Mathematical model for estimating probable cyclic variations in Martian atmosphere during solar activit

Lichtenfeld, K.

Vachon, D. N.

Weidner, D. K.

English

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FI bk(JAHY, 190,8	 DOC ()Ni f N T Nei, CHS0221
AN ESTIMATE
OF THE SOLAR CYCLIC VARIATION
OF THE MARTIAN UPPER ATMOSPHERE
D. N. VACHON, D. WEIDNER. K. LICHTENFELD
i	 (PAGES) -9E)_'
(NASACR ^' R AX R AD NUMBER) (CATEGORY)
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AN E8TIMATIC OF THEBQf.AIt CYCLfC
LATIt3N OF TI1E MAITEAN UPPER
	
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SUMUMV
A semi-empirical model of the Martian atmosphere Is pre
seated. This model is modified by means of an empirical
formulation to provide ra estimate of probable cyclic variations
In the Martian upx or atmosphere. The resulting variations are
compared to those encountered in the Earth's atmosphere said
on this basis appear reasonable.
The results indloate that the Martian atmospheric density at
I t 000 kilometers during a period of high solar activity is likely
to be three orders of magnitude greater than it is during a
period of low solar activity. The results therefore suggest
that the upper atmosphere density profile inferred from the
Mariner IV flyby experiments is likely is be substantially
different from that which will be inferred from the Mars 148
experiments.
may WOW
TABLE OF CONTZNTS
section	 Phze
ABBTRACT# of 009 * 609#0 000000000	 1
I INTRODUCTION** 2
2 MEAN ATMOSPHERE MODEL 0 3
3 PREDICTED SOLAR FLUX. 0
4 EX ISPHERE
4.1	 Temperature Variation
4.2	 Altitude of Exomphore Base
5 THERMOSPHERE
S o I	 Altitude of Bass
5,2	 Thermal Gradient 0 0 it
5. 3	 Altitude of Top of Thermosphere 12
6 VARIATION OF ATMOSPHERIC DENSITY a 0 0 0 0 0 0 17
6. 1	 Diurnal Variation	 .	 .	 .	 .	 .	 . . . 17
6.2	 Solar Cyclic Variations 17
7 CONCLUSIONS ** 21
8 REFERENCES 0 0 0 0 0 22
Ifl"`-`° „-: :fid ^^
	*.°'^•',x *^5"r6^^*we Wit- .^.r^--.-^ `-^a . ^.*^y.. ^- 	 `^ -
TILT OF tLLUSTUTIONE
ZIUM Pan
2-1 Temperature Profile in Ream At	 re Model of Mars . 4
2-2 Molecular Weight Profile to MeanAtmosphere Model of Mars	 .	 .	 .	 . d
2-3 and Kxtreme Density Profiles of the Martian Atmospheres 6 k
LIST OF TABLZB
3-1 Predicted Values of the 10.7-Centimeter Flux.	 .	 •	 • 7
-1 Martian Zxospheric Temperature a	 as a Function of the 10.7-
Centimeter Solar Flux(e) .	 .	 .	 ,	 •	 .	 •	 .	 .	 •	 .	 •	 •	 .	 .	 •	 . Q
4-2 Comparison of the Harris and Priester Model Temperatures at
3000 k and 420 Ion i 	.	 •	 •	 •	 •	 •	 •
6-1 Altitude Variation of the Thermal Grad ient eK/km) in the Earth's
Tharmorphere as a Function of Solar Activity •	 • i6
6--2 Altitude Variation of the Thermal Gradient (OK/km) in the Martian
Thermosphere as a Motion of Solar Activity. 14
5-3 Integrated Thermal Gradients (OK/km) in the Martian Thermosphere
as a Function of Solar Activity .	 .	 .	 .	 .	 .	 .	 .	 .	 •	 .	 . 16
6-1 Distribution of Density at 1000 Kilometers in Models of the r
'terrestrial
 
and Martian Atmospheres
6-2 Variation of the Martin, Atmospheric Density (g/co) at 704
Kilometers as a Function Of Kolar Activity •	 •	 • 20 k
4
9
R
r
k
2S
tit
i
AN ESTIMATE OF THE SOLAR CYCLIC VAMA71ON OF THE
MA92UN UPPXR ATMOSPHERE*
by
AEdTRACT
A semi-empiriosl model of the Martian stmosp6ore is presented. This model is modified
by means of an empirical formulation to provide an estimate of probable oyclic variations in
the MArtlan upper atmosphere. The resulting variations are ooampared to those encountered
In the Earth's atmosphere and on this basis appear reasonable.
i
INCT'ION 1
INTRODUCTION
Defining the deity pr^ile of the Martian Gaper atts^aaipheredensit 	 is somewhat of a problem,
sings it can be expected that the structure of the outer atnaospbera will be greatly influenced
by solar variations In muob the same mawwr as Is the zartbls atmo ►spberc It Is expected
that the density at high altitudes (greater than 200 ion) will be greatest during periods of
high solar aotivity, as is the cue in the RartbOs uppee atmosphere. Thus, an estimate of
the probable solar oyolio-related variation of the upper atmosphere of Mare can be of
assistanoe in reduoing the uncertainty rage of density variation likely to be experienced in
ow given year. In addition, such an estimate % ^xdd provide a means of relating derived
density profiles from fly-'by experiments made at different periods of tines.
The purpose of this paper is tot
W
i
UCTION p
NUN A	 snit! UODZL
lgMYl model am aasooiated extretn• e'!velope Me revs,onsly been! dev^loa-- by
D. weldner In 1967 and Weidner and Hosealtlne In 1967. The model was bmW in part on
the results of a number of theorrtloal etudlse on the struoturs and chemical kinetics of the
atmosphere, {a, & Chamberlain
 and Mozlroy 1966, Donahue 1006g FJeldbo, st al. -1 ,
Johnson - 1985, and Smith and Bsudler • 1966N The results of others were thus taken into
Account in the awy whiob included cansideratioia oft the various l rlrrststi 	 Of the
Mariner IV data, the diffusion and possible esoap #r of the Martian 8xosphario psea, the
1goo
goo
0 400	 Go	 loo	 1000
TgMMATURK (No
1000
•iWil! mm m M009L
goo
	
Nam 1009 L
mmmw# .,rr MAXIMUM M 9L
goo
too
Q
to—is 10-14 la-l0	 10	 4 Z
OmITY (am C.00)
1#1 2
71pre 2-& Man and Zctr a Density Profiles of the M*r1 Atmospheres
i
rA
yip
I
F
•
r	
U! fMON 3
k	 PRRIXCTRD BOLAR FLUXG
Na^
rear	 10-22 wa
E3ft4MO
110-22 watts/m2/02gl
1871 180 to 180
1973 110 to 135
1878 70 to 80
1884	 70
1888	 208 to 228
75 to 85
280 to 810
805 to 828
140 to 17 5
88 to 110
Tabu 9-1. Pra ICW Values at the 10* 7-CSSUmetar Floc
7
s°^	
.- «dz^v.=:!_°aF^ears-.is.^,^ma scw_>-:.. an..,,,,^...:^:,,yaf. ..., ._^-ar: ^^.....s•.,i^7px........_^._.ab;d... _.w sn.n.-.+^^_ ys^w.r,.::.:.^^,.^... ..s=;-.r.._wls.,wwa.^-,: ..^.m.^..+^a ..- .:.:..^^.... ,...,,._ _ .,—. .. _. 	 .. ,.^:
1
ZZCUON 4
MECO iZRZ
4.1 TZMPR Ti1RZ VARIA71ON
The empirical relation between the exospheric temperature and solar activity (Vachon and
Horsey - 1963) was found to be consistent with the temperature values derived from the
Mariner IV data (Vachon-1966). On the basis of this agreement, the empirical relation
appears acceptable at this time. Data from the Mars 169 fly-by may provide an opportunity
to check the relative validity of the relation for periods of high solar activity. For the
present, it is assumed that the empirical relation will provide a reasonable estimate of the
exoupheric temperature variation as a function of solar activity.
The temperature minima (Tn) are taken to occur at 0400 while the maxima (Tx) occur at 1400
for any value of the 10.'7-centimeter solar flux (8). The minima and maxima are obtained by
the following formulation:
T
n 
= 1.943 + 275
T _ 3.083 + 372
x
k	 +
TOale 4-1. Martian ftospherioTsmps—I re (°IK) N a	 = of the 10.7-Centimeter
solar Flux (t)
K)
solar Flvac e
70 100 160 200 260
im, ^a 411 469 666 663
Offmomm
760
ima 686 677 629 982 1134
(1962) temperature values at 420 kilometers and the temperature value at 2000 kilometers,
well within the Earth's exosphere, is given in Table 4-2.
Table 4-2 Comparison of the Harris and Priester Model Temperatures at 2000 bm and
420 km
Solar Flux (6)
T (oK) 230 200 130 100 70
Minima
8000 km 1892 11109 944 737 612
420 km 1383 1156 938 732 609
Maxima
2000 km 2121 1768 1409 1046 827
420 km 2068 1739 1394 1039 822
The empirically derived base altitude of the exosphere will be discussed in section 6o s siaces
p	 as sated above*
 it is expected to be related to the selected values of the thermosphere thermal
gradient.
I
30
RM
aeECTION 6
THERM011PHERE
6« 1 ALTITUDE OF SAW
The atmosphere of Mars at high altitudes is expected to exhibit a region of temperature
Increase due to recombination heating. The altitude at which this beat source occurs has
recently been estimated at about 90 kilometers (Gross, et, &L - 1066), 100 kilometers
(Donahue - 1966), and < 140 kilometers (Chamberlain and McElroy - 1066N Dared on
evaluations of the Mariner IV data (Vachon - 1966 and Vachon and Llohten feld - 1967) the
base of the thermosphere was calculated as being around 106 kilometers. For our purposes,
the base of the thermosphere is taken as being at an altitude of 100 kilometers. To simplify
further calculations, it is assumed that conditions at 100 kilometers remain constant in
time and space. Thus, we introduce a fixed boundary condition at 100 kilometers, which
contains all of the inherent limitations contained in the same assumption mad3 in regards to
the Earth's upper atmosphere, sP g, , the density at the boundary altitude is held constant in
time and space, although it is known to vary substantially. In the Harris and Priester model
(1962)9
 it is found that a fixed boundary exists at an altitude of 120 kilometers. Considering
that the Harris and Priester model provides a reasonable fit to the observed conditions at
altitudes in excess of 200 kilometers, fine assumption of a fixed boundary condition appears
permissible as a means of developing models of the atmospheric structure above 200 kilo-
motors for use in orbit decay evaluations.
The intensity of solar vadiation at the Martian orbital distance is *bout half that incident at
the Earth's distance. Blnce the thermosphere ►
 is a by-product of photodissocistion and
reaaabination, it will be assumed that the Martian thereto sphere thermal gradients are
equal to half the value of the Earth's thermosphere thermal gradients. This is an admittedly
crude assumption for it totally neglects the disfereaoss in the chemical kinetios of the two
atmospheres. The thermal gradients for three selected altitude intervals, as well as the
equivalent over the three intervals, is given in 'Table 5-1 for the Earth, and In Table 5-2 for
Mars as a function of solar activity.
From the values presented in Table 5 -29 it to obvious that the estimates of the altitude
variation of the Martian thermal gradients, based on values for the Earth's thermosphere,
decrease much more rapidly than those used in Martian atmosph ers models, However,
based on evaluation of the Mariner IV data (Vachon - 1986 9
 and Vachon and Licbtenfele -
1967)0
 th+e thermal gradient over the altitude range of 106 to 138 kilometers, during a perlud
of low solar activity, was found to He within the limits of 1 0. 50 K1km.
i
Table 6-1. Al *x% Ysrtatlm of dw TUrwd tlradist
(°K/I=) & zarst•	 as a Fwwtioa of solar Activity
Sol" Flux (s)
250 900 180 100 70Al	 td (long
220 to 190
Minima 8.72 V.83 4.94 8118 2.08
12.68 10058 8028 8.70 9099
20MIft ivaa
r3420
xima
1132 0198 0.74 0089 0.40
maxima 9.82 2.64 1.76 0.97 0688
to 200
minims 0.24 0619 0115 0111 0008
Maxima 0096 0.06 0138 0.17 0110
420 to 120
Minima 9.48 2.67 1.94 1020 0.88
Maxima 8.70 4.61 3.46 2.28 10861
4
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^^^
-	
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^	
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'` ".. >	 -^^	 .. --<..:;	 -:,u r.e'^,YT..}-...^ ire
	
*,'...'wR * .per.:-°1^s
	 ^ «4-	 +r -r ,.....^,8.. ww^...... -.^sa.-.:.^,*y... 	 _-.-.^cr se^..^a^u..rr^._ ,...,as...	 ux^u..y.:..... _	 -^+.+w,.T.r..^..w,.	 _.
1'
a	 i
sto fit the condition of a fixed base altitude for the	 awe as thermal gradients
are defend t upon the chemical idnotica of the at phere, which ware largely gorede it
Is file that modifying the gradient values would be better than introducing a variable exosphere
bass altitude. Vying the i h!egsated gradient values from Table 6-8 together with the
excspbers teNnperature from Table 4- i, the lowest altitude of the exaospMrs (460-kilometers)
was found to be associated with the highest i egrated thermal gradient (0.86o K/j=) and
th+e hilt excosphero temperature (1184 XK Since there is doubt that the excosph*"
Um"roture oould be this high, and that the 1, it
	
thermsl gradient is itself muoh
higher then the Smith and 8eutler values based on evaluation of the chemical kinstios, it was
dooided to Moot this condition as the basis for scaling. The nod lowest altitude of the
mosphero (483 kilometers) was found to be associated with an iategrateed thermal gradient
of 1, ?Q K/ing and an omphers temperature of 76er. The relt►tive agreement between
thei^ptxtgrated went of this oase and the model of Weidner and Hasseltine (1860 was
titan as a favorable aspeot, since their model Is based in part on an evaluation of the
chemical kinedoi. Farther, the ex caphere temperature value of 760°K is not out of accord,
with most studies of the chemical kinetic* of the Martian upper atmosphere. Although,
Intuitively, the top of the thermosphere to expected to be lower than it is in the Earth's
atmosphere, for the present it is assumed that the top of the thermosphere on Mars is at an
altide_of 482 kilometers.
o -a. amw atad Tbormal Ondista i m) in tm Morulm Ttwrmoq*oro of a na uou
of	 r Aot vity
_
Iola rim (B)
T °K 060 200 150 _ 100 TO
vartablacospara
MID13 N 1671 16 413 0 ^ 0063 0* 40
Kivdma sees 240 1 79 1014 0, 7e
a lo 7l 146 1000 0095 00 80
maxims 20 40 Soso 1089 1. 49 1626
lei
UCUON 6
VAMA71ON OF ATMON iC DZWTY
	
i^
Sol INIM?TAL VANATtON
TU atmospheria density in the lamb 's upper atmosphsra at 1000 k0ometers aaria by
about we order of ma—aituds from a mUdmum at 0400 hours to a maximum at 1400 hours
durbg =Wmum sohr
 
activity periods, AW w O the m- pdt de of the diand variation of
d"ty is about a taetor of a duriap periods of low soar activity, 000asioually larger
are sncouattred em durft these periods.
®-1. lstr11-0-19loo adfDoneftyst;1000 Kgot astern In Models of	 Terrestrial and
Martion, A r .r"
Density (9/e0) RAW Remarks
Soo to 250 8 x 10"18 to 1.3 x 10'16 102 Harris and Priester
70 to 100 : x 10.1©
 to 1.7 x 10,18 101 Models of Earth's
70 to 260 2 x 10"t0
 to 1.8 x 104016 100 atmosphere at 1000 km
Men to Maximum 6.0't x 10.19 to 1,4x 10M16 2_3 x 10$ Weidner and
minimum to Moen 60 03 x 10"22
 to 0. 97 x 10-19 1,03 Hasseltine models of
Minimum to 0.02 x 10-22 to 1.4 x 10-18 0 x 105 Mars atmosphere at
MAXIMUM 1000 kin (Figure 2-3)
substltuttoa of the thermosphere thermal gradient values given in Table a-g, together with
the excephere twas"& attire values given in Table 4-1.. This rather simple modification
provides a means of estimating the probable variation of the atmosphere as a function of
solar activity for any Riven model. In the case of the "looted mean model, the resulting
range of density variation as a function of solar activity (Table 6-2) was found to ages closely
with that obtained from the Harris and Priestar (1962) models.
	 0
From the values in Table d-g, it is seen that the density at ,loo kilometers during a period
of high solar activity is likely to be almost three orders of magnitude greater than during a
Table 6•8. Variation of the Martin Atmospberie Density (g/oo) at 700 Kilometers as e
Function of Solar Aotivity
Solar Flux (8)
250
_
1a0 100 70
waima 5x1017 017
r
7x10'18 1.8x1018 0.2x10-1A
Maxims 4. Z x 10 16 018 8 x 10.17 S. 4 x 10"1? 8.0 Y 1.0 18
,
Based on the Mariner IV ionospheric eocperiment data, the base of the thermosphere may be
as low as 105 kilometers. The thermosphere integrated thermal gradient is expected to range
 °	 °In value from 0, b to J. 0 K/km during periods of low to high solar activity respectively,
u
raaTtM e
RZFZRZNCZ8
Chamberlain, J. W. and M. R. McElroy, "Martian Atmospheres the Mariner IV Occultation
Experiment, 11 8010006 166 (61) 9 1666.
Donahue, T. M. , "Upper Axwophere and lonospbers of Mars, 11 Science,  166 (763) 0 1966.
Fjeldbo, 4. , W. C. F jeldbo, and Von R. Eshleman, "Atmosphere of Mars: ]Mariner IV
Models Compared, t' Science 15366 (1618), 1966.
Galbraith, T. L. , "Personal Communication, " GZ -MS% 1967.
Gross, S. H. , W. E. McGovern, and L 1. wool, "Mara: Upper Atmosphere, 1' Scams
161, 1966.
Haxrie 1. and W. Friester, "Theoretical Mode for the Solar-Cycle Variation of the Upper
Atmopphere, 11 NASA-TN-D-1444,
 1966.
Vachon, D. N. , "On the Distribution of Density at Orbital Altitudes in the Martian Atmosphere,
GE-TM-6126-50
 1666.
vlobon, D. N, and K. Liohtenfeld, "Density at Orbital Altitudes is the Martian Atmosphere, it
Regional Symposium on Planetary Geology and Geophysics, AAd, 25-27 May 1967, Boston,
Massachusetts,
Weidner, D. K. , "Preliminary Models and Confidenos Envelopes for the Mors atmosphere, 11
Presented at the Planetary Mission Board ]Meeting, June 16, 1967 and at the Voyager Science
Panel Meeting, June 91, 1967 9 NASA-MBFC.
Weidner, D. IL and C. L. Hasseltine, "Natural Environment Design Criteria Guidelines for
US C Voyager Spacecraft for Mars 1973 Mission, 11 NASA-MSFC-TMX-69616, 1967,
sw


An estimate of the solar cyclic variation of the Martian upper atmosphere

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