Full report

Original page 1

NASA / TM--2002-211786 NASA Marshall Engineering Thermosphere Model-Version 2.0 J.K. Owens Marshall Space Flight Center, Marshall Space Flight Center, Alabama June 2002

Original page 2

The NASA STI Program Oflice...in Profile Since its founding, NASA has been dedicated to the advmlcement of aeronautics and space science. The NASA Scientific and Technical Infommtkm (STI) Program Office plays a key part in helping NASA maintain this impollant role. The NASA STI Program Office is operated by Langley Research Center, the lead center l)r NASA's scientific and technical information. The NASA STI Program Office provides access |o the NASA STI Database, the largest collection of aeronautical and space science STI in the world. The Program Office is also NASA' s institutional mechanism fi)r dissemina|ing the results of its research and development activities. These results are published by NASA in the NASA STI Report Series, which includes the following report types: TECHNICAL PUBHCATION. Reporls of completed research or a major significant phase of research that present tile results of NA S A progrmns and include extensive data or theoretical analysis. Includes compilations of significant scientific and technical data and infi_rmation deemed to be of contimfing relerence value. NASA's counterpart of peer--reviewed formal professional papers but has less stringent limilatkms on manuscrip| length and extent of graphic presentations. TECttNICAL MEMORANDUM. Scientific and technical findings that are prelmfinary or of specialized interest, e.g., quick release reports, working papers, and bibliographies that contain minmml aimotation. Does not contain ex|ensive analysis. CONTRACTOR REPORT. Scientific mid technical findings by NASA-sponsored contractors and grantees. CONFERENCE PUBLICATION. Collected papers from scientific and teclmical conferences, symposia, seminm's, or other meetings sponsored or cosponsored by NASA. SPECIAL PUBLICATION. Scientific, technical, or historical infolTnation fi'om NAS A programs, projects, and mission, often concerned with subjects having substantial public interest. TECHNICAL TtC4NSLATION. English-language translations of foreign scientific and technical material pertinent to NASA's mission. Specialized services flint complement the STI Program Office's diverse offerings include creating cns|om thesauri, building cns|omized databases, organizing and publishing research results.., even providing videos. For more inlormation about the NASA STI Program Office, see the fl_llowing: ® Access the NASA STI Program Home Page at http://www.stimasa.gov . E-mail your question via the Internet to help @ sit.nasa, gov = Fax your question to the NASA Access Help Desk at (301) 621----0134 * Telephone the NASA Access Help Desk at (301) 621-0390 Write to: NASA Access ttelp Desk NASA Center lk_r AeroSpace Information 7121 Standard Drive ttanover, MD 21076-1320

Original page 3

NASA / TM--2002-211786 NASA Marshall Engineering Thermosphere Model-Version 2.0 J.K. Owens Marshall Space Flight Center, Marshall Space Flight Center, Alabama National Aeronautics and Space Administration Marshall Space Flight Center o MSFC, Alabama 35812 June 2002

Original page 4

Acknowledgments The author recognizes and acknowledges the pioneering work of Luigi (]_ Jacchia and Jack W. Slowey, Smithsonian Astrophysical ()bservatory, on which tile NASA. Marshall iqngineering Thermosphere Model is based. In addition, the author wishes to thank (2.(3.3ustus, Computer Sciences Corporation, for his contributions to the fairing routine between tile lower thermosphere and the altitudes where seasonal/latitudinal variation of helium is importanL His input has greatly improved the performance of the computer program in this altitude region. 17{is contributions to the subroutine for calculating solar position are also gratefully acknowledged_ The author is also grateful to Keith O. Niehuss, Marshall Space Flight Center, and Steven Smith, Computer Sciences Corporation, for their considerable help and contributions toward solving computer programming issues. Thanks to their efforts, the computer program operates on a variety of platforms. Finally; the author is grateful to William W. Vaughan, The University of Alabama in ftuntsville, for his contributions and exten sire proofreading of the manuscript. His efforts have improved the cl ari ty and readability of the document considerably. Naturally, any errors or omissions are the sole responsi bility of the author. Available NASA Center for AeroSpace Information 7121 Standard Drive Hanove,; MD 21076-1320 (301) 621-0390 from: National Technical Information Service 5285 Port Royal Road Springfield, VA 22161 (703) 487-465(11

Original page 5

TABLE OF CONTENTS 1. BACKGROUND .......................................................................................................................... 2. DEVELOPMENT ......................................................................................................................... 2 2.1 Jacchia 1964 Model ............................................................................................................... 2 2,2 Jacchia 1970 Model ............................................................................................................... 2 2.3 Jacchia 1971 Model ............................................................................................................... 3 .................................................................................. 3 2.4 MSFC/J70 Orbital Atmosphere Model 2,5 NASA Marshall Engineering Thermosphere 2.6 NASA Marshall Engineering Thermosphere Model-1988 Version ...................................... 3 Model-1999 Version ...................................... 4 3. DESCRIPFION ............................................................................................................................ 5 .............................................................................................................. 6 3.1 Density Distribution 3.2 Variations ............................................................................................................................... 10 Thermosphere ................................................................ 15 3.3 Fairing Between Lower and Upper 3.4 Solar Position ......................................................................................................................... 15 ................................................................................................... 17 3.5 Thermodynamic Quantities 4. PROGRAM USAGE .................................................................................................................... 19 .................................................................................................................... 19 4,1 Input Parameters ................................................................................................................. 21 4.2 Output Parameters ................................................................................................................ 22 4.3 Sample Calculation 5. CONCd_dJDING REMARKS ....................................................................................................... 24 APPENDIX-- CORRESPONDENCE BY .lACK W, SLOWEY, SMITHSONIAN ASTROPHYSICAL OBSERVATORY, MARCH 27, 1978 ................................................................ 25 REFERENCES ................................................................................................................................... 29 BIBLIOGRAPHY .............................................................................................................................. 30 iii

Original page 6

LIST OF FIGURES neutral density models ........................................... 5 . Statistical evaluation of thermospheric 2, Variation in daily F10.7 flux in 1983 ..................................................................................... 3. 10 12 Variation in 3 hourly geomagnetic index, ap, in 1983 .......................................................... LIST OF TABLES . INDATA array definition ...................................................................................................... 19 2. Summary of output parameters ............................................................................................ iv 22

Original page 7

LIST OF ACRONYMS AND SYMBOLS Ar argon CH coronal hole CME coronal mass cjection CPU central processing unit EUV extreme ultrmTiolet GRAM-99 Global Reference Atmosphere Model-- 1999 Version I--te helium ISES International Space Environment Service J64 .lacchia 1964 J70 Jacchia 1970 J71 .lacchia 1971 JD Julian date MET Marshall Engineering Thermosphere MET-V2.0 Marshall Engineering Thermosphere Model-Version 2.0 MKS meter-kilogram-second MSFC Marshall Space Flight Center N2 nitrogen oxide O oxygen [Ol atomic oxygen 02 oxide [0 2] molecular oxygen density SAO Smithsonian Astrophysical Observatory UT universal time UTC coordinated universal time UV ultraviolet

Original page 8

NOMENCLATURE Ap planetary geomagnetic index (24-hr average) average (13-mo smoothed) planetary geomagnetic index a coefficient ap planetary geomagnetic index (3-hr value) b coefficient CN coefficient C coefficient coefficient C n Cp constant pressure constant volume C v d number of days E diflerence between the apparent solar time and the mean solar time (equation of time) solar flux F10.7 F10.7 average over six solor rotations g acceleration due to gravity g mean anomaly go gravitational acceleration at sea level Gx gradient H solar hour angle i individual species (index) K logarithmic representation of geomagnetic measurements planeta_ S geomagnetic index k coefficient L mean longitude M constant M molecular mass 1H parameter N number density NA Avogadro's number vi

Original page 9

NOMENCLATURE (Continued) n number of Julian days P constant qo volume fraction of a species m the atmosphere R quantity; universal gas constant R E effective radius assuming a spherical Earth T local temperature t UT m minutes IL exospheric temperature Y length of a tropical year altitude Zb base fairing height thermal diffusion factor; solar right ascension 13 constant 7 constant A incremental change solar declination obliquity of the ecliptic A longitude of the point for which the calculation is being performed solar ecliptic longitude P total mass density vii

Original page 10

TECHNICALMEMORANDUM NASA MARSItALL ENGINEERING THERMOSPHERE MODEL-VERSION 2.0 1. BACKGROUND The region of the Earth's atmosphere between about 90- and 500-km altitude is known as the thermosphere. The region above _:500 km is known as the exosphere. The temperature m the lower thermosphere increases rapidly with increasing altitude from a minimum near 90 km but eventually becomes altitude independent at upper thermospheric altitudes. This asymptotic temperature, known as the exospheric temperature, does not vary with height at any given time due to the extremely short thermal conduction time. However, the exospheric temperature does vary with time because of solar activity and other factors discussed below. The neutral thermosphere is important for two reasons: (1) Even at its low density, it produces significant torques and drag on orbiting spacecraft and orbital debris, and (2) the density/height profile of the atmosphere above 100-km altitude modulates the flux of trapped radiation encountered at orbital altitudes. The state of the neutral thermosphere is most conveniently described m terms of a mean, with spatial and temporal variations about that mean. The NASA Marshall Engineering Thermosphere (MET) model of the Earth's atmosphere at spacecraft orbital altitudes has evolved, based on work conducted at Marshall Space Flight Center (MSFC), over a long period of time. The model is based on the extensive work of Luigi Jacchia and his colleagues at the Smith sonian Astrophysical Observatory (SAO) during the 1960's and 1970's and was developed primarily for application to satellite orbital lifetime prediction, mission analysis relative to fllture reboost requirements, etc. This Technical Memorandum describes the second version of the MET model, attributes of the atmosphere at orbital altitudes, and the methods used to model those attributes. Short-period atmospheric waves are localized in both time and space in a way that has thus far been unpredictable. Consequently, these waves are not explicitly included in NASA Marshall Engineering Thermosphere Model-Version 2.0 (MET-V 2.0). Thermospheric winds are also not included. At low latitudes (less than 28.5°), wind speeds range from 100 to 200 m/s. At high latitudes (greater than about 65°), speeds can be 1,500 m/s or more. Rapid (minutes) changes in wind direction (to 180°), probably driven by gravity waves, have been observed by a satellite.

Original page 11

1. DEVELOPMENT 2.1 Jacchia 1964 Model Reference 1 contains a description of the Jacchia 1964 (J64) model. It provides tables of atmospheric density and composition computed for a wide range of exospheric temperatures, starting from a fixed set of boundary conditions at 120 km. The diffusion equation is integrated following empirical temperature profiles of exponential form capable of reproducing the densities derived from atmospheric drag effects on satellites. Formulae are given that relate the exospheric temperature to solar and geomagnetic activity and allow for the diurnal and semiannual variations. The response of the density at the 200-kin level to different types of heating is briefly discussed. In the mid-1960's, personnel of the Aerospace Environment Division at MSFC were responsible for providing orbital altitude density inputs for satellite orbital decay prediction. They began studies to determine which atmospheric model, when combined with the appropriate orbit propagation program, would most accurately predict the observed decay histories of 39 satellites. Since the observed satellite decay histories were already available, a number of available models of the thermosphere were selected for testing in appropriate orbital lifetime computer programs. Because the satellites had decayed prior to the start of the study, actual values of proxy input parameters (described in sec. 3) required by the roodells were used. These proxy parameters were representative of actual solar conditions that occurred during the decay periods of the satellites. The .I64 model, described in reference 1, had the best performance statistically of the models studied and, therefore, was selected for use by MSFC. 2.2 Jacchia 1970 Model The .lacchia 1970 (J70) model, described m reference 2, is patterned after the 1964 model. The main differences consist in the lower height (90 km instead of 120 km) of the constant boundary surface and a higher ratio of atomic oxygen to molecular oxygen density ([O]: [02] ) = 1.5 at 120 km instead of 1.0). Mixing is assumed to prevail to a height of 105 kin; diffusion occurs above this height. All the recognized variations that could be connected with solar, geomagnetic, temporal, and geographic parameters are represented by empirical equations. Due to the great similarity between the 1964 and 1970 models, and confirmation from observed data of the existence of the major differences, the decision was made by MSFC personnel to use the newer model. One key difference fiom the J64 model, in which the temperature-induced density bulge remained on the equator all year, was that the J70 model bulge followed the latitudinal excursions of the Sun. 2

Original page 12

2.3 Jacchia1971 Model In 1971, SAO published the Jacchia 1971 (J71) model) Although an effort was made m the earlier models to increase the ratio of [O] to [O2], new observational evidence showed that the increase had not been large enough. This model was an attempt to meet as closely as possible the composition and density data derived for a height of 150 km by Von Zahn 4 on the basis of all the available mass spectrometer and extreme ultraviolet (EUV) absorption data. Mixing is assumed to prevail to a height of 100 kin; diffusion occurs above this height. All the recognized variations that can be connected with solar, geomagnetic, temporal, and geographic parameters are represented by empirical equations. Some of the previous Jacchia model equations have been revised, not only in their numerical coefficients but also in their form, as a result of new analyses. The J71 model was not considered to be as representative of the atmospheric density as the .U0 model relative to use in satellite orbital lifetime prediction programs. However, it contained some aspects that proved useful m improving MSFC's thermospheric modeling capability. 2.4 MSFC/J70 Orbital Atmosphere Model An unpublished study by em'ironmental personnel at MSFC showed that the J70 model could be improved by incorporating the J7l model formulations of seasonal/latitudinal variations in the lower thermosphere density below 170 km and seasonal/latitudinal variations m helium (He) above 500 kin, while retaining the orbital decay prediction accuracy of the J64 model. Reference 5 contains a description of the MSFC/J70 Orbital Atmospheric Density model, a modified version of the J70 model. The algorithms describing the MSFC/J70 model are provided as well as a listing of the computer program. The estimated future 13-too smoothed values of solar flux ( F10.7 ) and geomagnetic index (Ap), which are required as inputs for the MSFC/J70 model when computing future estimates of orbital altitude density conditions, are also discussed. 2.5 NASA Marshall Engineering Thermosphere Model-1988 Version The modifications made and used in the MSFC/J70 Orbital Atmosphere Density model spuriously introduced step function increases in density requiring minor fairing modifications for their elimination. In the late 1980's, this fairing routine was added, minor programming errors were corrected, and the complete program was made more understandable and user friendly. In addition, the calculation of atmospheric thermodynamic properties was included, and the entire program was updated from FORTRAN IV to FORTt_-_N 77. These modifications known as the MET model used at MSFC. and additions produced the first version to be Reference 6 contains a description of the MET model-1988 Version, which is a modified version of the MSFC/J70 Orbital Atmospheric Density model. The modifications to the MSFC/J7() model required for the MET model are described, graphical and numerical examples of the models are included, as is a listing of the MET model computer program. Major differences between the numerical output from the MET model and the MSFC/J70 model are discussed.

Original page 13

In the courseof usingthismodelandplottingtheresults,it wasdiscoveredthatdensity discontinuitieswereoccasionallypresentovercertaingeographiclocations.Theseweretracedto an occasionalproblem,with the integrationroutineusedin themodel.It wasreplacedwith a moreaccurate numericalintegrationalgorithmto solvetheproblem.Reference7 containsa detaileddescriptionof the replacementintegrationschemefor theintegrationof thebarometricanddiffusionequationsin theMET model.Thisintegrationschemeis baseduponGaussianquadrature.Extensivenumericaltestingreveals it to benumericallyfaster,moreaccurate,andmorereliablethantheMSFC/J70modelintegration scheme(a modifiedform.of Simpson'srule),whichwaspreviouslyusedin theMET model.Numerous graphicalexamplesareprovided,alongwith a listingof the modifiedformof theMET modelin which subroutineINTEGRATE(usingSimpson'srule)is replacedby subroutineGAUSS(whichusesGaussian quadrature). 2.6 NASA Marshall Engineering Thermosphere Model-1999 Version While reviewing the 1988 version of MET, it was determined that the model would not correctly adapt to the change of the approaching new millennium While performing this update, it was decided to also update the calculation of the solar position to use the more recent standard epoch, J2000.0, which corresponds to January 1.5, 2000, or Julian date (JD) 2451545.0. This is the standard epoch now recommended for use in dynamical astronomy. An improvement to the model was also achieved m calculating the solar coordinates. A low precision ephemeris for the Sun can be calculated using relatively simple equations. 8 This simpler scheme for computing the solar position requires fewer arithmetic calculations, yet it maintains more than adequate accuracy. The apparent coordinates of the Sun are obtained to a precision of 0°.01; i.e., better than an arc minute, and the equation of time to a precision of 0.1 min between 1950 and 2050. The other significant modification to the 1988 version of the MET model is in the fairing subroutine, which controls the transition from the lower altitude density profile to that of the upper altitude region where seasonal/latitudinal variation of He is significant. The previous version of this subroutine made the transition in a series of small steps. The new scheme introduced in MET-V 2.0 provides a smooth functional form for the transition. The developmental MET-1999 Version was incorporated into the MSFC Global Reference Atmosphere Model-1999 Version (GRAM-99). 9 4

Original page 14

1. DESCRIPTION TheMET-V 2.0 is a semiempiricalmodelusingthestaticdiffusionmethodwith coefficients obtainedfrom satellitedraganalyses.It is basedon the 1988version6,7 of MET and work done on the 1999 version, developed flom the Jacchia series of models. Most of the following description also applies to the 1988 and 1999 versions of the MET model. With the proper input parameters, specified below, an approximate exospheric temperature can be calculated. With exospheric temperature specified, the temperature can be calculated for an3,' altitude between 90 and 2,5(i)(i)km from an empirically determined temperature profile. In the original development phase of the Jacchia model, the prime objective was to model the total neutral mass density of the thermosphere by adjusting temperature profiles until agreement between modeled and measured total densities (derived from satellite drag observations) was achieved. Agreement between modeled temperatures and those derived from later satellite drag and in situ measurements was not always achieved. Thomson-scatter radar temperature measurements generally show that the diurnal temperature maximum lags the density maximum by a couple of hours, whereas in the MET-V 2.(i)model, the temperature and the density maxima and minimal are in phase. Studies of the accuracy with which thermospheric models estimate the neutral density have shown that an apparent "barrier" exists at the 15-percent level, and models have not thus far been able to achieve better performance. A recent study of this type by Marcos et al. 9 has shown that, historically, this level of accuracy was first achieved by the J70 and J71 models. Figure 1 illustrates this point. The MET-V 2.0 model was not explicitly included in this study. However, since MET-V 2.0 incorporates the best aspects of Jacchia's 1970 and 1971 models, it clearly perfbrms at the current 15-percent accuracy state-of-the-art in thermospheric neutral density calculation, while being easier to use than other approaches. It was also derived explicitly for use in operational satellite/spacecraft drag applications, unlike most then-nosphenc density models. The MET-V 2.0 model reflects the J70/J71 models' accuracy results. 35 3O "7" _.2. 25 20 "N, 15 { 10 g AE-C (68 °) [] AE-D (90 °) B AE-E (20 °) m $3-1 (98 °) IIII--'i'--i US62 J64 U166 170 171 173 J77 MSI877 MSIS79 MSIS83 MSB86 Nedel and Year Figure 1. Statistical evaluation of thermospheric neutral density models. 5

Original page 15

Theessenceof theMET-V 2.0 modelis thecalculationof atmosphericdensityin two major regions:thelowerthermosphere(altitude90km_ z -< 105 kin) and the upper thermosphere (z > 105 km). Between the base of the thermosphere (assumed here to be at 9(i)kin) and 105 km, turbulent mixing is assumed to predominate, and diffusion dominates at higher altitudes. The density lot all points on the globe at 90-km altitude is assumed constant and mixing of atmospheric constituents prevails to 105 km Between these two altitudes, the mean molecular mass varies as a result of dissociation of [02] to [O]. An empirical process is employed in the determination of the mean molecular mass distribution between 90 and 105 km, such that the ratio of [0] to [(i)2] is 1.5 at 120 kin. This makes it agree more closely with observations as reviewed by Von Zahn. 4 The input parameters required by the program are altitude, latitude, longitude, date (month, day, and year), time (hour and minute), 3 hourly geomagnetic index (linear or logarithmic), and the daily 10.7-cm solar radio flux and its average over six solar rotations referenced to the midpoint. These parameters and their application will be discussed further m section 4. They are essentially the same as provided by the 1988 version of the MET model, but with changes made to the computer program to improve the representativeness of the model's output products and efficiency of the computation. 3.1 Density Distribution 3.1.1 Barometric and Diffusion Equations Density between 90 and 105 km is calculated by integration of the barometric equation. In the lower thermosphere, the atmospheric density is computed by integrating the barometric equation: P(z)=P9°(JIT)JexPI-J:o m (1) RT(z) ' where M is the mean molecular mass, g is the acceleration due to gravity, T is the local temperature (all of which are functions of altitude z), and R is the universal gas constant 8.31432 J K -1 mole -1. The lower boundary (z90 = 90 kin) is assumed to have the following conditions: P90 = 3.46 × 10 ...9g cm ---s r90 : 183K Mg0 = 28.878 g mole ---1. For altitudes above 105 km, the diffusion equation for each of the individual species (0 2, O, N 2, He, and Ar) is integrated upward from the 105-km level. The number density for an individual species in the altitude range 90 _<z -< 105 is calculated using a partition function based upon the sea level composition, and this calculation establishes the values for N105 used below. For N 2, Ar, and He, the number density is given by P(Z)NA n(i) = %(5 28.96 6 (2)

Original page 16

wherei denotes the species (N 2, Ar, or He), qo(i) is the appropriate volume fraction for species i, and N A is Avogadro's number. The values of qo(i) used in Mt?TI'-V 2.(i) are 0.78110 for N 2, (i).2(i)955 for (i)2, 1.289 × 1(i)-5 for He, and 0.009343 for At. For O and 02, the equations used are n - 2P(Z)NA_ 1 l M(z) and P(Z)NA [ n- __ --[1+qo(O2)]-1 a(z) [28.96 respectively. M(z) (3) 28.96 (4) J In the upper thermosphere (z > 105 km), the density computation is accomplished by integrating the diffusion equation: N(z)=NI05() exp- (5) )5 RT(z) where N is the number density of the specms for which the calculation is being done, c_,is the thermal diffusion factor (zero for all species except He, for which a value of -4).380 is used), and the lower boundary is at 105 kin. It should be noted that, in this case, the molecular mass Mis a constant, since the concern is for only one species at a time. In both cases, MET-V 2.0 computes the integral using Gaussian quadrature. The number density of H is assumed to be negligible below 500 km and in diffusive equilibrium above this altitude. Thus, the lower boundary is taken to be at 500 km for this constituent, and its number density at this lower boundary is given empirically by log10 NSO 0 = 73.13 - 39.401og10 Too+ 5.5(log10 Too)2 , (6) where 1_ is the exospheric temperature given by equation (25). The integration of the diffusion equation then proceeds upward from 500-kin. altitude. 3.1.2 Composition In the lower thermosphere (90 km < _<105 kin), the mean molecular mass is computed empirically using the equation 7

Original page 17

6 % (z,- 100;* (7) = n----O where the coefficients, c n, are used to fit the profile in this region. The result of equation (7) is then used m the barometric equation, equation (1), to calculate the total mass density, p. The values of c n used in the MET-V 2.0 model are, following Jacchia, 2 28.15204, -0.085586, 1.284 x 10 -4, -1.0056 × 10 -5, -1.021 × 10 -5, ] .()544 × 10 -6, and 9.9826 × 10 -8, respectively. In the upper thermosphere (z > 105 kin), the number densities for the individual species are determined by integrating the diffusion equation; i.e., from equation (5), with the values at the lower boundary (105 km) given by equations (2)-(4). The total mass density is then given by 6 Mi(z)N i(g) i =1 NA and the mean molecular weight is (8) M. (z) - P(Z)N A (9) 6 i=1 where i denotes the individual species (N 2, 02, O, Ar, He, or H). 3.1.3 Gravity Field The altitude coordinate system used in the MET-V 2.0 model is referenced to the "surface" of the geoid. However, the gravitational field is computed by assuming a spherical planet with an effective radius, R E = 6356.766 kin, where the gravitational acceleration at sea level is assumed to be go = 9.80665 m s2. These two values are self-consistent and correspond to values of go and R E at a latitude of 45 ° 32' 40" with centrifugal acceleration included. Thus, the gravitational acceleration as a function of altitude is given, for purposes of the model, by the equation g(z) - go Il+-J 3.1.4 Temperature Profile The temperature varies both temporally and spatially, but its basic profile is defined by a boundary value it90 = 183 K and an reflection point at zx = 125 kin. The temperature at the inflection point is defined empirically by 8

Original page 18

exp(k-T ) , (11) Tx = a + bT_ o + c where the coefficients a, b, c, and k- are 444.3807, 0.02385, 392.8292, and 0.0021357, respectively 2 and T is the exospheric temperature from equation (25). For the low altitude portion of the profile; i.e., for 90 < z < 125, the temperature is defined by a fourth degree polynomial: 4 T(Z) = Tx + cn(Z-Zx) n n=l (12) where the coefficients c are determined by requirements placed on the derivatives of the profile. Since the lower boundary of the MET-V 2.0 model is taken to be, essentially, the mesopause, the temperature there must be T(90) = 190 = 183 K, and the gradient there (being a minimum) must be G o = 0. At the inflection point, the second derivative must be zero, and the gradient G x must satisfy the condition 4 z x - 9(i) < Gx < 2 (13) in order to have no inflections in the region 90 < z < zx. A value of 1.90 for G x was found by experimentation to be best 2, so MET-V 2.0 uses 1.9 77v-" 7i_0 -1.9 " C 1 z x - 90 c 2 - 0 Tv- 79 0 (14) 35 (15) % = -1.7 7;. - _")o _ .7_7-- _")o (16) (z x - 90) 3 353 ,4 =-0.8 L. - 7;0 __0.8 C- 7;0 07) (,7.x - 90) 4 354 For z > .:r;i.e., ,7.> 125 km, the temperature profile is calculated using the empirical relation T(z) = Tx+Atan -1 ' z -z X I+B z-z x , (18) where A= 2(7, - 7.), B = 4.5 × 10---6for z in kin, and u = 2.5. 9

Original page 19

3.2 Variations 3.2.1 Solar Activity Solar electromagnetic radiation at ultraviolet (UV) and EUV wmTelengths changes substantially with the level of solar activity. Thus, thermospheric density is strongly dependent on the level of solar activity. An average 11-yr solar cycle variation exists; similarly, a "typically" 27-day variation in density exists, which is related to the average 27-day solar rotation period. Variations, however, tend to be slightly longer than 27 days early in the solar cycle when active regions occur more frequently at higher solar latitudes and slightly shorter than 27 days later in the solar cycle when the active regions occur more frequently closer to the Sun's equator. Coronal holes and active longitudes also affect this average 27-day variation. Changes in the thermospheric density related to changes in level of solar (and geomagnetic) activity; e.g., flares, eruptions, coronal mass ejections (CMEs), and coronal holes (CHs), can begin ahnost instantaneously (minutes to hours), although more often a lag of a day or more occurs. Various surrogate radices are used to quantify radio flux, designated t" 10.7. Although EUV radiation measured flom the ground. The Fro7 can be measured levels of solar activity; one is the 10.7-cm solar heats the atmosphere, this radiation cannot be flom the ground and correlates well with the EUV radiation. Figure 2 shows the variability of the Fro7 index during a period of low solar activity. 200 180 160 140 A g 120 100 =* 80 - 60- 40- 20 .... 0 .... i- T ] T 7--7 f f T--T T i 31 61 91 121 151 181 211 241 211 301 331 361 Day Number Figure 2. Variation in daily/"10.7 flux m 1983. The exospheric temperature is computed in the MET-V 2.0 model from a base state temperature parameterized using the 10.7-cm solar radio flux. Then several variations due to diurnal variations, geomagnetic activity, and semiannual variations are added to the base state to form an empirical estimate 10

Original page 20

of the exospheric temperature. The base state equation is for the global minimum of the exospheric temperature distribution (which occurs at night) when the planetary geomagnetic index ap (or Kp) is zero (see sec. 3 for an explanmion of these indices): (19) . = 383 + 332_._ 10.7 + 18(F10.7 -/T10.7) where f'10.7 is the 10.7-cm (2,800 MHz) solar radio flux in units of 104 Jansky (a Jansky is defined as 1(i).26 W 111.2 Hz -1 bandwidth). The bar over F10.7 indicates an average over three solar rotations prior to the day for which we are doing calculations and three solar rotations alierward; i.e., six solar rotations, for a total of 162 days as used by Jacchia in the model development. (See appendix.) 3.2.2 Diurnal Rotation of the Earth induces a diurnal (24-hr period) variation (diurnal tide) m thermospheric temperature and density. Due to a lag in response of the thermosphere to the EUV heat source, density maximizes around 2 p.m. local solar time for orbital altitudes at a latitude approximately equal to the subsolar point. The lag decreases with decreasing altitude. Similarly, minimum density occurs between 3 and 4 a.m local solar time at about the negative of the subsolar latitude; i.e., in the diametrically opposite hemisphere. In the lowest regions of the thermosphere (120 km and bellow), where characteristic thermal conduction time is on the order of a day or more, the diurnal variation is not a predominant effect. Harmonics of the diurnal tide are also induced in the Earth's atmosphere. A semidiumal tide (period of 12 hr) and a terdiurnal tide (period of 8 hr) are important in the lower thermosphere (below ,-=160 km fk)r the semidiurnal tide and much lower fk)r the terdiurnal tide). Because of large damping effects of molecular viscosity, these diurnal harmonic tides are not important at orbital altitudes. The diurnal variation is included in MET-V 2.0 under the assumption that the daytime maxmmm 7)4 and nighttime minimum temperatures occur at latitudes which are diametrically opposed to one another on the geoid; i.e., they occur at latitudes q) equal to +5s, respectively, where ?5s is the solar declination. This is accomplished by writing the exospheric temperature as Tl::(l+RsinmO) Il+Rc°sn-7 (20) d(COSmTl--sinmOll77+R )]' where the fitting parameters are R = 0.31, m = 2.5, and n = 3 and the arguments of the trigonometric functions are I"1= Id)+ 8sl/2, 0 = IO+ 8sl / 2, Vd = H + [3+ p sin (H + ?9. The diurnal variation is contained in the expression for rd in which H is the solar hour angle measured from upper culmination (the computation of which will be discussed in section 3.4) and the constants fi, p, and ?'are determined from obserwttions to be -0.6457718, 0.1047198, and 0.75()49] 6, respectively; i.e., -37 °, 6 °, and 43 °, respectively. The quantity R is really 7_i/2 _,-1 and is known to be correlated with solar activity and with geomagnetic activity) Reference 2 provided equations for 11

Original page 21

computingR from mmual running means of/k)_ or from averaged F10.7. It was concluded from later analyses that the available data were insufficient to establish the rules of the variation, so using a constant, average value of R was the best approach. 3 MET-V 2.0 uses the average value from the J70 model, 2 as reflected in the 1988 version of MET. 3.2.3 Geomagnetic Activity Interaction of solar wind with the Earth's magnetosphere (referred to as geomagnetic activity) leads to a high-latitude heat and momentum source for the thermospheric gases. Some of this heat and momentum is convected to low latitudes. Geomagnetic activity varies, usually having one peak in activity just prior to and another just after the peak activity of the solar cycle as defined by the 10.7-cm solar radio flux. Also, larger solar cycle peaks are associated with more intense geomagnetic activity. A seasonal variation of geomagnetic activity occurs with maxima in March (++1too) and September (+1 mo) each year. This variation is possibly related to the tilt of the Sun's rotational axis toward the Earth. There are two geomagnetic indices that may be used in the MET-V 2.0 model. A logarithmic representation of the maximum range over which the magnetic field components vary is designated K. Values of K may range from zero to 9, and cover a 3-hr interval. The K values from 12 standard stations at latitudes from 48 ° to 63 ° and l_drly evenly distributed in longitude are averaged to obtain the planetary index, Kp, used in MET-V 2.(i). The other index, which may be used m MET-V 2.0, is ap, which is a linear index derived from Kp and ranges from zero to 400. Sometimes a 24-hr average of the 3 hourly a o values is quoted, in which case the convention is to designate it Ap. Although high-latitude ionospheric current fluctuations drive the magnetic field fluctuations observed at these stations, the magnetic field fluctuations do not drive the thermosphere. Thus, good correlations are not always found between observed density changes and the ap index. Pigure 3 shows a year of ap data during a period of low solar activity. 25O 20O 150 = lOO @ 50 61 91 121 151 181 211 241 271 301 331 361 DayNumber Figure 3. Variation in 3 hourly geomagnetic index, ap, m 1983. 12

Original page 22

WhenthelogarithmicK v index is used, MET-V 2.0 computes the adjustment to the exospheric temperature using Big = 28 Kp + 0.03 but if the linear av index is used, the equation exp(-0.08 ap)] (22) Arlg = ap + 10011 - exp(hp) (21) is used. There is a time lag between changes m the geomagnetic indices and temperature variations which averages -_6.7 hi; so, whichever index is used, its value should be from a time =6.7 hr prior to the time for which the exospheric temperature is to be computed. 3.2.4 Semiannual This variation in thermospheric density is still poorly understood, but it is believed to be a conduction mode of oscillation driven by a semiannual variation in Joule heating in the high-latitude thermosphere (as a consequence of a semiannual variation m geomagnetic activity). The variation is latitudinally independent and is modified by compositional effects. The amplitude of the variation is height dependent and variable from year to year with a primary minimum in July, primary maximum in October, secondary minimum in January, followed and altitude dependence of the semiannual oscillation to another. This variation is important at orbital altitudes. The MET-V 2.0 formulation of the semiannual by a secondary maximum in April. Magnitude vary considerably from one solar cycle variation is accomplished through the exospheric temperature. The variation is roughly propo_ional to the 10.7-cm solar radio flux and may be computed as where d 1+si _rs=__+0.1145,, / _ k _ Y 2 (23) +42o3 . __ (24) with d being the number of days since January 1 and Ythe length of a tropical year; i.e., 365.2422 days. Note that d is not the day number of the year. 13

Original page 23

Havingcomputedthevariousadjustmentsasdescribedabove,theexospherictemperature is givenby (25) whichprovidestheappropriatevaluefor usein equations(6) and(11)for computingtheH number densityat500km andthetemperatureattheinflectionpointof thetemperatureprofile,respectively. 3.2.5 Seasonal/Latitudinal Thetotalmassdensityis modifiedfurtherby theeffectsof seasonal/latitudinaldensityvariation of thelowerthermospherebelow170-kinaltitudeandseasonal/latitudinalvariationsof Heabove 500km.Thesetwo effectswereincorporatedinto MET-V 2.0usingtheequationsdevelopedby Jacchia for his 1971themlosphericmodel) 3.2.&1 Lower Thermosphere.Thebarometricanddiffusiondifferentialequationsweresolved by assumingfxed boundaryconditionsatz = 90 km. In reality, the values at that height vary as a function of both season and latitude. These seasonal/latitudinal variations are driven in the thermosphere by the dynamics of the lower atmosphere (mesosphere and below). Amplitude of the variation maximizes in the lower thermosphere between about 105 and 120 km and diminishes to zero around 200 kin. Although the temperature oscillation amplitude is quite large, corresponding density oscillation amplitude is small. This variation is not important at orbital altitudes. Computation of this variation in MET-V 2.0 follows the J71 model) In the interest of simplicity, the boundary conditions are left fixed, and the density variations are computed using the empirical relation (26) Alogl0 p(z) = S(z,) _ P sin 2 q) , where (27) S(z) = 0.014(z- 90) exp[-0.0013(z - 90) 2] and P=sm d+100 . (28) This equation is only applied below z = 170 kin, since the effect on density variation is negligible above this altitude, 14

Original page 24

3.2.$.2 Helium. Satellitemassspectrometershavemeasureda strongincreasein Heabovethe winterpole.Overa year,theHe numberdensityvariesby a factorof 42at275km, 12at4(i)(i)kin,anda factorof 3 or 4 above500km Formationof thewinterHe bulgeis primarilydueto effectsof global scalewindsthatblow fromthesummerto thewinterhemisphere.Amplitudeof thebulgedecreaseswith increasinglevelsof solaractivitydueto increasedeffectivenessof exospherictranspo(tabove500kin, carryingHebacktothe summerhemisphere.Also, a very weakdependenceexistsof Hebulgeamplitudeon magnitudeof thelowerthermosphericeddydiffusivity. As wasjust noted,theseasonal/latitudinalvariationof Hedecreaseswith increasingaltitude. However,He is a sufficientlysmallfractionof thetotal densityatlow altitudesthatits seasonal/ latitudinalvariationis negligiblebelow_0500kin. Above500kin, MET-V 2.0usestheequation (29) lOgl0n(He) = lOgl0 n(He) + 0.65 - [sin3/4 ) 8s/-sin3 41 216,1) where g is the obliquity of the ecliptic, following the J71 model) 3.3 Fairing Between Lower and Upper Thermosphere In order to produce a smoother, more continuous transition from the densities computed below 500 km to those computed above, a fairing algorithm is applied to the base 10 logarithm of the total density and He number density for altitudes between 44() and 500 km. The faired density is given by (30) p(z) = pl(Z)C(z) + p2(z)[1- C(z)] , where p is the density before adj usting for the seasonal/latitudinal variation of He and ,92 i s the density afterward, and the fairing coefficient is C(S) = cos 2 [3(Z-Zb)/2] , (31) where zb is the base fairing height at which the fairing calculation begins, 440 km in this case. The fairing coefficients have been chosen such that a gradual transition occurs from the density variation below 440 km to the variation above 500 kin. 3.4 Solar Position It is evident from the preceding discussion that a key element in the computation of densities in the MET-V 2.0 model is the exospheric temperature, and decimation. The solar declination is given by which in turn depends upon the solar hour angle (32) 6 s = sin-1 (sine sin )_s) , 15

Original page 25

wheree.is the obliquity of the ecliptic; i.e., the angle between the plane defined by the Earth's equator and the ecliptic plane, and '_s is the solar ecliptic longitude. Due to Earth's nutation, the obliquity of the ecliptic is not constant. (Nutation is the slight periodic wobbling motion of the Earth's rotation axis caused by the varying distances and relative directions computed as of the Sun and Moon.) In MET-V 2.0, it is (33) = 23°.439- 0°.0000004n , where n is the number of Julian days from J2000.0 for the Julian date (JD) corresponding to the date specified m the input n = JD- 2451545.0 . (34) The Julian date is computed using the Eli egel and Van Flandem algorithm.l° The solar ecliptic longitude can be computed by _'s = L + l°.915sing + 0°.020sin2g , (35) where L is the mean longitude corrected for aberrations and g is the mean anomaly; i.e., the mean angle from pericenter travelled from some arbitrary starting time assuming constant angular speed. These may be computed from L = 280 ° .460 + 0° .9856474n (36) and (37) g = 357°.528+ 0°.9856003n , respectively. The solar hour angle is the angle between the local meridian and the right ascension of the Sun. It is given by t H = -- - 180°.0 + A + E , (38) 4 where t is UT in minutes, A is the longitude of the point for which the calculation is being performed, and E is the difference between the apparent solar time and the mean solar time. E is known as the equation of time, and it may be computed to a good approximation by E=L-a where the solar right ascension cxis given by , (39) (4O) o: = tan -1 (cose tan _s) • 16

Original page 26

3.5 Thermodynamic Quantities As an option, MET-V 2.0 computes some thermodynamic quantities, which were computed without option in the 1988 version of MET, but were not included in previous neutral thermosphere codes used by MSFC. The change to have these calculations be optional was incorporated to provide economy of CPU time for those applications; e.g., total density for satellite lifetime predictions, that do not use these thermodynamic quantities. These include the pressure, pressure scale height, specific heat at constant pressure, specific heat at constant volume, and the ratio of the specific heats. The equations used to calculate these quantities are presented in sections 3.5.1 through 3.5.3. 3.&l Pressure The pressure is calculated directly from the equation of state under the assumption that the atmosphere behaves essentially as an ideal gas. Since the number of moles of gas is given by the ratio of the mass of the gas to its molecular weight and the ratio of the mass of the gas to its volmne is its density, the pressure at altitude z is given by p(z) = M(z) 3.5.2 Pressure Scale Height . (41) The pressure scale height is, by definition, the inverse of the integrand in equation (1). It may be observed from equation (1) that this is.just the change in height required to change the density of a gas of molecular mass M by e-1 in an isothermal atmosphere. To compute this quantity in the MET-V 2.(i) model, it was observed that solving equation (41) lbr RT and substituting the result into the definition of the scale height gives p(z) (42) It(z) - p(z)g(z) where t-I(_) is the pressure scale height at altitude r. 3.5.3 Specific Heat Capacities Under the assumption of an ideal gas, it can be shown by statistical mechanical methods that the molar specific heat at constant volume, c v of a monatomic gas is 3R/2, and for a diatomic gas it is 5R/2. It can also be shown from the definitions of c v and cv (the molar specific heat at constant pressure) that, assuming an ideal gas, cp is the sum of cv and the universal gas constant R. Then, the ratio of the specific heats, 7 - cp / c v , is 5/3 for a monatomic gas and 7/5 for a diatomic gas. Therefore, the ratio of specific heats in the thermosphere is calculated in the MET-V 2.0 model using the weighted average 17

Original page 27

1.67[n(O) + n(Ar) + n(He) + n(H)] + 1.4[n(O2) + n(N2) ] (43) n(O) + n(Ar) + n(He) + n(H) + n(O2) + n(N2) Using the equation of state and the fact that R = cp- c v in equation (43) yields 6 H(z)g(z) Then, the specific heat at constant pressure is (44) (45) %(z) = 7(z)% (z) . 18

Original page 28

1. PROGRAM USAGE 4.1 Input Parameters The MET-V 2.0 model (code available from author) is designed to be very easy to use. Four basic types of input parameters are required by the model: time, location, solar activity, and geomagnetic activity. These may be provided to the model using the sample driver program provided, which reads an input data. file, puts the data into the INDATA array, and calls the primary subroutine MET. The user is free to replace the driver program with his/her own, or to integrate MET-V 2.0 model into a larger program, to suit the needs of the project. Note that the INDATA array, and therefore all of its elements, is REAL*4. Table 1 presents a summary of the contents of the INI_-)ATA array. Note that the year is input as a four-digit number, while the month, day, hour, and minute are all required to be input as two-digit numbers. The first column contains the array element number; the second colmnn identifies the corresponding parameter; the third column indicates the appropriate range of values, where applicable; and the fourth column identifies the proper units for that parameter, where applicable. Note that INDF/FA(9) controls whether INDATA(12) is interpreted as ap or Kp, and INDATA(13) controls whether the additional thermodynamic quantities are calculated. Table 1. INDATA ElementNn. Parameter 1 Altitude 2 Latitude 3 Longitude 4 Year 5 Month 6 Day 7 Hour 8 Minute array definition. Range Units 90 to 2,500 Kilometers ....90 to 90 Degrees -180 to 180 Degrees 1950 to 2050 01 to 12 01 to 31 O0to 23 O0to 59 9 Geomagneticindex type 1(Kp) or 2(ap) 10 10.7--cmsolar flux 0 to 400 104 Jansky 11 Average10.7-cm solar flux 104Jansky 0 to 250 12 Geomagneticactivity index 0 to 400 (ap) 13 Thermodynamicsflag 0 to 9 (Kp) 0 or 1 19

Original page 29

There are three general categories of applications for the MET-V 2.0 model: (1) After-the-fact calculations of densities, (2) real-time (or near real-time) calculations of densities, and (3) future applications in which density estimates are required for sometime in the future. In each case, the time and location inputs are selected and entered according to the same rules. When entering the time, the year is entered in four-digit lbrm, while the month, day, hour, and minute for which the calculation is to be done are each entered in two-digit form with the hour and minute being the coordinated universal time (UTC). For the position desired, enter the altitude in kilometers and geographic latitude and longitude in decimal degrees of the spacecraft location at the time of application. Note that the longitude is measured fi:om the Greenwich meridian eastward. The selection of inputs for the solar and geomagnetic activity parameters depends upon which application category applies to the calculation as discussed in sections 4.1.1 through 4.1.3. 4.1.1 After-the-Fact Calculations This type of calculation is required for times more than 81 days in the past, such as the analysis of data from a space mission or testing model performance using observed orbital parameters for one or more spacecraft. In this case, solar activity is specified using the prexious day's value of the lO.7-cm solar radio flux and the centered (about the day for which the calculation is to be done) average of the lO.7-cm solar radio flux over six solar rotations (162 days), /-510.7.The geomagnetic index, either ap or Ap, is the 3 hourly index value from 6 to 7 hr prior to the time of application. 4.1.2 Real-Time Calculations When the application requires that the density calculations be made for the current time, or less than 81 days in the past or future, averaging the observed 10.7-cm flux over six solar rotations as described above is clearly not possible. In this case, the previous day's value of the 10.7-cm solar radio flux is still used for the daily F10.7 value. However, for the average value, observed values are used where available, and the estimated future 13-mo smoothed value of the 10.7-cm solar radio flux is used as an estimate for the balance of the time period (for which observed daily/"m7 values are not available). These estimated future values of/=10.7 are published by the International Space Environment Service (ISES) and are available electronically via the internet (connect to http://sec.noaa.gov/SolmCycle and retrieve the "Table of Predicted Values With Expected Ranges"). The observed ap or Kp from 6 to 7 hr prior to time of application is still appropriate for this application category except for the time period up to 81 days in the future, when the estimated future value of Ap is used. 4.1.3 Future Calculations When the calculations of densities must be done for a date more than 81 days in the future; e.g., for estimating orbital lifetimes, the problem becomes more dependent upon estimates of future average values for the 10.7-cm solar radio flux, F!l0.7, and the average planetary geomagnetic index, Ap. Now neither the daily nor the ] 62-day average 10.7-cm solar radio flux is known from observations, nor is the 3 hourly geomagnetic activity. In this case, the future estimate of the 13-too smoothed value of F10.7 from ISES, as described in section 4.1.2, is used as an estimate of both the previous day's value of the 10.7-cm solar radio flux input and of the 162-day average value. On average, a value of _12 may be used for the 13-mo smoothed estimate of the A-p index for use as an estimate of the 3 hourly geomagnetic index input. 2O

Original page 30

Forfutureneutraldensitycalculations,theaccuracyof thecalculationdependsprimarily upon two l_lctors: (1) Theability of thethermosphericmodelto representthe observedneutraldensityusing the observedvaluesof solarradioflux (proxyfor solarEUV heating)andgeomagneticactivity usedin thedevelopmentof themodel. (2) Theaccuracywith whichfuturesolarradioflux andgeomagneticactivitycanbeestimated for useasinputsto thethermosphericmodel. As notedin section3, theMET-V2.0 modelhasanaccuracyof _15percent,whichis thecurrent state-of-the-allfor thermosphericdensitymodelcalculations.However,asnotedby Vaughanetal.,12 themajorsourceof nncertaintyfor futurethermosphericneutraldensitycalculationsis theestimation of futuresolarEUV heatinput. 4.2 Output Parameters Upon completion of the calculation, the MET-V 2.0 model passes the results back to the calling routine through the OUTDATA and AUXDATA arrays, both of which are REAL*4. These calculated results include the exospheric temperature, temperature at the input altitude (z), number densities for each constituent, the mean molecular mass, total mass density and its logarithm., and when desired, gravitational acceleration at z, total pressure, pressure scale height, molar specific heat capacities at constant pressure and constant volume, and the ratio of the specific heat capacities. All of these parameters are expressed in MKS units. Table 2 details the output arrays. The first column identifies which element of which output array contains the data for the parameter in the second column. The notation used is AUX for the AUXDATA array (produced when themlodynamic quantities are computed) and OUT for the OUTDATA array. For example, AUX 2 indicates element 2 of the AUXDATA array, and OUT 5 indicates element 5 of the OI.£I'DATA array. The third column gives the MKS units for the parameter identified in column 2. The total mass density, temperature, and individual species number densities all have the same phase variation in the MET-V 2.0 model. 21

Original page 31

Table2. Summaryof outputparameters. Location Parameter OUT 1 Exospheric temperature OUT 2 Temperature OUI-3 N2 number derlsity OUl- 4 02 number density OUT 5 0 number density OUT6 Ar nurnber density OUT7 He number density OUT 8 H number density OUT 9 Average molecular weight OUT 10 Total mass density OUT 11 Loglo mass density ou-r 12 Total pressure AUX 1 Local graviIy acceleration AUX 2 Ratio--specific heats AUX 3 Pressure scale height AUX 4 Specific heat constant p AUX 5 Specific heat constant v 4.3 Sample Units Kelvin (K) Kelvin (K) Molecules per cubic meter (m -3) Molecules per cubic meter (rn 4) Atoms per cubic meter (m-3) Atoms per cubic meter (m-3) Atoms per cubic meter (m-3) Atoms per cubic meter (m-3) Kilograms per kilo-mole (kg kmol-1) Kilograms per cubic rneter (kg rn-3) Pascal (Pa) Meters pet second squared (rn s-2) Meters (m) m2 s-2 K-1 m2 s--2 K--1 Calculation Suppose one wants MET-V 2.0 model results, including thermodynamic quantities, for a point at lat. 45 ° N., long. ] 20 ° W:, and 350-kin altitude on January 20, 1969, at 19:11 UTC. The 10.7-cm solar radio flux for the preceding day (136 × 104 Jan sky) would fJrst be found, then the average 10.7-cm solar radio flux be computed over six solar rotations (162 days, _+81 days) centered on January 20, 1969 (155 x 104 Jansky). Then find the value of the geomagnetic index (ap = 9) at =6.7 hr earlier; i.e., at about 12:29 UTC on January 20, 1969. Using these values for a sample run with the driver program supplied with MET-V 2.0, the input data file (see table 1) reads as follows: Altitude = 350.00 Latitude = 45.00 Longitude = -120.00 Year = 1969.00 Month = 1.00 l:)ay = 20.00 Hour = ] 9.00 Minute = 11.00 Geomagnetic Index Type = 2.00 10.7-cm Solar Flux = 136.00 Average 10.7-cm Solar Flux = 155.00 Geomagnetic Activity Index = 9.(:)(:) Thermodynamics Flag = ] .00 22

Original page 32

Notethatin theMET-V 2.0modellongitudeis positivetowardtheeast,so120° westlongitudeis enteredas-120. Performingthis runwill resultin the creationof a file namedOUTPUT.TXTcontaining thefollowingoutput(all outputin MKS units): Exospherictemperatme = 1031.207K Temperature = 1019.849K N2 nm-nberdensity = 0.3289E+14/m3 02 numberdensity = 0.1660E+ 13 /m3 = 0.2811E+15 /m3 O numberdensity A numberdensity = 0.5398E+10 /m3 He nmnberdensity = 0.5449E+13 /m3 H numberdensity = 0.1000E+07 /m3 Averagemolecularwt. = 17.110 Totalmassdensity = ().9123E-11 kg/m3 = -11.040 Log10massdensity = 0.4521E-05 Pa Totalpressure = 8.80982 m, sec-2 Localgray.acceln. = 1.64095 Ratiospecificheats Pressurescale-height = 56254.6 m = 1244.11 m2.sec-2.K-1 Specificheatcons.p = 758.168 m2.sec-2.K-1 Specificheatcons.v 23

Original page 33

1. CONCLUDING REMARKS Using current or past observations of solar radio flux and geomagnetic activity as inputs to the MET-V2.0 model will produce thermospheric density estimates with an accuracy of _15 percent. However, using future estimates of these input values from generally accepted statistical models 01o physical solar model is currently available for use) will result in significantly (order of magnitude effects) reduced accuracy for the calculated thermospheric density values. These are key considerations to the prediction and statistical confidence of satellite orbital lifetimes, orbital insertion altitudes, reboost requirements, etc. for which the MET-V2.0 model (and its predecessors) was developed. 24

Original page 34

APPENDIX--CORRESPONDENCEBY JACK W. SLOWE_ SMITHSONIAN ASTROPHYSICAL OBSERVATORY, MARCH 27, 1978 25

Original page 35

SMITHSONIAN ASTROPHYSICAL 60 GARDEN STREET CAMBRIDGE, TELEPHONE Dr. William W. Vaughan, Chief Atmospheric Sciences Division ES811 Bui]dii_g 448] George C. Marshall Space Flig_rt Cerrter Marshall Space F]ig_rt Cerrter, Alabama 36812 Dear B:J]I: INSTITUTION OBSERVATORY NIASSACHUSETTS 02138 617 864-7910 March 27, 1.978 It occurs to me that I promised to get back to you on the subject of smoothing to obtain the mean value of the solar flux. This hasn't quite reached the top of my list of "things to do today," but I' 11 have a go at it anyway. Concerning the gaussian smoothing procedure given on page 20 of the 1977 Jacchia model, the "recoma-c_ended" value of _ should have been 70 days. This is the value we _ ve used since we first began to use the method ourselves. Of course, I'm sure that we couldn't distinguish between quoted. The association with "three solar this and the value of 71 days that kS rotations" may have been the result of poor arithmetic following this lesser corruption but, chicken or egg, it is not appropriate and should be deleted. In the gaussian method, the scale factor _ should not be confused with the larger interval over which the iuean is to in question the weight of an included value appreciable. You have to go to an interval be taken. At an interval _ from the time of F would be 1/e .... .37, which is quite of about 3T before the weights really become insignificant. It is this limit, 3T .... 210 days, that we apply to determine "final*' values of F with the gaussian method. limit is applied both forward and backward assumed to be a centered mean of the values Concerning the older iuethod, in whioh mean, the statement on the same page of the means take--over s total of six solar rotations It should be emphasized that the in time: as in the older method, F is of F. F is taken as an unweighted running 1977 model that the model was based on is oorreot. The unfortunate as--sociation of F with the mean over three solar rotations that was made in both the 1970 and 1971 models is, again, not a correct reflection of our actual practice. I can' t recall the exact chronology, but we may still have been getting F from a hand--drawn curve through the monthly mear:s event, when we did finally put the determination wber: these models were published. In any of F on a more formal basis, we found that a total of six rotations were necessary to represent F "correctly" as we saw it. We have used this value (i 3 rotations) used this interval in connection with this computations I' ve made concerning Skylab. 26 ever since. In particular, I have kind of smoothing in all of the model

Original page 36

-2- Of course, I don' t claim that anything of F is necessarily "best." It is all based matter. I hope, however, that I have clarified and _recommended " for use with the atmospheric Sincerely yours, JWS/p1 P.S. If I can possibly meet deadlines for a paper. we do with regard to the determination on our own subjective feelings in the what is consistent with our practice models that result. New York meeting, I" 11 be happy to submit 27

Original page 37

REFERENCES 1. Jacchia,12.(_3.:"Stalc I)i ffusionModelsof the UpperAtmospherewith EmpiricalTemperature Profiles,"Smithsonian Contributions to Astrophysics, Vol. 8, pp. 215-257, 1965. 2. Jacchia, L.G.: "New Static Models of the Thermosphere and Exosphere with Empirical Temperature Profiles," Smithsonian Astrophysical Observatory Special Report No. 313, 1970. 3. Jacchia, L.G.: "Revised Staic Models of the Themlospllere and Exosphere With Empirical Temperature Profiles," Smithsonian Astrophysical Observatory Special Report No. 332, 1971. 4. Von Zahn, U.: "Mass Spectrometric Measurements of Atomic Oxygen in the Upper Atmosphere: A Critical Review," J. Geophys. Res., Vol. 72, pp. 5933-5937, 1967. 5. Johnson, D.L.; and Smith, R.E.: "The MSFC/J70 Orbital Atmosphere Model and the Data Bases for the MSFC Solar Activity Prediction Technique," NASA IM-86522, Marshall Space Flight Center, AL, November 1985. 6. Hickey, M.P: "The NASA Marshall Engineering Marshall Space Flight Center, AL, July 1988. 7. Hickey, M.P: "An Improvement in the Integration Thermosphere Model," NASA CR-179359, Procedure Used in the NASA Marshall Engineering Thermosphere Model," NASA CR-179389, Marshall Space Night Center, AL, August 1988. 8. Anon., The Astronomical Ahnanacfor llle Year 1991, p. C24, U.S. Government Printing O_lice, Washington, DC, 1990. 9. Justus, C.G.; and Johnson, D.L.: "The NASA/MSFC Global Reference Atmosphere Model-1999 Version (GRAM-99)," NASA I37[--1999-209630, Marshall Space Flight Center, AL, May 1999. 10. Marcos, EA.; Bass, J.N.; Baker, C.R.; and Borer, W.S.: "Neutral Density Models for Aerospace Applications," AL4A 94.---0589, 32d Aerospace Sciences Meeting and Exhibit, Reno, NV, January 10-13, 1994. 11. Fliegel, H.E; and Van Flandern, T.C.: "A Machine Algorithm for Processing Calendar Dates," Commtm. Assoc. Comp. Mach., Vol. 11, p. 657, 1968. 12. Vaughan, W W.; Owens, J.K; Niehuss, KO.; and Shea, M.A.: "The NA SA Marshall Solar Activity Model For Use In Predicting Satellite Lifctime," 1999. Adv. ,Space Res., Vol. 23, No. 4, pp. 715-719, 29

Original page 38

BIBLIOGRAPHY Anderson,B.J.;andSmith,R.E.:"NaturalOrbitalEnvironmentGuidelinesfor Usein AerospaceVehicle Development,"NASA I3/I-4527, June 1994. Anon., "Guide to Reference and Standald Atmosphere Models," AIAA G-OO3A-1996, American Institute of Aeronautics and Astronautics, Reston, VA, 1997. Anon., "Models of Earth's Atmosphere (90 to 2,500 km)," NASA SP---8021, March 1973. Anon, UIS. Standard Almosphere, 1976, U.S. Government Printing Office, Washington, DC, October 1976. Banks, R M.; and Kockarts, (3.: Aeronomy, Academic Press, New York, 1973. Bates, D.R.: "Some Problems Concerning the Terrestrial Atmosphere Above About the 100-kin Level," Proc. Royal Soc. London, Vol. 253A, pp. 451--462, 1959. Bramson, A.S.; and Slowey, J.W.: "Some Recent hmovations in Atmospheric Density Programs," Af'CRL----TR----74----0370, Air Force Cambridge Research August 15, 1974. Laboratories, Hanscomb Air labrce Base, MA, Chamberlain, J.W.; and Hunten, D.M.: 7?wory of Planetary Atmospheres. An Inm)duction to Their Physics and Chemistry, Academic Press, Orlando, FL, 1987. Champion, K.S.W.; Cole, A.E.; and Kanto_; A.J.: "Standard and Reference Atmospheres," in Handbook of Geophysics and the Space Environment, A.S. Jursa (ed.), pp. 14-1-14-43, Air Force Geophysics Laboratoly, Hanscomb Air Force Base, MA, 1985. Crowley, G.,:"Dynamics of the Earth's Thermosphere: A Review," in U.S. National Report lo Inlernalional Union of Geodesy and Geophysics, M.A. Shea (ed.), pp. 1143-1165, American Geophysical Union, Washington, DC, 1991. De Lafontaine, J.; and Hughes, R: "An Analytic Version of Jacchia's 1977 Model Atmosphere," Celes. Mech., Vol. 29, pp. 3-26, 1983. Dreher, RE.; and Lyons, A.T.: "Long-Term Orbital Lifetime Predictions," NASA TP-3058, 1990. Fuller-Rowell, TJ.; Rees, D.; Quegan, S.; Moffett, R.J.; and Bailey, GJ.: "Interactions Between Neutral Thermospheric Composition and the Polar Ionosphere Model," J. Geopkys. Res., Vol. 92, pp. 77447748, 1987. 3O Using a Coupled Thermosphere-Ionosphere

Original page 39

Jacchia,L.G.:"ThermosphericTemperature,Density,andComposition:NewModels,"SAC)Special ReportNo. 375,SmithsonianAstrophysicalObservatory,Cambridge,MA, March1977. Johnson,D.L.: "Sensitivity/ComparisonStudyBetweentheJacchia1970,1971,and1977Upper AtmosphereDensityModels,"NASA _IM-82534, 1983. Johnson, R.M.; and Killeen, T.L. (eds.), The Upper Mesosphere and Lower Thermsophere: A Review of E_7)erimenl and "lheory, American Geophysical Union, Washi ngton, DC, 1995. Justus, C.G.; Jeffries III, W.R; Yung, S.R; and Johnson, D.L.: "The NASA/MSFC Global Reference Atmospheric Model-1995 Version (GRAM-95)," NASA IM-4715, Marshall Space Flight Center, AL, August 1995. Marcos, E A. ;Bass, J.N. ;Baker, C.R.; and Borer, W.S.: "Neutral Density Models for Aerospace Applications," AIAA 94---0589, 32d Aerospace Sciences Meeting & Exhibit, Reno, NV, January 10-13, 1994. Mueller, A.C.: "Jacchia-Lineberry Upper Atmosphere Space Center, Houston, TX, October 1982. Density Model," JSC-18507, NASA Johnson Nazarenko, A.I.; Kravchenko, S.N.; and Tatevian, S.K.: "The Space-Temporal Variations of the Upper Atmosphere Density Derived from Satellite Drag Dma," Adv. Space Res., V>l. ] 1, pp. (6)155-(6)160, 1991. Rees, D. (ed.): 7he COSPAR International Reference Pergamon Press, Oxford, NY, 1989. Atmosphere 1986, Part I: 7he 7_ermosphere, Rees, M.H.: Physics and Chemistry of the Upper Atmo,sphere, Cambridge Univ. Press, Cambridge, UK, 1989. Rishbeth, H.: "F-Region Storms and Thermospheric pp. 513-524, 1991. Dynamics," J. Geomag. Geoelectr. Suppl., Vol. 43, Roble, RG.; Ridley, E.C.; Richmond, A.D.; and Dickinson, R.E.: "A Coupled Thermosphere/Ionosphere General Circulation Model," Geophys. Res. [,ell., Vol. 15, pp. 1325-1328, 1988. Smith, R.E.: "The Marshall Engineering Thermosphere (MET) Model," Physitron, Inc., December 1995. Vallance Jones, A. (ed.), Environmenzal _ffects on Spacecrafl Pos#ioning and Trajectories, Geophysical Monograph 73, IUGG Vol. 13, American Geophysical Union, Washington, DC, 1993. Whitten, R.C.; and Poppoff, I.G.: Fumlamentals of Aeronomy, John Wiley & Sons, New York, 1971. 31

Original page 40

REPORT DOCUMENTATION PAGE Fc_rmApproved OMB No. 0704-0188 PuNic reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operation and Reports. 1215 Jefferson Davis Highwav Suite 1204 Arlington, VA 22202-4302, and to the ©ffice of Management and Budget, Paperwork Reduction Project (0704=0188), Washington, DC 20503 1, AGENCY USE ONLY (Leave Blank) 2, REPORT DATE June 2002 4. TITLE AND SUBTITLE 3, REPORT TYPE AND DATES COVERED Technical Memorandum 5, FUNDING NUMBERS NASA Marshall Engineering Thermosphere Model-Version 2.0 6. AUTHORS J.K. Owens 7. PERFORMING ORGANIZATION NAMES(S) AND ADDRESS(ES) George C. Marshall Space Flight Center Marshall Space Flight Center, AL 35812 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) National Aeronautics and Space Administration Washington, DC 20546-0001 11. SUPPLEMENTARY NOTES 8, PERFORMING ORGANIZATION REPORT NUMBER M-1051 10. SPONSORING/IVlONITORING AGENCY REPORT NUMBER NASA/TM-- 2002-211786 Prepared by Space Science Department, Science Directorate 12a. DIBTRIBUTION/AVAILABILITYBTATEMENT Unclassified-Unlimited Subject Category 46 Nonstandard Distribution 13. ABSTRACT (Maximum 200 words) 12b. DISTRIBUTION CODE This Technical Memorandum describes the NASA Marshall Engineering Thermosphere Model--Version 2.0 (MET-V 2.0) and contains an explanation on the use of the computer program along with an example of the MET-V 2.0 model products. The MET-V 2.0 provides an update to the 1988 version of the model. It provides information on the total mass density, temperature, and individual species number densities for any altitude between 90 and 2,500 km as a function of latitude, longitude, time, and solar and geomagnetic activity. A description is given for use of estimated future 13-too smoothed solar flux and geomagnetic index values as input to the model. Address technical questions on the MET-V 2.0 and associated computer program to Jerry K. Owens, Spaceflight Experiments Group, Marshall Space Flight Center, Huntsville, AL 35812 (256-961-7576; e-mail Jerry.Owens @msfc.nasa.gov). 14. SUBJECT TERMS 15. NUMBER OF PAGES 4O thermosphere, atmospheric on-orbit density, satellite orbital lifetime _. PRICECODE _z.SEcuRi_c[ABsi_i_ATiON _ SECURiTYCLASSiFiCATiON191SECURITYCLASSIFICATION20i LiMiTATIONOFABSTRACT OF REPORT OF THIS PAGE Uncl assi fled Unclassified NSN 7540-01-280-5500 OF ABSTRACT Uncl assi fled Unlimited Standard Form 298 (Rev, 2-89) Prescribed by ANSI Std. 239 18 298 102

Original page 41

National Aeronautics and Space Administration AD33 George C. Marshall Space Flight Center Marshall Space Flight Center, Alabama 35812