Nasa Technical Note Atmosphere

7/28/2019 Nasa Technical Note Atmosphere

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NATI ONAL AERONAUTI CS AND SPACE ADM NI STRATI ON

TECHNI CAL NOTE D- 612RANGE OF DENSI TY VARI ABI LI TY FROM SURFACETO 120 KM ALTI TUDE

0. E. Sm t h and H B Chenowet hSUMMARY

A r e- ent r y space vehi cl e devel opment pr ogr am such as Pr oj ect Apol l o,r equi r es a knowl edge of t he var i abi l i t y of at mospher i c densi t y f r om t hesur f ace of t he ear t h t o r e- ent r y al t i t ude (120 km). Thi s r epor t summar i zest he dat a on densi t y gi ven i n t he most r ecent l i t er at ur e on t he subj ect .The range of at mospher i c densi t y wi t h r espect t o t he ARDC 1959 ModelAt mospher e i s det er m ned and shown graphi cal l y.Fr om t he sur f ace to 30 km al t i t ude abundant i nf or mat i on on densi t yi s avai l abl e. Fr om 30 to 90 km al t i t ude t he summar i zed r epor t s of obser -vat i ons made at a l i m t ed number of st at i ons have been used. Bet ween 90

and 120 km al t i t ude t he densi t y i s somewhat specul at i ve, t her e bei ng butf ew measur ement s avai l abl e. Ther ef or e, t he qual i t at i ve val ues f or t hevar i abi l i t y of densi t y above 30 km must be consi dered t ent at i ve.Var i at i ons of at mospher i c densi t y by l at i t ude and seasons made i tnecessary t o devel op a f am l y of cur ves r at her t han a si ngl e pr of i l e.Thr ee cur ves ar e pr esent ed t o show t he r ange of densi t y devi at i on ver susal t i t udes wi t h r espect to the ARDC 1959 Model At mosphere. Each cur vei s used f or a speci f i c l at i t ude r ange and season.

I NTRODUCTI ONSt at ement of t he Pr obl em

There exi st s a need t o know t he var i at i on of at mospher i c densi t ywi t h r espect to a st andar d densi t y pr of i l e f or t he pur pose of f l i ghtmechani cal and aer odynam c heat i ng st udi es i n r el at i on to Pr oj ectApol l o and ot her r e- ent r y bodi es.t o st at e t he var i at i ons of densi t y i n terms of conf i dence l i m t s rel a-t i ve t o a st andar d densi t y pr of i l e, t hi s i s not possi bl e. St at i st i calmet hods do not per m t a val i d det er m nat i on of var i ances usi ng ahet erogeneous sampl e, such as woul d r esul t by combi ni ng f r equency di s-t r i but i ons of densi t y f rom di f f er ent l ocat i ons t aken at di f f er ent t i mes.Fur t her mor e, suf f i ci ent dat a have not been accumul at ed t o det erm ne

Whi l e i t woul d be most desi r abl e


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v a r i a n c e s f o r a g re a t number of lo ca t io ns above 30 lun.another approach t o t he problem must be made.

Therefore ,

A Proposed F i r s t ApproachA proposed approach i s t o d et e rm i ne t h e r an ge of d e n s i t y v a r i a b i l i t yw i t h r e s p e c t t o a s t and ard de ns i t y p ro f i l e (i.e.zARDC 1959).

approach is a t t r a c t i v e b ecause of c e r t a i n r e s t r i c t i v e c o n d i t i on simposed.as fo l lows ( r e f . 36):

ThisThe r e s t r i c t i v e c o nd i t io n s a pp l i c a b le t o P r o j e ct APOLLO a re

a.b.

C .

d.

e.f .

Re-entry occurs a t a n a l t i t u d e o f a p pr ox i ma t el y 120 km.The re-entry body performs a maneuver i n t he 60 t o 80 kma l t i t u d e r e g i o n s .tude , ascends t o 80 km, and th en proceeds t o impact .The range from re-entry34 d eg re e s of l a t i t u d e .The o r i e n t a t i o n of t h e f l i g h t pa t h r e l a t i v e t o g e o gr a ph i c alc o o r d i n a t e s of t h e ea r t h i s unknown.The coo rdi nat es of t h e impact a re unknown.The time of y e a r , month , and day f o r t he ope ra t i on a r eunknown.

I t descends from 120 lan t o 60 km a l t i -

t o i mp ac t i s e q u i v al e n t t o a bo ut

The above co ndi t i on s make i t necessary t o de t e rmine a d en s i t y p r o -f i l e t h a t i s r e p r e s e n t a t i v e f o r a ny l a t i t u d e , l o ng i t ud e , a l t i t u d e ,season, and t i m e of day. T h e magni tude o f t he r ange o f de ns i t y va r i a -b i l i t y must a l s o be d e te rmin ed w i t h r e s p e c t t o a r ep r e sen t a t i v e a t mo s -p he r ic d e n s i t y p r o f i l e .

Thi s approach w i l l be developed, s ince i t i s t h e o n l y a v a i l a b l ep rac t i ca l method .A Proposed Second Approach

A proposed second approach i s t o e s t a b l i s h r e f e re n c e d e n s i t y pro-f i l e s f o r l a t i t u d e s , s e as on s, and t i me of day. A more r e a l i s t i c d e n s i t yp r o f i l e and v a r i a b i l i t y t h a n e s t a b l i s h e d by t h e f i r s t approach could beachieved i f t h e r e s t r i c t i o n s d , e , and f i n p ar ag raph above could be removed.I t may be p oss ib l e f rom th e p re l i minar y eva lua t io ns based on th e de ns i typ r o f i l e i n t h e f i r s t app ro ach t o d e t er mi ne t h e app ro xi ma te a l t i t u d er an ge and f l i g h t mechani ca l r e l a t i o n sh i p s . Th i s i n fo r ma t i on , t o g e t h e r .w i t h a remova l of r e s t r i c t i o n s d , e , and f , would make i t p o s s i bl e t op r e sen t a more r e f i n e d d e n si t y d t i t u d e and d e ns i t y v a r i a b i l i t y r e l a t i o n -s h i p f o r a p a r t i c u l a r o p e r a t i o n .


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LI ST OF TABLESTabl e Page

I Thermal Model of t he At mospher e ....................... 4I1 I onospher e Model ...................................... 5111 Number Densi t i es f or Anal yt i cal Model of Ther mospher e . 6IV Typi cal Low and Hi gh Lat i t ude Summer and W nt er Densi t yPr of i l es .............................................. 11V Hi gh Al t i t ude Measur ement of At mospher i c Par amet er s ... 14VI Densi t y Devi at i on Summary ............................. 15

LI ST OF I LLUSTRATI ONSFi gur e

1 Compar i son of ARDC 1956 and 1959 Model At mospher es .... 172 Range of Densi t y Devi at i on f r omARDC 1959 ModelAt mosphere f or Nor t hern Hem spher e .................... 183 I deal i zed Range of Densi t y Devi at i ons f r omARDC 1959Model At mosphere ...................................... 19

. 4 Maxi mum and M ni mumDensi t y Var i abi l i t y I nf er r ed f r omTher moel ect r i c Pr oper t i es ............................. 205 Ampl i t ude of Di ur nal Densi t y Var i at i on, Day Posi t i ve-Ni ght Negat i ve ........................................ 21


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This second approach w i l l n o t b e deve loped f u l l y i n t h i s r e p o r t ,s i n c e it i s i n t e r d ep en d en t on many f ac t o r s i n t h e f i r s t app ro ach.However, t h e second approa ch w i l l be scru t i n i ze d and developed i n ageneral form. A sp ec i f i c form would invo lve s tu dy in co ns i s t e n t wi tht h e p r el i m in a ry n a t u r e o f t h i s r e p o r t .

A Proposed Third ApproachA t h i r d ap p r o ach i s t o e s t a b l Fs b a d e ns i t y p r o f i l e by u t i l i z i n g

obse rva t io na l and p red i c t i on t echn iques. To b e u s e f u l i n P r o j e c tApollo, th e p re d ic t io n must be va l i d over a f i ve-day per iod .requ i remen t p rese n t s d i f f i c u l t i e s . Our presen t knowledge o f t h e a tmos-phere above 30 km a l t i t u d e i s based upon ex t r ap ol at io n of a tremendousamount of da ta i n th e f i r s t 30 km wi t h very l i t t l e d a t a above t h a t l ev e l .The p r i n c i p a l s i t e s a t which atmos pheri c de ns it y measurements above 30 kmhave been made and which a r e av ai la bl e fo r refer enc e, a re l i m i t e d t o :

This

a. For t Chu rch i l l , Canadab. Wallops Is la nd, Vi rg in iaC. White Sands Miss i l e Range, New Mexicod. Guame. Woomera, A u s t r a l i af . Cape Canaveral , Fl or id ag. Fo rt Greel ey, Alaska

Li mi ta t i ons of measur ing accuracy, f requency of measurement, a l t i t u d erange, sampling area , and coord ina t ion o f measurements prevent th e t h i r dapproach from being pr ac t ic a l a t t h i s t i m e .

SUMMARY OF THERMODYNAMIC RELATIONSHIPS I N THE ATMOSPHEREThermal Model o f t h e Atmosphere

B efo re d i s cu s s i n g t h e o bse rv ed v a r i ab i l i t y o f amb ient d e n s i t y andt h e po ss ib le mechanism whereby t he de ns i t y changes w i th t i m e , i t appearsap pro pr i a t e f i r s t t o r evi ew th e nomencla tu re o f an atmospheri c modelbased on tem per atu re and io n con cen tra tio n. The therm al model summarizedi n t a b l e I i s t h e model cons idered mos t de sc r i p t iv e f o r t h e purpose o f t h i sr e p o rt . The d a t a i n t a b l e I were based on Ni co le t ' s work ( ref . 21).

I t sh ou l d be no ted t h a t t h e r e i s a wide d i f f e r e n c e o f o p i n i ono n t h e a l t i t u d e r e g i o n s whi ch c o mp ri se the s t ra tosphere and mesosphere .


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4For exampl e, Chapman ( ref . 32), i n measur ement s based on t emper at ure,r est r i ct s t he st r at ospher e t o t he l ayer bet ween 8 and 22 km and t hemesosphere t o t he r egi on bet ween 22 and 90h.

TABLE ITHERMAL MODEL OF THE ATMOSPHERE

Regi onEar t h' s sur f aceTrosposphereTr opopause

St r at ospher eSt r atopauseMesospher eMesopaus eTher mosphere

Ther mopause

Descr i pt i onTemper at ur e 275 2 20 KTemperat ur e decr eases wi t h al t i t ude.Al t i t ude, 0 t o 13 5 kmTemper at ure m ni mum 210 20 KAl t i t ude, 13 2 5 km, decr easi ng f r omequat or t o pol esTemperat ur e i ncr eases wi t h hei ght .Al t i t ude, 13 i t o 50 5 kmTemper at ur e maxi mum 273 20 KAl t i t ude, 50 i kmTemperat ur e decr eases wi t h hei ght .Al t i t ude, 50 2 5 t o 85 2 5 kmTemper at ur e m ni mum 190 2 25 KAl t i t ude , 85 2 5 kmTemperat ur e i ncr eases wi t h hei ght .Al t i t ude, 85 f 5 t o 175 km wi t h t heupper l i m t not f i r m y establ i shedThe begi nni ng of an i sot her mal l ayerat 175 lan al t i t ude

El ect r on Densi t y Model of t he At mosphereThe i onospher i c r egi on i s gener al l y consi der ed t o begi n at 60 lunal t i t ude and t o extend upward t o 600 km al t i t ude. However , due t o t hewi de var i at i on of t he hei ght s of t he l ayer s of maxi mum i on concent r a-t i on (denot ed as D, E, F;, F , and B suggest ed G r egi on) , i t i s di f f i -

cul t t o est abl i sh f i xed al t i t ude l i m t s f or t hese r egi ons wi t hi n t hei onosphere. The model gi ven i n t abl e I1 i s t aken f r om Mur gat r ogd ( ref . l!


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TABLE I1I ONOSPHERE MODEL

Layer ( Regi on) Hei ght (km El ect r on Densi t i es cm 3DEF1F2

60 - 10090 - 120160 - 220250 - 500about 600

4

5*1. 5 x 101. 5 x 102.5 1051. 5 x l o63 . 0 x 106

*The hi gh el ect r on densi t y of about 3. 0 x 106 el ect r ons~ m - ~ ,nown as "Spor adi c E- Regi on, " of t en exi st s l ocal l yi n pat ches near 120 km al t i t ude.Composi t i on Model of t he At mospher e

The ARDC 1956 and 1959 Model At mospheres ar e Based on t he assump-t i on t hat t he ai r i s homogenous i n composi t i on up t o 90 kmal t i t ude.Above 90 km t he mol ecul ar scal e t emper at ur e i s used t o def i ne t hei deal gas r el at i onshi p. However , t he text f or t he ARDC 1959 ModelAt mospher e ( ref . 17), suggest s t hat t he mean mol ecul ar wei ght used f ort he 1956 Model At mospher e i s pr obabl y more r epr esent at i ve of t he act ualat mospher e f or l ow l at i t udes. Thi s woul d be i n agr eement wi t h Ni col et(re f . 20) who concl udes t hat di ssoci at i on over For t Chur chi l l appear st o begi n near 80 km i n J ul y and 96 km i n March. As of December 1959,no di r ect measur ement f or t emper at ure had been made above 80 km (ref .ZO, and pr essur e had not been measur ed above 120 kmbeen measur ed above 120 km Ther ef or e, no at mospher i c model yetexi st s whi ch i s r el at ed by obser ved val ues of t emper at ur e, pr essur e,densi t y, and composi t i on f or al t i t udes bet ween 80 t o 120 km and above.

Onl y densi t y has

Bates ( ref . 2) has gener at ed val ues of densi t y i n t he al t i t uder egi on 120 t o 80 km f r om anal yt i cal l y der i ved val ues f or t he composi -t i on. I n t he equat i ons def i ni ng composi t i on he assumes f or 120 kmdi f f usi ve equi l i br i um a gi ven t emper at ur e, and a ver t i cal t emper at ur egr adi ent . The r esul t i ng densi t y pr of i l e i s i n r easonabl e agr eementwi t h sat el l i t e dat a. Fr om t hese and ot her assumpt i ons, Bat es gi vest he number densi t i es of 0, 02, and N2 f or al t i t ude and t emperat ur eas shown i n t abl e 111.


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TABLE 111

A 1ti udeZ(W1201401601802002503003504004505006 007 0800

NUMBER DENSITIESFORANA L Y T I C A L MODEL OF THERMOSPHERE

TemperatureT W(K)

380776938

10031031104810501050105010501050105010501050

1.8 x 10l14.7 x 1o1O2.6 x l o lo1.7 x l o l o1.1 x 1o1O4.9 l o 92.1 lo99.4 x lo8

1.9 x lo84.2 x l o 8

7766

8.8 x 101.9 x 104.4 x 101.0 x 10

3.95 x l o l l

2 l o 99 x l o 8

0.4 x l o 87.9 l o 71.5 lo7

5.6 x 1g9

63 x 106 x l o 5

1.2 lo52.6 1041.2 l o 3

16.4 x 103.6

2.4 x lo1'4 x 101(

1.6 x lo1(7.8 x 1 094.1 lo9

2.2 x lo8

1.3 lo7

8.2 lo55.7 l o 44.3 1033.5 x l o 2

89.2 x 10

75.2 x 10

3.2 x l o 6


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Radi at i on and i t s Cont r ol of t he At mospher eTheor et i cal l y i t i s possi bl e t o det er m ne t he t her mal st r uct ur e of

t he ear t h' s at mosphere, and t hus i nf er t he densi t y st r uct ur e, i f onecan obt ai n sat i sf act or y sol ut i ons t o t hr ee physi cal equat i ons.equat i ons, as st at ed by Schocken. ( r ef . 26) ar e as f ol l ows: Thesea. An equat i on of st at e:

p RT = MP.b. An equat i on of hydr ostati c equi l i br i um

dP = - g dzc. An equat i on of r adi at i ve t r ansf er :

where:P = ressureR = uni ver sal gas const ant!d = mol ecul ar wei ghtT = t emper at ureg = accel er at i on of gr avi t yz = geomet r i c hei ghtK, = mass absorpt i on coef f i ci entI , , = i nt ensi t y of penci l of r adi at i onJu = sour ce f unct i onS = t hi ckness of at mospher i c l ayer i n di r ect i on ofpr opagat i onP = densi t yv = f r equency of penci l of r adi at i on

At t he pr esent t i me t hr ee f act or s pr ecl ude sat i sf act or y sol ut i onst o t hese equat i ons.observat i onal het er ogenei t y of t he dat a and, t her ef or e, (3) a l ack ofknowl edge of t he di st r i but i on f unct i ons and boundar y val ues i nvol vedi n t he di f f er ent i al equat i ons.

These f act or s ar e (1) i nsuf f i c i ent basi c dat a (2)


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8VARIABILITY OF DENSITY RELATIVE TO A STANDARD DENSITYPROFILE - FIRST APPROACH

Choosing a S t and a rd D en si t y P r o f i l eThe p r i n c i p a l r e f e r e n ce so u r ces of a t mosp h er i c i n f o r ma t i o n f o r t h e

upp er s t r a t o sp h e r e and h i g h e r , are t h e ARDC 1956 and ARDC 1959 ModelAtmospheres. These are i n g r e a t d i sa gr ee me nt f o r a l t i t u d e s a bove 50 h.The d e n s i t y d a t a f o r t h e ARDC 1956 and ARDC 1959 Model Atmospheres arecompared i n f i g u r e 1 by e x p r e s s i n g t h e d i f f e r e n c e p e rc e nt a ge d e v i a t i o nfrom the ARDC 1959 va lu es . For example, t h e ARDC 1 95 9 d en s i t y i s 18%h i gh e r t h a n t h a t of t h e ARDC 1956 a t 120 km a l t i t u d e and becomes 90%lower a t 300 km a l t i t u d e . D i sc rep anc i e s b et ween s a t e l l i t e d a t a and t h eARDC 1956 v a l u e s r e s u l t e d i n t h e 1 959 r e v i s i o n. The r e l a t i v e d i f f e r e n c e sbetween the ARE 1956 and the ARDC 1959 v a l u e s f o r t e m p e r a t u r e , p r e s s u r e ,mean molecular weight , and densi ty are shown i n f i g u r e 1.

It i s now t h e co nsen su s of o p i n i o n by au t h o r i t i e s* i n t h e f i e l dt h a t t h e i s ot h e rm a l l a y e r f o r bo t h t h e ARDC 1956 and the ARDC 1959 modelsbeginning a t 11 km ( g e o p o t e n t i a l k i l o m e t e r s ) i s t o o t h i c k , t h a t t h etemperature at 32 km i s t o o l ow, and t h a t t h e s t r a t o p au s e (50 km ) i sabout 1O K t o o h igh. These op in i ons are der ived f rom IGY r o c k e t d a t aan a l y s i s .

P l a n s are und er way t o make a p p r o p r i a t e r e v i s i o n s of t h e ARDC 1959Model Atmosphere to conform t o t h e l a t e s t f i n d i n g s d e r i v ed from t h eo b s e r va t i o n a l d a t a f o r all a l t i t u d e s above 11 g e o p o t e n t i a l k i l o m e t e r s .

Range of Density Over t h e Nort her n HemisphereR e la t iv e t o t h e ARDC 1959 Model Atmosphere

F or t h e p ur po se of t h i s r e p o r t , t h e ARDC 1959 Model Atmosphere ha sbeen ado pt ed t o compare t h e r an ge o f d e n s i t y v a r i a b i l i t y o v e r t h eNorthern Hemisphere . The p r in c i pa l sources used i n ob t a in ing the r angeof d e n s i t y v a r i a t i o n o ve r t h e No rt he rn Hemisphere r e l a t i v e t o t h e ARDC1959 Model Atmosphere are as f o l l o w s :

a . 0 t o 30 km References 25, 27, and 29b. 30 t o 9 0 km References 1, 11, 19, and 22c. 90 t o 200 km References 7 , 8, 10, 12, 16 , 17, 23, and 31

From the su r fa ce t o 30 km a l t i t u d e t h e r e i s abundant atmosphericd e n si t y i n fo r m at i o n a v a i l a b l e f o r t h e p ur po se s of t h i s r e p o r t . Of p a r t i c u -l a r be ne f i t were th e r ep or t s by Vaughan ( re f . 29) and S i ssenwine ( r e f . 27 ) ,

Conference of U . S . Committee on Ext ens ion of t h e Stan dar d AtmosphereWorking Group, January 16-17, 1961, Mass achus etts I n s t i t u t e of Technology.


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wh ich p r e sen t f o r s e l ec t e d s t a t i o n s t h e monthly mean d ev i a t i o n o fd en s i t y f r o m t h e ARDC 1959 Model Atmosphere and th e va ri a nc e of d e n s i t yf rom the monthly values .

I n t he 30 t o 90 km a l t i t u d e r e g i o n , i n d i v i d u a l d e n s i t y o b s e r v a t i o n sa re seldom rep or t ed i n t h e l i t e r a t u r e and one must r e l y on th e summarizedr e p o r t s of o t h e r i n v e s t i g a t o r s . F or t h i s r e p o r t , t h e i n d i v i d u a l d e n s i t yo b s e r v a ti o n s f o r F o r t C h u r c h i l l ( r e f . 1) and f o r Whi te Sands Mi ss i l eRange (ref. 32) were used. I t w a s from these d a t a t h a t t h e r an ge o ft h e d e n s i t y d e v i a t i o n from t h e ARDC 1959 Model Atmosphere w a s d e t e r -mined, as d ep i c t ed by t h e s o l i d curwe i n f i g u r e 2. The curves la be le d( l ) , ( 2 ) an d ( 3 ) i n f i g u r e 2 r e p r e s en t the d e n s i t y d e v i a t i o n s from t h eARDC 1959, de r ived f rom Nordbgrg' s " typ i ca l " l ow l a t i t u d e den s i ty p ro -f i l e s and " t y pi c a l" h i gh l a t i t u d e w i n t e r and summer p r o f i l e s (ref. 22 ) .Note, however, only t h e modulus of th es e de vi at io ns i s i l l u s t r a t e d . T h eh ig h l a t i t u d e " t y p i c a l " p r o f i l e s a r e based on 10 r o c k e t g re na de f i r i n g sa t F o r t C h u r c h i ll . I t must be cons idered t h a t t he re Ps some d i s p e r s i o ni n t h e d e n s i t y ab ou t t h e s e " t y p i ca l " w i n te r p r o f i l e s , p ro du ci ng an ev enl a r g e r r a ng e of d e n s i t y v a r i a t i o n s a bo ut t h e ARDC 1959 d e n s i t y p r o f i l e .A s a co n se r v a t i v e e s t i ma t e o f t h e u pp er l i m i t of t h e d e n s i t y v a r i a b i l i t yw i t h r e s p e c t t o t h e " t y p i c a l " w i n t e r p r o f i l e , t h e a mp li tu de o f t h es e a so n al v a r i a t i o n was added t o t h i s mean and i s i l l u s t r a t e d as curve 4,i n f i gu re 2. S i n ce no ev a l u a t i o n was p o ss i b le t o assess t h e e r r o r s i nt h e i n d i v i d u a l d en s i t y measu rement s an d th e d en s i t y i n f o r ma t i o n w a sex t r ac t e d from many so u r ces , t h e r e s u l t i n g r ang e of d e n s i t y r e l a t i v et o t he ARDC 1959 Model Atmosphere m u s t be cons idered t en t a t iv e between30 and 100 km a l t i t u d e , and i n t h e a l t i t u d e r e g i o n between 100 and 200km t h e d en s i t y d ev i a t i o n s a r e somewhat sp ecu l a ti v e . The i s o l a t ed p a r t sa t 110 km and 200 k m a l t i t u d e s a re take n from Horowitz (r ef . 8 ) andN i c o l e t ( r e f . 20), r e s p e c t i v e l y .

For t h e purpose of ap p l i c a t io n o f t he r ange of de ns i t y de v i a t io nv e rs u s a l t i t u d e s w it h r e sp e c t t o t h e ARDC 195 9 Model Atmosphere , a nempir ical formula has been devised s u c h t h a t a family o f cu r ves g i v i n gt h e d e v i a t i o n s v e r s u s a l t i t u d e c an be d et erm ine d by a r b i t r a r i l y s e l e c t -i n g d i f f e r en t v a l u e s f o r o n ly one p ar amet er . Th i s eq u a t i o n is:

where:a = 100, 225, and 400b = 0.01842 lan-ly = a l t i t u d e i n km 0 = y


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10

Of course , t h e re s ul t i ng dev ia t i on s determined by th e above equa-t i o n s are id ea l i ze d. By comparing f i gu re s 2 and 3 i t c a n b e s e e n t h a tt h e cu r v e f o r &= 20% over -es t imates t h e range o f t h e de ns i ty devia -t i o n s i n t he f i r s t 30 km a l t i t u d e , p ro babl y u n de r -e s t ima t es t h e d evi a -t ion f rom 40 t o 70 km, and then exceeds th e p robable r ange o f de v i a t io nsabove 90 km.f o r c=+ lo%, 2 15%, and + 2% ( h e r e a f t e r r e f e r r e d as 10, 15, and20% c u rv e s) c ou ld prove h e l p k i n u s i n g t h e s e values f o r s pa c e re-en tr y problems. The 20% cur ve sh ou l d r ep r e sen t t h e r an ge o f d en s i t ydev ia t ion fo r t h e e n t i r e Northern Hemisphere from th e ARDC 1 95 9 d en s i t yp r o f i l e . Th e 15% cur ve sh ou ld r ep r e s en t t h e r an ge f o r d en s i t y f o r mid-l a t i t u d e s , a n d t h e 10% c ur ve f o r l ow l a t i t u d e s .used with some r e s e r v a t i o n f o r the low l a t i t u d e s i n t h e a l t i t u d e r e g i o nf r o m 0 t o 30 km, f o r i t is known t h a t t h e d e n s i t y d e v i a t i o n a t 15 kma l t i t u d e over Guam can be as much as 22% h i g h e r t h a n t h e ARDC 1959d e n s i t y v a l u e ( ref . 32). A s ano the r example, th e annual mean den si tyo v e r P a t r i ck A i r Force Base a t 13 km i s 13% h i g h e r t h a n t h e ARDC value.I n b ot h c a s e s i t i s t h e b i a s t h a t c o n t r i b u t e s m ainl y t o t h e v a r i a n c eof t h e t o t a l r an ge o f d e n s i t y d e v i a t i o n from t h e ARDC d e n s i t y i n t h eupper t r o p o s ph e r i c l e v e l f o r t h e s e low l a t i t u d e s .more cl os el y approximate th e upper l i m i t of t he range from ARDC 1959a t h i g h l a t i t u d e s i n winter t h a n f o r a ny o t h e r s e as on o r l o c a t i o n .

Some qual i fying remarks concerning th e r ange o f dev i a t io n

The lO%.curve m u s t be

The 20% curve should

Unless one r ecogn i zes t h er e a re a l t i t u d e s a t which t h e v a r i a t i o no f d en s i t y i s a maximum and a minimum, t h e n t h e r e i s no b a s i s f o r makinge x t r ap o l a t i on s o r i n t e r p o l a t i o n s f o r t h e v a r i an c e of d e n s i t y v e rs u sa l t i t u d e i n t o those r eg i ons no t support ed by obse rva t iona l data . Thisphenomenon is widely observed and i s s up po rt ed by t h e o ry f o r t h e f i r s t30 km a l t i t u d e , and t o a more l i m i t e d ex t en t abo ve t h i s a l t i t u d e . Byway of an an al og y w it h t emp era t ur e , r a d i a t i o n ab so r p t i o n , e l ec t r o nd e n s i t y , and from t h e l i m i t e d o bs er ve d d e n s i t y d a t a , t h e a l t i t u d e s a twhich t h e d en s i t y v a r i a t i o n i s a maximum and minimum a r e es t ima t ed t obe a s i l l u s t r a t e d i n f i g u re 4.

V A R I A B I L I T Y OF DENSITY WITH LATITUDE,SEASONS, AND TIME OF DAY - SECOND APPROACH

A r e fe renc e a tmosphere i s a s p e c i a l purpose atmospheric model basedon emp i r i ca l o b se r v a t i o n s and ex p r es sed i n an an a l y t i c a l form such t h a tthe parameters are i n h e r en t l y co n s i s t en t w i t h b o th t h e o b se rv ed q u an t i -t i e s and r ig o rou s ly connected by phy s i ca l equa t ions .a , refe ren ce a tmosphere w a s pre se nt ed by Smith ( r e f . 28) i n a r e p o r te n t i t l e d " A Reference Atmosphere f o r Pa t r i ck Air Force Base, Flor ida."I t i s p o s s i b l e , a t l e a s t i n p r i n c i p l e , t o e s t ab l i s h a r e f e r e n c eatmosphere f o r space ve hi cl e re-e nt r y which would re pre se nt th e meanatmosphere for a g i ve n r e -e n tr y f l i g h t p at h.information would l i m i t th e mean de ns i t y to :

This concept o f

P r esen t b a s i c a t mo sp h er i c


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11

A l t i t u d e(b)

a. L a t i t u d i n a l v a r i a t i o n o nl y f o r a l t i t u d e s above 30 km.

Low L a t i t u d e* P I

( % I

b. S ea so na l r e f e r e n c e p e r i o d s f o r a l t i t u d e s above 30 km

-2 -22-1 -282 -38-4 -50-6 -55.4 -48

c. X maximum a l t i t u d e of 90 lan.

- 11.1- 15.9- 24.3- 32.0- 37.9- 33.3

d. Only in fe r r ed i n fo rmat ion concern ing th e var i an ce wi thr e sp ec t t o t h e mean d en s i t y f o r a l l a l t i t u d e s .I t i s an t i c i p a t e d t h a t t h e outcome of t h e f i r s t approach as p r esen t edi n s ec t i o n 111, and wi th ad d i t i on a l knowledge ga ined of t h e cha rac t e r -i s t i c s of t h e s p a c e r e - e nt r y body as t h e program progre sse s , w i l l d e t e r -mine t h e f e a s i b i l i t y o f d ev el op in g a r e fe rence a tmosphere fo r a p a r t i -c u l a r o p er a t io n .

As an in t e r i m measure i t may be w e l l t o c o ns i de r t a k i n g a previewof what t he expec ted reduc t ion of t h e b i as i n t h e mean density wouldb e b y s e l ec t i n g a r e f e re n c e de n s i t y p r o f i l e ov er t h a t of t h e ARDC 1959d e n s i t y .

Nordberg (ref . 22) con cl u des t h a t t h e v a r i a t i o n o f t h e mean d en s i t yfrom month t o month i s small i n t h e a l t i t u d e r eg io n from 30 t o 90 kmf o r l ow l a t i t u d e s ( 35 de g re e s n o r t h a nd 35 degree s sou th ) . Therefore , anannual mean de ns i t y pr of i l e would repr ese nt only a s l i g h t b i a s i n t h emonthly mean de ns i t y f o r t h i s region . Using Nordberg 's " t ypi ca l" lowl a t i t u d e , " t y p i ca l " h i gh l a t i t u d e summer and w i n t e r d e n s i t y p r o f i l e s ,comparisons are made as shown i n t ab l e I V .

TABLE I V'JTPICAL LOW AND H IGH LATITUDE SUBdMER A ND WINTER DENSITY PROF'ILES

304050607080

-10-5-a-12-15-15

High Lat i tude ISummer Ninter I Seasonal Amplitud

t = Summer- =Winter


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13

For al t i t udes up to r adi osonde cei l i ng of about 30 km t he di ur nalvar i at i on i s smal l and can be negl ect ed f or most pur poses.DENSI TY MEASUREMENTS AND PREDI CTI ONOF DENSI TY - THRDAPPROACH

Obser vat i onal Met hods f or Det er m ni ng Densi t yThe convent i onal met hod of maki ng atmospheric,measurements for thef i r s t 30 km i s t he r adi osonde.schedul ed r adi osonde measur ement s t aken over t he past t wo decades hasmade i t possi bl e t o pr esent t he mai n f eat ur es of t he atmosphere st r uc-t ur e, up to t he l ower st r at ospher e. W t h t he ever - i ncr easi ng demands

i mposed by t he devel opment of m ssi l es and sat el l i t es t here has beena r api d devel opment of met hods and t echni ques t hat extend t he measur e-ment of at mospher i c quant i t i es to hi gher and hi gher al t i t udes. TheI GY has pr oduced emphasi s on coor di nated schedul i ng and i ncr easi ngt he f r equency of upper at mospher i c measur ement s t hrough r ocket exper i -ment s. Some of t he mor e r ecent devel opment s i n at mospher i c measur e-ment s are summar i zed i n t abl e V.

The wor l d- wi de net wor k of r egul ar l y

I n addi t i on t o t he met hods pr esent ed above, t he observat i ons ofmet eor s by r adar , doppl er met hods usi ng pul se or cont i nuous wave t ech-ni ques, and r adi o pr opagat i on st udi es as wel l as vi sual and phot ogr aphi cobser vat i ons have pr oduced i nf or mat i on on t emper at ur e, wi nd, t ur bul ence,di f f us i on, and densi t y i n t he al t i t ude r egi on f r om80 t o 100 kmGr eenhow r epor t s measur ement s f or densi t y ( ref . 5 ) , t ur bul ence ( ref . 6 ) ,and di f f usi on ( ref . 4 ) usi ng met eor t r acer t echni que.yi el ds l ar ge er r or s i n t he i ndi vi dual obser vat i on such t hat a l ar gesampl e i s r equi r ed i n or der to r educe t he physi cal measur ement byst at i st i cal t echni ques.

Thi s met hod

I t i s not ed t hat each of t he t echni ques l i st ed i n t abl e V i s l i m t e di n al t i t ude r ange, and accuracy of measur ement , or bot h.Ther e must be an i mpr ovement i n obser vat i onal t echni ques t o i ncl udemeasur i ng accur acy, al t i t ude r ange, f r equency of obser vat i ons, andcoor di nat ed schedul e of obser vat i ons f or a l ar ger number of l ocat i onsbef or e an adequat e descr i pt i on of t he st r uct ur e and behavi or of t heat mospher e can be made. These r equi r ement s ar e a prerequi si t e f orpr edi ct i on of at mospher i c paramet ers.

Pr edi ct i on or For ecast f or Densi t yThe ul t i mat e goal woul d be a pr edi ct i on t echni que t hat woul d besuper i or t o that of est abl i shed st at i st i cal means and var i ances obt ai n-

ed f r omhi st or i cal dat a. The f act s ar e that even wi t h t he pr esentwor l d- wi de net wor k of r adi osonde obser vat i ons a f i ve- day f or ecast f orspeci f i c at mospher i c par amet er s i s f ar f rom bei ng a r eal i t y. The


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-

300rlI0M

3 30 0a 3 o DI I0 0M M

'G0cu5-4a>0aJn

QE:a30curl

I0M

E4:00rlI0M

aL5a *L a J5 Lm aL aL kg i 3

3ro(DI0rl

-WE:.rlcncnaJbo*I0a5haE:.tiC

a

..0*samL0LLaaL

zL0aE:0E:.daY,E:00hEaJ

*aJQ

E:a-Pa8.eQ O

0 0.ti rlLa J Q> E :

(d

:n

kL c uLw

h*.d0!2n

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E:aJc*mrnar lL0LLw

h-P.d2an

e0riE:ac*mmaJ-h*.rlmE:an

z0*rl

h+.rlE:an

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aL7*alLm aQ aE : E.d a5 =k

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r la3+)E:.rlLaaP4a

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boE:.rlP0LaI-Pcbo.rlr lc0LaaL

..


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15

maj o r co n t r i b u t i o n a f o r e c a s t f o r t h e a t mo sp he ri c d e n s i t y t o t h e s p ac eve h i c l e r e - en t r y p roblems would be t o r educe th e var i anc e and b i a s whicha re in he re nt i n t h e proposed second approach, i. e., t h e es t a b l i sh mento f r e fe rence a tmospheres .

I t i s i n t h e h ig h l a t i t u d e s a nd i n t h e a l t i t u d e re g io n ne a r 50 kmt h a t t h e l a r g e s t random* v a r i a t i o n o f d e n s i t y i s known t o oc cur .s a t e l l i t e a l t i t u d e s v a r i a t i o n s i n d e n s i t y have been a s s o c i a t e d w i t hv a r i a t i o n s of s o l a r f l u x ( re f. 9), b u t t h e magn it ud e o f t h e v a r i a t i o n sr e l a t i v e t o th os e a t 50 km has no t been es t a b l i s hed . ) There are o ccas i o n si n l a t e w i n t e r and e a r l y sp r i n g d u r i n g w hi ch a l a r g e o r g an i zed w a r m masso f a i r moves from eas t t o west a t h i gh l a t i t u d e s i n t h e u ppe r s t r a t o -sph ere . Th i s phenomenon i s r e f e r re d t o as ab ru pt warming, and was f i r s tr ep or t ed by Sherhag i n 1951 and 1952. One re po r t ( ref . 32) d e s c r i b i n gt h e o ccur r ence o f s t r a t o sp h e r i c warming o v e r F o r t C h u r c h i l l d u r i n g a two-day period, Janu ary 27-29, 1958, r e p o r t s t h a t t h e d e n s i t y a t 50 km a l t i -t u d e i n c r e a s e d 799, o v e r t h a t o f J an ua r y 27. An o r d e r of magnitude f o rt h e t emp er at u r e v a r i a t i o n d u r i n g p e r io d s o f s t r a t o sp h e r i c warmings i ssu g ges t ed t o b e 47K by Nordburg (r ef . 22). I t i s premature to suggestth a t t h e magni tude and periods o f t he se ou tbreaks cou ld be predicted .

( A t

CONCLUSIONS AND RECOMMENDATIONSThe r a ng e o f d e n s i t y d e v i a t i o n v e r s u s a l t i t u d e s w i t h r e s p e c t t o t h e

ARM: 1959 Model Atmosphere can be summarized from figures 2 and 3 f o rs p e c i f i c a l t i t u d e s as shown below i n t a b l e V I .Table V I

*The r e f e r en c e t o r andom v a r i a t i o n as used here i s t o i n f e r t h a t t h eq u a n t i t y i s n o t s e q u e n t i a l l y p r e d i c t a b l e f or a l ong per iod of t i m e .


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16

a. The lHo c urve f o r r a nge o f de n s i t y s hou ld be us ed f o rl ow l a t i t ude s be l ow 35 de gre e s N both summer and winter,a nd fo r h i gh l a t i t u d e s above 55 de g re e s N i n summer.

b. The 15% curve f o r range of de ns i t y should be used f o rm i d - l a t i t u d e s summer and winter.c. The 20% c urve f o r r a nge o f d e ns i t y s hou l d be use d f o rh ig h l a t i t u d e s i n wi n te r and f o r t h e e n t i r e N or th er n

Hemisphere.I t i s recommended t h a t t he se i de a l i z ed den s i ty cu rves be used t o

de p i c t t he a mpl i t ude of t h e d e n s i ty ran ge r e l a t i v e t o t h e 4RDC 1959Model Atmosphere f o r space re -en t ry s t u d ie s u n t i l more p re ci se knowledgeof t he s t r uc tu re of atmospheric de ns i t y becomes av a i l a b l e .

The f a c t t h a t t h e r e are t w o a l t i t u d e regions of maximum wind shouldbe cons idered as a po t e n t i a l p rob l e m area r e l a t i v e t o t h e s pa ce v e h ic l er e - en t ry s t ud i e s . The se a l t i t u d e r e g i o ns fo r t he Nort hern Hemispherea r e 5 t o 15 km, and 50 t o 75 km. I n the se two regi ons , th e mean windf o r some la t i tu d e s can be i n the ord er of magni tude of 50 m/sec and100 m/sec , respec t ive ly .


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AltitudeIIIIIIIIIIII

17

0

0

0

0

1I:I

I: III I

4I' II I

I 'Y 1.- e re12.- Tm re1AM re1.-- A T re1. -----5-- A P re1(x AHDC 56 - x ARE59) 100A X re1 $ = X A R E 59

- loo - 50 0 +50 +loo +150 +200 7LFigure 1. Comparison of ARDC 1956 and 1959 Model Atmospheres


21/27

i akm A l t i t u d e 8200

180

1.60

140

120

1.00

SO

60

40

20

0

I/

1. Low Lat . ( A n n u a l ) From Nordberg 'sI 2 . H L a t . Summer7 " y p i cal. I3. E4 . Est imated L i m i t of Density Range

5 . From r e f . 3. and 326. From r e f . 27 and 298. From r e f . 17

L a t . WinterJ ~ r o f i ~ . e se f . 22i\\\ '(. From r e f . 8\\\ \\\\\\\\\

\\1///

Range ofI k n s i t y Deviati on

I I I 1 I I I *20 40 00 L C J. 00 I 20 140

Figure 2. Range of Density Deviation from ARDC 1959 Model Atmospherefor Northern Hemisphere


22/27

tan A1 . t i :,ude 19

Acre1 = + G ebY)-b 0. ~3842 k m - '7 -, = AI - t i t u d c imV a l i d f o r a l t i t u d e range: 0 = y e 1 2 5 km

Range ofDens i ty Devia t ion

0 9 3 -40 - 60 280 - loo -120 -14C$1 1 I 1 1 I I --Figure 3 . Idealized Range of Density Deviations from ARDC 1959Model AtmosphereFfGURE 3


23/27

20

km 1200

180

160

L40

L20

LOO

80

60

40

20

0

~~

:itude

Thermopause

Thermosphere

0.100micron

0.100to1.176

micron

0.176to

0.300micron

F 2 layerIF1 layer

Thermostructure RadiationAbsorptions ElectronStructure

min

sax

1 in1min1min

jlDensityVariability

Figure 4 . Maximum and Minimum Density Variability Inferred fromThermoelectric Properties


24/27

21Ltitude..

I

. .

/

, -

2. Gree-fiow ?tar.-$3. Ilordberg ref. 224, Inferred frcer Temperature5. Wan-Cheng Chiu Ref. 33ref. 34

/ 1. Jacchia r d . 9 I

I

- - - ! . , . . . . . . . . . . . - - ... . . . .!I .

I. . . . . . . - . . . . - . .-7. . . , ~, t , i. ~n te rpo la t i ed . .; . - . j . . . . .......... . . . . . . .,. . .,no Observed h t a i . i; . _j . . I 1 . ; - _ _ . : . . . . . . . . . . . , . ...... ......I - 7 --. , i ' .

- *. . . . . . . . . . _ _ . . . . . . . . . .... . 1 .-.-.,... :! . ! , ' .

. _. ,

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. . . . . . . . . . . . . . . . . . . .. . ..... ..1 .

I

, I 1 . %lur6al- i -It I I ,Density Dpviation50 .is(-a5 f j 0 ,

Figure 5. Amplitude of Diurnal Density Variation, Day PositiveNight Negative


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2 2

BIBLIOGRAPHYBandeen, N .R . , St r a u d , W.G., Nordberg, W,, and G r i f f i t h , "The Meas-urement of Temperature, De ns it ie s , Pr es su re and Wind Over F or tC h u r c h i l l , Canada by Means of t h e Rocket Grenade Exp eri men t," USARDLTechnical Report 2076.

1

2.

3.4.

5.

6.

7.

8.

9.

10.

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12.

Bates , D.R . , "Some Problems Concerning the T e r r e s t r i a l AtmosphereAbove t h e 100 km Level , " Proceeding of t h e Royal Socie ty S e r i es A ,Mathematical 8 Ph y s i c a l Sc i e n c e s No. 1275, Volume 253, datedDecember 29, 1959.Chandrasekhar, S.J . , "Radi at ive Tr an sf er ," Oxford Pr es s , dat ed 1950.Greenhow, J.S., "Eddy D i f f u s i o n and I t s Effec t on Meteor T r a i l s , "J o u r n a l of Geop hysica l Res earch , Volume 64, No. 12, December 1959.Greenhow, J.S ., and Hal l , "Diurnal V ar i a t io n o f Dens i ty and Sca leHeigh ts i n th e Upper Atmosphere," Jo ur na l of Atmospheric andT e r r e s t r i a l Physics, Volume 18, dated June 1960.Greenhow, J.S. and Neu fel d, E.L., "Measurements of Tu rbu len ce i nt h e 8 0 t o 100 km Region From t h e Radio Echo Obs er va ti on s of Me teors ,"Jo ur na l of Geophysical Research, Volume 64, No. 12, December 1959.Harowitz, R. and LaGow, H.E. "Upper A i r Pressure and Dens i tyMeasurements From 90 t o 220 km With t h e Viking 7 Rocket ," Jo ur na lof Geophysical Research, Volume 62, No. 1, March 1957.Horowitz, R., LaGow, H E. and G iu li a n i , J .E., "Fall-Day Auroral-ZoneAtmospheric S t r u c t u r e Measurement from 100 t o 188 km," J o u rn a l o fGeophysical Research, Volume 64, No. 12, December 1959.J a c c h i a , L u i g i G., "A Va ri ab le Atmospheric De nsi ty Model FromS a t e l l i t e A c c e l e r a t i o n s , " R es ea rc h i n Sp ace Sc i en c e Sp e c i a l R ep or tNo. 39, Smithsonian I n s t i t u t i o n Astro physi cal Observatory, March 1960.Johnson, Francis S., "Pressure and Tempera ture Equal iza t ion a t 200km Al ti tu de ," Jo ur na l of Geophysical Research, Volume 65,August 1960.Jones , L.M., Pe t e r s o n , J .W . , and Oth ers , "Upper-Air Den sit y andTemperature: Some Va ri at io ns and an Abrupt Warming i n t h e Meso-sp he re ," J ou rn al of Geophysical Research, Volume 64, No. 12,December 1959.Kallmann, H,K. and Juncosa, M.L., "A P re li m in ar y Model AtmosphereBased on Rocket and S a t e l l i t e Data," Rand RM-2286 ASTIA Doc. No.A207752, October 1958.


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BI BLI OGRAPHY13. Ki ng- Hel e, D G. and Wal ker , "Var i at i on of Upper - At mospher e Densi t ywi t h Lat i t ude and Season: Fur t her Evi dence f r omSat el l i t e Or bi t s, "Nat ur e, No. 4715, Mar ch 1960.14. Kupper i an, J . E. , Byr an, E. and Fr ei dmann, H. H. , "Mol ecul ar OxygenDensi t i es i n t he Mesospher e at For t Chur chi l l , " At mospher i c andTer r est r i al Physi cs, Vol ume 16, No. %, Oct ober 1959.15. Menzel , et al . , ' I Fundament al For mul as of Physi cs, " Pr ent i ce Hal l :N. Y. 1955.16. M khnevi ck, V. V. , Dani l i n, D. S. , and Ot her s, "Some Resul t s of t heDet erm nat i on of t he St r uct ur al Par amet er s of t he At mosphere Usi ngthe Thi r d Sovi et Ar t i f i c i al Ear t h Sat el l i t e, " Tr ansl at ed f r om"Ar t i f i ci al Ear t h Sat el l i t es No. 3, "Academy of Sci ences USSR,Moscow, 1959, NASA TT F- 13 (Techni cal Transl at i on F- 13) , May 1960.17. M nzner , R. A. , Champi on, K. S. W, and Pond, H C. , "The ARDC ModelAt mospher e, 1959, ''Ar For ce Sur veys i n Geophysi cs No. 115,August 1959.18. M nzner , R. A. , and Ri pl ey, W S. , "The ARDC Model At mospher e, 1956, r 'Ai r For ce Surveys i n Geophysi cs No. 86, December 1956.19. Mur gut r oyd, R. J . , "W nds and Temperat ur es Bet ween 20 kmand 100 km-A Revi ew, " Quar t er l y J our nal of Royal Met eor ol ogi cal Soci et y, Vol ume83, No. 358, Oct ober 1957.20. Ni col et , M , "Const i t ut i on of t he At mospher e at I onospher i c Level s, "J our nal of Geophysi cal Research, Vol . 64, No. 12, December 1959.21. Ni col et , M , "Hi gh At mospher e Densi t i es (To Expl ai n Sat el l i t e Obser -

vat i ons, Model s of t he Thermospher e must Al l ow f or Di f f usi on andOt her Factors) , " Sci ence, Vol . 127 No. 3310 J une 1958.22. Nor dber g, W, "Seasonal , Lat i t udi nal and Di ur nal Var i at i ons i n theUpper Atmosphere, " Pr oposal t o COSPAR f or " I nt er nat i onal Ref erenceAt mospher e" a pr i vat e communi cat i on, November 1960.23. Nosenzo, L. V. and Sl ezak, D. A. , "Densi t y Var i at i ons i n t he UpperAt mospher e, " (A Thesi s), Massachuset t s I nst i t ut e of Technol ogy,J une 1960.24. Pr i est er , W, Mar t i n, H A, , and Kr amp, K. , "Di ur nal and SeasonalDensi t y Var i at i ons i n t he Upper At mospher e, " Nat ur e, Vol ume 188,Oct ober 1960.


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