16908\) (27)
k2 8 CO + 0 + M - t C02 + M
Carbon dioxide absorpt ion cross sec t ions are smal le r by an order of magnitude
with respec t t o t h e equivalent molecular oxygen cross sec t ions . The rate
c o e f f i c i e n t k2* is s t i l l doubtful , (Kaufman, 1968) but i s considered very
slow. A t 293'K Clyne and Thrush (1962) found K2* < 8 x
In summary, it can be s a i d t h a t t h e chemistry o f atmospheric carbon
oxides i s a t t h i s time p r a c t i c a l l y unknown.
26
3. RATES OF IONIZATION
3 .1 Introduct ion
Several sources of i on iza t ion can ac t i n t h e atmosphere below 90 km.
The most important one i s considered t o be , a t t h i s time, s o l a r Lyman-alpha
r ad ia t ion ion iz ing n i t r i c oxide. However, t h e u n c e r t a i n t i e s about t h e meso-
sphe r i c concentrat ion of t h i s cons t i t uen t which were mentioned i n t h e last
chapter , make d i f f i c u l t a co r rec t estimate of t h e r e l a t i v e importance of Lyman-
alpha and o t h e r r a d i a t i o n i n t h e ion iza t ion of t h e D region.
and u l t r a v i o l e t r a d i a t i o n of 1027-1118A wavelengths between 85 and 90 km, and
S o l a r X-rays 0
cosmic rays below 70 km, are capable of i on iz ing t h e atmospheric gas. A t n igh t ,
s c a t t e r e d Lyman-alpha r a d i a t i o n and p r e c i p i t a t e d e l ec t rons could be e f f e c t i v e
sources o f i on iza t ion between 70 and 90 km.
3.2 Ion iza t ion by So la r Lyman-Alpha
A very i n t e n s e r ad ia t ion is emit ted from t h e sun a t a wavelength o f
1215.7;. I ts photon f l u x i s equal , f o r average low s o l a r a c t i v i t y , t o 2.7
-1 - 2 -1 photons cm-2 sec equiva len t t o 6 e rg c m sec . The hydrogen Lyman-alpha
l i n e o r i g i n a t e s i n t h e absorbing region between t h e photosphere and t h e
chromosphere.
through t h e r a d i a t i v e recombination with e l ec t rons . Lyman-alpha r a d i a t i o n
is mostly absorbed by 0 and an i n t e r e s t i n g fact i s t h a t one of t h e absorp-
t i o n "windows" of molecular oxygen atmosphere corresponds t o t h e same
The k i n e t i c energy of s o l a r protons i n t h a t region is l o s t
2
wavelength as shown i n Figure 11. The corresponding absorption cross sec t ion
is
as
by
20 2 o ' = 1.04 x 10 c m 02
low as 65-70 km. The
t h i s r a d i a t i o n , below
(Watanabe, 1958), Lyman-alpha r ad ia t ion can pene t r a t e
only atmospheric cons t i t uen t t h a t can be ion ized
90 km, i s n i t r i c oxide, and it becomes a s t rong
27
30
Firgure 11. Absorption coefficient of molecular oxygen in the far ultra- violet (Watanabe, et al., 1953).
28
source of i on iza t ion i n t h e D region. NO i on iza t ion cross sec t ion is
= 2 x cm2 (Watanabe, 1954). With cross sec t ion and f l u x da ta it
is poss ib le t o compute t h e ra te of NO i on iza t ion by Lyman-alpha.
done by using t h e expression:
This i s
qLa(h) = IS' [NO] exp(- s e c x IS 1; d[021 d h) O2
NO
where q
concentrat ion, and x is t h e s o l a r zen i th angle .
Chapman funct ion f o r angles g r e a t e r than 80".
i nd ica t e s t h e ra te of i on iza t ion , h t h e a l t i t u d e , b racke ts i nd ica t e La
Sec x i s s u b s t i t u t e d by t h e
By using Mitra (1968) and Pearce (1968) n i t r i c oxide d i s t r i b u t i o n s
shown i n Figure 3, d i f f e r e n t rates are computed and are drawn i n Figure 1 2 .
The Pearce da ta r e s u l t s i n a very la rge ra te o f i on iza t ion which overdraw t h e
e f f e c t s of X-rays and i n p a r t , o f cosmic rays as e f f e c t i v e sources of i on iza t ion
as w i l l be seen below.
3.3 Ioniza t ion by X-Rays
Quasi-thermal X-ray emissions of wavelength < l O O i o r ig ina t e s i n t h e
corona of t h e sun. This r ad ia t ion is h ighly va r i ab le as is shown i n Figure
13, reproduced from de J a g e r (1967). 0
Sola r X-rays of wavelength between 1 and 40A can pene t r a t e i n t h e D
region down t o an a l t i t u d e of 50 km, ion iz ing a l l t h e cons t i t uen t s of t h e
mesosphere. However, t h e low photon f luxes ava i l ab le during low s o l a r
a c t i v i t y are not capable o f producing important i on iza t ion below 85 km.
Under such condi t ions t h e X-ray cont r ibu t ion t o t h e formation o f t h e D
region i s l imi t ed t o i t s upper p a r t . During s o l a r f l a r e s when t h e X-ray
f luxes inc rease by seve ra l orders o f magnitude, t h i s r ad ia t ion increases
g r e a t l y t h e ion iza t ion o f a l l t h e D reg ion .
29
0
6,
I\- -
30
0
-1
-2
-3
-4
-5 I- / 5 10 2 0 50 100
W A V E L E N G T H ( A )
Figure 13. S o l a r x-ray emission f o r various s o l a r condi t ions. The curves drawn are based on measurements i n th ree wavelength bands, as ind ica t ed by t h e heavy b a r segments. o f t h e assumed x-ray emission funct ions used t o reduce t h e photometer responses t o t h e p l o t t e d energy f luxes . values observed a t t he e a r t h ' s d i s tance above t h e atmosphere (from H. Friedman, 1963).
The slopes of t h e b a r segments a r e t h e s lopes
The energy f luxes refer t o
3 1
A summary of t h e absorpt ion and ion iza t ion cross sec t ions f o r X-rays
and 0 and N has been given by H i n t e r r e g e r e t -- a l . (1965) and are reproduced
i n Table 4, t oge the r with t h e i r estimates of photon f luxes f o r q u i e t condi-
t i o n s of low s o l a r a c t i v i t y .
t o X-rays of wavelength from 1 t o 401, can be computed by using t h e expression:
2 2
From t h e s e da t a t h e r a t e of i on iza t ion due
where i represents wavelength, j cons t i t uen t , and t h e o the r symbols have
been def ined above. Ohshio -- e t a l . (1966) using Hin ter reger -- e t a1 . (1965)
cross sec t ions , computed t h e ra te o f i on iza t ion produced by a u n i t photon
f l u x f o r a l l s o l a r r ad ia t ion . 0
They included t h e band from 1 t o 40A X-rays.
With t h e i r da t a and t h e f luxes of Table 4, t h e ra te of i on iza t ion f o r undis-
turbed low s o l a r a c t i v i t y a re a l s o shown i n Figure 7.
3.4 Ioniza t ion of Metastable Molecular Oxygen
Recently (Hunten and McElroy, '1968) it has been suggested t h a t a major
region could be t h e ion iza t ion of t h e source of i on iza t ion i n t h e upper D
metastable spec ies 0 ( Ag) by s o l a r
band 1027-1184A. Ioniza t ion of t h e
less energy than t h e non-excited 0
1 2
0
2
u l t r a v i o l e t r ad ia t ion on t h e wave length
metastable molecular oxygen r equ i r e s
1 Experimental measurements of 0 ( Ag) 2
shows t h a t i t s concentrat ion is la rge i n t h e mesosphere as i s shown i n Figure
1 4 , taken from Hunten and McElroy, (1968). The ra te of i on iza t ion obtained
by t h e same authors i s a l s o shown i n Figure 1 2 .
3.5 Ioniza t ion by Prec ip i t -a ted Electrons
I t i s known t h a t t h e aurora l e x c i t a t i o n and ion iza t ion i n t h e lower
ionosphere i s produced mostly by t h e p r e c i p i t a t i o n of ene rge t i c e l ec t rons
i n t h e atmosphere (Hul tqvis t , 1965 and references the re in ) . Electrons
32
n
E Y - 90 I- I c3 -
1 Figure 14. The concentrat ions of 02( Ag) above 70 km, from the dayglow measure- ment of Evans, e t a l . (1968). The smooth vers ion shown dashed was used f o r t he ca l cu la t ions i n t h i s paper .
--
33
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34
p r e c i p i t a t i n g i n t h e region of t h e South At l an t i c anomaly (Ghielmetti -- e t a l . ,
1965; Paulikas _.- e t a l . , 1966 and references the re in ) can be a s u b s t a n t i a l
source of i on iza t ion i n t h a t a rea , both a t n igh t and i n t h e day (Zmuda, 1966).
In J u l y 1964, O'Brien -- e t a l . (1965) measured f o r t he f irst time simul-
taneously, both t h e f lux o f p r e c i p i t a t i n g e l ec t rons (E - > 40 keV) and nightglow
emissions i n c uding t h e 39148, l i n e using rocket techniques. On t h a t occasion,
they recorded a f lux of 40 e l ec t ron cm-2 s e c - l .
-- e t a l . (1969) have measured d i r e c t l y t h e f lux of daytime and nighttime ene rge t i c
p a r t i c l e s with a system of Geiger counters aboard rocke ts . Values of p a r t i c l e s
f luxes as a function of l a t i t u d e obtained are shown i n Figure 15. The same
author computed t h e r a t e o f ion iza t ion t h a t i s drawn i n Figure 16. The f igu re
a l s o shows t h e rate of i on iza t ion computed by using O'Brien -- e t a l . (1965)
p a r t i c l e f l u x and assumed spectrum. This computation has been c a r r i e d out
by using t h e formulation of Lazarev (1967) which i s e s s e n t i a l l y t h e same as
developed by Rees (1963) bu t more adequate f o r a complete computation.
Tulinov (1967) and Tulinov
I t has been shown (Radicel la , 1968) t h a t nighttime ioniza t ion i n t h e
upper D region can be explained assuming ioniza t ion by e l ec t ron p r e c i p i t a t i o n .
H i s computations were based upon a chemical scheme t h a t w i l l be discussed
i n t h e next chapter and on the r a t e o f night t ime ioniza t ion given by
Ivanov-Kholodyny (1965). By using the same formulation given by Radicel la
(1968) and t h e r a t e of i on iza t ion obtained from O'Brien -- e t a l . (1965) da ta ,
t he e l ec t ron dens i ty shown i n Figure 1 7 is computed. The f igu re a l s o shows
an experimental p r o f i l e measured by Mechtly and Smith (1968a). I t can be
seen t h a t measured e l ec t ron p r e c i p i t a t i c n can produce a t n ight t h e necessary ion i -
zat ion i n t h e upper D region.
35
.. L (eart I I
Figure 15. Flux measurements of precipitating energetic particles.
36
pz
M
‘E
M
‘0
-
37
38
3.6 Ion iza t ion by Cosmic Rays
Almost f o r t y years ago Hulburt (1930) used Mi l l i kan ' s measurements t o
Nicolet compute ion iza t ion by cosmic r ad ia t ion i n t h e region below 60 km.
and Aikin (1960), i n t h e i r e a r l y theory of t h e D region, a t t r i b u t e d t h e
ion iza t ion of t h e lower p a r t of t h a t region t o g a l a c t i c cosmic r ays .
o f t h e r a t e of i on iza t ion produced by g a l a c t i c cosmic rays i s shown a l s o i n
Figure 7.
given by Arnold and Pierce (1963):
Values
The computed values were obtained by using t h e empir ical r e l a t i o n
(y = 1964)] q = 1.5 x 10 [MI COS 0 [ l - - 2 2 - 18 -4
where
- 3 -1 q = ion p a i r production (cm sec )
0 = geomagnetic l a t i t u d e
y = y e a r
[MI = n e u t r a l gas dens i ty .
39
4. NEGATIVE-ION CHEMISTRY I N THE D REGION
4 .1 Laboratory Measurements of Negative-Ion Reaction Rates
On t h e bas i s o f t h e known labora tory measurements of attachment r eac t ions
and mesospheric composition it appears t h a t t h e b a s i c process o f negat ive- ion
formation i n t h e D region i s :
with a r a t e coe f f i c i en t (Phelps, 1967) :
600 -29 300 - - k33 = 1 . 4 x 10 (7) e T .
Other three-body attachment reac t ions involving minor cons t i t uen t s a re
unimportant. React ion :
e + ~ + k34 o - + o * 3 (34)
i s very slow (Fehsenfeld and Ferguson, 1968) and as a r e s u l t , 0- is not
considered as an i n i t i a l negat ive ion of importance. I t should be considered
3 a l s o t h a t b inary attachment reac t ions involving heavy neu t r a l s l i k e NO
- 3 -1 could have ra te c o e f f i c i e n t s as high as c m sec .
Molecular oxygen negat ive ions are s h o r t l i ved because e l ec t rons can
be detached from them by c o l l i s i o n with atomic and exc i t ed spec ie s , and
because they can charge exchange with n e u t r a l molecular spec ies .
The only abundant atomic spec ies i n t h e D region is atomic oxygen which -
r e a c t s r ap id ly with 0 - 2 - - k35
O 2 3 + 0 + 0 + e (35)
40
- 10 where k = 3 x 10 (Fehsenfeld -- e t a l . , 1967). Also t h e exc i t ed spec ies
0 ( Ag) detaches e l ec t rons through:
34 1
2
- 1 k36 O2 + 0 2 ( Ag) -+ 2 O2 + e
-10 where k = 2 x 10 (E. E . Ferguson, 1968 p r i v a t e communication). 36
Recently, s eve ra l charge exchange reac t ions have been measured i n
the labora tory . In p a r t i c u l a r :
- k37 - +
2 o2 + o3 -t o3
- k38 - O2 + NO2 -+ NO2 + O2
(37)
(38)
- 10 -9 where k = 3 x 10
and Ferguson, 1968; Rutherford and Turner, 1967).
(Fehsenfeld -- e t a l . , 1967) and k38 = 1 x 10 (Fehsenfeld 37
The r eac t ion :
- k39 - O2 + NO -f NO2 + 0 (39)
suggested by Nicole t (1965b) has been found t o be slow i n labora tory measure-
ments, Ferguson (1967). A t t h i s time, r eac t ion (35) appears as t h e b a s i c
charge exchange f o r 0
70 km where it w i l l eventua l ly provide an e f f e c t i v e process i n formation
of NO2 .
- Reaction 36 could be important only a t n i g h t below 2 .
-
Poss ib le three-body r eac t ions leading t o t h e formation of heavy and
s t a b l e nega t ive ions should be inves t iga t ed i n t h e labora tory because of
t h e i r p o t e n t i a l importance a t D-region he igh t s . Experimental observat ions
o f negat ive ions s p e c t r a Narcisi (1968), f o r example, suggest t h e presence
o f heavy negat ive ions below 100 km.
41
- Negative ion 0 can exchange i ts charge with molecular spec ie s : 3
k40 - 2
- + co2 -+ cog + 0 O 3
- + o k41 -
N03 O 3 + NO -f
10 where k40 = 4 x 10-
Fehsenfeld -- e t a l . , (1967). Reaction (40) is always more e f f e c t i v e than
reac t ion (41) because t h e r a t i o [CO,]/[NO] is much l a r g e r than one below
and k41 = 1 x 10-l ' a t room temperature, as found by
90 km, a l s o i f
are accepted. -
NO3 i s a
can react with
(1967)
L
t h e l a rge values es t imated by Barth (1966) and Pearce (1968)
- s t a b l e negat ive ion . This i s not t h e case with CO which
atomic oxygen regenera t ing 0 2
3 -
as shown by Fehsenfeld -- e t a l . ,
- %2 - cog + 0 -+ o2 + co2
-11
Another poss ib l e reac t ion is :
where k42 = 8 x 10 .
- k43 - C 0 3 + NO -+ NO2 + C 0 2 143)
where kl l = 9 x
e f f e c t i v e than (43) i f :
(Fehsenfeld -- e t a l . , 1967). Reaction (42) is more
[NO1 - k43 [O] >> - [NO] 2 10-1 k42
I t can be s a i d s a f e l y t h a t above 55 km during daytime and above 70 km a t
n igh t , r eac t ion (42) i s t h e main charge exchange process o f CO -
How ever , 3 .
42
- t h e formation of O2
through r eac t ions (35) and (36), tend t o produce an excess of e l ec t rons
below 90 km during both daytime and night t ime, contrary t o t h e experimental
evidence. To avoid t h i s d i f f i c u l t y i n studying night t ime D region, Radicel la
(1968) pos tu l a t ed another fast charge exchange r eac t ion deal ing with a s t a b l e
negat ive ion , suggested o r i g i n a l l y by Whitten and Poppoff (1964) :
by (42) and t h e r ap id detachment t h a t takes p l ace
k44 - 03- + N 2 -+ NO2 + NO (44)
assuming k
s tudied t h i s r eac t ion i n t h e labora tory and found it t o be very slow (k
< 1 0 - l ~ cme3 s e c - l ) a t room temperature.
= 10 -13 - + '. However, F. C. Fehsenfeld (p r iva t e communication 1968) 44
44
I t must be not iced , however, t h a t t h e f i n a l i m p l i c i t equation used by
Radice l la (1968) i n order t o compute night t ime e lec t ron-dens i ty p r o f i l e s f o r
s t eady- s t a t e condi t ions (see h i s Appendix 2 , Equation A12) i s independent of
t h e p a r t i c u l a r reac t ion t h a t produces t h e s t a b l e negat ive ion .
i s formally i d e n t i c a l with. equation below.
That equation
F ina l processes t h a t involve e l ec t rons and s t a b l e negat ive ions i n t h e
D region are recombination and mutual n e u t r a l i z a t i o n . The r a t e c o e f f i c i e n t
f o r d i s s o c i a t i v e recombination:
+ k13 e + X Y -+ X + Y (45)
has been analyzed r ecen t ly by Biondi (1967).
A value of k45 = 7 x a t 200'K (D-region temperature) with a temperature +
dependence o f t h e type T - l appears t o ' b e reasonable, when XY : NO'.
43
The present experimental knowledge about t h e rate of mutual n e u t r a l i -
zat ion :
(46) k46 M- + XY+ -+ n e u t r a l s
is not very good. However, a r a t e c o e f f i c i e n t k = 4 x f o r atmospheric
ions has been measured by Hirsch e t a l . (1967) and t h i s value agrees with
the t h e o r e t i c a l es t imate of k = 5 x 10 by Baulknight and Bortner (1964).
46
-- -8
46
A summary of t h e rate c o e f f i c i e n t s of negat ive- ion reac t ions is given
i n Table 5 . In t h e above discussion, w e confined our a t t en t ion on a r a t h e r
reduced number of r eac t ions involving t h e major cons t i t uen t s and t h e minor
cons t i t uen t s of l a r g e r concentrat ion.
f i c i e n t s f o r t h e many negat ive- ion reac t ions involving t h e known minor
atmospheric cons i tuents including hydrogenous compounds. (DASA Reaction Rate
Handbook:
ion chemistry of t h e normal D region.
4 .2 General Schemes of D-Region Negative-Ion Chemistry
A simple inspect ion o f t h e r a t e coef-
1967) shows t h a t they a re of very l i t t l e importance i n the negat ive-
Let r eac t ion (33) be t h e i n i t i a l s t e p i n t h e formation of nega t ive
ions .
wr i t t en :
Time va r i a t ions of t h e i o n i c spec ies a t a given a l t i t u d e can be
dCel d t = cq + 6[O2-][P11 - B[e][MI2 - a,[e][XY']
dtM-l d t = y [O,-] [P,] - a i [XY+] [M-]
44
where b racke t s i n d i c a t e concentrat ions
are n e u t r a l molecules o r atoms, M is t h e atmospheric gas as a whole, N-
is t h e f i n a l molecular s t a b l e nega t ive ion , XY
p o s i t i v e ion , and cq is t h e ion p a i r porduction r a t e due t o t h e sum of a l l
poss ib l e sources o f i on iza t ion . a a 6, y , 6 a r e , r e spec t ive ly , rate e' i'
c o e f f i c i e n t s of recombination, mutual n e u t r a l i z a t i o n , attachment , charge
exchange and detachment. I t can be assumed a l s o t h a t :
e ind ica t e s e l e c t r o n , Ply P2""
+ is t h e general molecular
because t h e s t a b l e nega t ive ion w i l l be always more abundant than o the r -
When : 2 - intermediate nega t ive ions l i k e 0
is assumed, i . e . when s t eady- s t a t e condi t ions are considered, so lu t ions o f
Equations (47), (48) and (49) w i l l not be changed i f in te rmedia te charge
exchange r eac t ions take p lace . The s t eady- s t a t e so lu t ion of Equation (48)
gives :
By s u b s t i t u t i o n i n 47 t h e following equation is obtained:
45
where :
can be c a l l e d an "ef fec t ive atta,chment factor" .
Equation (SO), i t can be wr i t t en :
Taking i n t o account
Tnis system of equations can be solved i n terms of e and N- i f t h e ion-
p a i r function and coe f f i c i en t s a re known.
wr i t t en as follows:
An imp l i c i t equation i n Bef f i s
which i s formally equal t o Equation A12 of Radice l la (1968).
e lec t ron densi ty is known an i m p l i c i t equation i n B
If t h e
is: eff
Equations (47) t o (49) have been w r i t t e n considering only t h e detachment
process with a rate 6[Pl ] [02-]. If an addi t iona l process with a r a t e
1 6 ' [ P l ' ] [0, ] i s taken i n t o account, reac t ions (56) and (57) are formally
maintained, but now is :
46
Y [P21 B [MI - -
Bef 6[p1] + ~ ' [ P ~ T I + y[p2]
If t h e charge exchange with ra te y [P,] [02-] i s such t h a t :
Y [P21 >> 6 [P1l
Equation (23) reduces t o :
2 B e f f = BWI
Another p o s s i b i l i t y appears i f t h e charge exchange r eac t ion o r chain of
reac t ions i s no t capable o f producing a l a rge concentrat ion of s t a b l e nega t ive
ions . The e f f e c t w i l l be:
'eff <<
t h a t i s equiva len t , i n terms of e
t o :
(62)
sc t ron L m s i t y , t o reducing Equation (26)
A f i n a l case r e s u l t s i f an add i t iona l attachment process i s pos tu l a t ed with
1 a r a t e B [XI, where X i s an unknown cons t i t uen t , and such t h a t Equation (23)
becomes :
From t h e above d iscuss ion it i s clear t h a t each of t h e d i f f e r e n t forms o f
@eff ref lects a d i f f e r e n t negat ive- ion scheme. I t i s poss ib l e now t o analyze
47
t h e problem of t h e apparent cont rad ic t ions between daytime-measured e l ec t ron
d e n s i t i e s and NO concentrat ion. If measured NO concentrat ion (Pearce, 1968)
i s accepted toge the r with r eac t ions (33) (34), (35), (36), (37), (40), (41) ,
(42), (43), (45), and (46), which r ep resen t t h e most accepted s e t , and which
w i l l refer as the ”bas ic schemes”, t h e e f f e c t i v e attachment f a c t o r w i l l b e
wr i t t en as:
k43 [NO1
k43[NOl + k42[01 2 1 (65)
P I + 7 LO2( &)I k43[NOl ’eff =
+ LO3] k43[NOl + k42[01
As it i s mentioned before , during daytime, above 55-60 km, and at n igh t above
70-75 km:
Then :
where :
This case corresponds then t o t h e condi t ion given by Equation (63). The
e l ec t ron d i s t r i b u t i o n can be computed by using Equations (58) and (66) and
t h e ion -pa i r production ra te given i n Chapter 2 when Pearce (1968) NO
48
concentration i s adopted.
mental da t a and it can be seen t h a t below 85 - 90 km t h e e lec t ron densi ty is
much l a r g e r than expected on the bas i s of experimental evidence (Mechtly and
Smith, 1968b).
The r e s u l t i s shown i n Figure 18 toge ther with experi-
By using t h e b a s i c sequence p lus an addi t iona l f a s t charge exchange
of the type given by Radicel la (1968):
k36 0- + x -f x- + o3 3
where :
The e f f e c t i v e attachment f a c t o r w i l l be:
which is equivalent t o Equation (60). Again by using (58) and (69) t h e e l ec t ron
densi ty is computed and it ' is shown i n Figure 19. Once more, t h i s t h e o r e t i c a l
computation shows a l a r g e r e l ec t ron densi ty than what expected experimentally.
This is a l s o t h e case i f a f a s t charge exchange reac t ion of t he type:
- + x + k70 x - + 0 2 O2
such t h a t :
is accepted. The e f f e c t i v e attachment f a c t o r reduces then t o :
49
8
h
s E 80 W
Q, 0 3
.b-
e .- - Q
70
60 IO’ IO3
Figure 18. Comparison of daytime electron densities. Experimental by Mechtly and Smith (1968b); theoretical from Equations (58) and (66) and NO concentration by Pearce (1968).
50
n
E Y
a 0 3
Y
c 4- .- - a
90
80
70
60 I
IO lo3
lectron Density ( C
Figure 19. Comparison of daytime electron densities. Experimental by Mechtly and Smith (1968b); theoretical from Equations (58) and (69) and NO concentration by Pearce (1968).
51
which is formally equal t o Equation (61). The computed electron densi ty f o r
t h i s case is shown i n Figure 20 ,and again no agreement is reached with the
experiment a1 da ta .
The only p o s s i b i l i t y l e f t i n order t o obtain an agreement between t h e
experimental e lec t ron densi ty and the measured NO concentration is t o search
f o r new attachment react ions f a s t e r than the attachment t o O 2 between 70 and
90 km. I t can be computed by using Equation This i s done by means of B e f f .
(59), daytime experimental values of [NO] and [e], and accepted deionization
coe f f i c i en t s . The e f f ec t ive attachment f ac to r can be a l so derived theo re t i ca l ly
from (69) and (71). Figure 2 1 shows these computed values of B
be seen t h a t t he p r o f i l e based upon experimental data , is qu i t e d i f f e r e n t from
the two theo re t i ca l p r o f i l e s .
o f [NO] and [e] and theo re t i ca l computation is t o pos tu la te a binary attachment
react ion of t h e type:
I t can e f f '
The only way t o conc i l i a t e experimental values
e + Z W + k49 z- + y
where Z- is a s t a b l e negative ion and such t h a t :
k7*[ZW] >> k [0 ]* 33 2
o r :
which corresponds t o Equation (64).
52
90
80
70
60 101
EX P ERI MENTA L
I
I d lo3
Figure 20. Comparison of daytime electron densities. Experimental by Mechtly and Smith (1968b); theoretical from Equations (58) and (71) and NO concentration by Pearce (1968).
I o4
53
a a
n
l- -I
;I z W I
II: W
a
X
W
I
0
a: LL
W
I- - n
h
- 'V
a, v)
v
1
c 0
0
0
LL
t
a,
L
V 0
c
E
c t
a a,
>
V
a,
W
.- t rc
rc
0
0
P- (D
54
Accepting reac t ion (72) where [ZW] could be a heavy n e u t r a l , and a
- 3 -1 experimental i n Figure * 'eff t e n t a t i v e r a t e coe f f i c i en t k % lo-' cm s e c
21 w i l l i n d i c a t e t h a t t h e spec ie [ZW] would be a minor cons t i tuent with a peak
concentration of % 5 x 10 a t around 80 km. Such a minor contamination a t t h a t
72
6
height could be accepted, but i ts eventual na ture i s a t t h i s time unpredictable .
Possible conglomerates of n e u t r a l p a r t i c l e i n t h e region of low temperature
could form heavy n e u t r a l s .
In summary it can be s a i d , t h a t the negative-ion chemistry can be repre-
sented by an e f f e c t i v e attachment coe f f i c i en t B e f f as shown by Equation (54)
which takes d i f f e r e n t forms depending upon t h e negat ive- ion processes involved.
To c o n c i l i a t e t he high values of [NO] given by Pearce (1968) with experimental
values of e l ec t ron dens i ty and recombination, and mutual n e u t r a l i z a t i o n r a t e s ,
a new attachment process m u s t be pos tu la ted . This should be able t o form a
s t a b l e negat ive ion and could be a f a s t b inary reac t ion involving heavy neu t r a l
molecular compounds o r conglomerates formed under t h e low temperature condi t ions
o f t h e D region. However, f u r t h e r complications appear i n the lower mesosphere
where the experimental values of B e f f suggest t h e exis tence of f a s t detachment
reac t ions .
55
APPENDIX I
1. SOITRCES OF DAT,!
1.1 Introduct ion
The computations f o r t h e oxygen atmosphere were based on Equations
(7) and (8) of t h e t e x t .
the Kaufman adopted da ta i n Table 1.
The values of k 3 , k4 and k5 were taken from
The O2 and 03 absorpt ion cross sec t ions and t h e s o l a r photon f lux a re
tabulated i n Table A l . The same da ta i s shown graphica l ly i n Figures 3 and 4 of
the t e x t . A l i s t o f t h e references from which t h e cross sec t ions and
f luxes were taken i s given i n Table A 2 . The s o l a r f l u x i s t h e unat tenuated
photon f l u x outs ide t h e e a r t h ' s atmosphere. The da ta numbers i n Table A 2
r e f e r t o those i n Table A l . Below 2425w t h e 0 2 absorption cross sec t ions a re
very small according t o Hunt (1963) S.40 123, s o cor rec t ions below 2425 A a r e
assumed t o be zero f o r t hese ca l cu la t ions . Between 1775 A and 1975 A t he
s o l a r f lux was read fron a graph i n t h e Handbook o f Physics a t 5 j n t e r v a l s .
These values were then averaged over 50 A i n t e r v a l s t o give an average f l u x
f o r each 50 i n t e r v a l .
0
0 0
0
0
1 . 2 Neutral Atmosphere Parameters io21 , [MI
The a t t enua t ion o f s o l a r r ad ia t ion as it passes through t h e atmosphere depends
on the number of absorbing molecules between t h e a l t i t u d e of i n t e r e s t and the
outs ide of t h e e a r t h ' s atmosphere. For these ca l cu la t ions 02 was assumed t o be the
only spec ies which s i g n i f i c a n t l y a t tenuated t h e s o l a r f l ux . From 300 t o 120 km, t h e
values o f [O ] were obtained from t h e U.S. Standard Atnosphere Supplement 1966
f o r the 3 cases: Winter Podel, Exospheric Temperature = 1000°K, Sumper tlodel,
r xospheric Temperature = 1 O 0 O o Y , and Sprinp/Fa11 Podel, rxospheric Temperature =
1000°K.
2
Relow 120 km it was necessary t o convert t h e absolute atmospheric dc,nsity
56
Table A 1
PHCTON FLUX PHgTflV FLIlX 0 2 A R S O P R . 0 3 A A Z W ' 4 . D A T U M CENTR4L WAVFLENGTH NUMRES kbVELENGTH INTERVAL
(8) 1.0
53.0 3 1450. 50.0 4 1500. 50.0 5 1550. 50. n 6 16C0. __ 50.0- - - __ 7 1650. 50.0 8 9
10 11
13 14 15 16 17 18 19 20 2 1 22 23 24 25 26 27 78 29
31 32 33 34 35 36 77 38 39 40 4 1 42 4 3 44 45 46 47 48 49 50 51 52 53 54 55 - 56 57 58 59 60 61 62 63 64 6 5
. _=- .
30 -
...
1700. 1750. 1775. 1780. 1785. 1790. 1795. 1 e o o . 1PP5.
1P15.
. - - _- ._
i e i o .
1820. 1825.
i e35 . 1e4n.
1830.
1P45. l P 5 0 . 1855. 1Et9. 1Ft5. 1E70. 1 E75. i e p n . i e ~ 5 . 1eso. 1 P95. 1900. 19c5. 1910. 1915. 1920. 1$25. 1920 . 1975. 1540. 1945. 1950. 1555. 1960. 1565. 1570. 1S75. z r t n . 2r50. 2100. 2150. 2200. 2250. 2 2 0 0 . 2=50. 2400. 2450. 75C0. 2550. 2600. 2650. 2 7 C 0 .
50.0 50.0
7.5 5.0 5.0 5.0 5.0 5.0 5.0 5.9 5.0 5.0 5.0 5.0 5.0 5.0
5.0
5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.n 5.0 5.0 5.0 5.0
5.0 5.0
5.0 5.0 . 5.0 5.0 2.5
57. 0 53.0 50.0 50.6 -
50.0 50.0 50.0 50.0 50.0 50.0 50.0
50.0
-_
5. n
5.0
5 . 0
5.0
5.0 -
50. n
50.0
50.0
.. .
.. -
P E R INTERV L P E R PNGSTROM CR"ISS-2X (cm- ) (phot. cm-* sec-' Ax-') (phot. cm-' sec-l x-l)
2.70OD 11 7.701E 11 1.100D-2P 1.4500-17 1.R300 11 3.660F O R 1 .4400- 17 3.7000 in 7.4O0F O R
7.3000 i~ 1.469E 39 1 I ?ROD- 17 1.330D 1 1 A . R1nD- 1 9
4.8700- 1 R
1.11201)- I R 1.0hOD 17 7.123E 19 3 -0R00- 19
1.2750 11 7.550F 1'
7.3701)- 18 i . 4 0 9 ~ i n 7.0nnn 11
6.0880 10 2 . 4 3 ~ ~ i n 7.5309-7n i . 7 ~ n 0 - 2 0
1.3280 1 1 7.656F 10 I . 63n0-2n i . - ~ q i d Ti 7 .-mF-i-T-- -- 1.77on- 7 0 1 . 4 0 7 ~ 11 7.R14F 11 2 . 0 5 ~ - 2 " 1.515ll 1 1 7.079~ i n I . 7nnn-20 1.5870 11 3.174F 10 2 . 6 7 c i n - ~ ~ 1.6600 11 3.323F 10 1.1700-2n
I . 1900-70 I . R M P 11 3.612E 16- -1 . iwm-7n 1.RR0D 11 3.76'3F 10 4. s n n n - 7 I 1.977D 1 1 3.Oc4F 10 7.0400-21 2.0610 1 1 4.122E 17 4.~~1-n-2 I 2 . i m n 11 4.300E 17 I .4300- 3 1
6.6400-21 2.44717 11 4.R94F I ? i .430n-7 1 2.57no 11 5.147F 10 1.57nn-71
1.7370 11 3.4hhE 10
2.24RD 11 4.496E 19 5.6 ? I D - 7 1 2.3470 i i -- 7.6qTF m---
2.6710 11 5.347F 17 5 .n7oD-71 2.0300-21 z . R i 9 r 11 5.63qE 1 1
2.9710 1 1 5.R47F l? 4 -430D-77 3 . n m n 11 h . 1 4 T - 1 Ci I .45nn-21 3.1971) 1 1 6 . 3 9 4 ~ i n 1 .77'30-21 3.3480 11 6.696s 19 7.5hnn-27
3,7810 11 7.5h7E In R . ROD-77
4.2930 11 R.5P6F 10 4 . 3 ~ 0 - 77
? . 2 8 n ~ - 2 2
3.5nnn 11 7.7130~ 1 0 7.0600-77 3.62RD 11 7.256F i n 6.3700-27
3.9350 1 1 - - - - -7 .870f -17 -----?.qRPD=77 4.1390 11 4.276E 10 1.3800-27
4 . 4 5 ~ 11 R.90'lF 10 6.450D- 2 2 4.6550 11 9.310F 13 4 . ~ 6 2 n 11 9.774E l o 1 . '000-77 4.9720 11 9 . r i 4 C 10 0.44n0-21 5.27RD 11 1.156F 11 1.RQPD-22 5.4380 11 .I.lRRF 11 1 . q ~ ~ n - 2 2
P.R7PD-77 1.111F 1 1 5.6490 1 1 5.8600 11 1.172F 11 5 .8500-23 5.974n 11 1.195E 1 1 5.9700-73 6.2R60 11 - 1.257E-Tl-- l-.P3Pn-2? - 3.7500 11 7.0350 1 2 1 . ~ 7 ~ 1 1 1.7nno-73 9.271ll 12 l.454F I 1 1 . 1 ~ 0 - 7 3
- 4.8500-23 1.307E 11
1.5300 13 3.7hCIE 11 4.6000- 24 2.5930 1 3 5.186s 11 7.9000- 74 3;-627h- IS-----h.854F I1 -- $ . 4 n n ~ - ? 4 - -- 3.9570 1 3 7.914F 11 4.mno-24 4.1610 1 3 9.372E 11 3.1000-74
__ -
3.7790 13 4.1000 13 4.8020 13
7 . 1 7 6 ~ 13
1.6961-1 14
4.7740 1 3
9.1461) 1 3 1.3320 14
7.55RE 11 R . 2 0 0 E 11 9 . 6 0 4 ~ 11 0.548E 11 1.435E 12 1.R29F 1 7 2.664E 12 3.392E 1 2
1 . 5 2 0 ~ 14- _ _ _ _ 3.341)E 12 50.0 - - 2750. -_ ._ - 3;3-76F 12--
66 67 zeco. 50.0 1 . h R 86-1 4 68 2e50. 59.0 2.4350 14 4.873F 1 2 69 2900. 50.0 3 . 7 ~ 9 0 14 7.574E 17
- - __ - _. __ -
70 2950. 50. n 4.6700 14 4.349E 17 4.5981) 14 9.196E 12 71 3000. 50. 0
72 3~50. -50.0 _ _ 5.174D 14 1.077E 13 73 3100. 50.0 5.92 ne - i 4 l.IR%F 13 74 . . '150. 50.0 6.4400 14 1.294E 13
1.367E 17 7 5 3200. 50.0 6.R34D 14 3250. 50.0 8.3240 14 1 . 6 6 h F 17 3300. 50.0 9.5350 14 1.907F 1 3 77
- ____
76 .
9.3439 14 1.R69E 17 9 . 4 ~ 2 0 1 4 - - - - 1.RS6F 17 - - --
78 3350.
80 3450. 50.0 1.0140 15 2 .72RF 13 81 2 5 0 0 . 50.0 t.038n 15 7.976F 1 7
?0.? .-. - - =E- 3400:- 50.0
1.530D-24 1.99OD-24 n.O 0.0 0.7 9.Q
0.0 n.0
9.q o; n q.n O.n P.9 0.0
b.O '1.0
' . 0
0.9
q.n
o.n
82 4750. 500.0 2.5060 16 5.012E 13 9 . p 83 1250. 510. 0 2.575C 14 5.150F 1 3 9.9 7.3600-21 84 5750. 500.1 2.7570 16 5.514F 13 0.0 1.9430- 7 1
503.0- -2.69An 16-- - - - 5 .3c ) f iE-13 7,n - --- 7.6hW-71 e5- - --t250; - - _ _ e6 6750. 500.0 2.6nzn 16 5.294E 13 0.0 1 . 5 3 w - 2 1 e 7 1250. 500.0 2.4740 16 4.94Rf 17 0.0 5.2 7 nn-2 7
57
TABLE A2
Data Numbers
1-50
51-87
Data Numbers
1-10
15,25,35,45
51-87
@2 Absorption Cross Sections
Wavelength
12151, 1375i-1975i
1975;- 35 2 S i , 45 O O i - 75 00;
p)3 Absorption Cross Sections
Wavelength
12 15i , 13751- 1775;
1800;, ISSO;, 19OOx, 1950;
1975i-3525i, 4500i-- 750d
Source
A
B
Source
C
D
D
Between 1775i and 19751, all cross sections not listed in this table are smooth curve interpolations of Hunt's data.
Data Numbers
1-50
51-81
82-87
S o l a r Flux
Wavelength
1215i, 1375;-1975a
19751- 3525i
4 5 0 06; - 75 0 0 1
Source
E
F
G
58
TABLE A2 SUPPLEMENT
A . Huffman, Robert E . , DASA Reaction Rate Handbook, October 1967, Chapter 10, PHOTOChEMICAL PROCESSES, page 10-7, Values read from graph, General Electrical Company Missile and Space Divis ion, Space Sciences Lab., Phi ladelphia , Penn.
B . Hunt, B. G . , Technical Note SAD 123, Weapons Research Establishment, June 1963, Adelaide, South Australia, page 2 2 .
C . Craig, Richard A . , The Upper Atmosphere, Meteorology and Physics, 1965, Academy Press , N . Y . , Ed. J . Van Mieghem, page 168 read from graph, Chapter 4, The Sun's Radiation and t h e Upper Atmosphere.
D . Hunt, SAD 123 , page 24.
E . Handbook of Geophysics, Data Numbers 1-9 from page 16-16, Data iiumbers 9-50 read from graph page 16-11.
F . Tousey, Richard, Space Science Reviews, Vol. 2 , 1963, The Extreme U l t r a v i o l e t Spectrum of t h e Sun, page 22 .
G . Handbook Geophysics, page 165.
59
given i n t h e U . S . Standard Atmosphere Supplement 1966 t o EO,] and [MI by
using the mean molecular weight and the percent composition of 02.
the d e n s i t i e s were converted t o [0 ] and [MI by assuming a constant mean molecular
weight of 28.96 (CIRA 1965) and constant r a t i o o f [ 0 2 ] t o [MI of .2091 f o r a l l
seasons.
[0], .and [A] given i n C I R A 1965 page 1 2 .
Below 90 km
2
This r a t i o was ca lcu la ted from t h e 90 km values o f [ N 2 ] , [0 1 , 2
A t 120 km the mean molecular weight
and percent composition of 0 t o M f o r ea.ch season was ca lcu la ted from data
i n t h e U . S. Standard Atmosphere Supplement 1966. Between 90 and 120 km
2
t h e mean molecular weight and t h e percent composition were assumed t o vary
l i n e a r l y with a l t i t u d e s o as t o match t h e boundary values of 90 and 120 km.
The boundary values of composition and mean molecular mass a t 90 km and 120 km
are given i n Table A 3 .
c a l cu la t e t h e i n t e g r a l f [02]dh which is used i n the ca l cu la t ion o f t h e
photodissociat ion rates.
i n t e g r a l .
The r e s u l t a n t values o f [02] were then used t o 300 km
z
Above 300 km [O,] contr ibuted neg l ig ib ly t o t h e
The photodissoc ia t ion ra te J of t h e k th cons t i tuent was ca lcu la ted k
according t o t h e formula:
Eo2] dh) 300 km J = okA R exp(-secx IS (0 ) k A A A 2 J
where: okA = t he average value of t h e photodissociat ion cross sec t ion of the
k th cons t i tuent i n t he Ath wavelength in t e rva l
R = t h e t o t a l . s o l a r photon f l u x with wavelength i n t h e Xth i n t e r v a l
secx = t he secant of t h e s o l a r zeni th angle x A
CI (0 ) = t he average absorpt ion c ross s e c t i o n of O2 i n t h e Ath i n t e r v a l A 2 300 km S [0 ]dh = t he i n t e g r a l o f t h e O2 concentrat ion from 300 km t o Z , t h e z 2
a l t i t u d e o f i n t e r e s t .
60
TABLE A3
Summer
Winter
Spring/Fall
Summer
Winter
Spring/Fall
90 km Mean Molecular Mass
28.96
28.96
28.96
120 km Mean Molecular Mass
26.76
27.12
26.90
Composition
20.91%
20.91%
20.91%
Compos it i on
13.17%
14.40%
13.61%
61
In t h e ca l cu la t ion o f t h e photodissociat ion r a t e s , i t was assumed t h a t
only 0, s i g n i f i c a n t l y a t tenuated s o l a r r a d i a t i o n .
t h e quantum e f f i c i e n c y f o r 0
t h e molecule r e s u l t e d i n the d i s soc ia t ion o f t h a t molecule. Thus, t h e
I t was a l s o assumed t h a t
and O3 was un i ty ; i . e . every photon absorbed by 2
absorpt ion cross sec t ions a r e the same as t h e photodissociat ion c ross sec t ions .
1 . 3 I n i t i a l Values f o r t he Oxygen Atmosphere
I n i t i a l values o f 0 and O 3 were ca l cu la t ed f o r l a t i t u d e s ranging from 45"N
t o 45's i n 15' i n t e r v a l s with a constant s o l a r dec l ina t ion o f 23.5"N. The
appropr ia te temperature p r o f i l e s f o r t h e ra te c o e f f i c i e n t s , as well as [O,],
and t h e [O,] i n t e g r a l s , were obtained from t h e da t a i n U.S. Standard Atmosphere
Supplement 1966. The s o l a r zeni th angle used i n computing the photodissociat ion
rates was ca lcu la ted from the formula:
cosx = s i n ( 1 a t i t u d e ) s in(dec1ina t ion) + cos(latitude)cos(declination)
The s teady s t a t e concentrat ions o f 0 and O3 were approximated by:
3
k3, k4, kS are t h e Kaufman reac t ion r a t e s given i n Table 1 o f t h e t e x t .
J2, J3 = photodissoc ia t ion rates of 0 , and 0
[ O ] , [ 0 2 ] , [MI, [ 03 ] a r e the concentrat ions of 0 , 02 , M, and 03 , r e spec t ive ly .
1.4 Time-Dependent Oxygen Atmosphere
respec t ive ly . 3
The time-dependent oxygen atmosphere used t h e values of [ O ] and [0 ] from
The b a s i c da t a f o r r eac t ion 2
t h e s t eady- s t a t e approximation as i n i t i a l values .
ra tes , temperatures, c ross -sec t ions , s o l a r f l uxes , and [0 ] p r o f i l e s were
i d e n t i c a l i n both models. The time dependence was incorporated i n t o t h e
2
6 2
s o l a r zeni th angle x i n t h e form cosx =
cos ( l a t i t u d e ) cos (dec l ina t ion) cos (hour
s in ( l a t i t u d e ) s i n (dec l ina t ion) +
angle) whe.re t h e hour angle uniformly
increased a t t h e ra te o f 24 hours p e r day. An approximation t o t h e Chapman
funct ion was used f o r t h e s o l a r zen i th angle x between 80" and 90" t o lessen
e r r o r s due t o t h e curvature o f t h e atmosphere. The values o f t he Chapman
funct ion Ch(x,x) were taken from M.V. Wiles. ( In t h i s no ta t ion x = s o l a r
zeni th angle , and x = h+Re - where h i s t h e a l t i t u d e of observat ion above t h e e a r t h ' s
su r f ace , Re is t h e rad ius o f t h e e a r t h , and H i s t h e s c a l e he igh t of 0 2 at t h a t
a l t i t u d e . ) A t t h e a l t i t u d e s and d e n s i t i e s involved, t h e r e s u l t a n t values c?f
x were q u i t e l a rge , o f t h e order o f 1000. To approximate t h e Chapman func t ion ,
the region between 80" and 90" was broken i n t o 1" i n t e r v a l s . Within each
i n t e r v a l t he Chapman funct ion was approximated q u i t e well as a l i nea r funct ion
o f x about t h e value a t x = 1000. When x L 90" a l l d i s soc ia t ion rates were
se t t o zero because t h e s o l a r r ad ia t ion must pass through very dense l aye r s
o f 02 f o r l a r g e r values of x.
rough approximations because only absorpt ion by O2 is considered.
a t sunse t t h e sun's rays must pass through dense layers o f t h e atmosphere so
t h a t absorpt ion by cons t i t uen t s such as 0 3 a l s o becomes important.
of the time-dependent oxygen atmosphere are depicted graphica l ly i n Figures A 1
through A24.Nmerical t abu la t ions o f t h e 0 and 03 va r i a t ion during a 24 hour
per iod are given i n Table A4 t o A37.
f o r 90 km; 80 km, 70 km, and 6 0 km f o r each o f t h e l a t i t u d e s 45", 30", 15",
O " , -15", - 3 0 ° , -45" f o r a constant s o l a r dec l ina t ion of + 2 3 . 5 " , corresponding
t o a summer s o l s t i c e i n t h e + l a t i t u d e s .
a t 85 km, 75 km, and 6 5 km f o r +45O l a t i t u d e and dec l ina t ion o f 2 3 . 5 " . The
so lu t ions f o r each l a t i t u d e and a l t i t u d e were generated u n t i l t h e concentrat ion
H
Near s u n r i s e and sunse t t h e equations are only
In r e a l i t y
The r e s u l t s
P r o f i l e s were computed and p l o t t e d
In addi t ion , p r o f i l e s were computed
63
of 0 3 a t successive noons was wi th in 5% o f each o the r o r u n t i l a vaximum time
o f 6 d s y s was reached. A t a l l a l t i t u d e s , except 90 km, t h e so lu t ions
s t a b i l i z e d t o wi th in 5% a t successive noons before s i x days passed, and at
90 km the Dro f i l e s i n d i c a t e t h a t s t a b i l i z a t i o n would have been reached wi th in
another 24 hour per iod.
64
D
c
7
9
0
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9
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9
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0
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la
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cc .7
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65
66
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NWILHklLN23NW
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67
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68
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69
LRT=45 a
00 D
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fiLT=70.00
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0
54.00
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12.00
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90.00 16.02
112. @O
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TIME
[HOURS1
Figure A4
70
M
c3
LL
=u
0
LRTL-U
5.00 D
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=23.50 R
LT=65.00
10 6 : 00
12.00 TI ME (HO
clR51
/
I 18.00
24.00 30.00
!0 6.00
12.00 18.00
2Y. 00 30.00
1 I ME (HOURS)
LRT=Ll5.00
DE
C=23.50
fiLT=60.00
J0 6 ~ 00
12.00 ia.00
24, OD 30.00
T I ME (HOURS)
Figure A4
(continued)
71
0 0
0
0
II t- __I
CII
0
m
M
Tu I1 i, W
0
0
0
0
I1 t.
-I
m
a
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00.21 00'11
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0 0
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72
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73
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Figure A7
75
Y
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M
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Figure A7 (continued)
76
00
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0
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Figure A10
80
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Figure A10 (continued)
81
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0 6.00 12.00 1
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Figure A13
85
LRT=C. CC OEC=23 50 FlLT=GC. OC
io 6.00 12.00 TIME lHBURSl
, G O 2G.00 30. 00
0 0
m I 0.00 6.00 12.00 18.00 2U. 00 3G. 00
T I M E [HOURS)
Figure A13 (continued)
86
87
D 0
N 2
D 0
3'
N
0
_c_
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_
0
m
'1
88
\
0
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105
- - _ _ _ _ _ _ _ _ _ _ _ . ___ --- ................................................................................................... .--------- TabJJiAs --_---- ... ---_----_____-______ .... Table A4
L A T I l L D E = 45.C OEG ALTITUDE= 90.0 KH LATITLDE= 45.C CEG ALTITUCE= 85.C KH
---__.- - DECL INAT ION=23.5 DE6
/ TICE(HR-CIK) N(0) NI133)-- T I C E ( kR- M,A F: I N ( C ) . N ( C 3 I .................................................................................... ....................... _ _ ...................... _ _ .............. c- 7 4.786E 11 1 . 3 3 4 ~ oa c - 7 2.455E 11 5. L29€ 08
..................................................................................................................................................... 0 - 3 1 4.i?98€ 11 1.343E 08 C-31 2.512E 11 5 . 2 0 0 ~ oa 1- 7 4.eS8E 11 1.349E 08 1- 7 2.570E 11 5.284E 0 s 1-3 1 4.898E 11 1.358E 08 1-3 1 2.570E 11 5.358E 08
2.630E 11 5.432E 98 2- 7 4.898E 11 1.361E 08----' 2- 7 2 -31 4 . 8 9 8 ~ 11. ;?;;E ;;. 2-? 1 2.630E 11 5.5C8E 08
........ 4 - . .i .................................... .--i. r S 8 ~ E .~ a.. ............. .-.4 .... ....... ....--_;.'-;E;-;-; ..................................
5-3 ~. 1 ............. .~ 5.012E .c.l-2F. l-f 11 ............ .~. 1.390E . 3.9 F. .~f 0 8 . . ,- ............................ 5-31 '9.-821;4 2.818E ~- 'I.l. 11 ............. 5-.9.~ 5.888E ~~. ~ . ~ - 08 ......
............................................................... ................................................................................ 3- 7 5.012E 11 3- 7 Z.tS2E 1 1 5.572E 08 3-3 1 5.C12E 11 i . 3 a 0 ~ 0 8 3 - 3 1 5.649E 08
5.012E 11 - 5.715E Of! 4-3 1 5.C12E 11 1.387E 08 4-? 1 2.754E 11 5.781E 08 5- 7 5.012E 11 1.384E 38-- 5- 7 2.818E 11 5.821E Of!---
-
--
6- 7 t -3 1 5.C12E 11 1.396E O e t - 3 1 2.884E 11 5.970E 08
2.065E 09 7-33 5.C12E 11 1.390F C 8 7-33 2 . ~ 8 4 ~ 11 5.957E 08
4.603F OF a-45 2.030E 11 2.042F 1 C 8-44
9-59 4.78tE 11 8.472E 09 1c- c 2.291E 11 3.802E 10 lo ..=~. ............ 4--'r86-~..~.I ............... 4..~66m. .99 ..................................... 2-*.~-8-a-E---l.i .............. 4--4.6-f-E..fC .....
11- c 4.786E 11 1.C7ZE 1 C 11- c ' 2.C89E 11 4.898E 1 c 11-30 4.6f7E 11 1.148t Tr-- - 11-3C 1.950E 11 . -
12- c i . a 6 2 ~ 11 5.888E 1 0 12- c 4.677E 11 i.z-Tc ........... 4-.WYE-.fZ'1 Z e - ~ 8 E . 1c ................................ .............. 6;TbZE -IC- - . - 12-3c 6.607E IC 13- c 4.571E 11 .1*349E 1c 13- c 1.6tOE 11
7.413t I C 14- C 4.467E 11 1.445E 1 C 14- C 1.479E 11 7.079E 1 0 14-30 .? 3 1.41VE-17T-." 14-3C 1.3ROE 11 15- c 4.365E 11 1.514E 1 C 15- 0 1.318E 11 7.586E 10,
. . 15 5~ ............... 4 . T a - ~ ~ - 1 T ............. 1 . . 5 4 - E ~ . . ~ C ............................................................. f-T.6.z62F'.l.o-. ... - 1.230E 11
I t- c 4.266E 11 1.585E 1 C 16- C 1.148E 11 7.943E 1@
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_- 8- 7 5.C12E 11 3 e- 7
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1C-30 ... -
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18-37. 4.365E 11 1.21tE o e l f - 3 7 1.995E 11 4.140E 08 19- 19- ? 1.995E 11
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106
. . . ..,.Table A6.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tabls-BI ........................ ............. LA? I ?lCE?..45, !XG. ................. ALTITUDE=- 75-.C Kr CAT 1' l?E=..!eC.DE.!? ..................... A L T I T " C E = .??.@. !?
I
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1- 7 2.6SZE 11 3 ; I t i f 09 1- 3 2.C42E 1 1 8.53lE C9 2.089E 11 8.67CE 09 1-33 2 ec.2.L 3.228E 05 _. 1-37 . ...
R.f7OE 09 2- 7 2.754E 11 3.285E 09 2- 3 2.089E 11 2.19eE 11 8.851F 09 2-33
8.933E 09 3- 3 3.388E 6i; 3- 7
4- 1 3.475E 09 2 .138E- - l l -. 8.914.~ 3s . 4-37 . -. . ~. .
.2. .*.~7.0 .i .l. 2.630E 11 3.119E 09
.______._- -. - - - - .. -. __ - - . . . . 2.el8E 2...a.84.E f i 11 . . 3.342E OS .......... 2T.13 . . . . . z.;i?BE i.i . . . . . . .
4 - 3 2-33 2.138E 11 8.954F c 5 . . . . . . . . ~~ ~ . _ _ ~ ............... 3-37 ; :!?;:E".: ;. ?.43tE c9
2.951E ' ~ ~ i E ~ 11 -.
5-37 ;.-;;;E..;; 8.974F 09 3.5CEE 09 4-37
3. 5-4.Ti-. .C9̂ - . 5- 1 1 5- 3 2.138E 11 8.933E 09 5-33 2.138E 11 8.872E 09 3.540E 09
3.54eE 0 9 t- 1 t - 3 3 2.089E 11 8.69CE 09 6-33 2.951E 11 3.548E 05
7- 7 2 . 9 5 1 ~ i-i . - 3.532E 09 2.C42E 11 e-.-55.1F 05 7-33 2.951E 11 3.5CEE 09 7-33 2.C42E 11 8.414E 0 9
2.138E 11 ~
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9-30 l .175E 11 I . ? l E E 11 9-15 1.259E 1 0 1.514F 11 I C - c IC-30 11- C 11-3c 12- c 12-3c 13- 0 13-3C 14- C 14:3P-
8.71CE 1 0 t.607E 1 0 - 4.898E 1 0 -3 -
2.692E 10 1.595E. 1 0 - 1.479E 10 1.C9EE 1 0 - e.147E 09 W T Z T -0 T---
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1.778E 11 1.82CF 11 1.820F 11 1.862E 11 1.86ZE 11
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1-:862F 11 1 . C O O E 0 8 1.585E 11 ~. 2A .o-9.-
2.421E 09 1.862E 11 IC: 5 1 . C C C E 08 1.585E 11 1 . 5 8 5 ~ . . i i
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le-? 1 i . e 6 2 ~ 11 2.265E 09 1.514E 11 6.339E 09 6 . 2 8 n T . - --
16-31 Tf . ~ ~ . . ~ -r'-29 ;4p '04-. - - - - 17- 1 1.514E 11
1.514E 11 6.266E 0 9 6.261F OS
1.905E 11 2.249E O S 17-37 l e - ? If!-- 3
6.324E 05 6.5SfE. 0 5
g 1 3 ; 1.950E 11 2.3C7F 0 5 ---2.33>E- 09 15- 7 1.549E 11
6.486E 09 15-37 1.995E 11 2.388E 09 15-33 1.C49E 11 ~~- 1.622E 11 6.761E 09 2.089E 11 2.489E C9
21- 3 l.658E 11 7.063E 09 21-?7 2:lEeE 11 2.624E 0 9
2- 22- 7 7.261E g 5 22-37 2.344E 11 2.754E 09 2 2 - - 3 2 1.778E 11 7.413E 09
~ ii. 2 - 23-37 2.455E 11 2.8S7E 05 23-33 I . ~ O Z E 11 7.780F 09
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107
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c- 1 c-3 1 1- 7
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11-3c 12- 0 12-3c 13- c 13-3C
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1.995E 10 1.995E 1C 1 . ~ 9 6 ~ 11 1.413E 1c 4- 3 5.623E 10
1.380E LC 4-3 1 C.495E 1C 1.95CF 1C 1.9mF- 1C 1.C72E 11 5- 7 5.37CE 1 0
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. 14-45 5.754E 1C 5..7546 lC
15-45 . 1.CCOE 08 5.154E 1C
lt-31 4.C74E 10 1.475E 1C 17- 3 3.581E 1 0 17-33 3.981E 1 0 1.413E 1C l..f- .'I;443F .1C
4.169E 1 0 1.445E 1C
15-31 4.461E 10 1.585F 10 1 - 6 m 1 6 20- 7 4.671E 10
2E-37 . .. .. 4.786E 10 1.698E 1C 21- 3 5.C12E 10
16- 7 1.CCOE 08 5-:? 5.4 E - i c -- 1.413E r--
. . . ... - . . . . 4..~7-4.6E...I0 _. -..
. . ~
-.
.. . . ...._..
i 1-9 1 9.333E 1 0 1.175E 1C 21-91 5.129E 10 1.820E 1C
1.C23E 11 1.318E 1C . . . . . - . . . . . . . -. - - - . . . . . - . . . . -. -. 23-31 . . 5.023E 1 0 1.995E 10 .23-3! - - . . . . . . . -. . . . . - .
108
,. Table A10 . . . . . . . . . . . -81.1.. .................
LA T I 7 1 0 E = 4 5 ..C -0 E G ALTITUDE= 40.C _K! ~. ~ LA71 r c =. . 'P *c .CEG.. ALTITUDE= 90.C KP .......................
c- 0 c-3c 1- c 1-3c 2- c 2-3c 3- c 2-3c 4- c 4-3c 5- 0 5-3c t- c 6-3C 7- c 7-? 1 e- 3 e-33 9- 7 S-31
1c- 7 IC-31 11- -7 11-33 12- 7 12-33 l ? - 7 13-33 14- 7 14-33 15- 3 15-77 I t - 1 I t - 3 1 17- 1- 17-3 1 l e - 1 ]@-?I 15- 1 15-21
-2cz f -
i C - t l 21- 1 21-31 22- 1 22-3 1 8- 1 23-2 1
_ _ _
__
3.311F 1 0 3.311F 1 C 3.311E 10 3.311E 1 C 3.311E 1 0 3.311E 1C
.. 3*311ELC_- _ _ _ - 30_236E 1 C 3.236E 1 0 3.236E 1 C 3.23CE 1 0 3.236E 1 C 3 . 2 3 6 ~ i e 3.162E 1 C 3.162E 1 0 3.162F 1C 3.C90E 1 0 3.090E 10 3.C20E IC 2.951E 10 2.e84E 1 0 2.818F 1 0 2.C97E 1 0 2.57CE 13 2.455F 10
- - 1. .TTFE 7x8- -- l.CO0E 08 1 . C C O E 08 - - l . O @ O E 08
_. - - .- . 3.020E IC 2.951E - 1 C 2.@84E 1 C 2.818E I C 2.692E 1 C 2.570F 1 C 2.455F 10
- -4.67TE 1c 4.671F 1 C 4.677E IC 4.677E 1 C
-
1.CCCF 08 4.677E 1 C 1 . C C C E 08 4.677F 1 C 1.000E 08 4.677E 1@ 1 . C T C E 08 4.677F 1C i . r o o E 0 8 4.677E I C
-4 i677E 10 I.COCE 0 8 1 . C C C E 08 4.677F 10 1 . C C O E 68 4.677E 1 C L . C @ C E 08 4.677E L C 1 . C C O E 08 4.677E I C 2.291F 10 2.291F 1 C
--2.2397 10 2.291E 1 C 2.291E 13 2.291E 1 C 2.344E 10 2.344E 1 C 2.455E 1 C 2.455E 1 C 2.57CE -10 2.570E IC
2.63CF 1 C 2.63CE 1 0
2 . e ~ ~ i o 2.e18F 1 C 2.951E ZO 2.951F 1 C 3.020E 1 0 3.C2OE 1 C 3.C9CE 10 3.090E IC 3.162E 1 0 3.162E 1 C 3 ; l X Z T D - - - T . l 6 2 F IC 3.236E I C 3.236F 10
- - - - - - - __
. ____
1 3 4 ~ 16 7 . T 5 - G I C ---_ _
-..
c- 1 4 . 6 7 7 ~ 1 1 l. lC4E 08 C-37 .4..'@EE 11.. 1.114F 08 1- 1 4.786E 11 1.117E O e
2- 1 4.1@6E I1 _ - 1-31 4.786E 11 __ 1.121: - ? e
1.130F 08 1.138E 08 2-77 4.PS8E 11 1.138E 08 3- 1 4.fSRF 11
3-77 4.eSAE 11 1.148F O @ 1.146E O P 4- 1 4.898E 11 1.153E 0 @ 4-71 ___ -~ 4.@9(3E ~ 11
5- 1 4.898E 11 l.- l5rF-a@
t - 1 4.898E 11 1.153E C8 1.159F 0P t - 3 7 4.898E 11
7- c 4.898E 11 ?.C@3F 0.2 7-44 4.898E 11 2.911F OS 8-29 4.786E 11 4.842E 09 e-59 4.786E 11 5.834F OS 5-29 4.786E 11 6.637F 0 9 9 - 5 9 4.677E 11 7.295E 09
IC-20 4.677F 11 7.81CE C S 4.571E 11 8.26CE 09
11-30 4.571E 11 8.610E 9 9 12- 0 4.571E 11 @.8S2F 0 9 12-3c 4.467E 11 9.141E OS 13- c 4.467E 11 9.333E C 9 13-30 4.365E 11 9.484F C S
5-37 4.RSBF 11 1.156~ o e
~. - __ - - __ __ ________ -
-1J:- ?- _______ - __
14- C 14-30 15- c 15-3C I t - c It-3C 17- 0 1 7 - c 17-33 1 P - 3 I@-37 15- 1 19-37 i c - 1 2 C- 3.1 2 1 - . 1 ;1-37
___._I__ __
- _ . - - - - - -
4.165E 11 4.266E
ll--- -
4.266E I 1 4.266E 11 '
- ___
4.16SE 11 4.169E 11 4.074E 11 4.C74E 11 4.169E 11 4.169E 11 4.165E 11 4.169E- 11
-. __
~~
4.26CE 11 4.266E 11
-.
4.266E 1.1 4.266E 11 4.266E 11
9.616E 09 9 . m E 69 9.817F 09 9.886F 09 9.954E OS 1.OCCF 1 C 1.OOCF 1 C
9.852E 37 9.860F 0 7 q.@84F 07 9.877F C7 9.935E 07 9.9 3 6E- Of 1 . C O O E C'8 1 . C C Z E O R 1.C12E o e
_ _ _ -
i.corE IC
-
_ _ 22- 1 4.265E 11 1.014E 9 e 2 2 - 3 ! - 4.365E 11 1.C23F O@
-TX'FZT -% E 23- 1 4.3zmri- i ~
1.038E O P 23-37 4.467E 11
109
1 1 0
D E C L I N A T ION=23.5 DEG 1 ICE l PR-MI& Nl03) T !HE ( t -R -MIh 1 k l C 3 1
111
. . . . - . . . - .. - . . . - - .. . . . - -. . - . - . . . . . e- 3 1.778E 11 1.342E 0 9 c - 3 ? ... l . 862E 11 . !r3'!? 0s 1- 3 1.905E 11 1.439E 0 9
1.486E 0 9 1-37 2- 3 2.C42E 11 1.528E 0 9
3- 3
1 - 9 9 5 E 11 __I______ -
-2-3.7. ._. , . . 2 2.089E ..i3TE.;li... 11 .__ ..-. ..l~ 1.570E 607E 0 9 09. -
2.188E 11 1.644E O S
1.702E 0 9 4-37 2.291E 11 5- 7 2.291E 11 1.718E 0 9
2.291E 11 1.726E O S 6- .j 2.291E 11 1 .- 730 E 0 9
3-37. ... ___..__ .. .. 4- 3 2.239E 11 1 . 6 7 . i ~ - 0 9
5-33 . . .. .. - ...._ -.. . ... - .-
-.__ . _. . - -
2.239E 11 5.998E 09 6-3C 7-15 4.169-E l o 7-45 1.479E 11 5.754E 1 0
-KmE-r- n m - I-€-- e- 30 9.12CE 10 8.318E LC
9-36 8:913E 1% IC- c 6.026E 10 9.333E 1 C
. .. ..i..7TaE..i..l ._.. -.. ...
- .
12- 0 2.570E 10 1.047E 11 13-70 1 i 6 4 7 E 11
1.072E 11 1.672E 11
._. . . . - . . . . -. . . . -. . . . . . - -. . . -. . - - - - -. . . . - - - -. . . . -. . . . . . . . . -. c- 3 1.175E 11 1.C96E 1 0 C-31 1.175E 11 1.096E 1 G 1- 1 1.202E 11 1.122E 1 C
2- 3 1.23OE 11 1.148E 16-
3- 1 1.230E '11 1.148E 1 C
. - . - . . . . . . - . -. . -. . . . - - -. . . . _ _ - - - - -. . . - - _ _ -. . . . -. . . -. .. . . . . . , 1-33 1.230E 11 i . 1 4 a ~ i c
. 2 _..... 2-3 1 1.230E 11 L.!48F. ?C .. . _ _ 3-33 1.230E 11 1.148E LC 4- 3 230E 11 1.148E 1 C 4 -31 -r;202E 11 1.122E 1 C 5- 3 1.175E 11 1 ~ ~ 6 ~ 1 ~ ~ - - 5-33 1.148E 11 1.072F 1 C 6- 3 6-3c 8.511E 1 0 3.311E 1 C .. . . - ~. .. ...._....___ s - T 1 - ~ ~ ' . ~ . 9 -. - 4".55*F ~ ~ . 6 . . . 7- 7 7-37 1.112E 0 9 1.000E 11
1 * 0 2'fE-TT--- 8-15 1.CCOE 0 8 8-45 I.COOE oa 1.023E 11 ...._.......... .___ -. .'i'.c~CE'~o.8 _.____.....__ 1.0.23E.ll 9 -15 9 -45 1.COOE 08 l..023E 11 ~. .. .. . . . i' .c.0~dc.~~.ij8 _.__...__.____ l-..G..z.--. . .
1c -7c . 3F 11 11- c T.000E 0 8 1.023E 11 11-30 1.OCOE 08
11
1?- c 1.COOE 09 1.023E 11
.. _..._ ..__..__._....___ ...---.--..------.-.-.. . .-. . . .
l-.-C47E.1C '
. . .. . .~ .... . .. . . . - ~ .... ~ ~ - ~ ~ . .I.l
-.-
1.023E f - 7 . . . . . . . -. . . 12- . -. . . . c . - . . . . - . . . - - - -. i . c c o E . . - - - - .. _ _ . oa . - - . -. - - - - - 1.023E -. . - -
12-30 1.CCCE 08 1 . 0 2 3 ~ i i . -
13-30 l.b@OE 08 1.023E- ti . . - . . -... .... .. .. - ._..... . ~...
1.023E 11 1.02 3 E 7 1 .-
14- 0 1.C96E 10 1.072F 11 14- 0 1.COOE 08 B ; n - * T ~ ; c n r T T ' - .. - 14-30 I.CCOE OR 14-30
15- 0 t.998E 09 1.096E 11 1.C23E 11
16- 0 4.508E 0 9 1.096E 11 - 16- c 1.000E 08 1.023E 11 6- 30. . __. . - . .... 3;-6~2 E-~7J--. .--_ _.. . - 17- 0 2.9C4E 0 9 1.096E 11 17- 0 i . cooE ca 1.023f 11
17-31 2.312E 0 9 .1.096E 11 I.COOE O R 1.C23E 11 18- 7 18-33 8.913E- 10 8.414E 0 9 18-33 1.148E 11 8.551E 08
lS- 7 . . 1s- 3 8.913E 1 0 a . 4 3 3 ~ 09 -..B-81.dE *a 8.531F 0 9 19-31
20- 7 t 11 9.441E --O-K--- 2c- 1 9.333E 1 0 B.67CE 0 9 20-23 9.55CE 1 0 8.892E 0 9 2C-33 1.288E 11 9.795E 08
1;-026E- os 21- 3 9.772E 10 9.12DF-oq- 21-33 1.413E 11 1.064E 0 s 2 1-33 1.COOE 11 9.397E 09
22-33 1.549E 11 1.159E 0 9 22-3 1 1,072E 11 9.954F. 09
22-33 1.660E 11 1.25fE 09 23-33 1.122E 11 1.047E 10
_- -_-____
15-30 - _._...-_____.-~____.~-~~-~-.....__.-.....____. ,.
Z-.-OV6E. 11 l t - 3 0 1.COOE 08 1.023E 11
1.096t 11 --n=r!r----- 2 . 6 0 0 ~ 09 17- 15 1.COOE 08 ._ -.
1.023E 7
. - . . .. . . . . . . . .. . . . - . . . . . . . . . . . -. . - . - - - - - - -. . - . - -. . . -. - - -. . - . . . . . .. . -. -. . .. .i..l-t'SE.gl .
1.202E 11 8.892€ 08 19-23 9.120E LO
. . .. -. . - . . . . . -. . . . -. . . . . . . . . . . . . . -. . . . . . .. . . . , . . . - - . -. . . ~ - ~ ~ . .,. . . . . .
..2-~; --,- ..- . .. _ _ _ _ T - - ~ ~ $ ' I V E - ~ Z _ _ _ _ _ i .____..- I-.~L'lVE..OF-.. . l-..c.2.~.E--l 4..6.6-o-~. .064 .._. .
.~~4vE-ll .
22- 3 . ' A 1
-2T-T- 1.622 t 11 1 * z n - 23- 1 1.C9tE 11 1.023E 10 ..____ _. ...
112
Table A19 . . . . . . . . Table . A 2 8 _ . .................. ............................................................................
. . LATITLO€= 0.0 OEG ALTITUDES 90.F KFI LA7 IPl DE =. I? .o DE!? .................... ALTI T"I)E=..bO *P..K!... .......................................................................
-~ - .- - . OECLINATION=23.5 DEG T I F E (PR-MIh 1 N ( G ) & ( c 3 ) - 7lPEtPR-Flh l Nt C ) N ( C 3 )
. . ...................................... ........................................................................ c- c 3.715E 10 3.0 9 0 E -10- c- 7 4.074E 11 8.935E 0 7 4eC74E 11 8.973E 0 7 c-31 3.715E 1 0 3. C9QE -10 0-33
1- 1 3.715E 1 0 3.090E L C 1- 7 4.16% 11 9.054E 07 4.169E 11 9.084E 0 7 -. 1-.33 3.715E L O 3.090E 1 C - 1-33
2- 3 3.715E 1 0 3.020E L O 2- 7 4.169E 11 9.14ZE. 0 7 4.169E 11 9.180E 0 7 2-3;. 3.631E 1 0 3 e C 2 0 E 1 C 2-33
2-33 3.548E 10 2.884E 10 3-37 4.266E 11 9.256E 07 4- 3 3.467E 1 0 2.818E 1c 4- 1 4.266E 11 9.311E 0 7 4-33 3.388E 10 2.754E L C 4-37 4.266E 11 9.307E 0 7 5- 3 2.23CE 1 0 2.692E
r ~ - - - - - - - 5- 1 4.26CE 11 9.37LE 07 -
........................................ .............................................................................
................................................................................................................................. 3- 3.63LE 1 0 2.951E L C 3- 3 4.169E 11 9 . 2 ~ ~ .a7
.................................................................................................................................
._
5-33 3.C90E 1 0 2.570E 1 C 5-37 4.266E 11 9 . 3 4 5 ~ a 7 e - . . . . 2- 4.~1.E..1.0-'--- .. .-.r;4-~S.E..lC.. .................................. 4-r-6-~E-il .............. r-6-~5F-Ue...
7; 7 . . . . . ..i...G.o .6E..o ........ 5..~lzi- i.c ................................. 4. . i~-~E-- i l .............. 3- * -7a F - 0-4 - - -
e-37 1.000E 08
t- 0
7-29 t- 30 3.29tE 09 4.677E L O 0-44 4.266E 11 2.244E 99
7-33 1 . C C C E 08 5.012E L O 7-59 4.169E 11 4.529E 09 5.012E 16 . . 4.074E 11 e----.- 1.00aE 08 5.012E 1 C e- 59 4.074E 11 5.623E 09 5;81~E Io 4--Ii74-~-ri .... 9- 3. . . . . . . . c % ~ ~ . .668 ........... ................................. .................
6.324E 09 3.$81E 11 6.5f7E 09
10-33 1 . C O O E 08 5.012E L O 11- 0 3.981E 11 6,776E 09 6.934E 09 7.079E 09
~ .Io 11-3 1 12- .7 -
_. e-29
9-29 6.ClZE'-669 - - .ic.~- 9-37 .............. T-~.*.~.~ 1 . C O C E 08 0-8 5.012E 10 9-59 3.981E 11 ............. T..oO12E.ID ...........................................................................
-- 11-15- 1.CGOE 08.---.' 11-30 3.890E 11 5 . 0 1 2 ~ i a 12- a 3.890E 11
. - 10-30
..l %6CE. .6B . . . . . . . . . ____- - IT . 3-a ............. B-B-662-~-Yf ............. .b.9. .... 1.656E 08 . . .
~ l.6- . . . . -I..6C16E.'0 ...... 5-.6TzF l.~
16-37 i.cooE a 8 5.012E 10 17- 7 1.COOE 08 5.012E
13- C 3.e02E 11 7.261E 09 _. ........... ............. i-3-~ .3-6 ............ .=. . . ~ ~ ~ - l
14-3C
7;328FCSV .14- c 3.715E 11 7.396E OCi
7.430E 09
_. 3.715E 11
1 . C O O E 08 5 . ~ 1 2 ~ i o ...... r. .~6a-E- iT I ......... - ~ . l.~ . .~
12-37 12- 7 13-32 1 . C O O E 08 5.012E 10
' 15- 0 3.631E 11 7.464E 09 ---r--7 1. c 0 aE7J--;mr-
1.000E 08 5.012E 10 ....I- . ~ ~ - * ~ . . 6 - ~ ........... ..5-0r2E . ro ........................................................... T7-9-~E..o.9.. . 14-37 i5- =I . ' 15-3C 3.631E 11 15- 33 1.OOOE 08 5.1112~ io 16- C 3.631E 11 7.534E 09 4-5TiT'0.9-..
17- 0 3 . 5 4 ~ 11 7.568E 09
............................................................. .. l t -3C 3 . 5 4 8 ~ 11
18- 0 3.467E 11 7 , 5 8 0 ~ a 9 le- c 17-30 3.467E 11 7.586E 09
................................ --3--7~-~E--i1 .............. 7'5B-6-E--6.~..
..................................................... ---~--~~-l-E..~-7-. .... 18-33 3.548E 11 . 7.775E 07 19- 7 3.548E 11 1q-33 3eC48E 11 7.815E 0 7
20- 3 2 . 9 b l E 1 0 19-33 2.818E 10 2.291E L O
.... . z l - ~ -3 ............. ~ - - ~ 3 - ~ E - + 0 .............. 2..~63.cF.L.~. ................................. 3.-.6.3631-E--1i ------------..,.- 42.~.E..6T-. ..
............... ' "J8 -~~-T0 .............. ~ . . ~ * - ~ E . . i ~ ............... ..z-2 .... 7. ............. 3---6-~~-~---l-i .............. ..62ZE--6T-. ...
__ 2.399E 10 2c- 7 .* L48t 11 7.841t 07
20-33 3 . ~ 9 0 ~ i o 2.512E 1 C 2C-33 3.631E 11 7 . 8 7 6 ~ a 7 -. 21- 7 21-21 3.311E 1 0 2.692E 1 C 21-32 3.631E 11 7.958E 0 7
8.061E 0 7 8.136E 0 7
23-31 3.031E 10 3.020E 1 C 2 3 - 3 3 3.715E 11 8.178E 07
........... - - *. . d
- 22-31 3.f48E 1 0 2.884E LO 22-33 3.715E 11 23- 3 . 5 i o 2e951F 1 C 22- 7 3.71% 11
................................................................................................................................................
113
114
.. ... .. ~ . ... . .T&le.AZ2 ..... .~ .. .. .. .
... .. LA7.!1lOE.~..C,_C__P_E_G_ ..... . . . . .. ALTITUCE= . . . . ._ . ~ ~ 60.0 . K P . LATITLDE=-15.C CEG ALTITUDE= 90.C K Y ~
._ -. -. -. CECLINATION=23.5 DEG . ----__ TI C E (HR-C I K 1 N(%) N(C3 J TIME ( PR-M IN ) N(O1 N(03)
- -. .. .. ._._ ~ . .... c- c 3.631E 10 3.020E 1 C ' c - 7 3.548E 11 7.@3lE 07
3.715E l o _ _ _ 3.020E 1 C 3,548E 11 7.865E 07 1- 1 3.715E 10 3.020E 1 C 1- 7 3.631E 11 7.933E 07 1-3 1 3.631E 1 0 3.020E 1 C 1-33 3.631E 11 7.961E 0 7 2- 3 3.631E 10 2.951E LC 2- 7 3.631E 11 8.C24E 07-
_ _ a!-?.- ...._____._....._.______________________~~.~~.... ..c:s I. . .._.________._____....
2-33 3.631E 10 2.951E 1 C ... 2-33 3.631E 11 .8.C43E 0 - - 2.887F 3- 3 3.548E 10 3- 7 3.715E 11
3-33 3.467E 10 2.818E LC 3-33 3.715E 11 8.108E 0 7 3.715E 11 8.140E 07 4- 3 3.388E 10 2 . 7 5 4 ~ - i o 4- 7
4-33 3.236E 10 2.692E 1 C 4-33 3.715E 11 5- 3 3.162E 10 2.57CE lC- - - - - 5- 7 3.715E 11 8.187E 07
5-3c ' 3.715E 11 8.187E 07 5-3 1 ?.020E 10 2.455E 1C 6- 0 2.512E 10 2.570E. 1.0 6- 7 6-37 1.COOE 08 5.012E 1 0 t - 4 4 3.715E 11 2.9C4E 09
6~-~E--il .._.____ 4--0.9.3S..b4 i-.-~-o-c-~..o-8. 5-~.C.~2E. .l.o . . ~. . _ _ _ .............__________________
7- 3 7-29 ... 8- 3 1.000E 0 8 7-37 __ 1.COOE 08 5.012E 1 0 7-59 3e631E 11 4.71OE 09
5. o-rx- i r - 8-29 3 2 4 8 E 11 5.212E 09 a-45 1.COOE 08 5.012E 10 8-59 3.548E 11 5,6365 09 . . . .q.-. .~ . - -_ - -. . _. . . ~ . ~ ~.€. - ~ ~ . - - - -. . - -. . . . 5. ~ 1~~ . . . . . . . - - - __. . . . . . -. . . .- _ _ - - -. __. ~.4 .~.~. . Yf. _ _ _ ____. . . . . 5. %t o - ~ .@ 9
- . . . . . . .. . . -. -. . __. . . . . - . - - - - - - - - -. . . . . . . . . . . . . 8.098E 07.- - -
.- . . . . . . . . . - -__ - - -. - - . . . . . . - - - - - - - - - - - - -. - _-. - - - - - _ _ _ -. -. . -. .. -. - - .. -. - - . . . . . . . . . . . . . . . _. - - - _ _ _ _ - ___. . . . . . . . - -. - - -. . . . . . . .
\ 8.159E 07 __ - - .. ... 3-1Y5F.i1 -.-.----.-....€.- 54~E.'89.. . .. . . . . . . . . . . -. . - - . - -. . . . . -. . -. . . . . . . - -. - . - . . . . . -.
.. . ........._
. . 9-29 3.-
9-37 1.00CE 08 5.012E 1 C 9-59 3.467E 11 6 - 2 5 2 F 09
115
! OECLINATION=Z3.5 DEG TIFE(HR-WI#) N t O ) N ( E 3 ) TIME(HR-HIN) N(C) N(C3) -
a- 1 1.549E 11 1.164E 09 0- 3 . IeC7ZE 11 9.931E 09
1- 7 1.698E 11 1.265c 09 1- 1 1.C96E 11 1.023E 10 1-33 ' . l.738E 1 1 1.306~ alj 1-31 1.122E 11 1.047E 1C
a-37 1.022E 11 1.227E 09 0-33 1.C72E 11 1.000~ io .. ... __.______.__..__..______________________------.--------
2- 7 1.778E 11 1.349E a9 2- 3 1.122E 11 1.047E 10
116
117
c-33 1.148E 11 6.761E 08 c-3 7 1.000E 11 7.656E 09 . 1- 3 1.175E 11 7.C47E 08 1- 3 1.023E 11 7.762E 09
__-____ 1-37 1.230E 11 1-37 1.047E 11 7.852E 09 2- 1 1.288E 11 2- 3 1.C47E 11 7.925E
Oq--.-
. .. -. . . . . . . . . - - -. - . - -. - - -. . - - - - -. - -. .. - - -. . - - -. . - - -. -. . -. - - . . . -. .
118
.. -. . . . . . . . . . . . . . - -. - - - -T&b- Am.. ._. . . - -. . . . . . . . . . . ~. . . . . . - _ _ _ _ _ _ _ _ _ _ -. -. _. . . . . . . . . . . . __. . . _. -&&Z+-Ag.. . . . ._. .__.___ ._ . . . . . . . . . .
- - ...-..-- LATITlDE=-3C.C CEG ALTITUOE= 6n.c K M LATITlDE=-45.C CEG ALTITUDE= 90.0 KP
CECLINATION=23.5 OEG -__ - --_--_______ T I R E m-N I N 1 N ( C I R ( C 3 ) T I C E ( l ' R - C I N ) N(0) h ( C 3 ) ________.___._..............~.~--~.-.-~--~~~~~~~~~~.~~.~~~~~~~~.~~~~...
3.548E 10 2.57CE LC 0- 7 . 2.951E 11 4.889E 0 7 c- -0- -.-- . -....._..____ ..____........ . .
0-33 3.54EE 1 0 2.512E 1 0 0-3 1 2.951E 11 4.872E 07 1- 3 3.548E 10 2.512E 10 1- 7 2.951E 11 4.934E 0 7
___ 1-3 1 3.548E 1 0 2.512E 1 0 1-33 2.951E 11 4.953E 07 2- 3 3.467E 10 2.512E 1 0 2- 7 3.020E 11 4.9 7 1 E T - -
. . -2 -33 3.467E 1 0 ........__ 2.455E I C . 2-3 1 3.02CE 11 4.972E 0 7 2.3996 .i.O. . ._._........._.............~~..~~~~----~~~~~-.--~-----~-~---~~~~~.~-~.~~~..~ 3- 1 3.388E 1 0 3- 7 3eC20E 11 5.015E 0 7 3-31 3.311E 10 2.344E 1 C 3-33 3.020E 11 5.028E 0 7 2. 291E io. . 5-b'9eE'.07 .- 4.~. __._... ......
4-3 1 3.020E 1 0 2.188E 1 0 4-33 3.020E 11 5.082E 08 ' 5- 0 2.884E 10 2.0 89E-10- -- -- 5 -14 3.020E 11 1 . 2 6 5 r -
5-44 2.951E 11 .. 1.60CE 0 9 6- 7 6-37 7' - i...ca-o.E--* 1.000E 0 8 4.898E 1 0 6-44 2.951E 11 1.968E 0 9
2.153E 0 9 4-xm?-lc---- 8-29
7-37 1.CCOE 08 L . C O 0 E 08 e- 7 2.884E 11 2 .188 t 09
------.-....-.....__-~--~~. ....._..__.___.......
3.162E 10 4- 3 3.OZCE 11
- 1-.-e2OF-v9--- - __. ... ___.._ _............. 2..q451E..11 ....___.___... 5-37 . - . - - - - - 1.000E l'-o.o.~.E..o.~ 0 8 4.898E 4 98E '.io LO .
. 5: E.€. yc . . . . . . . . . . .. . . . .. . .~. -2 q.. . . . . . . . . .. . .Z - - ~ -8-~E--I ~-. -. -_. -. - - -. . ~ . .o 9qF. o.4. . . - __ 4.898E 1 0 7-59 2e884E 11 - ' . -
119
120
121
23-31 5.37CE 1 0 23-31 3.388E 10 1.778E 1 0 ~. . . ~~~ ~ ~ ~ .- -~ ~ ._- .
1 2 2
2 . CObIPUTATIONAL CONSIDERATIONS
The e n t i r e computer program used i n numerical i n t e g r a t i o n o f t h e 0 and 03
d i f f e r e n t i a l equat ions i s given i n Tables A38 through A42. Many important notes
a r e contained on t h e comment cards wi th in each subprogram. A l l computations
d i r e c t l y involved i n t h e numerical i n t e g r a t i o n of t h e d i f f e r e n t i a l equations
were done i n double p rec i s ion t o decrease round-off e r r o r s .
wr i t t en i n Fortran I V f o r t h e IBM System/360. The ac tua l numerical
The program i s
in t eg ra t ion is done by t h e DRKGS Subroutine which is provided f o r t h e IBM
System/360 by IBM. The i n t e g r a t i o n was done by means of t h e fou r th order
Runge-Kutta formulae i n t h e modif icat ion due t o G i l l . The comment cards i n
Table A42 conta in more information on t h i s method. The maximum absolu te e r r o r
i n concentrat ion p e r i n t e g r a t i o n was l imi ted t o a f a c t o r of roughly .0005 times
the i n i t i a l value of t h e concentrat ion f o r each cons t i t uen t 0 and 03. I t is
unl ike ly t h a t such e r r o r s would accumulate s i g n i f i c a n t l y as the i n t e g r a t i o n
proceeds because an excess o r dear th 0.f a spec ies r e s u l t s i n a corresponding
increase o r decrease of i t s r a t e of des t ruc t ion . During most of t h e
ca l cu la t ions t h i s e r r o r l i m i t was s a t i s f i e d while i n t e g r a t i n g i n 15-minute
jumps, bu t a t s u n r i s e and sunse t , t h e i n t e g r a t i o n i n t e r v a l dropped t o 1 second
o r less. The t y p i c a l I B M System/360 computer running t i m e f o r a 6-day p r o f i l e
of 0 and O3 was about 3 minutes.
Following is a l i s t of notes pe r t a in ing t o t h e programs. Additional
information i s contained on comment cards wi th in each program.
Main Program Table A38
ZQ12 = i n t e g r a l o f g2 from 300 km t o a l t i t u d e of i n t e r e s t , LAT = l a t i t u d e ,
DEC = dec l ina t ion TXPLOT, TYX, TYPLOT, SIZEX, SIZES a re cont ro l vec tors f o r
the "calcomp" p l c t t e r . A l l s ta tements of t h e form CALL CCP . . . are p l o t t i n g
123
124
Table A38 (Continued)
- - -_ L O G ( 1 0 ) flF 03 C O N C E N T R A T I O N v 3393.99 . . ____ I I S N 0114 C A L L C C P 5 A X [ 0 . 0 , 0 . 0 9 3 3 H
I s a . L ' . i y x ~ ~ C A L L C C P 5 A X (0.0 90.0 11 1 H T I M E (HOURS ) 9 - 1 1 v S I Z E X , O.O,TXPLOT) ~~~~-tGPb=~rtffWSYR3?N;T ; T x ~ T T ;fYX,. .-----I~-uIT6---------------- .................................................
..... TSN-UI-TB ........ 4~ ..... 'GoNTTmuE ..... ~ ..........................................................................
I S N 0115
I S N 0117 C A L L C C P l P L 1 S I Z E S ~ C . O v - 3 J
.. 1 S N U l L U L LCN m U t
'ISN 0119 3 C O N T I N U E
STOP ---------------------------- I S N 0121 TSN-uIZZ---------------- .................................................................
.
..............................................................................................................................
125
commands, W and S a r e used i n con t ro l l i ng p r in t -ou t . R = photon flux; S2 =
02 absorb. cross-x: S3 = O3 absorp. cross-x, t h e 13 VA values a re t h e y
i n t e r c e p t values f o r t h e Chapman funct ion approximations f o r 1" i n t e r v a l s
from 80" t o 93".
l i n e a r approximations f o r t h e 1" i n t e r v a l from 80" t o 93".
AUX, Y, X a r e descr ibed i n Table A42 .
The 1 3 V B values a r e t h e s lopes of t h e Chapman funct ion
PRMT, DERY, N D I M ,
The values of R , S2, and Se were incorporated i n t o t h e program i n a Bloch DATA
subprogram which was i n common with the l abe l l ed common /BFLUX/.
Subroutine FCT TABLE A39
This subrout ine is c a l l e d by t h e in t eg ra t ion rout ine DRKGS. I t ca l cu la t e s
the time r a t e of charge of 03 (DERY(2)) from t h e values of O(Y(2)) which
have been ca lcu la ted i n subrout ine DRKGS. Subroutine FCT c a l l s Subroutine
Flux t o c a l c u l a t e t h e d i s soc ia t ion r a t e Joz(F2) and Jog(F3).
Subroutine Flux TABLE A40
This subrout ine ca l cu la t e s t h e photodissociat ion r a t e s J 0 2 and Jog (F2 and
F3) as the s o l a r zeni th angle x changes.
zeni th angle. COSCHI i s ca lcu la ted from t h e l a t i t u d e , dec l ina t ion , and hour
angle i n subrout ine f lux . For x > 90", COSCHI is l e s s than zero i n ISN 13
s o a l l d i s soc ia t ion r a t e s a r e s e t t o zero i n ISN 14 and 15.
values a r e checked i n ISN 17 t o determine whether t h e Chapman funct ion
approximation i s required.
r a t e s F2 and F3 a r e summed over contr ibut ions from a l l 87 wavelength intervals
i n which s o l a r f l ux and cross sec t ion da ta were tabula ted . ISN 26 checks f o r
la rge negat ive arguments and s e t s cont r ibu t ions from such terms t o zero t o
avoid an exponential underflow.
COSCHI = cos x where x is the s o l a r
For x > 90°, t he
From ISN 2 2 t o ISN 29 new values of t h e d i s soc ia t ion
126
Table A39
127
Table A40
128
Subroutine @OTP TABLE A41
This subrout ine cont ro ls t h e p r i n t i n g of t h e re levant da ta .
N I N = number "/ time t h a t output has been ca l l ed by t h e equation so lv ing
Subroutine DRKGS. Hence, it represents t h e number of i n t eg ra t ions t h a t have been
required t o t h a t po in t .
X = TIME i n seconds
CHI = Solar zeni th angle i n degrees ca l cu la t ed from the cosine o f ch i
ca lcu la ted i n Subroutine Flux. The d i f f e r e n t i a l equation rout ine i n t e g r a t e
f o r 6 days under t h e values of 0 3 concentrat ion a re with 5% a t successive
noons i n which case the program terminates by s e t t i n g PRMI(5) = 5.0 .
check and r e s u l t a n t terminat ion r e s u l t s i n ISN 29 through ISN 33.
This
ALAT, ADEC a re t h e l a t i t u d e and dec l ina t ion i n degrees. A t y p i c a l shee t
of output i s shown i n Table A43.
H and SH = i n t eg ra t ion increment.
Subroutine DRKGS TABLE A42
This i s a l i b r a r y subrout ine furnished by IBM. I t i s the subrout ine which
ac tua l ly i n t e g r a t e s t he d i f f e r e n t i a l equat ion. The subrout ine has been
modified s l i g h t l y by including t h e va r i ab le H i n t h e arguments of a l l Subroutine
Output statements t o t ransmi t t he in t eg ra t ion i n t e r v a l . Also the card DRKG
0216 has been replaced by t h e card, 25 CONTINUE, t o permit unl imited b i sec t ions
of the i n i t i a l i n t eg ra t ion i n t e r v a l .
129
1 Table A41
1800 S F C O N D S ( H A L F HOU9
r Y S3(49) 9 XHR I 4 9 1
THF R E S U L T 5 OF S U C C F S S I V E
130
Table A42
S U R R C U T I N F O R K G S ( P R M T , Y ~ C E R Y ~ N D I M ~ I H L F ~ F C T l n U T P , n U X ) c---- I i R KG DRKG
070 19 29 3 9 49 53
F D
b0 r TO S C L V F A S Y S T E C C F F I R S T ORDER '3ROTNAQY D I F F E R E N T I A L DRKG 79 c - - E O U A T I C N S W I T H G I V E N I N I T I A L VDLUES. D R K G 80 C D R K G 97
-T-----mn'E - DRKG 109 C C A L L DRKGS ( PRVT t Y 9 CERY 9 N C I M , I P L F , FCT,FIJTP, A l J X P Q Y G 11')
--c------ ---- P A T A R E T E R S F C T Ah0 OUTP R E O I I I R F AY E X T F R N A L S T P T E V F N T . QRKG 177
c - - D F S C R T P T I C N OF PPRPWETERS DRKG 140 C P R C T - D O I I P L F P R E C I S I D N I t ' P U T AYD D U T P U T VFCTOR W I T H DRKG 159
7: ~ D I M E h S I C N GREATFR T H A N O R F 9 U A L T O 5 1 W H I C H P R K G 160 r S P E C I F I F S T H E P A R A P E T E R S OF THE T N T E R V A L AND OF ORKG 170
ACCURPCY OND W H I C H S E R V F S F(3R C O M M U N I C A T I O N RETWEENDRKG 180 ~ - _-__ - -__ - . _ _ . . C O U T P U T S U P R C U T I N E ( F U P N I S H E C PY T H E USFQ) A N 0 0 R K G 199
SURROIJTINE DRKGS. E X C F P T P R Y T ( 5 1 THE COMPPYCNTS D R K 5 ?no .~--"--.--------
C ARE NOT OESTROYEC PY S l I H Q 7 U T I Y E ~ C R I < G S AND T H E Y ARF DPKG 2 1 9 --mrpTTr)- LOWER R C I J K C CF THE INTERVAL (TNDUT), P R K G 220
C P R C T ( 2 ) - U P P E R P C U h C C F T h E I N T E R V A L ( I N P U T ) . DRKG 239 vRMTT31- I N I T I A L I N C R F V F N T O F T H F I N D E P F Y O F V T V A R I A R L F n R K G 247
-t---------------- r ( I N P U T ) 9 DRKG 2 5 0
PRFTI47- U P P E R ERRCR R r U h C ( T N P U T ) . I F A B S r L I J T E F R R f l 9 TS "RKG ?6n --~---------------'
c GREATER T b A N P R M T ( 4 1 , I Y C R F Y F N T G E T 5 HALVEC). D R K G 270 - -'TF I N C R E P F N T IS L F S S T H A Y P R u T I 3 ) ANI7 A S S O L U T F DRKG 2 4 7 C E9RflR L E S S T H A N P R M T ( 4 ) / 5 3 , I N C R E M E N T G F T S DOIJSLED.DRKG 200
TFE U S E R B A Y CHAYGE P r l M T f 4 1 PY V F A N S O F H T S DRYG 3 3 0 -%---------------------------
C O U T P L T S U i ? R P U T I Y F . D P K G 310 --~---------------- FWT7-51-- XD I N P U T P A R A C F T E P . S U R R O U T I N F O R K G q I N I T I 4 L I Z F S DRKC 3 7 0 C P R M T ( 5 ) = 3 . I F T H E U S F R WAVTS TO T F Q M I N A T F l l R K G 379 C S U B R C U T I N E CRKG? 4 T A h Y ClJTPUT P O T V T , H E H 4 5 TO n F K G 343 C CHANGF P R M T l 5 1 T U NON-ZERO B Y Y E A N S flF SUHR'lUTINE n R K G 2 5 0
C F E 4 S I s L E I F I T S D l P F t v S I O t v I S D E F I N E D GREATEQ DPKG 3 7 9 T H A R 5. HCWEVFP SIJRQC'UTIYE OQKGS C O F S UGT R F W T P E n P K G 799 A N 0 CIJANGE THFM. N E V F R T H E L F T S T H E Y klAY C.F ( I 5 E F U L 0 R K G 390 C
; ( C A L L I N G CRKGS) WHICH ARE Q R T A I Y F C ' 9 Y S P F C I A L DRKG 41" Y A N I P U L P T I C N S W I T H O U T P U T D A T A I N S I I P R O I I T I N F n I J T P . DRKG 4 7 r l
-'~'------------..-
C Y - 9 0 U e L E D R E C I S I C N I h P U T VECTOR O F T Y I T I A L V 4 L U F S QQKG 4 3 9 I n F S T R O Y E C l . L A T F R O Y Y IS T H F R F S U L T I Y G VECTOP O F DPKG 440 -.c __--_ -. _ _ _ _ - -
C D E P F N r l E N T V D R I A R L E S C r M P U T F O AT I N T E Q M E D I A T F DRKG 450 -I------ P C I W T S x. DRKG 46'l
C DERY - O O l l @ L E P R E C I S I n N I N P U T V F C T f l R O F FRRf lQ W E I G H T S DRKG 470 - c---- - ( D E S T Q C Y E C ) . T H F SUM OF I T S CDMPONFNTS MlJST S E DRKC 4 8 7
C F G U A L TO I . L A T F P O h CEPY I S T H F VFCTI IR n F DRKG 490 c - - - - - - - D F P I V A T I V E S , W H I C H R F L f l Y C TO F U N C T I O N V A L U F S Y A T DRKG 50'7 C I N T E R M E C I D T E P O I N T S K. OPKG 5 1 0 L-- WTP - AN I h P U T VPLUEt W H I C H S D F C I F I F S T H E NUMrjFP I lF ODKC 520 - c - E Q U A T I C h S I N T H F SYSTEM. OPKG 530
C I H L F - AN OUTPUT V A L U E , W H I C F S P F C I F I E S T H F NUMRER OF DPKG 5 4 0 L T I T S E C T T O N S CF TIJE I N I T I A L I Y C Q E M E N T . I F TFLF G E T S P R K G 5 5 0 C G R E A T E R T H A N 109 S U D R O I J T I N F OPKGS R E T U R N S W I T H DPKG 5 6 0
€nRrJR C E S S P G E I H L F = 1 1 I N T O V A I N PROGOAM. FQROR n R K G 5 7 0 C MESSAGF I H L F = 1 2 CR I H L F = 1 3 APPEARS I W C A S E ORKG 580
PRMT131='5 CR I N C A S E S I G ~ r P 3 M T ( ? ) ) . N € . S f G N ( D ~ ~ T ( 2 ) - D R K G 5 9 0 C P R M T ( 1 ) 1 R E S P E C T I V E L Y e ORKG 600 L t L I - H t N m E OF AN F X T E R N P L S115901JTTVF USED. T Y I 5 QRKC 610 C S U R R O U T I N E C C C P U T F S T b E Q 1 5 H T H 4 N O SIDES D E R Y O F ORKG 629
THE-S'VSTFP T n G I V E N VALIJES X AND Y. TTS P A Q A M E T E R "RKG 630 C L I S T MUST RE X t Y v D F R Y . SURR' l lJTIVE F C T SHOULD DRKG 640
T J C T T I E S T R C Y X A N 0 Y. D R K G 65'7 C OUTP - T H E h P C E CF AK E X T E R N E L O U T P U T S U P R O U T I N F U S E D . D P K G 660
C NCNE CF T F E S E PARAMETERS ( E X C E P T , I F N F C E S S A R Y ? n R K G 6A0 P R M T t 4 1 , P R P T I 5 ) , . . . ) SHf lULD t l F CHDNGED R Y DQKG 690 -2----1---------------'--------.
C S U S R O U T I N E CUTP. I F PREOT(5) I S CHAYGFC TO V O Y - Z E R f l l O R K G 700 S U B R O U T I N E CRKGS I S T E R M I N A T E D . n R K G 719 -t"--------------------
C AUY - D r l U B L E P R E C I S I L N A U X I L I A R Y STOQACE ARRAY W I T H 9 D Q K G 720 .-- - ROWS BNC NOIC C C L U Y N S . DRKG 730 r - O R K G 740
C D P K G 1-m
---ULTP. F U R T H E R C C P P C N E h T 5 C F VFCTOR PRMT ADE m c G ---c------^------------------
"-c------------'--------.
FER H n N O I h G R E S U L T V A L U F S T r l T P F M A I N PRPGQAC O P K G 4nq --
--c-----------------------------
--c------------------------------
--c-----------------------------
--c-----------------------------
L 1 TS P B R A M E T E R L t S T Y U S T B F X , Y , O E R Y , I H L F , N ~ I M I P R M T ~ D R K G 670
131
Table A 4 2 ( C o n t i n u e d )
-e----------- w-mm-- -- DRKG 7 5 0 C THE PROCEDURE T F R Y I h A T E S A Y D R E T U R V S TO C A L L I N G PROGRAM, I F DRKG 760
TTT-PORFTFlnN 10 E I S E C T I O N S OF T H E I N I T I A L I N C R E M F N T ARE D R K G 770 C NECESSARY T O G E T S A T I S F A C T C R Y ACCUPACY (ERROP MESSAGE D R K G 78'l l, I n r F = m 7 D R K G 797 C ( 2 1 I N I T I A L I N C R E C E N T I S EQUAL TO 3 OR H A S WRONG S I G N DRKG 800
1TRRCJR MESSAGES I P L F = 1 2 OR f H L F = 1 3 1 , DRKG 311) C ( 3 1 T H E WHOLE I N T E G R A T I C V I N T E R V A L I S WORKED TH4f IUCHv DRKG 820
T+T SURRUUTINE OUTP H A S CHANGFC P R M T ( 5 ) TO YON-ZERO. D R K G 8 3 3 C D R K G 849 L 5 L W ES AND F U N C T I C h SUPPRDCRACS WEQUIRFO DRKG 850
DRKG 860 C T H E E X T E R N d L ?URKOUTINFS F C T I X , Y v D E ? Y ) A N D O t J T P t X r ~ r 0 E ~ Y , I H L F r h D I P * P P M T ) W S T I?€ FU"N1SHED B Y TFIE U S E R e D R K G 870
C ORKG 880 c------------ NETHpu---- DRKG 890 C F V 4 L U 4 T I O N IS DONE E!Y PFANS O F FOtJRTH ORDER RUNGE-KUTTA DRKG 900 t rumulxE I Y T H F ~ C O I F I C A T I O N DUF T O G I L L . ACClJRACY IS D R K G 910 C T E S T E D C C M P A R I h G THE R E S U L T S C F THF P 9 G C C D U R F h I T H S I N G L E n R K G 9 7 0 c---------- X R D D O U B L E I h C R t Y E Y T . D P K G S t 0 C S U R P C U T I N E C R K G S A U T C Y A T I C A L L Y A D J U S T S T H E I N C R F M F N T D U R I N G O P K G 9 4 7
T H E W O L F C O C P U T A T I C N P Y FIALVIWG OR D O U B L I Y G . I F YORF T H A N DRKG 950 C 10 B I S E C T I O N S C F TFrE I h C R E M E N T ARE N F C E S S A R Y TO G E T D P K G 5 6 0 L SAff^PFbM3RY OCCURACY, 1HF S U R 4 0 U T I N F PETURNS W I T H DQKG 9 7 D C F P R O R MFSSAGE I H L F = 1 1 I N T r V A I N P R W P A V . 0 9 K G 9 8 9
TU GFT FULL F L F X I P I L I T Y IF: fUTPUT, AN O U T P U T SURRCU'INE DRKG 997 C MUST R E F U Q N I S H E O B Y THE USFR. D R K G l O O O
C R A L S T O W W I L F . M A T H F M A T I C A L VETHODS FOR O I G I T A L COMPUTERS, D R K G l n 7 ' 1 D R K G 1 033
c D P K G J 040 c- - - --- ................................................................... D R K G I 0 5 ~ C OR K G 1 '760 c - - - D R K G l O R O C O R K G I c'90
i3R KG 1100
P R K G I 1 2 0 I S N O C 0 4
I s h CCCS C C L S L F P R F C C S I O F , O D E S 6 1Tc77+1* hTTp- 0 Q K G 1 1 3 7
I S N 0007 1 A U X 1 9 , 1 ) = . 3 6 6 b 6 6 6 6 6 6 6 6 6 6 6 6 6 7 C ~ ~ D E R Y ~ I ) OR K G 1 143 T = P R Y T t I 1 n R K G l 1 5 3 IsN ~~~ _.________._
I S N C C C S X F N D = P R W T l 2 ) W' K G 1 1 6 i ) I yhl flcrc--------------- P Z p R u T 7 7 ) ~QKT;I 170 ISN O C l l P R N T ( 5 ) =9* PO ns K G 1 1 RO
_--_-------- -
---_--------- *----------------
------- -cI----------------l---
.-------------c--------------~-
--_---------- c---------,.----- __________-__
__-_---___--- -___--__---_- c---------------
_____-___---_ c------ -____-_-
-------------t--'-----------
L, WFU Y C R K I t t h C O N t 1963, PP.11'1-127.
- F f l R - T E F E R E N C E p S E E DR K G 1 P 1
___.___._____
_____.________-__
-mrmm------- DtTEn'S7P.N Y t 1 ) ,OERY 1 1 1 t AUX (8 7 1 ) , A ( 4 ) , 8 ( 4 ) C ( 4 ) 9 P R M T 1) OOUSLE P R F C f S l r h P R ~ T , Y , C E P Y ~ A ~ J X ~ ~ , ~ ~ C ~ X ~ X C N C ~ H ~ ~ J , B J ~ C J , R I I ~ ~ ~ , D R K G l 1 1 9
. - _ _ 1 P F L T
---- CELT FT. T1 X 9 Y 9 DE R Y 1 D Q K G 1 1 9 9 C D R K G 1 2 0 n C '----'+RRCR T F S T D R K G l 210
I S N O C 1 3 I F ( H " ( X F N n - Y ) ) 7 8 r 3 7 9 7 DO K t 1 2 2 7 O R K G 1 2 3 9 c ------- - -
C P R E P A R A T I O N S FOR RUNGF-KCTTA WFTHOO n R K G l 2 4 0 -mm------z-nrr=-o mt! nn K G 1 2 5 0
I S N C C 1 5 A ( 2 ) = .2 9 2 R 93 2 1 8 8 1 7 4 5 2 4 8 0 C n R K G 1 2 6 9 6~T7=1.7fl7~~67811865475DC D Q K G I 77'7 T s N - ~ ~ 6 - - --.-- --. --
ISN C C 1 7 ~ ( 4 ) = . 1 6 6 ~ 6 h 6 6 6 6 6 6 h 6 6 6 7 ~ @ O P K G 1 7 9 n PI rj =7. n3 n R K G 1 7 9 0 'r SN'VCTB-- .___--- _-. --
I S N C C 1 9 ec 2 1 = l e 0 3 D R K G l 7 0 0 IS4 C C L U P I 5 1 = I .DT DQ K G 1 310 I S N O C 2 1 P ( 4 ) =2.00 D R K G 1 3 7 0
----TZN-~OC*Z----'---------' 7TTT';mT DR K G l 3 3 i ) I S N @ C 2 3 c ( 2 ) =. 7 1 2 8 9 3 2 I 3~ 1 3 4 5 2 4 5 0 ~ OPKG1-347
DR K G 1 7 5 3 -----TSN-'U074---------------- n P K C , 1 7 6 0
L O R K G I 371 I S N O C 2 5 C ( 4 ) = . 5 D I :
C P P E P A R 4 T I O N S OF F I R S T RUPiCE-KUTT4 S T E P D R K G l 3 e 0 -U~T-~--I~-T-, m-w 0 P K G 1 79r)
I S N C C 2 7 4 U Y ( 1 r I 1 = Y ( I J ~ K G I 4n0 O P K G L 4 1 0 NlXT7;TT =TmY C I
ISN @ E 2 9 AUX( 3 , I I =n.03 D R K G 1 4 7 7 I S N 5 n u n 6 7 I7xJ.U') VKGI 43n I S N O C 3 1 I R E C = O 09 K G 1 4 4 0
p=w*w- -- - 519 K G 1 4 5 i) I S N C C 3 3 I H L F =-1 O R K G 1 4 6 9
I S N 0035 I F N D = r ) W K G 1480 - - - D R K G ? 4 4 0 C n R K G 1 5 0 3
D R K G l 5 1 9 C - - - - - - - T l X R T 5 - A RUNGF-KUTTA S T F P I S N O C 3 6 4 I F ( ( X + H - X F Y D ) " H I 7 9 ~ , 5 D R K G l 5 7 9
- 5 F=XFND-X n R K G l 5 3 0 I ~ - % D J T ' _ _ _ _ -
I S N 00?8 6 I € k r ) = l f 3 9 K G 1 5 4 7
. . . _ _ _ - - - .__
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T C T T T - T ; ~ ~ ~ - J ~ ~ 1 ~ 6 5 4 7 5 0 ~
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-.--131F-%~p---'------------
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132 Table A42 (Continued)
D S K G i 5 5 0 D R K G l 56'3 DQ K G 1 5 7 0 n R K G 1 5 8 0 D Q K G 1 5 9 3 DR K G 1600 D R K G l 6 l O DR K G I 6 2 0 O R K G 1 6 3 0 D R K G 1 6 4 0 DR K G 1 6 50 D R K G l 6 6 0 O R K G 1 6 7 0 DR K G 1680 DP K G 1 6 4 6 P R K G 1 7 0 0 D R K G 1 7 1 3 DR K G 1 7 20 D R K G 1 7 3 0 n R K G 1 740 C P K G 1 7 5 3 P Q K G 1 7 6 0 D R K G I 77'3 n P KG 1 7 8 0 D 9 K G 1 7 9 0 OR K G 1 PO0 OR K G l R 1 0 DQ K G 1 870 D R K G I R 7 0 D Q K G l A 4 0 D R K G l P 5 0
O F ACClJRACY O R K G I P h ' 7 N K G 1 e70 ORKG1 8 8 0 OR K G 1890 D R K G l 9 0 ' 7 DR YG 1910 D R K G l 9 7 3 D R K G 1 9 3 0 D R K G 1 9 4 0 n R K G 1 9 5 0 n R K G 1 9 6 0 D R K G 1 9 7 0 D R K C 1 9 R O D R K G l 9 9 0 O R K G 2 9 0 0 n R K G 7 O I 0 D R K G 2 0 2 0 tlQ K G 2 q 3 0 D K K G 7 0 4 0 D R K G 2 0 5 3 D P K G 2 0 6 0 DR K G ? P 7 0 D R K G 7 0 8 0 n R K G 2 0 q n D Q K G 7 1 0 O P R K G Z I 10 DP K G 2 1 2 0 O P K G 2 1 3 0 D R K G 2 140
PR K G ? 1 5 0 D R K G 2 170 DP K G 2 1 8 0 DRKGZ 19 '3 D R K G 2 7 0 0 n R K G 2 2 I 0 0 P K G 7 2 2 0 n P K G 7 233 D R K G 2 2 4 3 D R K G 2 2 50 D R K G 2 2 6 0 DR K G 2 2 70 RRKGZ 7 P 9 D R K G 2 2 4 7 D R K G 7 3 0 0
D Q K G 2 3 7 0 n ~ ~ w 3 1 7
133
f DR K G 2 330 D R K G 7 1 4 0 DR K G 2 3 5 0 D R K G 7 3 6 0 D R K G 2 3 7 7 DR K G 2 3 8 0 O R K G 7 3 9 0 DRKG240C) D R K G 2 4 1 9 OK K G 7 4 2 0 D R K G 2 4 3 0 O R K G 2 4 4 0 DP KG2 4 5 3 O R K G 2 4 6 0 DR K G 2 4 7 0 f l P K G 7 4 8 1 DR K G 7 4 9 0 D R K G 2 5 0 0 OR K G 7 5 1 9 DR !<G 2 5 2 'I D R K t 2 5 3 0 DR KG 2 5 4 0 i lR K G 2 5 5 '3 PRKG7 500 ORKGZ 5 7 0 OR KG 7 5 87 DR K G 2 5 4 3 RP K G 7 6 0 0 DP K G 7 6 1 @ n R K t 2 6 2 0 DR K G 2 6 7 0
134
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