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NASA / TM--2000-210279 Mars Global Reference Atmospheric Model 2000 Version (Mars-GRAM 2000): Users Guide C.G. Justus Computer Sciences Corporation, Huntsville, Alabama B.F. James Marshall Space Flight Center, Marshall Space Flight Center, Alabama May 2000

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The NASA STI Program Office...in Profile Since its founding, NASA has been dedicated to the advancement of aeronautics and space science. The NASA Scientific and Technical Information (STI) Program Office plays a key part in helping NASA maintain this important role. The NASA STI Program Office is operated by Langley Research Center, the lead center for NASA's scientific and technical information. The NASA STI Program Office provides access to 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 for disseminating 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 PUBLICATION. Reports of completed research or a major significant phase of research that present the results of NASA programs and include extensive data or theoretical analysis. Includes compilations of significant scientific and technical data and information deemed to be of continuing reference value. NASA's counterpart of peer-reviewed formal professional papers but has less stringent limitations on manuscript length and extent of graphic presentations. TECHNICAL MEMORANDUM. Scientific and technical findings that are preliminary or of specialized interest, e.g., quick release reports, working papers, and bibliographies that contain minimal annotation. Does not contain extensive analysis. CONTRACTOR REPORT. Scientific and technical findings by NASA-sponsored contractors and grantees. CONFERENCE PUBLICATION. Collected papers from scientific and technical conferences, symposia, seminars, or other meetings sponsored or cosponsored by NASA. SPECIAL PUBLICATION. Scientific, technical, or historical information from NASA programs, projects, and mission, often concerned with subjects having substantial public interest. TECHNICAL TRANSLATION. English-language translations of foreign scientific and technical material pertinent to NASA's mission. Specialized services that complement the STI Program Office's diverse offerings include creating custom thesauri, building customized databases, organizing and publishing research results...even providing videos. For more information about the NASA STI Program Office, see the following: • Access the NASA STI Program Home Page at http ://www.sti.nasa.gov • E-mail your question via the Internet to help@sti.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: 7. NASA Access Help Desk E NASA Center for AeroSpace Information | 7121 Standard Drive w. Hanover, MD 21076-1320 | m ,ira mE P_ _= z i E

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NASA / TM_2000-210279 Mars Global Reference Atmospheric Model 2000 Version (Mars-GRAM 2000): Users Guide C. G. Justus Computer Sciences Corporation, Huntsville, Alabama B.F. James Marshall Space Flight Center, Marshall Space Flight Center, Alabama National Aeronautics and Space Administration Marshall Space Flight Center • MSFC, Alabama 35812 I May 2000

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Acknowledgments The authors thank James Campbell, NASA Jet Propulsion Laboratory, for support provided through the Mars Characterization for Future Missions Program. We gratefully acknowledge Dr. R.M. Haberle and Jim Schaefer, NASA Ames Research Center, for assistance in running their Mars General Circulation Model (MGCM), Dr. S.W. Bougher and Steffi Engel, University of Arizona, for model runs and special analysis of their Mars Thermospheric General Circulation Model (MTGCM), and to Dr. A.EC. Bridger, San Jose State University, and Dr. J.R. Murphy, New Mexico State University, for special post-processing and analysis with the NASA Ames MGCM. We also express thanks to the National Science Foundation and the National Center for Atmospheric Research for supercomputing facilities support to the University of Arizona for running MTGCM. Special thanks also go to Belinda Hardin, Computer Sciences Corporation, for her expert assistance in preparing this report and to Margaret Alexander, MSFC Environments Group, for skillfully editing the draft. Available from: NASA Center for AeroSpace Information 7121 Standard Drive Hanover, MD 21076-1320 (301 ) 621-0390 National Technical Information Service 5285 Port Royal Road Springfield, VA 22161 (703) 487-4650 ii

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PREFACE These improvements to the NASA/MSFC Mars Global Reference Atmospheric Model (Mars-GRAM 2000) were sponsored by the Environments Group, Engineering Systems Department, Engineering Directorate of the NASA Marshall Space Flight Center. For those unfamiliar with earlier versions of Mars-GRAM, NASA Technical Memorandum 108509 "Mars Global Reference Atmospheric Model (Mars-GRAM 3.34) Programmer's Guide", and NASA TM 108513 "A Revised Thermosphere for the Mars Global Reference Atmospheric Model (Mars-GRAM Version 3.4)" and NASA/TM-I999-209629 "Mars Global Reference Atmospheric Model (Mars-GRAM) Version 3.8: Users Guide" are recommended. These reports are available electronically from the NASA Marshall Space Flight Center Technical Report Server at http://intl's.msfc,nasa.govlmtrs/ or from the Marshall Space Flight Center area of the NASA Technical Report Server at Internet address http://techreports.larc.nasa.gov/cgi-bin/NTRS For information on obtaining Mars-GRAM additional copies of this report, contact Environments Group Mail Code ED44 Marshall Space Flight Center, AL 35812 Attn: Ms. Bonnie James Phone: (256) 544-6985 E-mail: bonnie.[ames@msfc.nasa, gov Examples of output from the University 2000 (or earlier) code and data, as well as of Arizona Mars Thermospheric General Circulation Model (MTGCM) are available for browsing by interested readers at the following web site: http.'//www.lpl, arizona, edu/_sengel/thermo, html This web site has a constantly-changing archive of available MTGCM case runs for use by the scientific community at large. iii

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Table of Contents Section Title Page 1. Introduction .............................................................................................................. 1 New Features of Mars-GRAM 2000 ........................................................................ 2 Mars General Circulation Model Input Data ........................................................ 2 2.1. I Introduction to MGCM and MTGCM Data .............................................................. 2 2.1.2 Evaluation of MGCM and MTGCM Tidal Components" ........................................... 2 2.1.3 Interpolation Methods ............................................................................................... 3 2.2 Longitude-Dependent (Terrain-Fixed) Wave Model ............................................ 4 2.3 Earlier Mars-GRAM Versions and Climate Factors ............................................. 4 2.4 Simplified Perturbation Model ............................................................................. 5 2.5 Background Dust Level and Dust Storm Conditions ............................................ 5 2.6 Choice of West or East Longitude ........................................................................ 5 2.7 New File Name Input Options .............................................................................. 6 3. How to Run Mars-GRAM ............................................................................................... 7 3.1 How to Obtain the Program .................................................................................. 7 3.2 Running the Program ............................................................................................ 7 3.3 Program Input ....................................................................................................... 8 3.4 Program Output ................................................................................................... 12 4. Sample Results ............................................................................................................... 13 4.1 Model Variations with Latitude, Season, Height, and Time of Day ................... 13 4.2 Comparisons with Observations ......................................................................... 15 5. References ...................................................................................................................... 20 Appendices A° Headers for Mars-GRAM 2000 Output Files ..................................................... 22 B. Example NAMELIST Format Input File ............................................................ 25 C. Sample Output LIST File .................................................................................... 28 D. Summary of Files Provided with Mars-GRAM 2000 ......................................... 37 E. Example Application of Mars-GRAM in a Trajectory Code .............................. 39 F. Details of MGCM and MTGCM Data Files ....................................................... 41

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List of Illustrations Title Pa_gg__ Variation of daily average atmospheric density with latitude and season (Ls angle) at 100 km altitude ................................................... 13 4.2 Temperature at 3 AM local solar time at Ls 270 ° versus height and latitude ...................................................................................... 14 4.3 Temperature at 3 PM local solar time at Ls 270 ° versus height and latitude .... '".ii_.'..i(i' ............ i.......... ........................................... 14 4.4 Eastward wind at 3 AM local solar time at Ls 270 ° versus height and latitude ...................................................................................... 15 4.5 Eastward wind at 3 PM local sol time at Ls 270 ° versus height and latitude ...................................................................................... ! 6 4.6 Atmospheric density measured during entry and descent by Mars Pathfinder, and modeled by Mars-GRAM 2000 for the same date and time ................................................. ,............................. 16 4.7 Average temperature observed at l-m height by Mars Pathfinder lander compared with Mars-GRAM 2000 values near beginning and end of Pathfinder operations ....................................... 17 4.8 Observed average daily maximum, minimum, and average surface air temperature (1.6-m level) from Viking 2 lander and Mars-GRAM 2000 modeled surface air temperature for a full Mars year .......................................................................................... 17 4.9 Gradient of atmospheric density with latitude (% per degree) as measured by Mars Global Surveyor accelerometer at 130-kin altitude on inbound and outbound legs of each periapsis pass during phase 1 aerobraking ............................. 18 | 4.10 Atmospheric density at periapsis measured by Mars Global i Surveyor accelerometer during phase 2 aerobraking, ! compared with modeled density from Mars-GRAM 3.8 and ik Mars-GRAM 2000 ..................................................................................... 19 | vi

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Mars Global Reference Atmospheric Model 2000 Version (Mars-GRAM 2000): Users Guide 1. Introduction The Mars Global Reference Atmospheric Model (Mars-GRAM) is an engineering - oriented model of the atmosphere of Mars. Recent documented applications of Mars-GRAM include aerobraking operations of Mars Global Surveyor, 1 prediction and validation of Mars Pathfinder hypersonic aerodynamics, 2 and aerothermodynamic and entry dynamics studies for Mars Polar Lander, 3 among others. Earlier Mars-GRAM versions 48 were based on ad-hoc parameterizations to data observed by the Mariner and Viking missions. The current Mars-GRAM version (Mars-GRAM 2000) is based on input data tables of output from the NASA Ames Mars General Circulation Model (MGCM) 9,f° and the University of Arizona Mars Thermospheric General Circulation Model (MTGCM). II'12 Fully global in scope, and based o11 first-principles physics (e.g. atmospheric thermodynamics and equations of atmospheric motion), both MGCM and MTGCM have been somewhat "tuned" to insure that they represent Mariner and Viking results at the locations and times for which these data are available. Work on MGCM and MTGCM continues, to ensure that these models agree as well as possible with recent results from Mars Pathfinder and Mars Global Surveyor. Section 2 of this report describes the MGCM and MTGCM data and how they are applied in Mars-GRAM 2000. Other new Mars-GRAM features are also described in section 2. Section 3 explains how to obtain the Mars-GRAM code and data files, and how to set up and run the program. Sample results are presented in section 4. Appendices A through F provide additional details of Mars-GRAM 2000 input and output files and how to interpret program results.

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1. New Features of Mars-GRAM 2000 2.1 Mars General Circulation Model Input Data 2.1.1 Introduction to MGCM and MTGCM Data Earlier Mars-GRAM versions used ad-hoc parameterizations, derived from Mariner and Viking data, to represent temperature versus height, latitude, longitude, time of day, and Ls, and to prescribe surface pressure versus latitude, longitude, time of day, and Ls. Ls is celestial longitude of the Sun, as viewed from Mars. It gives time of year and Mars season. Ls = 0 is Northern spring equinox; Ls = 90 ° is Northern summer solstice, etc. In Mars-GRAM 2000, all data-derived parameterization relations are replaced by input data tables, based on information from the NASA Ames Mars General Circulation Model (MGCM) 9'I° and the University of Arizona Mars Thermospheric General Circulation Model (MTGCM). tl'u These tables give variation of temperature, density, pressure and wind components with height, latitude, time of day, and Ls. The tables also provide boundary layer data at 5 m and 30 m above the surface as a function of longitude, latitude, time of day, and Ls. MGCM data tables cover altitudes ranging from the surface to 80 km. MTGCM data tables cover 80 to 170 km-altitude. A modified (latitude-longitude dependent) Stewart-type thermospheric ,nodel 6 is still used for altitudes above 170 km, and for dependence on solar activity. The Stewart-type thermosphere model starts at a lower boundary condition at the height of the 1.26 nbar pressure level (height ZF). Between 80 km and height ZF (which is typically at about 125 km), MTGCM data are used directly. Above 170 km, modified Stewart-type thermosphere model data are used directly. Between height ZF and 170 kin a fairing process is used that smoothly transitions from MTGCM values to Stewart-type model values. Details and formats of Mars-GRAM's MGCM and MTGCM data files are given in Appendix F. To make file transfer easy, these files are provided in ASCII format. For run-time speed it is best to read the files in binary form. A program (discussed in Appendix F) is provided to convert ASCII format MGCM and MTGCM data files to binary files on the user's machine. 2.1.2 Evaluation of MGCM and MTGCM Tidal Components For each atmospheric parameter (temperature, pressure, densityl wind components) MGCM and MTGCM data tables provide a diurnal (daily) mean value, and amplitudes and phases of diurnal and semi-diurnal tidal components. Tidal values for each parameter are computed from the relation 12] + A 2 • Cos[r_ (t - _b2)/ 6 ] (2.1) Tide = A 0 + A t • Cos[ _ (t - _bl) / where t is local solar time in hours, A 0 is diurnal mean value of the given parameter, A I is amplitude of the diurnal tide component, d_l is phase (local time in hours) of the diurnal component, A 2 is amplitude of the semi-diurnal hours) of the semi-diurnal cornponent. MGCM and MTGCM tidal coefficients tide component, and dp2 is phase (local time in are provided at 5 kin-height increments [starting at 0 km relative to datum level, and going to 80 km (MGCM) or 170 km (MTGCM)]. MGCM coefficient data are provided at 7.5 degree-latitude spacing, while MTGCM data have 5-degree 2

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latitudespacing. Both MGCM andMTGCMdataareat every30 degreesof Ls angle,and includethreelevelsof dustopticaldepth(tau= 0.3, l, and 3). MGCM tidal coefficients are also provided at heights of 5 m and 30 m above local topographic height level at 9 degree-longitude spacing (for the same latitudes, Ls values, and dust optical depths). 2.1.3 Interpolation Methods Equation 2.1 is used to evaluate each atmospheric parameter, at the desired local solar time t, at "corners" of a multi-dimensional "box" of grid points that contain the desired interpolation location, Ls (time of year), and dust optical depth (tau). Multi-dimensional interpolation routines are used to evaluate all atmospheric parameters at locations between the MGCM or MTGCM grid-points. For data above the surface layer, interpolation is threedimensional in latitude, Ls, and tau. For surface layer data (5 m or 30 m), interpolation is fourdimensional in longitude, latitude, Ls, and tau. Interpolation is logarithmic for tau, and linear for all other dimensions. Interpolation to desired height (z) is done by first doing multi-dimensional interpolation at two height levels (zl and z2) from grid-point altitudes just above and below z. Above the surface layer, zl and z2 are at the 5 kin vertical grid spacing of the MGCM or MTGCM data. Near the surface layer (5 m and 30 m above surface height), altitudes zl and z2 are adjusted as appropriate. Temperature T(z), and wind components u(z) and v(z) are found by linear interpolation on height. Pressure p(z) is found by first computing pressure scale height H = (z2 - zl) / In[ p(zl) / p(z2) ] and evaluating pressure p(z) from the hydrostatic p(z) = p(z I ) exp[ (z I - z) / H ] (2.2) relation (2.3) Gas law "constant" R is evaluated from pressure, p, density, p, and temperature, T, at heights zl and z2 by R(zl ) = p(z I) / [p(z I ) T(z I) ] R(z2) = p(z2) / [p(z2) T(z2) ] (2.4) (2.5) Density p(z) at height z is then determined by the gas law relation and a linearly-interpolated R value, R(z) p(z) = p(z) / [R(z) T(z) ] (2.6) Winds at heights less than 5 m above the surface are evaluated from a logarithmic boundary layer profile relation u(z) = u(5) Zn(z/z0) / tn(5/zo) v(z) = v(5) In(z/z0) / tn(5/zo) (2.7) (2.8) where the surface roughness parameter z 0 is taken to be 0.03 m.

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2.2 Longitude-Dependent (Terrain-Fixed) Wave Model Tide components evaluated by equation (2.1) depend only on local solar time. Implicitly, this equation also depends on longitude. At any given instant, solar time varies at a rate of one hour for every 15 ° of longitude. During aerobraking operations, accelerometer measurements by Mars Global Surveyor 13 revealed large-amplitude longitude-dependent wave patterns for atmospheric density. Being in a sun-synchronous orbit, Mars Global Surveyor passed through each periapsis at essentially the same local solar time. Nevertheless, it found large-amplitude variatigns that tended to repeat as a function of periapsis longitude. The density variations were of the form of longitude-dependent (i.e., terrain-fixed) wave patterns. Mars- GRAM 2000 includes a model for these longitude-dependent waves (LDW) of the form LDW = B 0 + B 1 Cos[ rc (;_ - _ 1) / ! 80] + B 2 Cos[ n (_. - 2) / 90 ] + B 3 Cos[ 7(k - @3)/60 ] (2.9) where _, is longitude (in degrees), B 0 is a mean wave perturbation offset, B I, B2, and B 3 are amplitudes and _1, _2, and q_3 are phases (longitudes) for wave-l, wave-2, and wave-3 components. The term wave-n means the wave component has n peaks and troughs through 360 degrees of longitude. LDW perturbations computed by equation (2.9) are applied as a multiplier to the mean density and pressure computed from MGCM and MTGCM data, as interpolated by methods described in section 2.1.3. Wave model coefficients for equation (2.9) can be input from the NAMELIST format input file (see Appendix B), or from an auxiliary file of timedependent wave model coefficients (see sections 3.2 and 3.3). Values of LDW coefficients may be determined empirically, such as by accelerometer observations, _3 or theoretically from wave characteristics of Mars General Circulation Models. _4 For altitudes below I00 km, LDW perturbations are assumed to diminish in magnitude at an exponential rate, namely, LDW(z) = LDW(100) exp[ ( z - 100) / S ] (2.10) where S is the wave scale parameter Wscale, from the NAMEL1ST format input file. 2.3 Earlier Mars-GRAM Versions and Climate Factors Previous versions of Mars-GRAM allowed model output profiles to be adjusted (e.g., to better fit data profiles provided from MGCM output). These adjustments were accomplished with "climate factors" (CF0 through CF75 to adjust temperature fro,n 0- to 75-kin altitude, CFp to adjust surface pressure, deltaTF to adjust temperature at 1.26-nbar level, deltaZF to adjust height of the 1.26-nbar level (height ZF), and deltaTEX to adjust exospheric temperature. With Mars:GRAM 2000 based directly on MGCM and MTGCM output (below 170 kin), none of these climate factors are needed any longer (except deltaTEX, which still allows adjustment of exospheric temperature). Adjustment of Mars-GRAM 2000 model output can still be affected by choice of dust optical depth (input parameter Dusttau), and by longitude-dependent wave parameters (discussed in section 2.2).

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2.4 Simplified Perturbation Model In previous Mars-GRAM versions, a perturbation model, based on terrain-influenced gravity waves 5 was used. In the previous model, perturbation magnitudes are proportional to terrain relief (height above surrounding topographic heights), and depend on temperature gradients (through the Brunt-Vaisala frequency), air density. In addition to being complicated produce perturbation magnitudes that appear and on tile ratio of surface air density to local to evaluate, the previous model was found to to change too rapidly from place to place in response to changes in topography and temperature gradients. For Mars-GRAM 2000 a simplified perturbation model is introduced that does not require evaluation of surface density or temperature gradients. Perturbation magnitude (standard deviation, aD) in the new model (as a fraction of mean density) is given as a function of height, z, (km) and topographic surface height, z s, (km) by the relation crD = 0.0l (25+Zs)exp[(z-100)/40] A maximum value of 0.3 is imposed on crD. l) 2.5 Background Dust Level and Dust Storm Conditions Background (nondust storm) dust optical depth (tau) can be specified by the input parameter, Dusttau (see section 3.2). Interpolation routines (discussed in section 2.1.3) interpolate logarithmically between tau values for both MGCM and MTGCM input data. If Dusttau = 0 is input, a prescribed Viking-like seasonal variation of dust optical depth is used, in which case variation oftau with Ls (in degrees) is specified by tau = 0.65 - 0.35 Sin(n Ls/180) (2.12) A model for global or local-scale dust storms _ is retained. In Mars-GRAM 2000, input value for dust storm intensity (input parameter, INTENS) is equivalent to peak dust optical depth for the storm. The program does all necessary interpolations on dust optical depth as it varies with time (Ls, and as it varies with space, for local storms). 2.6 Choice of West or East Longitude The astronomical community (and "official" US Geological Survey maps of Mars) use West longitude positive (0 to 360°). Engineers and spacecraft navigation teams tend to use East longitude positive (0 to 360°). A program switch (input parameter, LonEW) allows Mars- GRAM 2000 users to select either East Longitude positive, or West Longitude positive. Default (LonEW=0) is West Longitude positive. The LonEW switch also determines if the longitudedependent wave model phase values (_1 through • 3 in equation 2.9) are in West or East Longitude.

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2.7 New File Name Input Options Options are now provided whereby the user can specify a name for the NAMELIST format input file, for the (optional) trajectory input file, and for the (optional) file of longitudedependent wave parameters. Users can also specify path names to the directories where the MGCM, MTGCM, and other input data reside. Upon executing the program, the user is prompted-to enter a name for the NAMELIST input file. Trajectory file name is specified by input parameter, TRAJFL. Name for thelongitude-dependent wave parameter file is given by input parameter, WaveFile. Path names for COSPAR and topographic data and for MGCM and MTGCM data are parameters, DATADIR and GCMDIR, respectively. See details in Appendix B. = | ! B i = z = i z

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1. How to Run Mars-GRAM 3.1 How to Obtain the Program All source code and required data files are available from a file transfer protocol (tip) server at NASA Marshall Space Flight Center. The ftp site also contains example input and output files and "readme" files. To obtain the program source code and data files by ftp, see contact information in the preface. See Appendices D and F for summaries of the program and data files available on the tip site. 3.2 Running the Program There are two ways to run Mars-GRAM: driver program (such as a trajectory program) (1) as a subroutine in a (user-provided) main and (2) as a stand alone program, using a NAMELIST format input file, in which values for all input options are provided. To use Mars- GRAM as a subroutine, see discussion in Appendix E and use example file dttmytraj.f (available in the ftp file distribution) as a guide. File README2.txt (available in the ftp file distribution) also discusses use ofdumytraj.fas an example for using Mars-GRAM as a subroutine. The steps involved in setting up and running Mars-GRAM in stand-alone mode are the following: • Compile and link the three FORTRAN source code files marsgram.f, marssubs.f, and setup.f, into an executable program (assumed to be called marsgram) Make sure that necessary data files ARCHGTS.DAT (topographic height information) and COSPAR.DAT (COSPAR model atmosphere pathname is specified by parameter DATADIR data) are in an appropriate directory (whose in the NAMELIST format input file) Compile and run the makebin.f program (see Appendix F) and convert the ASCII format MGCM and MTGCM data files provided to binary form (see Appendix D); this conversion process needs to be done only once on each user's machine Make sure that the binary format MGCM and MTGCM data files (see Appendices D and F) are in an appropriate directory (whose pathname is specified by parameter GCMDIR in the NAMELIST format input file) • Prepare a NAMELIST format input file (whose name is specified at run time) with the desired values of all input options (example in Appendix B) If trajectory input mode (rather than automatic profile mode) is desired, prepare a trajectory input file (whose name is set by parameter TRAJFL in the NAMELIST input file) containing time, height, latitude, and longitude (further discussion below) • If time-dependent coefficients for the longitude-dependent wave model are to be used, prepare a file (whose name is specified by parameter WaveFile in the NAMELIST format

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input file); this file contains one set of coefficients per line: time (seconds from start time) and wave model coefficients (B0 through (I)3, defined in section 2.2; further discussion below) Run the program by entering its executable name (e.g., marsgram); the program automatically opens and reads the NAMELIST input file (and the TRAJFL file, if trajectory mode is used), the data files, ARCHGTS,DAT and COSPAR.DAT, all MGCM and MTGCM binary data files, and the WaveFile file (if time-dependent coefficients are used) If the program is run in profile mode, the user provides (in the NAMELIST format input file) fixed values for increments of time, height, latitude, and longitude, in this mode, the program automatically increments position until the desired number of positions (NPOS) are evaluated. In trajectory mode, Mars-GRAM TRAJFL file. If constant values of longitude-dependent these are read in as part of the NAMELIST coefficients, values are read from the WaveFile reads time and position information from the wave model coefficients are used, values for input file (section 3.3). For time-dependent file. Each set of coefficients applies from the time given with the coefficient data, until a new time and set of coefficients are given (on the next line of WaveFile). The last set of coefficients in WaveFile applies indefinitely, beginning with its given time. 3.3 Program Input Appendix B gives a sample of NAMEL1ST format input file for Mars-GRAM 2000. Whether the subroutine or stand alone version is used, input variables whose values must be supplied in the INPUT file are as foIIows: LSTFL Name of LIST file (example LIST file in Appendix C); for a listing to the console in the stand alone version enter filename CON. OUTFL Name of OUTPUT file (discussion of this file in Appendix A) TRAJFL (Optional) trajectory input file name; file contains time (seconds) relative to start time, height (kin), latitude (degrees), longitude (degrees West if LonEW=0 or degrees East if LonEW= I; see below) WaveFile (Optional) file for time-dependent wave coefficient data (file description under parameter iuwave, below) DATADIR Pathname to directory for the COSPAR data and topographic height data GCMDIR Pathname to directory for MGCM and MTGCM binary data files MONTH Month (1 through 12) for initial time MDAY Day of month for initial time

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MYEAR Year for starting time, a 4-digit number; alternately years 1970-2069 can be input as a 2-digit number NPOS Maximum number of positions to evaluate, if an automatically-generated profile is to be produced; use 0 if trajectory positions are to be read in from a TRAJFL file IHR Initial time, hour of day UTC (GMT) IMIN Initial time, minute of hour SEC Initial time, seconds of minute LonEW Longitude switch, 0 for input and output with West longitude positive (default) or 1 for East longitude positive Dusttau Optical depth of background dust level (no time-developing dust storm, just uniformly mixed dust), 0.3 to 3.0 (if 0.0 is input, a Viking-like annual variation of background dust is assumed) ALSO Value of areocentric longitude of the Sun (Ls, in degrees) at which a dust storm is to start; use a value of 0 if no dust storm is to be simulated; dust storm can be simulated only during the season of the Mars year for which Ls is between 180 and 320 degrees INTENS Dust storm intensity, measured as peak dust optical depth of the storm, with allowable values ranging from 0.0 (no dust storm) to 3.0 (maximum intensity dust storm); intensity value (if> 0) must be greater than Dusttau RADMAX Maximum radius (km) a dust storm can attain, developing according to the parameterized space and time profile of build-up and decay in the program; if a value of 0 or more than 10 000 km is used, the storm is taken to be of global dimensions (uniformly covering the planet), but still assumed to build tip and decay in intensity according to the same temporal profile DUSTLAT Latitude (degrees, North positive) for center of dust storm DU STLON Longitude (degrees, West positive if LonEW=0, or East positive otherwise) for center of dust storm -22 F107 10.7 cm solar flux in its usual units of 10 W/cm 2 at average Earth orbit position (! AU); solar flux is automatically converted by the program to its value at the position of Mars in its orbit STDL Standard deviation parameter for short-term variations in Stewart nlodel thermosphere; normal value is 0; allowable range is from -3.0 to +3.0

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NR1 Seedvalue(integer)for randomnumbergenerator;allowablerangeis 1 to 29 999;to doMonte-Carlosimulationswith a varietyof perturbations,usea different randomnumberseedon each model run; to repeata given perturbationsequenceon a latermodelrun, usethe samerandomnumber seedvalue NVARX x-codefor theplotableoutput(x-y pairsfor line graphsor x-y-z tripletsfor contourplots);AppendixA lists the variablesassociatedwith the x-code (e.g.,if NVARX = 1, x outputfor plotting is heightabovethe reference ellipsoid) NVARY y-codefor contourplotoutput(x-y-ztriplets);useay-codevalueof 0 for line graph (x-y pair) plots; AppendixA lists y-codevaluesand parameters represented LOGSCALE Parameterto controlunitsof outputvaluesof densityandpressureon output plot files; a valueof 0 meansuseregulardensityandpressureunits(kg/m3 andN/m2); 1 meansto outputlogarithm(base-10)of the regularunits; 2 meansto outputpercentagedeviationfrom COSPARvaluesof densityand pressure FLAT Latitudeof initial pointto simulate (degrees, Noah positive) FLON Longitude of initial point to simulate (degrees, West positive if LonEW=0; East positive otherwise) FHGT Height (km) of initial point to simulate above the reference ellipsoid DELHGT Height increment (km) between successive steps in an automatically generated profile (positive upward) DELLAT Latitude increment (degrees, Northward positive) between successive steps in an automatically generated profile DELLON Longitude increment (degrees, Westward positive if LonEW=0; Eastward positive otherwise) between successive steps in an automatically generated profile DELTIME Time increment (seconds) between steps in an automatically generated profile deltaTEX Additive adjustment to modify temperature (K) of the exosphere (asymptotic temperature approached at very high altitudes), nominal = 0 rpscale Multiplicative factor for density and wind perturbation magnitude (I = nominal) 10

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NMONTE Number of Monte Carlo runs during one executionof the program; new/different starting random numbers are automatically generated for each of the Monte Carlo profiles (or trajectories) iup Option controlling output of LIST file and graphics output files (0 = none, other than 0 (default) indicates generate these flies) WaveA0 Mean term of longitude-dependent wave multiplier for density WaveA 1 Amplitude of wave-1 component of longitude-dependent wave multiplier for density Waveph i I Phase of wave-1 component of longitude-dependent wave multiplier (longitude, with West positive if LonEW = O, East positive otherwise) WaveA2 Amplitude of wave-2 component of longitude-dependent wave multiplier for density Wavephi2 Phase of wave-2 component of longitude-dependent wave multiplier (longitude, with West positive if LonEW = 0, East positive otherwise) WaveA3 Amplitude of wave-3 component of longitude-dependent wave multiplier for density Wavephi3 Phase of wave-3 component of longitude-dependent wave multiplier (longitude, with West positive if LonEW = O, East positive otherwise) iuwave Unit number for (Optional) time-dependent wave coefficient data file "WaveFile" (or 0 for none); WaveFile contains time (sec) relative to start time, and wave model coefficients (WaveA0 through Wavephi3) from given time to next time in the data file Wscale Vertical scale (km) of longitude-dependent wave damping at altitudes below 100 km (10<=Wscale<=10 000 kin) Two auxiliary input files are required (in addition to the MGCM and MTGCM input data fifes). Auxiliary file ARCHGTS.DAT contains topographic height data (height, kin, above the reference ellipsoid datum level). File COSPAR.DAT contains COSPAR reference wflues of temperature, density, and pressure as a function of height. If the (pre-computed) trajectory mode is used (NPOS=0), trajectory data must be read from a file (whose name is specified by the input parameter TRAJFL). Each line of TRAJFL is a position and time for which to compute atmospheric parameters. TRAJFL input lines contain time (seconds, from initial time), height (kin, relative to reference ellipsoid), latitude (degrees, North positive), and longitude (degrees, West positive if input switch LonEW=0, or East longitude if LonEW=l). For automatically-generated profiles, output is generated until the maximum number of positions (NPOS) is reached. For trajectory positions read in from TRAJFL file, output is generated until end of file is reached. I1

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If time-dependentwaveparameters(WaveA0throughWavephi3)aredesired,theseare input from the file whosepathnameis specifiedby parameterWavefileon the NAMELIST formatinputfile. Parameteriuwavedetermineswhethertime-dependentWaveFilevaluesare reador not(iuwave= 0 meannoWaveFitedata;otherwiseiuwaveistheWaveFileunit number). Eachdataline in the WaveFile file contains time (seconds) relative to start time, and wave model coefficients (WaveA0 through Wavephi3). Wave parameter values apply from the given time on each data line until the time given on the subsequent data line. Time-dependent wave parameters read in from WaveFile supercede any values given in the NAMELIST format input file. 3.4 Program Output There are three general types of program output: (1) a "LIST" file (name specified by LSTFL parameter) containing header and descriptor information, suitable for printing or viewing by an analyst (example LIST file in Appendix C), (2) an "OUTPUT" file (name specified by OUTFL parameter) containing one header line and one line per output position, suitable for reading into another program for additional analysis (description in Appendix A), and (3) a set of "plotable" output files, or graphics output files, i.e., text files suitable for input to a graphics program (descriptions in Appendix A). The graphics output files contain either x-y data pairs or x-y-z data triplets, determined by the selected values for the x-code (NVARX) and y-code (NVARY). If line-graph (x-y pair) data is the selected plot output option, then y-code = 0 is input. If contour plot (x-y-z triplet) data is the selected plot output option, then a non-zero value of y-code is input. See the list of codes for x-code and y-code in Appendix A. If the user desires to suppress the LIST, OUTPUT and graphics output files (so that output can be handled in a user-provided program), setLIST file unit number (iup) to 0 in the NAMELIST format input file. The unit number associated with the "screen" output (iu0 or iustdout), normaIly 6 in the stand alo,le version, can be set to any other value, by changing the assigned value of iustdout at program code line MGRM 15, and re-compiling the program. 12

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1. Sample Results 4.1 Model Variations with Latitude, Season, Height, and Time of Day Because of its small mass, the atmosphere of Mars has low heat capacity and little physical inertia. Therefore, it responds dramatically to changes in heat input (such as diurnal and seasonal changes in solar radiation) and mechanical forcing (such as winds flowing over strong topographic relief). This fact is illustrated by Figure 4.1, which shows seasonal and latitudinal variations of daily average atmospheric density at 100-kin altitude. This figure shows seasonal variation by almost a factor of 30 between southern winter solstice (Ls = 90 °) and southern summer solstice (Ls = 270 °) in the south polar region at this altitude. Figures 4.2 and 4.3 illustrate temperature versus height and latitude at Ls = 270 °, with tau = 0.3 and moderate solar activity, at 3 AM and 3 PM local solar time, respectively. Nearsurface temperatures at 3 AM show strong inversion. Near-surface temperature inversions between about 30 ° and 60 ° N latitude are also evident at 3 PM. Sharp north-south temperature gradients are seen from the surface to about 40-km altitude near the north polar cap edge (about 60 ° N). Strong diurnal changes in temperature (differences between 3 PM and 3 AM values) are seen in northern latitudes above about 150 km and in southern latitudes near the surface. DailyAverage Denslly (kg/km"3) at 100 km tau = 03 , , I , , I , , 1 , , I,, l , ; | i ; I , , I ' 1 I ' ' I l ' I l l 90 IE'lll_\ ",,o..._..///tlllNk\k l.,--" \ ,o 1' / 30- -30 -60 °o ./,r?,,.-7.,. .,.,,..,,-, .7 , 0 30 60 90 120 150 1.80 210 240 270 300 330 360 Ls, degrees Figure 4. i. Variation of daily average atmospheric density with latitude and season (Ls angle) at 100 km altitude. Density units are kg/km 3. Dust optical depth (tau) is 0.3. 13

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Temperature (K) at 3 AM Local Time Ls = 270 Dust OD = 0.3 Moderate Solar Activity 40 17 %0 -so -3o o 30 60 _o Latitude, degrees time at Ls 270 ° versus height and latitude. Dust Figure 4.2. Temperature at 3 AM local solar optical depth (tau) is 0.3 and solar activity is moderate. Temperature (K) at 3 PM Local Time Ls = 270 Dust OD = 0.3 Moderate Solar Activity 180 _ 160 _ 140 E120 %6 - -co -3o o J 30 60 oo Latitude, degrees Figure 4.3. Temperature at 3 PM local solar time at Ls 270 ° versus height and latitude. Dust optical depth (tau) is 0.3 and solar activity is moderate. Figures 4.4 and 4.5 show zonal (Eastward) winds versus height and latitude at Ls = 270 ° with tau = 0.3 and moderate solar activity at 3 AM and 3 PM local solar time, respectively. A strong polar jet is evident at both times of day, centered at about 40 km altitude, near 60 ° N. 14

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Zonesof strong,oppositely-directedwindsaboveabout150-kmaltitudeexhibit largediurnal variation. 4.2 Comparisons with Observations As illustrated in Figure 4.6, Mars-GRAM 2000 compares favorably with observed atmospheric density measured during entry and descent of Mars Pathfinder._5 Model evaluation was at the same location, date, and time of day as the entry observations. Figure 4.7 compares temperature rneasured at a height of I m above the surface by Mars Pathfinder lander, with comparable temperature estimates from Mars-GRAM 2000. Pathfinder data represent averages of the entire period of its surface operation, with bars on the data points showing + I standard deviation. Model values are indicated for dates near the beginning and end of Pathfinder lander operations for dust optical depths (tau) of 0.5 and 0.6, the approximate values observed at these times. Observed average daily maximum, minimum, and average surface air temperatures (1.6 m level) from Viking 2 lander are compared with Mars-GRAM 2000 modeled surface air temperature in Figure 4.8. Model values assume an annual variation of dust optical depth (tau) between 0.3 and 1.0, given by equation (2.12). Large symbols show observed average daily Eastward Wind (m/s) at 3 AM Local Tim e Ls = 270 Dust OD = 0.3 Moderate Solar Activity 200 180 160 140 'i II t ._E.120 _:100 80 60 40 20 0 -90 -60 -30 0 30 60 90 Latitude, degrees Figure 4.4. Eastward wind at 3 AM local solar time at Ls 270 ° versus height and latitude. Dust optical depth (tau) is 0.3, and solar activity is moderate. 15

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Eastward Wind (m/s) at 3 PM Local Time Ls = 270 Dust OD = 0.3 Moderate Solar Activity 200 180 160 140 120 .100 I1) -1- 80 60 4o 20 0 -go -60 -30 0 30 60 90 Latitude, degrees Figure 4.5, Eastward wind at 3 PM local solar time at Ls 270 ° versus height and latitude. Dust optical depth (tau) is 0.3, and solar activity is moderate. Mars PathfinderEntryProfile I I July 4'11997 Mars ILO(aJ Time =[3AM I [ 14o 12o lOO __ 8o & I 60 4O ...... Mars-GRAM2000 l Pathfinde Observed 2O o lO-iO 10g 10e 10-r 10-6 10-5 10-4 10-3 10-2 Censily,kg/m*'3 Figure 4.6. Atmospheric density measured during entry and descent by Mars Pathfinder, t5 and modeled by Mars-GRAM 2000 for the same date and time. 16

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Mars Pathfinder Site 270 2601 _250 240 o.230 E220 I_o_210 200 t 190 180 170 • , I , , I , , I 1 • , = _ ] I n , I = = I 0 3 6 9 12 15 18 21 24 Local Time, Mars Hours Figure 4.7. Average temperature observed at l-m height by Mars Pathfinder lander compared with Mars-GRAM 2000 values near beginning Pathfinder data points indicate +l standard deviation. and end of Pathfinder operations. Bars on Viking 2 Lander Site VV'hModel Seasonal tau Variation 250 240 • A A .A , 2301 'Q,.,',.. ,==e 220 "210 ...... .....,.,•,= .-200 . 190 8 180 170 160 •• X4_20_X4.20b O_lyDaily AvgMax • "4.2 Oh= Deily M 150 ', .4 ...:.,. • qg,,-, " 140 i , , i , , I , , I , , i , , i , , i , . i • , | , , I , , I , = i 30 60 90 120 150 180 210 240 270 300 330 360 Solar Longitude Figure 4.8. Observed average daily maximum, Ls, degrees minimum, and average surface air temperature (l.6-m level) from Viking 2 lander and Mars-GRAM 2000 mode]ed surface air temperature for a full Mars year. Model values assume an annual variation of dust optical depth (tau) between 0.3 and 1.0, given by equation (2.12). 17

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maximum,daily mean,anddaily minimumby 30 degreeLs intervals.SmalldotsshowMars- GRAM2000temperatureeveryfew hoursfor theentireMarsyear,fromwhichthe envelopeof daily maximumanddaily minimumcanbe inferred.BetweenaboutLs = 200andLs = 330, observeddataareinfluencedby two global-scaleduststormsthatoccurredduringthe Viking observationperiod.No duststormeffectsareincludedin theMars-GRAM2000simulationsin Figure4.8. Figure4.9 showsgradientof atmosphericdensitywith latitude(% per degree)as measuredby MarsGlobalSurveyor(MGS)accelerometer13at 130-kinaltitudeon inboundand outboundlegsof eachperiapsispassduringphase1 aerobraking,comparedwith modeled densitygradientfromMars-GRAM3.8andMars-GRAM2000.This figure shows that usage of MTGCM data input in Mars-GRAM 2000 results in considerable improvement in density gradient estimates over that of Mars-GRAM 3.8. Atmospheric density at periapsis measured by MGS accelerometer 13 during phase 2 aerobraking is compared in Figure 4.10 with modeled density from Mars-GRAM 3.8 and Mars- GRAM 2000. As evidenced by the "sawtooth" pattern in modeled values, particularly noticeable between orbits 700 and 900, much of the density variation with orbit is due to altitude changes from orbit-to-orbit. Additional large variations in observed density from orbit-to-orbit are due to observed longitude-dependent waves, 3 not represented in the model results, except by application of the mean coefficient (B 0 in equation (2.9)). Values of B 0 used in Figure 4.10 are 1.5 for Mars-GRAM 3.8 and 1.7 for Mars-GRAM 2000 results. At about the time of orbit 1200, MGS made its closet pass to the south (winter) pole. Figure 4.10 shows considerable improvement in representation of density near this zone for Mars-GRAM 2000 versus that for Mars-GRAM 3.8. Mars Global Surveyor Phase 1 Aerobraking 5 o 10 ' ' ' ' ' ' ' " ' ' ' ' ' ' " " ' ' " ' ' ' " " '" " ' ' " ' ' ' ' ' " ' " ' "i o o 0.°.._ °00o° o 000 0 , ' . oO cO ,v ° o° o o o 0 0 o o _ ".......-,----.--. o o o o o , o ---,.. -o oo.. oOoO-"oOoo o _ _ _ _ , 0 ".0 0 0 _ (][:;L, "0 "Or, ( 0 0 ------ M's-GRAM 38 o Accelerometer Observed -- Mars-GRAM 2000 O O o %_0 -- " -- "- ' _. ...s-15 ' ' ' I ' ' ' I ' ' " I ' ' * t ' ' ' I ' ' ' I ' ' ' I ' ' ' I ' ' ' I ' ' ' 0 20 40 60 80 MGS Orbit Number 100 120 140 160 180 200 Figure 4.9. Gradient of atmospheric density with latitude (% per degree) as measured by Mars Global Surveyor accelerometer 13at 130-km altitude on inbound and outbound legs of each periapsis pass during phase 1 aerobraking, compared with modeled density gradient from Mars- GRAM 3.8 and Mars-GRAM 2000. 18

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Mars Global Surveyor Phase 2 Aerobraklng 100 I I I o o g, 10 $ O 8 x --- M_-GRAMZ8 1.S Mars-GRAM 2000x 17 i i I 500 600 700 800 MGS Orbit Number I I t 1 k :_ <_ / l '! " T',' __F" I I 1 I 900 1.000 1.100 1.200 1.300 Figure 4.10. Atmospheric density at periapsis measured by Mars Global Surveyor accelerometer _3 during phase 2 aerobraking, compared with modeled density from Mars-GRAM 3.8 and Mars-GRAM 2000. 19

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1. References ° Lyons, D. T., Beerer, J. G., Esposito, P., and Johnson, M. D.: "'Mars Global Surveyor: Aerobraking Overview." Journal of Spacecraft and Rockets, Vol. 36, No. 3, pp. 307-313, 1999. . Gnoffo, P. A., Braun, R. D., Weilmuenster, K. J., et ai.: "Prediction and Validation of Mars Pathfinder Hypersonic Aerodynamic Database." Journal of Spacecraft and Rockets, Vol. 36, No. 3, pp. 367-373, 1999. , Queen, E. M., Cheatwood, F. M., Powell, R. W., and Braun, R. D.: "Mars Polar Lander Aerothermodynamic and Entry Dispersion Vol. 36, No. 3, pp. 421-428, 1999. , Justus, C. G.: "Mars Global Reference Analysis." Journal of Spacecraft and Rockets, Atmospheric Model for Mission Planning and Analysis." Journal of Spacecraft and Rockets, Vol. 28, No. 2, pp. 216-221, 1991. a | . Justus, C. G., James, B. F., and D. L. Johnson: "Mars Global Reference Atmospheric Model (Mars-GRAM 3.34): Programmer's Guide." NASA Technical Memorandum 108509, 1996. ° Justus, C. G., Johnson, D. L., and James, B. F.: "A Revised Thermosphere for the Mars Global Reference Atmospheric Model Memorandum 108513, 1996. Justus, C. G., James, B. F., and Johnson, (Mars-GRAM Version 3.4)." NASA Technical D. L.: "Recent and Planned Improvements in the Mars Global Reference Atmospheric Model (Mars-GRAM)." Advances in Space Research, Vol.19, No.8, pp.1223-1231, 1997. Justus, C. G. and James, B. F.: "Mars Global Reference Atmospheric Model (Mars-GRAM) Version 3.8: Users Guide." NASA Technical Memorandum 1999-209629, 1999. , Haberle, R. M., Pollack, J. B., Barnes, L J. R., et al.: "Mars Atmospheric Dynamics as Simulated by the NASA Ames General Circulation Model 1. The Zonal-Mean Circulation." Journal of Geophysical Research, Vol. 98, No. E2, pp. 3093-3123, 1993. 10. Barnes, J. R., Pollack, J. B., Haberle, R. M., et al.: "Mars Atmospheric Dynamics as Simulated by the NASA Ames General Circulation Model 2. Transient Baroclinic Eddies." Journal of Geophysical Research, Vol. 98, No. E2, pp. 3125-3148, 1993. 11. Bougher, S. W., Roble, R. G,, Ridley, E. C., et al.: "The Mars Tllermosphere: 2. General Circulation with Coupled Dynamics and Composition." Journal of Geophysical Research, Vol. 95, No. B9, pp. 14,81 I- ! 4,827, 1990. 12. Bougher, S. W., Engel, S., Roble, R. G., and Foster, B.: "Comparative Terrestrial Planet Thermospheres. 2. Solar Cycle Variation of Global Structure and Winds at Equinox." Journal of Geophysical Research, Vol. 104, No. E7, pp. 16,591 - 16,611, 1999. 20

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13.Keating, G. M. et al.: "The Structure of the Upper Atmosphere of Mars: In Situ Accelerometer Measurements from Mars Global Surveyor." Science, Vol. 279, No. 5357, pp. 1672-1676, 1998. 14. Bridger, A. F. C.: "Stationary Wave Activity Simulated by the NASA Ames MGCM Incorporating New MOLA Topography Data." Fifth International Conference on Mars, Pasadena, California, July 18-23, 1999. 15. Schofield, J. T., Barnes, J. R., Crisp, D., Haberle, R. M., Larsen, S., Magalhaes, J. A., Murphy, J. R., Seiff, A., and Wilson, G.: "The Mars Pathfinder Atmospheric Structure Investigation/Meteorology (ASI/MET) Experiment." Science, Vol. 278, pp. 1752-1758, 1997. 21

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Appendix A Headers for Mars-GRAM 2000 Output Files Mars-GRAM 2000 produces several output files suitable for passing to a graphics program for plotting and further analysis. Several of these files allow run-time selection from among several piotable parameters as the "X' parameter in an X-Y graph, or the "X and Y" parameters in an X-Y-Z graph. See the list of parameter selection codes at the end of this appendix. The graphics output file names and their descriptive headers are: File = Output.txt (or other name, as prescribed in the NAMELIST INPUT file) Time = time at_er initial input time (sec) Height = altitude above reference ellipsoid (kin) Lat = latitude (degrees, North positive) LonW/LonE = longitude (degrees, West positive or East Positive) DensAV = average (mean plus wave-perturbed) density (kg/m 3 or Log-10 ifLOGSCALE = 1 or % from COSPAR if LOGSCALE = 2) Temp = average temperature (K) EWind = eastward wind component (m/s, positive toward East) NWind = northward wind component (m/s, positive toward North) sigD = standard deviation for density perturbations (% of unperturbed mean) Ls = areocentrie longitude of Sun from Mars (degrees) Dust = dust optical depth File = DayData.txt (Daily averages for heights below 1.26 nbar level) Var_X = user-selected plot variable (determined by NVARX value) Var_Y = (Optional) user-selected plot variable (from NVARY value) TempDay = Local daily average temperature (K) PresDay = Local daily average pressure (N/m 2) DensDay = Local daily average density (kg/m 3) EWwnDay = Local daily average Eastward wind (m/s) NSwnDay = Local daily average Northward wind (m/s) File = Density.txt Var_X = user-selected plot variable (determined by NVARX value) Var_Y = (Optional) user-selected plot variable (from NVARY value) DENSLO = low (N average - 1 standard deviation) density (kg/m 3 or Log-10 or % from COSPAR, controlled by LOGSCALE) DENSAV = average (mean plus wave-perturbed) density (kg/m 3 or Log- 10 or % from COSPAR, controlled by LOGSCALE) 22

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DENSHI= high(- average+ 1 standard deviation) density (kg/m 3 or Log-10 or % from COSPAR, controlled by LOGSCALE) DENSTOT = total (mean plus perturbed) density (kg/m 3 or Log-10 or % from COSPAR, controlled by LOGSCALE) DustOD = dust optical depth File = Perturb.txt Var_X = user-selected plot variable (determined by NVARX value) Var_Y = (Optional) user-selected plot variable (from NVARY value) SigD -- standard deviation of density perturbations (% of unperturbed mean) DensRand = density perturbation from random model (% of unperturbed mean) DensWave = density perturbation from wave model (% of unperturbed mean) DensP = total density perturbation value (% of unperturbed mean) corlim = fraction of minimum step size for accuracy of perturbations (should be > i for insured accuracy of perturbations) S igU = standard deviation of wind perturbations (m/s) File = Thrmdata.txt (Thermospheric parameters for heights above 80 km) Var_X = user-selected plot variable (determined by NVARX value) Var._Y = (Optional) user-selected plot variable (from NVARY value) Tbase = temperature at 1.26 nbar level (K) Zbase = altitude of 1.26 nbar level (kin) F lpeak = altitude of F1 ionization peak (kin) MolWgt = mean molecular weight (kg/kg.mole) Texos = exospheric temperature (K) File = Tpreshgt.txt Var_X = user-selected plot variable (determined by NVARX value) Var_Y = (Optional) user-selected plot variable (from NVARY value) Temp = mean temperature (K) Pres = mean (plus wave-perturbed) pressure (N/m 2) TdegC = mean temperature (degrees C) Pres_mb = mean (plus wave-perturbed) pressure (rob) Hrho = density scale height (kin) File = Winds.txt Var_X = user-selected plot variable (determined by NVARX value) Var_Y = (Optional) user-selected plot variable (from NVARY value) EWmean = mean eastward wind component (m/s, positive eastward) EWpert = eastward wind perturbation (m/s) EWtot = total (mean plus perturbed) eastward wind (m/s) 23

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NSmean= meannorthwardwindcomponent(m/s,positivenorthward) NSpert= northwardwindperturbation(m/s) NStot= total(meanplusperturbed)northwardwind(m/s) Modelinputcodesusedtoselecttheplotablex andy parameters(VarX andVarY) are asfollows: Code Parameter .... ow ............. _ ................................. 1 Height (above reference ellipsoid, kin) 2 Height (above local terrain, km) 3 Latitude (deg.) 4 Longitude (deg.) West+ if LonEW = 0, East+ if LonEW = 1 5 Time from start (Earth seconds) 6 Time from start (Martian Sols) 7 Areoeentric Longitude of Sun, Ls (deg.) 8 Local Solar Time (Mars hours) 9 Pressure (mb) Run-time selection of these plotable parameters is made by the input variables NVARX and NVARY on the NAMELIST format input file (see section 3.3 and Appendix B). 24

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Appendix B Example NAMELIST Format Input File Following is an example of the NAMELIST format input file required by Mars-GRAM 2000. Values given are the default values assigned by the program. Only values that differ from the defaults actually have to be included in the NAMELIST file. $INPUT LSTFL = 'LIST.txt' OUTFL = 'OUTPUT.txt' TRAJFL = 'TRAJDATA.txt' WaveFile = 'null' DATADIR = 'C:\Mars\Mars2OOO\MGbindat' GCMDIR = 'C:\Mars\Mars2000\MGbindat' MONTH = 7 MDAY = 20 MYEAR = 76 NPOS = 41 IHR = 12 IMIN = 30 SEC = 0.0 LonEW = 0 Dusttau = 0.3 ALSO = 0.0 INTENS = 0.0 RADMAX = 0.0 DUSTLAT = 0.0 DUSTLON = 0.0 FI07 = 68.0 STDL = 0.0 NRI = 1234 NVARX = 1 NVARY = 0 LOGSCALE = 0 FLAT = 22.48 FLON = 47.97 FHGT = -5. DELHGT = 5.0 DELLAT = 0.5 DELLON = 0.5 DELTIME = 500.0 deltaTEX = 0.0 rpscale = 1.0 NMONTE = 1 iup = 13 WaveA0 = 1.0 WaveAl = 0.0 Wavephil = 0.0 WaveA2 = 0.0 Wavephi2 = 0.0 WaveA3 = 0.0 Wavephi3 = 0.0 iuwave = 0 Wscale = 20. 25

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SEND Explanation of variables: LSTFL = List file name (CON for console listing) OUTFL - Output file name TRAJFL - (Optional) Trajectory input file. File contains time (sec) relative to start time, height (km), latitude (deg), longitude (deg W if LonEW=0, deg E if LonEW=l, see below) WaveFile = (Optional) file for time-dependent wave coefficient data. See file description under DATADIR = Directory for COSPAR data parameter iuwave, below. and topographic height data GCMDIR = Directory for GCM binary data files MONTH _ month of year MDAY = day of month MYEAR = year (4-digit; 1970-2069 can be 2-digit) NPOS = max # positions to evaluate input file) IHR = UTC (GMT) hour of day IMIN = minute of hour (0 = read data from trajectory SEC _ second of minute (for initial position) LonEW = 0 for input and output West longitudes positive Dusttau = Optical depth of background dust storm, just uniformly 0 for a Viking-like annual ALSO _ starting Ls value (degrees) INTENS = dust storm intensity (0.0 be larger than Dusttau. longitudes positive; 1 for East dust level (no time-developing mixed dust), 0.3 to 3.0, or use variation of background dust for dust storm (0 = none) - 3.0). Storm intensity (>0) must RADMAX = max. radius (km) of dust storm (0 or >i0000 = global) DUSTLAT = Latitude (degrees) for center of dust storm DUSTLON = Longitude (degrees) (West positive if LonEW=0 ,or East positive if LonEW = i) for center of dust storm FI07 = 10.7 cm solar flux (10"*-22 STDL _ std. dev. for thermosphere W/cm**2 at 1AU) variation (-3.0 to +3.0) NRI = starting random number (0 < NRI < 30000) NVARX = x-code for plotable output See file xycodes.txt (l=hgt above ref. ellipse). NVARY = y-code for 3-D plotable output (0 for 2-D plots) LOGSCALE = 0=regular linear scale, l=log-base-10 scale, 2=percentage deviations from COSPAR model FLAT = initial latitude (N positive), degrees FLON = initial longitude (West positive if LowEW = 0 or East positive if LonEW = i), degrees FHGT = initial height (km), above ref. ellipsoid DELHGT = height increment (km) between steps DELLAT = Latitude increment (deg) between steps (Northward positive) DELLON = Longitude increment (deg) between steps (Westward positive if LonEW = 0, Eastward positive if LonEW = i) DELTIME = time increment (sec) betweensteps deltaTEX = adjustment for exospheric temperature (K) rpscale = random perturbation scale'factor (0-2) NMONTE = number of Monte Carlo runs iup = 0 for no LIST and graphics WaveA0 = Mean term of longitude-dependent WaveAl = Amplitude of wave-i component multiplier for density output, or unit number for output wave multiplier for density of longitude-dependent wave Wavephil = Phase of wave-I component of longitude-dependent wave multiplier (longitude, with West positive if LonEW = 0, East positive if LonEW = I) WaveA2 = Amplitude of wave-2 component multiplier for density of longitude-dependent wave Wavephi2 = Phase of wave-2 component of longitude-dependent wave multiplier (longitude, with West positive if LonEW = 0, East positive if LonEW = i) WaveA3 = Amplitude of wave-3 component multiplier for density 26 of longitude-dependent wave

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Wavephi3= Phaseof wave-3componentof longitude-dependentwave multiplier (longitude, with Westpositive if LonEW= 0, East positive if LonEW= i) iuwave - Unit number for (Optional) time-dependent wave coefficient data file "WaveFile" (or 0 for none). WaveFile contains time (sec) relative to start time, and wave model coefficients (WaveA0 thru Wavephi3) from the given time to the next time in the data file. Wscale = Vertical scale (k m) of longitude-dependent wave damping at altitudes below i00 km (10<=Wscale<=10,000 km) 27

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Appendix C Sample Output LIST File Following is LIST file output produced by standard input parameters given in Appendix B. Standard input is also provided to users (along with the program code and other data files) as file "input.std". Output data given here are provided as file "listmg2k.txt". Availability of these files allows users to make a test run after compiling Mars-GRAM on their own machine, and to electronically check their output by a file-compare process (e.g. the "diff" command in UNIX or the "fc" command in DOS). Note that, due to machine-dependent or compiler-dependent rounding differences, some output values may differ slightly from those shown here. These differences are usually no more than one unit in the last significant digit displayed. As shown here, the listing gives numbers in the DOS convention of not displaying zero-valued leading digits before the decimal place. Leading zeroes are given in the UNIX version of listmg2k.txt provided. If necessary for performing the output test, changes from UNIX format to DOS format can be accomplished with an editing program (e.g. changing all character strings " 0." to " ." and changing all "-0." to "-.", where "" indicates a blank space) Mars-GRAM 2000 (Version i) March, 2000 LIST file= LIST.txt OUTPUT file= OUTPUT.txt Data directory= C:\Mars\Mars2000\MGbindat\ GCM directory= C:\MarskMars2000\MGbindat\ Date - 7/20/1976 Julian Date = 2442980.0 UTC Time _ 12:30: .0 deltaTEX= .0 (Mars), standard deviation = .0 FI0.7 flux = 68.0 (I AU) 25.0 Random seed = 1234 Scale factor .000 .0 .000 .0 .000 .0 A0,Al,phil,A2,phi2,A3,phi3 = 1.000 = 1.0 Wave Scale - 20.0 km. Wave phases are in degrees of West Longitude Time (rel. to TO) = .0 sec. ( .000 Sols) Ls = 97.0 Dust = .30 Height - -1.54 km ( .00 km) Scale Hgt H(p) = 11.75 H(rho) = 13.27 km Latitude = 22.48 degrees Longitude = 47.97 W ( 312.03 E) degrees Sun Latitude = 25.00 deg. Mars Orbital Radius = 1.649 AU Sun Longitude = 108.77 deg. Local Time = 16.05 Mars hours Temperature = 234.9 K Pressure = 8.484E+02 N/m2 Density (Low, Avg., High) = i. 873E-02 i. 911E-02 1. 950E-02 kg/m 3 Departure, COSPAR NH Mean 4.7 % 6.8 % 8.9 % Tot. Dens. - 1.907E-02 kg/m3 Dens. Pert. - -.25% Wave -- .00% of mean Eastward Wind (Mean, Perturbed, Total) = 7.6 2.1 9.8 m/s Northward Wind (Mean, Perturbed, Total) = -3.0 -1.4 -4.4 m/s Time (rel. to TO) = 500.0 sec. ( .006 sols) Ls = 97.0 Dust 3 .30 Height m .00 km ( 1.33 km) Scale Hgt H(p) = 11.31 H(rho) = 13.25 km Latitude = 22.98 degrees Longitude = 48.47 W ( 311.53 E) degrees Sun Latitude z 25.00 deg. Mars Orbital Radius = 1.649 AU Sun Longitude = 110.80 deg. Local Time = 16.16 Mars hours Temperature _ 230.7 K Pressure = 7.437E+02 N/m2 Density (Low, Avg., High) = 1.672E-02 1.706E-02 1.740E-02 kg/m3 Departure, COSPAR NH Mean _ 7.9 % I0.i % 12.3 % Tot. Dens. = 1.700E-02 kg/m3 Dens. Pert. = -.34% Wave = .00% of mean Eastward Wind (Mean, Perturbed, Total) _ 14.1 -.9 13.2 m/s Northward Wind (Mean, Perturbed, Total) = -4.4 1.2 -3.3 m/s Time (tel. to TO) = 1000.0 sec. ( .011 sols) Ls = 97.0 Dust = .30 Height _ 5.00 km ( 5.65 km) Scale Hgt H(p) = 10.54 H(rho) = 11.90 km Latitude = 23.48 degrees Longitude = 48.97 W ( 311.03 E) degrees 28

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Sun Latitude = 25.00 deg. Mars Orbital Radius = 1.649 AU Sun Longitude = 112.83 deg. Local Temperature = 216.3 K Pressure Time = 16.26 Mars hours = 4.777E+02 N/m2 Density (Low, Avg., High) = 1 142E-02 1.169E-02 1.195E-02 kg/m3 Departure, COSPAR NH Mean = 15.4 Tot. Dens. = 1 203E-02 kg/m3 Dens. Pert. Eastward Wind (Mean, Perturbed, Total) Northward Wind (Mean, Perturbed, Total) Time (rel. to TO) 1500.0 sec. ( Height - i0.00 km ( 9.70 km) Scale % 18.1% 20.7 % = 2.93% Wave = .00% of mean = 6.6 -2.5 4.1 m/s = -3.2 -1.9 -5.1 m/s .017 sols) Ls = 97.0 Dust = .30 Hgt H(p) = 10.06 H(rho) = 11.32 km Latitude = 23.98 degrees Longitude _ 49.47 W ( 310.53 E) degrees Sun Latitude = 25.00 deg. Mars Orbital Radius = 1.649 AU Sun Longitude = 114.86 deg. Local Temperature = 20_.i K Pressure Time = 16.36 Mars hours = 2.973E+02 N/m2 Density (Low, Avg., High) = 7 469E-03 7.673E-03 7.878E-03 kg/m3 Departure, COSPAR NH Mean = 15.4 Tot. Dens. = 7 371E-03 kg/m3 Dens. Pert. Eastward Wind (Mean, Perturbed, Total) Northward Wind (Mean, Perturbed, Total) ........................................................................... Time (rel. to TO) = 2000.0 sec. ( Height = 15.00 km ( 14.63 km) Scale % 18.6 % 21.8 % = -3.94% Wave = .00% of mean = -2.9 -2.6 -5.4 m/s = 1.6 1.4 3.0 m/s .023 sols) Ls = 97.0 Dust = .30 Hgt H(p) = 9.55 H(rho) = 10.69 km Latitude = 24.48 degrees Longitude _ 49.97 W ( 310.03 E) degrees Sun Latitude = 25.00 deg. Mars Orbital Radius = 1.649 AU Sun Longitude = 116.89 deg. Local Temperature = 194.2 K Pressure Time = 16.46 Mars hours = 1.810E+02 N/m2 Density (Low, Avg., High) = 4 783E-03 4.932E-03 5.082E-03 kg/m3 Departure, COSPAR NH Mean = 14.7 Tot.Dens. = 4 848E-03 kg/m3 Dens. Pert. Eastward Wind (Mean, Perturbed, Total) Northward Wind (Mean, Perturbed, Total) Time (rel. to TO) = 2500.0 sec. ( Height = 20.00 km ( 19.57 km) Scale % 18.3 % 21.9 % = -1.70% Wave z .00% of mean -27.0 .0 -27.0 m/s = 9.0 -.6 8.3 m/s .028 sols) Ls = 97.0 Dust _ .30 Hgt H(p) = 9.02 H(rho) = 10.17 km Latitude = 24.98 degrees Longitude = 50.47 W ( 309.53 E) degrees Sun Latitude = 25.00 deg. Mars Orbital Radius = 1.649 AU Sun Longitude = 118.91 deg. Local Temperature _ 183.8 K Pressure Time = 16.56 Mars hours = 1.074E+02 N/m2 Density (Low, Avg., High) = 2 984E-03 3.090E-03 3.197E-03 kg/m3 Departure, COSPAR NH Mean = 13.5 Tot. Dens. = 3 153E-03 kg/m3 Dens. Pert. Eastward Wind (Mean, Perturbed, Total) Northward Wind (Mean, Perturbed, Total) Time (rel. to T0) 3000.0 sec. ( Height = 25.00 km ( 24.51 km) Scale % 17.5 % 21.6 % _ 2.01% Wave = .00% of mean -30.5 -4.3 -34.8 m/s = ii.0 .3 11.4 m/s .034 sols) Ls = 97.0 Dust = .30 Hgt H(p) = 8.50 H(rho) = 9.56 km Latitude = 25.48 degrees Longitude = 50.97 W ( 309.03 E) degrees Sun Latitude = 25.00 deg. Mars Orbital Radius = 1.649 AU Sun Longitude = 120.94 deg. Local Temperature = 172.9 K Pressure Time = 16.66 Mars hours = 6.184E+01 N/m2 Density (Low, Avg., High) = 1 818E-03 1.892E-03 1.966E-03 kg/m3 Departure, COSPAR NH Mean = 12.2 Tot. Dens. = 1 770E-03 kg/m3 Dens. Pert. Eastward Wind (Mean, Perturbed, Total) Northward Wind (Mean, Perturbed, Total) Time (rel. to TO) = 3500.0 sec. ( Height - 30.00 km ( 29.46 km) Scale % 16.8 % 21.4 % - -6.43% Wave = .00% of mean z -40.7 -.3 -41.0 m/s = 6.1 8.1 14.2 m/s .039 sols) Ls = 97.0 Dust = .30 Hgt H(p) _ 8.02 H(rho) = 8.82 km Latitude = 25.98 degrees Longitude _ 51.47 W ( 308.53 E) degrees Sun Latitude = 25.00 deg. Mars Orbital Radius = 1.649 AU Sun Longitude = 122.97 deg. Local Temperature - 162.3 K Pressure Time = 16.77 Mars hours - 3.445E+01 N/m2 Density (Low, Avg., High) = 1 073E-03 1.123E-03 1.173E-03 kg/m3 Departure, COSPAR NH Mean = 9.5 % 14.6 % 19.7 % Tot. Dens. = 1 146E-03 kg/m3 Dens. Pert. Eastward Wind (Mean, Perturbed, Total) 29 = 2.05% Wave = .00% of mean = -55.4 -.3 -55.7 m/s

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Northward Wind (Mean, Perturbed, Total) Time (rel. to TO) 4000.0 sec. ( Height - 35.00 km ( 34.40 km) Scale = 3.6 -6.2 -2.6 m/s .045 sols) Ls = 97.0 Dust = .30 Hgt H(p) = 7.64 H(rho) = 8.42 km Latitude = 26.48 degrees Longitude - 51.97 W ( 308.03 E) degrees Sun Latitude - 25.00 deg. Mars Sun Longitude = 125.00 deg. Local Orbital Radius = 1.649 AU Time = 16.87 Mars hours Temperature = 153.5 K Pressure = 1.854E+01 N/m2 Density (Low, Avg., High) = 6. 067E-04 6. 389E-04 6.711E-04 kg/m 3 Departure, COSPAR NH Mean = 4.2 % 9.8 % 15.3 % Tot. Dens. = 6.254E-04 kg/m3 Dens. Pert. = -2.11% Wave = .00% of mean Eastward Wind (Mean, Perturbed, Total) Northward Wind (Mean, Perturbed, Total) Time (tel. to TO) = 4500.0 sec. ( Height = 40.00 km ( 39.35 km) Scale = -65.8 -1.2 -67.0 m/s = -6.8 3.6 -3.2 m/s .051 sols) Ls = 97.0 Dust = .30 Hgt H(p) = 7.30 H(rho) = 7.86 km Latitude = 26.98 degrees Longitude = 52.47 W ( 307.53 E) degrees Sun Latitude = 25.00 deg. Mars Sun Longitude = 127.02 deg. Local Orbital Radius = 1.649 AU Time = 16.97 Mars hours Temperature = 144.5 K Pressure = 9.678E+00 N/m2 Density (Low, Avg., High) = 3.342E-04 3. 545E-04 3.747E-04 kg/m3 Departure, COSPAR NH Mean = -1.7 % 4.3 % 10.2 % Tot. Dens. = 3.800E-04 kg/m3 Dens. Pert. - 7.21% Wave = .00% of mean Eastward Wind (Mean, Perturbed, Total) Northward Wind (Mean, Perturbed, Total) ........................................................................... Time (rel. to TO) = 5000.0 sec. ( Height = 45.00 km ( 44.30 km) Scale = -75.6 8.3 -67.3 m/s = -6.6 -7.6 -14.1 m/s .056 sols) Ls = 97.0 Dust = .30 Hgt H(p) = 7.03 H(rho) = 7.37 km Latitude = 27.48 degrees Longitude = 52.97 W ( 307.03 E) degrees Sun Latitude = 25.00 deg. Mars Sun Longitude = 129.05 deg. Local Orbital Radius = 1.649 AU Time = 17.07 Mars hours Temperature = 137.7 K Pressure = 4.903E+00 N/m2 Density (Low, Avg., High) = 1.763E-04 i. 885E-04 2. 008E-04 kg/m3 Departure, COSPAR NH Mean = -9.1% -2.8 % 3.5 % Tot. Dens. = 1.786E-04 kg/m3 Dens. Pert. = -5.28% Wave = .00% of mean Eastward Wind (Mean, Perturbed, Total) Northward Wind (Mean, Perturbed, Total) Time (rel. to TO) = 5500.0 sec. ( Height = 50.00 km ( 49.26 km) Scale = -80.2 -5.0 -85.2 m/s = -17.3 -1.7 -19.0 m/s .062 sols) Ls = 97.0 Dust = .30 Hgt H(p) = 6.92 H(rho) = 6.85 km Latitude = 27.98 degrees Longitude = 53.47 W ( 306.53 E) degrees Sun Latitude = 25.00 deg. Mars Sun Longitude = 131.08 deg. Local Orbital Radius = 1.649 AU Time = 17.17 Mars hours Temperature = 133.1 K Pressure = 2.420E+00 N/m2 Density (Low, Avg., High) = 8. 915E-05 9. 625E-05 1.034E-04 kg/m3 Departure, COSPAR NH Mean = -17.4 % -10.9 % -4.3 % Tot. Dens. = 9.062E-05 k g/m3 Dens. Pert. = -5.85% Wave = .00% of mean Eastward Wind (Mean, Perturbed, Total) Northward Wind (Mean, Perturbed, Total) ........................................................................... Time (rel. to TO) = 6000.0 sec. ( Height = 55.00 km ( 54.22 km) Scale = -106.7 5.5 -101.2 m/s = -8.1 6.5 -1.5 m/s .068 sols) Ls = 97.0 Dust = .30 Hgt H(p) = 6.76 H(rho) = 6.36 km Latitude = 28.48 degrees Longitude = 53.97 W ( 306.03 E) degrees Sun Latitude = 25.00 deg. Mars Sun Longitude = 133.11 deg. Local Orbital Radius = 1.649 AU Time = 17.28 Mars hours Temperature = 134.1 K Pressure = 1.180E+00 N/m2 Density (Low, Avg., High) = 4.272E-05 4.662E-05 5.052E-05 kg/m3 Departure, COSPAR NH Mean = -27.8 % -21.2 % -14.7 % Tot. Dens. = 4.460E-05 kg/m**3 Dens. Pert. = -4.33% Wave = .00% of mean Eastward Wind (Mean, Perturbed, Total) Northward Wind (Mean, Perturbed, Total) .............. -- ............................................................ Time (tel. to TO) = 6500.0 sec. ( Height = 60.00 km ( 59.20 km) Scale = -93.0 -14.7 -107.7 m/s = 14.7 -6.0 8.6 m/s .073 sols) Ls = 97.0 Dust = .30 Hgt H(p) = 7.01 H(rho) = 6.75 km Latitude = 28.98 degrees Longitude = 54.47 W ( 305.53 E) degrees Sun Latitude = 25.00 deg. Mars Sun Longitude = 135.13 deg. Local 3O Orbital Radius = 1.649 AU Time = 17.38 Mars hours

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Temperature = 140.5 K Pressure Density (Low, Avg., High) = 1.932E-05 = 5.658E-01 N/m2 2°134E-05 2.337E-05 kg/m3 Departure, COSPAR NH Mean = -39.3 % -32.9 % -26.5 % Tot. Dens. = 1.953E-05 kg/m3 Dens. Pert. _ -8.48% Wave = .00% of mean Eastward Wind (Mean, Perturbed, Total) _ -27.2 -3.9 -31.1 m/s Northward Wind (Mean, Perturbed, Total) = 21.1 -14.5 6.5 m/s Time (rel. to T0) = 7000.0 sec. ( .079 sols) Ls = 97.0 Dust = .30 Height = 65.00 km ( 64.18 km) Scale Hgt H(p) = 7.10 H(rho) = 7.24 km Latitude _ 29.48 degrees Longitude _ 54.97 W ( 305._3 E) degrees Sun Latitude = 25.00 deg. Mars Orbital Radius = 1.649 AU Sun Longitude = 137.16 deg. Local Time = 17.48 Mars hours Temperature = 144.3 K Pressure Density (Low, Avg., High) = 9.122E-06 = 2.781E-01 N/m2 1.022E-05 1.132E-05 kg/m3 Departure, COSPAR NH Mean = -45.7 % -39.2 % -32.6 % Tot. Dens. = 1.029E-05 kg/m3 Dens. Pert. = .67% Wave = .00% of mean Eastward Wind (Mean, Perturbed, Total) = 24.3 -.i 24.1 m/s Northward Wind (Mean, Perturbed, Total) = 9.2 -12.0 -2.8 m/s ........................................................................... Time (rel. to TO) = 7500.0 sec. ( .084 sols) Ls = 97.0 Dust = .30 Height = 70.00 km ( 69.16 km) Scale Hgt H(p) = 6.99 H(rho) = 7.35 km Latitude = 29.98 degrees Longitude = 55.47 W ( 304.53 E) degrees Sun Latitude = 25.00 deg. Mars Orbital Radius = 1.649 AU Sun Longitude = 139.19 deg. Local Time = 17.58 Mars hours Temperature = 142.1K Pressure Density (Low, Avg., High) = 4.510E-06 = 1.377E-01 N/m2 5.137E-06 5.764E-06 kg/m3 Departure, COSPAR NH Mean = -48.3 % -41.2 % -34.0 % Tot. Dens. = 5.212E-06 kg/m3 Dens. Pert. 1.45% Wave = .00% of mean Eastward Wind (Mean, Perturbed, Total) = 28.3 .5 28.8 m/s = 7.0 9.3 16.3 m/s Northward Wind (Mean, Perturbed, Total) Time (rel. to T0) = 8000.0 sec. ( .090 sols) Ls = 97.0 Dust = .30 Height = 75.00 km ( 74.11 km) Scale Hgt H(p) = 7.24 H(rho) = 7.26 km Latitude = 30.48 degrees Longitude _ 55.97 W ( 304.03 E) degrees Sun Latitude = 25.00 deg. Mars Orbital Radius = 1.649 AU Sun Longitude = 141.22 deg. Local Time = 17.68 Mars hours Temperature = 136.8 K Pressure Density (Low, Avg., High) = 2.246E-06 = 6.742E-02 N/m2 2.607E-06 2.969E-06 kg/m3 Departure, COSPAR NH Mean = -49.8 % -41.7 % -33.6 % Tot. Dens. _ 2.530E-06 kg/m3 Dens. Pert. = -2.96% Wave = .00% of mean Eastward Wind (Mean, Perturbed, Total) = 8.6 -41.7 -33.1 m/s Northward Wind (Mean, Perturbed, Total) = -14.8 -8.3 -23.1 m/s Time (rel. to TO) = 8500.0 sec. ( .096 sols) Ls = 97.0 Dust = .30 Height = 80.00 km ( 79.06 km) Scale Hgt H(p) = 7.00 H(rho) = 7.16 km Latitude = 30.98 degrees Longitude _ 56.47 W ( 303.53 E) degrees Sun Latitude = 25.00 deg. Mars Orbital Radius = 1.649 AU Sun Longitude = 143.25 deg. Local Time = 17.79 Mars hours Temperature = 130.5 K Pressure Density (Low, Avg., High) = I.I08E-06 = 3.396E-02 N/m2 1.314E-06 1.521E-06 kg/m3 Departure, COSPAR NH Mean = -51.6 % -42.6 % -33.6 % Tot. Dens. = 1.309E-06 kg/m3 Dens. Pert. = -.42% Wave = .00% of mean Eastward Wind (Mean, Perturbed, Total) = 7.1 -61.4 -54.3 m/s Northward Wind (Mean, Perturbed, Total) = -6.1 6.9 .8 m/s ........................................................................... Time (rel. to TO) = 9000.0 sec. ( .I01 sols) Ls = 97.0 Dust = .30 Height = 85.00 km ( 84.00 km) Scale Hgt H(p) = 6.83 H(rho) _ 7.01 km Latitude = 31.48 degrees Longitude = 56.97 W ( 303.03 E) degrees Sun Latitude = 25.00 deg. Mars Orbital Radius = 1.649 AU Sun Longitude = 145.27 deg. Local Time = 17.89 Mars hours Exospheric Temp. = 206.0 K Tbase = 160.4 K Zbase = 120.2 km Solar Zenith Angle = 75.9 deg F1 peak Temperature = 127.2 K Pressure Density (Low, Avg., High) = 5.390E-07 = 133.1 km Mol.Wgt. = 41.50 = 1.672E-02 N/m2 6.562E-07 7.735E-07 kg/m3 Departure, COSPAR NH Mean = -53.9 % -43.9 % -33.9 % Tot. Dens. = 7.052E-07 kg/m3 Dens. Pert. = 9.5 -30.1 -20.6 m/s Eastward Wind (Mean, Perturbed, Total) 31 = 7.46% Wave = .00% of mean

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NorthwardWind (Mean,Perturbed, Total) = -9.4 -7.0 -16.5 m/s ........................................................................... Time (rel. to TO) - 9500.0 sec. ( .107 sols) Ls = 97.1 Dust = .30 Height = 90.00 km ( 88.95 km) Scale Hgt H(p) = 6.93 H(rho) = 6.90 km Latitude = 31.98 degrees Longitude = 57.47 W ( 302.53 E) degrees Sun Latitude _ 25.00 deg. Mars Orbital Radius = 1.649 AU Sun Longitude = 147.30 deg. Local Time = 17.99 Mars hours Exospheric Temp. = 205.6 K Tbase = 160.1 K Zbase = 120.3 km Solar Zenith Angle = 76.9 deg F1 peak = 133.8 km Mol.Wgt. = 41.83 Temperature = 126.0 K Pressure = 8.106E-03 N/m2 Density (Low, Avg., High) 2.579E-07 3.236E-07 3.892E-07 kg/m3 Departure, COSPAR NH Mean = -57.1 % -46.2 % -35.2 % Tot. Dens. = 2.988E-07 kg/m3 Dens. Pert. = -7.66% Wave = .00% of mean Eastward Wind (Mean, Perturbed, Total) _ 9.1 3.6 12.7 m/s Northward Wind (Mean, Perturbed, Total) = -14.8 -23.4 -38.2 m/s Time (rel. to TO) - i0000.0 sec. ( .113 sols) Ls = 97.1 Dust = .30 Height = 95.00 km ( 93.90 km) Scale Hgt H(p) = 6.76 H(rho) = 6.83 km Latitude _ 32.48 degrees Longitude _ 57.97 W ( 302.03 E) degrees Sun Latitude = 25.00 deg. Mars Orbital Radius = 1.649 AU Sun Longitude = 149.33 deg. Local Time = 18.09 Mars hours Exospheric Temp, = 205.2 K Tbase = 159.9 K Zbase = 120.4 km Solar Zenith Angle = 77.9 deg F1 peak = 134.5 km Mol.Wgt. = 41.58 Temperature - 126.0 K Pressure _ 3.982E-03 N/m2 Density (Low, Avg., High) 1.216E-07 1.581E-07 1.945E-07 kg/m3 Departure, COSPAR NH Mean = -60.6 % -48.8 % -37.1% Tot.Dens. = 1.199E-07 kg/m3 Dens. Pert. _ -24.16% Wave = .00% of mean Eastward Wind (Mean, Perturbed, Total) = 6.2 4.9 11.1 m/s Northward Wind (Mean, Perturbed, Total) = -22.3 -38.7 -61.1 m/s Time (rel. to TO) = 10500.0 sec. ( .118 sols) Ls = 97.1 Dust = .30 Height - I00.00 km ( 98.84 km) Scale Hgt H(p) = 7.09 H(rho) = 6.87 km Latitude = 32.98 degrees Longitude = 58.47 W ( 301.53 E) degrees Sun Latitude = 25.00 deg. Mars Orbital Radius = 1.649 AU Sun Longitude = 151.36 deg. Local Time = 18.19 Mars hours Exospheric Temp. = 204.8 K Tbase = 159.6 K Zbase = 120.5 km Solar Zenith Angle = 78.9 deg F1 peak = 135.3 km Mol.Wgt. = 42.08 Temperature = 126.7 K Pressure = 1.925E-03 N/m2 Density (Low, Avg., High) = 5.678E-08 7.689E-08 9.700E-08 kg/m3 Departure, COSPAR NH Mean = -64.3 % -51.6 % -39.0 % Tot. Dens. - 6.038E-08 kg/m3 Dens. Pert. = -21.48% Wave = .00% of mean Eastward Wind (Mean, Perturbed, Total) = .9 -11.6 -10.7 m/s Northward Wind (Mean, Perturbed, Total) = -30.2 -13.9 -44.1 m/s ........................................................................... Time (rel. to TO) = 11000.0 sec. ( .124 sols) Ls = 97.1 Dust = .30 Height _ 105.00 km ( 103.79 km) Scale Hgt H(p) = 6.99 H(rho) = 6.75 km Latitude _ 33.48 degrees Longitude - 58.97 W ( 301.03 E) degrees Sun Latitude = 25.00 deg. Mars Orbital Radius = 1.649 AU Sun Longitude = 153.38 deg. Local Time = 18.29 Mars hours Exospheric Temp. = 204.4 K Tbase = 159.3 K Zbase = 120.6 km Solar Zenith Angle = 79.9 deg F1 peak = 136.2 km Mol.Wgt. = 41.60 Temperature = 128.3 K Pressure = 9.645E-04 N/m2 Density (Low, Avg., High) = 2.644E-08 3.761E-08 4.877E-08 kg/m3 Departure, COSPAR NH Mean - -67.0 % -53,1 % -39.1 % Tot.Dens. = 2.563E-08 kg/m3 Dens. Pert. = -31.84% Wave = .00% of mean Eastward Wind (Mean, Perturbed, Total) = -6.8 -38.7 -45.6 m/s Northward Wind (Mean, Perturbed, Total) = -36.0 3.0 -33.0 m/s ........................................................................... Time (rel. to TO) = 11500.0 sec. ( .130 sols) Ls = 97.1 Dust = .30 Height _ 110.00 km ( 108.74 km) Scale Hgt H(p) = 7.49 H(rho) = 6.72 km Latitude = 33.98 degrees Longitude = 59.47 W ( 300.53 E) degrees Sun Latitude = 25.00 deg. Mars Orbital Radius = 1.649 AU Sun Longitude = 155.41 deg. Local Time = 18.40 Mars hours Exospheric Temp. - 203.9 K Tbase = 158.9 K Zbase = 120.7 km Solar Zenith Angle = 80.9 deg F1 Peak = 137.0 km Mol.Wgt. = 41.99 Temperature s 132.7 K Pressure = 4.779E-04 N/m2 Density (Low, Avg., High) = 1.273E-08 1.818E-08 2.364E-08 kg/m3 32

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Departure, COSPAR NH Mean = -69.3 Tot. Dens. = 1.875E-08 kg/m3 Dens. Pert. Eastward Wind (Mean, Perturbed, Total) Northward Wind (Mean, Perturbed, Total) ........................................................................... Time (rel. to TO) = 12000.0 sec. ( Height = 115.00 km ( 113.69 km) Scale % -56.1% -42.9 % = 3.11% Wave = .00% of mean = -14.5 5.1 -9.4 m/s = -38.2 -26.2 -64.4 m/s .135 sols) Ls = 97.1 Dust = .30 Hgt H(p) = 8.18 H(rho) = 7.07 km Latitude = 34.48 degrees Longitude = 59.97 W ( 300.03 E) degrees Sun Latitude = 25.00 deg. Mars Orbital Radius = 1.649 AU Sun Longitude = 157.44 deg. Local Exospheric Temp. = 203.5 K Tbase Solar Zenith Angle = 81.8 deg F1 peak Temperature = 142.1 K Pressure 6.128E-09 Density (Low, Avg., High) = Departure, COSPAR NH Mean = -72.1% Tot. Dens. = 8.655E-09 kg/m3 Dens. Pert. Eastward Wind (Mean, Perturbed, Total) Northward Wind (Mean, Perturbed, Total) ........................................................................... Time (rel. to TO) = 12500.0 sec. ( Height = 120.00 km ( 118.64 km) Scale Time = 18.50 Mars hours = 158.7 K Zbase = 120.7 km = 138.0 km Mol.Wgt. = 41.76 = 2.477E-04 N/m2 8.754E-09 1.138E-08 kg/m3 -60.2 % -48.3 % = -1.13% Wave = .00% of mean = -19.8 -25.9 -45.7 m/s = -38.7 -50.3 -89.0 m/s .141 sols) Ls = 97.1 Dust = .30 Hgt H(p) = 9.02 H(rho) = 7.64 km Latitude = 34.98 degrees Longitude = 60.47 W ( 299.53 E) degrees Sun Latitude = 25.00 deg. Mars Orbital Radius = 1.648 AU Sun Longitude = 159.47 deg. Local Exospheric Temp. = 203.0 K Tbase Solar Zenith Angle = 82.8 deg F1 peak Pressure Temperature = 155.8 K 3.058E-09 Density (Low, Avg., High) = Departure, COSPAR NH Mean = -74.3 Tot.Dens. = 3.028E-09 kg/m3 Dens. Pert. Eastward Wind (Mean, Perturbed, Total) Northward Wind (Mean, Perturbed, Total) ........................................................................... Time (rel. to TO) = 13000.0 sec. ( Height = 125.00 km ( 123.59 km) Scale Time = 18.60 Mars hours = 158.4 K Zbase = 120.8 km = 139.0 km Mol.Wgt. = 41.70 _ 1.357E-04 N/m2 4.369E-09 5.680E-09 kg/m3 % -63.3 % -52.3 % = -30.68% Wave = .00% of mean = -21.3 -14.8 -36.0 m/s = -40.7 -22.6 -63.4 m/s .146 sols) Ls = 97.1 Dust = .30 Hgt H(p) = 9.88 H(rho) = 8.44 km Latitude = 35.48 degrees Longitude = 60.97 W ( 299.03 E) degrees Sun Latitude = 25.00 deg. Mars Orbital Radius = 1.648 AU Sun Longitude = 161.50 deg. Local Tbase Exospheric Temp. = 202.5 K Solar Zenith Angle = 83.7 deg F1 peak Temperature = 171.0 K Pressure 1.618E-09 Density (Low, Avg., High) = Departure, COSPAR NH Mean = -75.6 Tot.Dens. = 2.607E-09 kg/m3 Dens. Pert. Eastward Wind (Mean, Perturbed, Total) Northward Wind (Mean, Perturbed, Total) ........................................................................... Time (rel. to TO) = 13500.0 sec. ( Height _ 130.00 km ( 128.54 km) Scale Time = 18.70 Mars hours = 158.1 K Zbase = 120.9 km = 140.1 km Mol.Wgt. = 41.54 = 7.856E-05 N/m2 2.296E-09 2.974E-09 kg/m3 % -65.4 % -55.1% = 13.53% Wave = .00% of mean = -19.0 -22.1 -41.0 m/s = -43.7 -3.0 -46.7 m/s .152 sols) Ls = 97.1 Dust = .30 Hgt H(p) = 10.73 H(rho) = 9.31 km Latitude = 35.98 degrees Longitude = 61.47 W ( 298.53 E) degrees Sun Latitude = 25.00 deg. Mars Orbital Radius = 1.648 AU Sun Longitude = 163.52 deg. Local Tbase Exospheric Temp. = 202.0 K Time = 18.80 Mars hours = 157.8 K Zbase = 121.0 km Solar Zenith Angle = 84.5 deg F1 peak = 141.3 km Mol.Wgt. = 41.51 Temperature = 185.3 K Pressure 9.290E-I0 Density (Low, Avg., High) = Departure, COSPAR NH Mean = -75.3 Tot. Dens. = 1.374E-09 kg/m3 Dens. Pert. Eastward Wind (Mean, Perturbed, Total) Northward Wind (Mean, Perturbed, Total) ........................................................................... Time (rel. to TO) = 14000.0 sec. ( Height = 135.00 km ( 133.50 km) Scale = 4.776E-05 N/m2 1.287E-09 1.645E-09 kg/m**3 % -65.8 % -56.2 % = 6.75% Wave = .00% of mean = -14.5 -15.7 -30.2 m/s = -48.2 1.8 -46.4 m/s .158 sols) Ls = 97.1 Dust = .30 Hgt H(p) = 11.41H(rho) = i0.01 km Latitude = 36.48 degrees Longitude = 61.97 W ( 298.03 E) degrees Sun Latitude = 25.00 deg. Mars Orbital Radius = 1.648 AU Sun Longitude = 165.55 deg. Local Exospheric Temp. = 201.5 K Tbase 33 Time = 18.91 Mars hours = 157.5 K Zbase = 121.0 km

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Solar Zenith Angle = 85.4 deg F1 peak = 142.5 km Mol.Wgt. = 41.29 Temperature - 195.9 K Pressure = 3.024E-05 N/m2 Density (Low, Avg., High) = 5.784E-I0 7.672E-I0 9.554E-I0 kg/m3 Departure, COSPAR NH Mean = -69.8 % -59.9 % -50.1% Tot. Dens. - 7.760E-I0 kg/m3 Dens. Pert. = 1.15% Wave = .00% of mean Eastward Wind (Mean, Perturbed, Total) Northward Wind (Mean, Perturbed, Total) Time (rel. to TO) - 14500.0 sec. ( Height _ 140.00 km ( 138.45 km) Scale = -9.0 -35.8 -44.8 m/s = -55.6 4.6 -51.0 m/s .163 sols) Ls = 97.1 Dust = .30 Hgt H(p) = 11.78 H(rho) = 10.69 km Latitude - 36.98 degrees Longitude = 62.47 W ( 297.53 E) degrees Sun Latitude = 25.00 deg. Mars Sun Longitude = 167.58 deg. Local Exospheric Temp. = 201.0 K Tbase Orbital Radius = 1.648 AU Time = 19.01 Mars hours = 157.3 K Zbase = 121.1 km Solar Zenith Angle = 86.2 deg F1 peak = 144.0 km Mol.Wgt. = 40.76 Temperature = 202.4 K Pressure = 1.964E-05 N/m2 Density (Low, Avg., High) = 3.760E-10 4.767E-10 5.765E-10 kg/m3 Departure, COSPAR NH Mean = -65.5 % -56.3 % -47.1% Tot. Dens. = 5.023E-10 kg/m3 Dens. Pert. = 5.37% Wave = .00% of mean Eastward Wind (Mean, Perturbed, Total) Northward Wind (Mean, Perturbed, Total) Time (rel. to T0) = 15000.0 sec. ( Height = 145.00 km ( 143.40 km) Scale = -3.4 7.9 4.5 m/s = -61.9 -30.1 -92.0 m/s .169 sols) Ls = 97.1 Dust = .30 Hgt H(p) = 12.10 H(rho) = 11.14 km Latitude = 37.48 degrees Longitude = 62.97 W ( 297.03 E) degrees Sun Latitude = 25.00 deg. Mars Sun Longitude = 169.61 deg. Local Exospheric Temp. = 200.5 K Tbase Orbital Radius = 1.648 AU Time = 19.11 Mars hours = 157.0 K Zbase = 121.2 km Solar Zenith Angle = 87.1 deg F1 peak = 145.6 km Mol.Wgt. = 40.47 Temperature = 205.2 K Pressure = 1.287E-05 N/m2 Density (Low, Avg., High) 2.485E-I0 3.062E-I0 3.630E-I0 kg/m3 Departure, COSPAR NH Mean = -64.8 % -56.6 % -48.6 % Tot. Dens. = 2.956E-I0 kg/m3 Dens. Pert. = -3.47% Wave = .00% of mean Eastward Wind (Mean, Perturbed, Total) Northward Wind (Mean, Perturbed, Total) Time (rel. to TO) - 15500.0 sec. ( Height _ 150.00 km ( 148.43 km) Scale = 1.8 25.3 27.0 m/s = -70.2 -8.4 -78.5 m/s .175 sols) Ls = 97.1 Dust = .30 Hgt H(p) = 12.34 H(rho) = 11.45 km Latitude = 37.98 degrees Longitude = 63.47 W ( 296.53 E) degrees Sun Latitude = 25.00 deg. Mars Sun Longitude = 171.63 deg. Local Exospheric Temp. = 200.0 K Tbase Orbital Radius = 1.648 AU Time = 19.21 Mars hours = 156.8 K Zbase = 121.3 km Solar Zenith Angle = 87.9 deg F1 peak = 147.3 km Mol.Wgt. = 39.99 Temperature = 204.7 K Pressure - 8.488E-06 N/m2 Density (Low, Avg., High) = 1.642E-I0 1.999E-I0 2.353E-I0 kg/m3 Departure, COSPAR NH Mean = -65.3 % -57.7 % -50.3 % Tot. Dens. = 1.989E-I0 kg/m3 Dens. Pert. = -.52% Wave = .00% of mean Eastward Wind (Mean, Perturbed, Total) Northward Wind (Mean, Perturbed, Total) Time (rel. to TO) = 16000.0 sec. ( Height = 155.00 km ( 153.45 km) Scale = 7.6 .7 8.3 m/s = -75.7 -1.6 -77.4 m/s .180 sols) Ls = 97.1 Dust = .30 Hgt H(p) = 12.43 H(rho) = 11.59 km Latitude = 38.48 degrees Lodgitude = 63.97 W ( 296.03 E) degrees Sun Latitude = 25.00 deg. Mars Sun Longitude = 173.66 deg. Local Exospheric Temp. = 199.4 K Tbase Orbital Radius = 1.648 AU Time = 19.31 _ars hours = 156.5 K Zbase = 121.3 km Solar Zenith Angle = 88.6 deg F1 peak = 149.3 km Mol.Wgt. = 39.44 Temperature = 202.8 K Pressure = 5.607E-06 N/m2 Density (Low, Avg., High) = 1.071E-10 1.313E-I0 1.560E-I0 kg/m3 Departure, COSPAR NH Mean = -68.2 % -61.0 % -53.7 % Tot. Dens. = 1.295E-I0 kg/m**3 Dens. Pert. = -1.39% Wave = .00% of mean Eastward Wind (Mean, Perturbed, Total) Northward Wind (Mean, Perturbed, Total) ........................................................................ Time (tel. to TO) = 16500.0 sec. ( Height = 160.00 km ( 158.48 km) Scale = 12.0 -2.1 9.9 m/s = -82.6 -2.0 -84.7 m/s _-- .186 sols) Ls = 97.1 Dust = .30 Hgt H(p) = 12.56 H(rho) = 11.73 km Latitude = 38.98 degrees Longitude = 64.47 W ( 295.53 E) degrees 34

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SunLatitude = 25.00 deg. Mars Orbital Radius = 1.648 AU SunLongitude = 175.69 deg. Local Exospheric Temp. = 198.9 K Tbase Solar Zenith Angle = 89.4 deg F1 peak Temperature = 200.3 K Pressure Density (Low, Avg., High) = 6.868E-II Departure, COSPAR NH Mean = -71.7 Tot. Dens. = 7.338E-II kg/m3 Dens. Pert. Eastward Wind (Mean, Perturbed, Total) Northward Wind (Mean, Perturbed, Total) ........................................................................... Time (rel. to TO) = 17000.0 sec. ( Height = 165.00 km ( 163.51 km) Scale Time = 19.41 Mars hours = 156.3 K Zbase = 121.4 km = 151.4 km Mol.Wgt. = 38.78 = 3.702E-06 N/m2 8.622E-II 1.051E-10 kg/m3 % -64.5 % -56.8 % = -14.89% Wave = .00% of mean = 16.4 .5 17.0 m/s = -89.4 53.1 -36.3 m/s .191 sols) Ls _ 97.1 Dust = .30 Hgt H(p) = 12.83 H(rho) = 11.90 km Latitude = 39.48 degrees Longitude = 64.97 W ( 295.03 E) degrees Sun Latitude = 25.00 deg. Mars Orbital Radius = 1.648 AU Sun Longitude = 177.72 deg. Local Exospheric Temp. = 198.4 K Tbase Solar Zenith Angle = 90.1 deg F1 peak Temperature = 198.3 K Pressure Density (Low, Avg., High) = 4.345E-II Departure, COSPAR NH Mean = -75.9 Tot. Dens. = 5.659E-II kg/m3 Dens. Pert. Eastward Wind (Mean, Perturbed, Total) Northward Wind (Mean, Perturbed, Total) ........................................................................... Time (rel. to TO) _ 17500.0 sec. ( Height = 170.00 km ( 168.53 km) Scale Time = 19.52 Mars hours = 156.1 K Zbase = 121.4 km = 999.9 km Mol.Wgt. = 37.96 = 2.458E-06 N/m2 5.661E-II 7.160E-II kg/m3 % -68.6 % -60.3 % = -.04% Wave = .00% of mean = 19.2 -26.1 -7.0 m/s _ -95.5 12.9 -82.5 m/s .197 sols) Ls = 97.1 Dust = .30 Hgt H(p) = 13.20 H(rho) = 12.10 km Latitude = 39.98 degrees Longitude = 65.47 W ( 294.53 E) degrees Sun Latitude = 25.00 deg. Mars Orbital Radius = 1.648 AU Sun Longitude = 179.75 deg. Local Exospheric Temp. = 197.8 K Tbase Solar Zenith Angle = 90.8 deg F1 peak Temperature = 197.3 K Pressure Density (Low, Avg., High) = 2.734E-II Departure, COSPAR NH Mean = -79.7 Tot. Dens. = 4.379E-II kg/m3 Dens. Pert. Eastward Wind (Mean, Perturbed, Total) Northward Wind (Mean, Perturbed, Total) ........................................................................... Time (rel. to T0) = 18000.0 sec. ( Height = 175.00 km ( 173.56 km) Scale Time = 19.62 Mars hours = 155.8 K Zbase = 121.5 km = 999.9 km Mol.Wgt. = 36.89 = 1.656E-06 N/m2 3.724E-II 4.842E-II kg/m3 % -72.4 % -64.1 % _ 17.58% Wave = .00% of mean = 21.7 -10.0 11.7 m/s = -100.8 -20.0 -120.8 m/s .203 sols) Ls = 97.1 Dust = .30 Hgt H(p) = 13.70 H(rho) = 12.37 km Latitude = 40.48 degrees Longitude = 65.97 W ( 294.03 E) degrees Sun Latitude = 25.00 deg. Mars Orbital Radius = 1.648 AU Sun Longitude = 181.77 deg. Local Exospheric Temp. = 197.3 K Tbase Solar Zenith Angle = 91.5 deg F1 peak Temperature = 197.0 K Pressure Density (Low, Avg., High) = 1.731E-II Departure, COSPAR NH Mean = -83.2 Tot. Dens. = 2.227E-II kg/m3 Dens. Pert. Eastward Wind (Mean, Perturbed, Total) Northward Wind (Mean, Perturbed, Total) Time (rel. to TO) = 18500.0 sec. ( Height = 180.00 km ( 178.59 km) Scale Time = 19.72 Mars hours = 155.6 K Zbase = 121.5 km = 999.9 km Mol.Wgt. = 35.59 = 1.134E-06 N/m2 2.464E-II 3.204E-II kg/m3 % -76.1% -68.9 % = -9.65% Wave = .00% of mean = 22.4 37.9 60.3 m/s = -104.2 49.7 -54.5 m/s .208 sols) Ls = 97.1 Dust = .30 Hgt H(p) = 14.28 H(rho) = 12.68 km Latitude = 40.98 degrees Longitude = 66.47 W ( 293.53 E) degrees Sun Latitude = 25.00 deg. Mars Orbital Radius = 1.648 AU Sun Longitude = 183.80 deg. Local Exospheric Temp. = 196.8 K Tbase Solar Zenith Angle = 92.1 deg F1 peak Temperature = 196.6 K Pressure Density (Low, Avg., High) = 1.151E-f1 Departure, COSPAR NH Mean = -85.4 Tot. Dens. = 1.267E-II kg/m3 Dens. Pert. Eastward Wind (Mean, Perturbed, Total) Northward Wind (Mean, Perturbed, Total) 35 Time = 19.82 Mars hours = 155.4 K Zbase = 121.6 km = 999.9 km Mol.Wgt. = 34.15 = 7.863E-07 N/m2 1.644E-II 2.137E-II kg/m**3 % -79.2 % -72.9 % = -22.94% Wave = .00% of mean = 22.9 11.9 34.8 m/s = -107.7 48.3 -59.3 m/s

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Time (rel. to TO) = 19000.0 sec. ( .214 sols) Ls _ 97.1 Dust = .30 Height z 185.00 km ( 183.62 km) Scale Hgt H(p) = 14.97 H(rho) = 13.06 km Latitude - 41.48 degrees Longitude = 66.97 W ( 293.03 E) degrees Sun Latitude = 25.00 deg. Mars Orbital Radius = 1.648 AU Sun Longitude = 185.83 deg. Local Time = 19.92 Mars hours Exospheric Temp. = 196.2 K Tbase = 155.2 K Zbase = 121.6 km Solar Zenith Angle = 92.7 deg F1 peak = 999.9 km Mol.Wgt. = 32.60 Temperature - 196.1 K Pressure = 5.535E-07 N/m2 Density (Low, Avg., High) = 7.748E-12 1.107E-If 1.439E-II kg/m3 Departure, COSPAR NH Mean = -87.3 % -81.9 % -76.5 % Tot. Dens. = 6.672E-12 kg/m3 Dens. Pert. = -39.73% Wave = .00% of mean Eastward Wind (Mean, Perturbed, Total) = 23.3 -27.4 -4.1 m/s Northward Wind (Mean, Perturbed, Total) = -iii.i 8.6 -102.5 m/s ........................................................................... Time (rel. to TO) _ 19500.0 sec. ( .220 sols) Ls = 97.1 Dust = .30 Height = 190.00 km ( 188.65 km) Scale Hgt H(p) = 15.77 H(rho) = 13.51 km Latitude - 41.98 degrees Longitude _ 67.47 W ( 292.53 E) degrees Sun Latitude = 25.00 deg. Mars Orbital Radius = 1.648 AU Sun Longitude = 187.86 deg. Local Time = 20.03 Mars hours Exospheric Temp. = 195.7 K Tbase = 155.1 K Zbase = 121.7 km Solar Zenith Angle = 93.3 deg F1 peak = 999.9 km Mol.Wgt. = 30.95 Temperature = 195.6 K Pressure z 3.958E-07 N/m2 Density (Low, Avg., High) = 5.275E-12 7.535E-12 9.796E-12 kg/m3 Departure, COSPAR NH Mean -88.9 % -84.1% -79.3 % Tot. Dens. - 6.191E-12 kg/m3 Dens. Pert. = -17.85% Wave = .00% of mean Eastward Wind (Mean, Perturbed, Total) = 23.5 -22.1 1.4 m/s Northward Wind (Mean, Perturbed, Total) = -114.6 -7.3 -122.0 m/s ........................................................................... Time (rel. to T0) = 20000.0 sec. ( .225 sols) Ls = 97.1 Dust = .30 Height = 195.00 km ( 193.68 km) Scale Hgt H(p) = 16.68 H(rho) = 14.04 km Latitude = 42.48 degrees Longitude = 67.97 W ( 292.03 E) degrees Sun Latitude'= 24.99 deg. Mars Orbital Radius = 1.648 AU Sun Longitude = 189.88 deg. Local Time = 20.13 Mars hours Exospheric Temp. _ 195.2 K Tbase = 154.9 K Zbase = 121.7 km Solar Zenith Angle = 93.9 deg F1 peak = 999.9 km Mol.Wgt. = 29.27 Temperature - 195.1 K Pressure = 2.877E-07 N/m2 Density (Low, Avg., High) = 3.635E-12 5.193E-12 6.751E-12 kg/m3 Departure, COSPAR NH Mean -90.2 % -86.0 % -81.8 % Tot. Dens. = 4.450E-12 kg/m**3 Dens. Pert. = -14.32% Wave = .00% of mean Eastward Wind (Mean, Perturbed, Total) = 23.5 6.6 30.1 m/s Northward Wind (Mean, Perturbed, Total) = -118.2 -10.9 -129.1 m/s 36

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Appendix D Summary of Files Provided Mars-GRAM 2000 Version 1 directory following files: with Mars-GRAM 2000 on the FTP server contains the marsgram.hst - history file summarizing various versions and changes marsfix.txt - history of minor code changes since first posting of Version 1 marsgram.f - source code for the "stand dumytraj.f - source code for the dummy alone" version main program trajectory version main program marssubs.f - subroutines used by both marsgram and dumytraj versions setup.f setup subroutines used by both marsgram and dumytraj versions ARCHGTS.DAT - data file for low resolution Ames GCM topographic heights COSPAR.DAT - data file for the COSPAR reference model atmosphere input.std commented test input file for reference case listmg2k.txt - list output file for reference case headers.txt - list of plotable output files and file header definitions READMEI.txt - this general program introduction file README2.txt - discussion of the dumytraj.f README3.txt - discussion of the MGCM and dummy trajectory program MTGCM input data files xycodes.txt - list of x-y plot codes (also given below) makebin.f program to read ASCII version MGCM and MTGCM data files and write out binary version (for faster reading on user machine) sfc05xxy.txt - MGCM boundary layer data at 5m height for dust optical depths 0.3, 1.0, and 3.0 number y (xx = 03, i0, 30), version sfc30xxy.txt - MGCM boundary layer data at 30m height for 3 dust optical depths xx, version number tpdloxxyotxt - MGCM 0-80 km temperature, 3 dust optical depths xx y pressure, and density data for uvloxxy.txt - MGCM 0-80 km EW wind and NS wind data for 3 dust optical depths xx, version number tpdhixxy.t×t - MTGCM 80-170 km temperature, y pressure, and density data for 3 dust optical depths xx, version number y uvhixxy.txt - MTGCM 80-170 km EW wind and NS wind data for 3 dust optical depths xx, version number y zfhgtsy.txt - Height ZF of 1.26 nbar level for all dust optical depths, version number y Plotable output files can be generated with data given versus several selected parameters. Generation of LIST file output and plotable output files is controlled by the value of iup on input. For Mars-GRAM 2000, a number of plotable each containing several parameters suitable output files are generated, for plotting. These plotable files have headers to help identify parameters in the files. File names and definitions of headers are Plotable x and y parameters and their code Values of x-code and y-code for Mars-GRAM Code Parameter Height (above reference ellipsoid, Height (above local terrain, km) Latitude (degrees) given in the file headers.txt. values are as follows: plotable output files km) Longitude (deg.), West positive if LonEW=0. East positive if LonEW=l Time from start (Earth seconds) Time from start (Martian Sols) 37

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7 Areocentric Longitude of Sun, Ls (degrees) 8 Local Solar Time (Mars hours = 1/24 Sols) 9 Pressure (mb) To compile marsgram and dumytraj under UNIX, to produce executable files marsgram.x and dumytraj.x, you can use the commands: f77 -o marsgram, x marsgram.f marssubs.f and f77 -o dumytraj.x dumytraj.f marssubs.f To compile marsgram and dumytraj under setup.f setup.f PC-DOS (for example, with Microsoft FORTRAN Powerstation), to produce executable files marsgram.exe and dumytraj.exe, you can use the commands: f132 marsgram, f marssubs.f setup.f and f132 dumytraj.f marssubs.f setup.f 38

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Appendix E Example Application of Mars-GRAM in a Trajectory Code With earlier versions of Mars-GRAM marstraj.f, was supplied. Beginning with alternate version of a (double precision) program (dumytraj.f) was included. Although a dummy trajectory program, Mars-GRAM version 3.8, an dummy trajectory calculating similar in general function to the original marstraj.f code, some details of dumytraj.f are different: (i) In the original marstraj.f, interaction to three subroutines - Call Setup(...) Call Randinit(...) Call Datastep(...) with Mars-GRAM was via calls These three subroutines are part of the Mars-GRAM 2000 code and are automatically available to be called whenever the Mars-GRAM 2000 code (marssubs.f and setup.f) is linked to the user's main trajectory driver program. IF YOU ALREADY HAVE A TRAJECTORY PROGRAM BUILT LIKE THIS, WITH CALLS TO SETUP, RANDINIT, AND DATASTEP IT MIGHT BE EASILY MODIFIED TO INCORPORATE Mars-GRAM 2000 SUBROUTINES WITHOUT USING THE APPROACH TAKEN IN DUMYTRAJ.F. Note, however, that the number of arguments in these subroutines has changed, so appropriate modifications in your trajectory programs must be made. (2) In dumytraj.f, interaction with Mars-GRAM 2000 is via three calls to one "wrapper" subroutine (named Marstraj), but with different values of three control parameters (isetup, jmonte, and istep) - Call Marstraj ...) with isetup=l Call Marstraj ...) with isetup=0, jmonte>0, istep=0 Call Marstraj ...) with isetup=0, jmonte=0, istep>0 where isetup = 1 triggers the call to the Setup subroutine, jmonte>0 triggers the call to the reinitialization process (including the call to the Randinit subroutine), and istep = i to MAXNUM is a counter for steps along the trajectory (with a call to the Datastep subroutine at each step). Marstraj is a subroutine in the dumytraj.f code, and must be included (along with the basic Mars-GRAM code setup.f and marssubs.f ) as a subroutine in the user's calling trajectory program. (3) In the original marstraj.f dummy trajectory main code, transfer of double precision (trajectory) variables to and from single precision (Mars- GRAM) variables was assumed to be done within the user's main trajectory code. In the dumytraj.f code this transfer is handled within the Marstraj subroutine (which must be included as a subroutine in the user's trajectory program). (4) In the original marstraj.f dummy trajectory main code, (single precision) values of position increments (DELHGT, DELLAT, and DELLON) were presumed to be calculated within the user's main trajectory program. In the dumytraj.f code, input variables to the Marstraj subroutine are current and next (double precision) position values (height, latitude, and longitude) and the position increments to be passed to the Datastep subroutine (increments of height, latitude, within the Marstraj subroutine. Regardless of which dummy trajectory and longitude) are computed code you decide to use as your starting model from which to build the interface to Mars-GRAM 2000 for your own trajectory code, it is worthwhile to read the comments embedded in the dumytraj.f code. These comments give more functions that are being performed. They 39 explicit descriptions of the also provide better hints

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about what to do if you are using predictor-corrector (or other) trajectory approaches that require mid-point corrections along trajectory steps and/or the use of density variations that occur within each trajectory step. Another feature of dumytraj.f Mars ephemeris values for sun latitude, is that it allows high precision longitude, and Ls angle to be passed from the trajectory program for use by Mars-GRAM 2000 subroutines. 40

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Appendix F Details of MGCM and MTGCM Data Files ASCII format MGCM and MTGCM data files are provided, each having values for amplitudes and phases of diurnal (24-hour period) and semi-diurnal (12-hour period) components. Generically, the amplitudes and phases are: A0 = Diurnal mean value of the given parameter A1 = Amplitude of the diurnal tide component phil = Phase (local time in hours) of the diurnal component A2 = Amplitude of the semi-diurnal tide phi2 = phase (local time in hours) of the component semi-diurnal component Tidal values for each parameter are computed from the relation Tide=AO+AlCos((pi/12)(time-phil))+A2Cos((pi/6)(time-phi2)) where time is the local solar time in hours. For temperature and wind components, the data files give amplitudes in the same units as those of the parameter (K for temperature or m/s for wind). For pressure and density, the data files give amplitudes in units of percent of the mean value (A0). A0 values for pressure are N/m2. A0 values for density are kg/m3. For each of three values of dust optical data files are provided (in ASCII format): depth, two MGCM boundary layer sfc05xxy.txt - MGCM boundary layer data at 5m height for dust optical depths 0.3, 1.0, and 3.0 (xx = 03, 10, 30), version number y sfc30xxy.txt - MGCM boundary layer data at 30m height for 3 dust optical depths xx, version number y Each record of these files contains Ls value, latitude, longitude, and tidal coefficients (A0, AI, phil, A2, phi2) for temperature, and for EW wind and NS wind components. For each of the same three dust opticaldepths, two ASCII format files of MGCM 0 to 80 km data are provided: tpdloxxy.txt - MGCM 0 to 80 km temperature, pressure, and density data for 3 dust optical depths xx, version number y uvloxxy.txt - MGCM 0 to 80 km EW wind and NS wind data for 3 dust optical depths xx, version number y Each record of the tpdloxx.txt files contains Ls value, height, latitude, and tidal coefficients for temperature and pressure. Only the A0 coefficient is given for density. Tidal variations in density are computed from those for pressure and temperature by the perfect of the uvloxx.txt files contains Ls value, coefficients for the Eastward and Northward For each of the same three dust optical of MTGCM 80 to 170 km data are provided: gas law relation. Each record height, latitude, and tidal wind components. depths, two ASCII format files tpdhixxy.txt - MTGCM 80 to 170 km temperature, pressure, and density data for 3 dust optical depths xx, version number y uvhixxy.txt - MTGCM 80 to 170 km EW wind depths xx, version number and NS wind data for 3 dust optical y Each record of the tpdhixx.txt files contains Ls value, height, latitude, and tidal coefficients for temperature, pressure, and density. Because of 41

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height variations in molecular weight, tidal coefficients are retained for all three of these thermodynamic components. Each record of the uvhixx.txt files contains Ls value, height, latitude, and tidal coefficients for the Eastward and Northward wind components. A single file, zfhgtsy.txt, provides for altitude ZF, the height of the 1.26 depths, version number y. Each record depth, Ls, latitude, and tidal coefficient tidal coefficient information nbar level, for all dust optical of this file contains dust optical values. Source code (makebin.f) is also provided for a program to read the ASCII format MGCM and MTGCM data files and write them out in binary format. After this ASCII-to-binary conversion is once completed, subsequent reading of the binary format files significantly shortens the time required to initialize Mars-GRAM 2000 on each run. 42

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REPORT DOCUMENTATION PAGE Fo,_ Approved OMB No. 0704-0188 Public reporting burden for this ¢o/isctlon of Information is estimated to average 1 hour per respoe,se, ir_uding the time for revtewlng klstruct_ns, Narchlng existing data sources, gathering and rnaintainklg the data needed, and completing and reviewing Ihe coflection of lnfon'naUon. Send comments regarding this burden esUmets or any other aspect of this collec_on of informaSon, including imggertlons for reducing _ burden, to Washington Headquarters Services. Directorate for Information Opetatioeb and Reports. 1215 Jefferson Davis Highway. Suite 1204, Arington. VA 22202-4302, and to the Office of Management and BtMget. Paperwork Reduction Project {0704-0188). Washington. DC 20503 1. AGENCY USE ONLY (Leave Blank) 2. REPORT DATE May 2000 4. TITLE AND SUBTITLE 3. REPORT TYPE AND DATES COVERED Technical Memorandum 5. FUNDING NUMBERS Mars Global Reference Atmospheric Model 2000 Version (Mars-GRAM 2000): Users Guide 6. AUTHORS e.G. Justus* and B.F. James 7. PERFORMINGORGANIZATIONNAMES(S)ANDADDRESS0ES) George C. Marshall Space Flight Center Marshall Space Flight Center, AL 35812 NAS8--60000 8. PERFORMING ORGANIZATION REPORT NUMBER M-980 9. SPONSORING/MONFrORINGAGENCYNAME(S)ANDADDRESS(ES) 10. SPONSORING/MONITORING National Aeronautics and Space Administration Washington, DC 20546-0001 11. SUPPLEMENTARY NOTES AGENCY REPORT NUMBER NASA/TM--2000-210279 Prepared by Environments Group, Engineering Systems Department, Engineering Directorate *Computer Sciences Corporation 1211. DISTRIBUTION/AVAILABILITY STATEMENT Unclassified-Unlimited Subject Category 18 Nonstandard Distribution 13. ABSTRACT (Maximum 200 words) 12b. DISTRIBUTION CODE This report presents Mars Global Reference Atmospheric Model 2000 Version (Mars-GRAM 2000) and its new features. All parameterizations for temperature, pressure, density, and winds versus height, latitude, longitude, time of day, and Ls have been replaced by input data tables from NASA Ames Mars General Circulation Model (MGCM) for the surface through 80-km altitude and the University of Arizona Mars Thermospheric General Circulation Model (MTGCM) for 80 to 170 km. A modified Stewart thermospheric model is still used for higher altitudes and for dependence on solar activity. "Climate factors" to tune for agreement with GeM data are no longer needed. Adjustment of exospheric temperature is still an option. Consistent with observations from Mars Global Surveyor, a new longitude-dependent wave model is included with user input to specify waves having 1 to 3 wavelengths around the planet. A simplified perturbation model has been substituted for the earlier one. An input switch allows users to select either East or West longitude positive. This memorandum includes instructions on obtaining Mars-GRAM source code and data files and for running the program. It also provides sample input and output and an example for incorporating Mars-GRAM as an atmospheric subroutine in a trajectory code. 14. SUBJECT TERMS 15. NUMBER OF PAGES 48 Mars Global Reference Atmospheric Model, Mars-GRAM, Atmospheric 18. PRICE CODE i Density, Atmospheric Temperature, Atmospheric Models, Winds 17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION OF REPORT OF THIS PAGE Unclassified Unclassified NSN 7540-01-280-5500 A03 19. SECURITY CLASSIFICATION 20.uMrrATIONOFABSTRACT OF ABSTRACT Unclassified Unlimited Standard Form 298 {Rev_ 2-89) Prescribedby ANSI Sld 239-18 298-102