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i

NASA/TM—2011–216467

The NASA Marshall Space Flight Center 

Earth Global Reference Atmospheric 

Model—2010 Version

F.W. Leslie

Marshall Space Flight Center, Marshall Space Flight Center, Alabama

C.G. Justus

Dynetics Technical Services, Huntsville, Alabama

June 2011

National Aeronautics and

Space Administration

Marshall Space Flight Center • MSFC, Alabama 35812
ii

Available from:

NASA Center for AeroSpace Information

7115 Standard Drive

Hanover, MD 21076 –1320

443–757–5802

This report is also available in electronic form at

<https://www2.sti.nasa.gov/login/wt/>
iii

TABLE OF CONTENTS

1. INTRODUCTION ............................................................................................................. 1

1.1 Background and Overview ............................................................................................ 1

1.2 Basic Description of the Global Reference Atmospheric Model 2010 .......................... 1

1.3 Summary of Significant Changes and Features for Global Reference 

 Atmospheric Model 2010 ............................................................................................. 3

1.4 Summary of Global Reference Atmospheric Model 2010 Characteristics .................... 6

2. TECHNICAL DESCRIPTION OF THE MODEL ........................................................... 8

2. 1 The Upper Atmosphere Section (Above 90 km) .......................................................... 8

2.2 The Middle Atmosphere Section (20–120 km) ............................................................ 9

2.3 The Lower Atmosphere Section (Surface to 10 mb) .................................................... 10

2.4 The Boundary Layer Model for Vertical Velocity ........................................................ 15

2.5 Water Vapor and Other Atmospheric Species Concentrations .................................... 22

2.6 Interpolation and Fairing Techniques ......................................................................... 23

2.7 The Perturbation Model ............................................................................................. 26

2.8 Perturbation Model Initialization ............................................................................... 30

2.9 Optional User-Selected Initial Perturbations .............................................................. 31

2.10 Optional Range Reference Atmosphere Data ............................................................. 31

2.11 Speed of Sound Calculation ........................................................................................ 35

3. SAMPLE RESULTS .......................................................................................................... 36

3.1 Large-Scale Perturbations ............................................................................................. 36

3.2 Density Perturbations ................................................................................................... 36

3.3 Revised Boundary Layer Model for Vertical Velocity ................................................... 37

3.4 Range Reference Atmosphere Data Option .................................................................. 38

4. GLOBAL REFERENCE ATMOSPHERIC MODEL 2010 USERS GUIDE ................... 40

4.1 General Program Review .............................................................................................. 40

4.2 Units, Coordinates, and Conventions ........................................................................... 40

4.3 The ‘atmosdat’ Input File ............................................................................................. 41

4.4 The Trajectory Input File .............................................................................................. 44

4.5 Random Number Seed Input File ................................................................................. 44

4.6 Output Data Files ......................................................................................................... 45

4.7 Description of Program Files and Subroutines ............................................................. 48

4.8 Setup of Global Reference Atmospheric Model 2010 ................................................... 49
iv

TABLE OF CONTENTS (Continued)

APPENDIX A—NATIONAL CENTERS FOR ENVIRONMENTAL PREDICTION 

REANALYSIS PROJECT CLIMATOLOGY DATA .................................. 53

APPENDIX B—COMPILING AND RUNNING GLOBAL REFERENCE 

ATMOSPHERIC MODEL 2010 ................................................................. 58

APPENDIX C—DESCRIPTION OF NAMELIST FORMAT INPUT FILE ....................... 66

APPENDIX D—SAMPLE OUTPUT OF GLOBAL REFERENCE 

ATMOSPHERIC MODEL 2010 ................................................................. 69

APPENDIX E—PARAMETERS AVAILABLE FOR SPECIAL OUTPUT .......................... 98

APPENDIX F—EXAMPLE APPLICATION OF GLOBAL REFERENCE

ATMOSPHERIC MODEL 2010 AS SUBROUTINES 

IN ANOTHER MAIN DRIVER ................................................................. 102

REFERENCES ....................................................................................................................... 109
v

LIST OF FIGURES

1. Summary of the atmospheric regions in the GRAM2010 program, 

sources for the model, and data on which the mean monthly GRAM2010 

values are based ........................................................................................................ 2

2. Average ratio of RRA surface wind speed to NCEP wind speed evaluated 

at the RRA surface altitude ...................................................................................... 11

3. Multisite average of surface wind speed ratio of hourly average wind speed 

to daily average wind speed ....................................................................................... 12

4. Multisite average of surface temperature ratio of hourly average temperature 

to daily average temperature ..................................................................................... 13

5. Observed diurnal variation of January hourly average surface 

wind speed at KSC .................................................................................................... 15

6. Sample vertical profile of large-scale wave perturbations using 

a large-scale wave perturbation model output ........................................................... 36

7. A plot of a 1,000 profile Monte Carlo run of density perturbation 

(in percent of the mean value) as a function of height. The 2- and 3-sigma 

envelopes are also shown ........................................................................................... 37

8. An example realization of the global distribution of: (a) The standard deviation 

of the vertical velocity in m/s, (b) the surface roughness in m, (c) the surface 

elevation in km, and (d) the mean horizontal surface wind in m/s ............................. 38

9. GRAM2010 (solid line) or RRA/GRAM2010 (dotted line) profiles 

of temperature along hypothetical parabolic trajectory between EAFB 

and WSMR with 100-km apogee .............................................................................. 39

10. Differences in density (solid line) and temperature (dotted line) between 

GRAM2010 and RRA/GRAM2010 values for the hypothetical trajectory 

used in figure 9 .......................................................................................................... 39
vi

LIST OF TABLES

1. Surface codes and associated zo values ........................................................................ 16

2. Sample output statistics for vertical wind standard deviation (m/s) 

from GRAM2010 ....................................................................................................... 20

3. Summary of KSC vertical wind estimates from data in table 3 of reference 33 ........... 22

4. List of RRA site data provided, file ‘rras2006.txt’ ....................................................... 33

5. Boundary layer output parameters .............................................................................. 47
vii

LIST OF ACRONYMS AND SYMBOLS

AFB Air Force Base

AFGL Air Force Geophysics Laboratory

AFMS Air Force Midlatitude Summer

AFMW Air Force Midlatitude Winter

AFSS Air Force Subarctic Summer

AFSW Air Force Subarctic Winter

AFTR Air Force Tropical

AMU Applied Meteorological Unit

Ar argon

ARL Air Resources Lab

ASCII American Standard Code for Information Interchange

BL boundary layer

CDAS Climate Data Assimilation System

CH4 methane

CIRA Committee on Space Research International Reference Atmosphere

CO carbon monoxide

CO2 carbon dioxide

COSPAR Committee on Space Research

DVD digital videodisc

EAFB Edwards Air Force Base

F10 solar radio noise flux at 10.7 nm (surrogate for extreme ultraviolet flux)

FTP File Transfer Protocol

GPS Global Positioning System

GRAM Global Reference Atmospheric Model

GRS Geodetic Reference System

GUACA Global Upper Air Climatic Atlas

H hydrogen

H2O water vapor

He helium

HWM harmonic wind model

IAU International Astronomical Unit

JB Jacchia-Bowman
viii

LIST OF ACRONYMS AND SYMBOLS (Continued)

kmr Kwajalein Missile Range

KSC Kennedy Space Center

LaRC Langley Research Center

lat-lon latitude-longitude

Lya Lyman alpha extreme ultraviolet radiation

MAP Middle Atmosphere Program

MET Marshall Engineering Thermosphere

MG2 double-ionized magnesium

MSFC Marshall Space Flight Center

MSIS Mass Spectrometer, Incoherent Scatter

MSL mean sea level

N2 nitrogen

N2O nitrous oxide

NCAR National Center for Atmospheric Research

NCDC National Climatic Data Center

NCEP National Centers for Environmental Prediction

NOAA National Oceanic and Atmospheric Administration

NRL Naval Research Laboratory

NRLMSISE Naval Research Laboratory Mass Spectrometer, Incoherent Scatter 

Radar Extended model

O atomic oxygen

O2 molecular oxygen

O3 ozone

PC personal computer

POR period-of-record

RH relative humidity

RRA Range Reference Atmosphere

Ruv cross-correlation of the horizontal and wind components

SI International Standard

SLF Shuttle Landing Facility

SODAR sound detection and ranging

TM Technical Memorandum

U.S. United States

UDF universal diurnal factor
ix

LIST OF ACRONYMS AND SYMBOLS (Continued)

url uniform resource locator

UT universal time

UTC universal time coordinated

WGS World Geodetic System

WMO World Meteorological Organization

WSMR White Sands Missile Range
x

NOMENCLATURE

A local wave amplitude

AQ large-scale amplification factor

A(z) data set, amplitude

B(z) data set

C faired variable

c(t) specific concentrations

cs the speed of sound

cs the monthly mean speed of sound

d boundary layer depth

dN neutral boundary layer depth

Dst index of worldwide geomagnetic storm level

El solar elevation

Emd solar elevation at midday

ER site elevation in km

F adjustment factor

F(h) surface wind adjustment factor as a function of height

FS(H) universal diurnal factor for wind speed as a function of hour

FT(H) universal diurnal factor for temperature as a function of hour

f coriolis parameter

f(z) fairing parameter

fL large-scale fractional variance

fnon factor for variance of nonsevere perturbation

fsev factor for variance of severe perturbation

g acceleration of gravity

G(El) time-factor multiplier

H hour

h topographic altitude in km

L local vertical correlation scale (small-scale perturbation) or Monin-Obukhov

scaling length (stability dependent) in meters

Lavg average scale size

Lh horizontal scale parameter

Lmax maximum scale size
xi

NOMENCLATURE (Continued)

Lmin minimum scale size

Lz vertical scale parameter

m wave number in the latitudinal direction

mn input value of month

n wave number in the longitudinal direction

nr net radiation index

Psev probability of severe perturbations

Ptail tail probability of a Gaussian distribution

p pressure

p monthly mean pressure

Q a uniformly distributed random number between 0 and 1

q Gaussian-distributed random number

R gas constant

Ri Richardson number

r autocorrelation value

rc cross-correlation

rq a correlation coefficient

rt concentration rate of change

rν a correlation coefficient

rμ a correlation coefficient

S wind speed

Sday wind speed daily average for a given month

SN National Centers for Environmental Prediction wind speed in m/s

SR Range Reference Atmosphere surface wind speed in m/s

su stationary eastward wind

sv stationary northward wind

sy stationary perturbation

T temperature or wave period

T monthly mean temperature

T(H) temperature as a function of local hour

TTot monthly mean temperature plus perturbations

t year

t0 initial time in concentration formula

U10 surface wind speed measured at the standard 10-m height above surface
xii

NOMENCLATURE (Continued)

U18 surface wind speed measured at the standard 18-m height above surface

u west-to-east component of wind

u

* friction velocity

um monthly mean eastward wind

V variable available on two-dimensional grid

v south-to-north component of wind

vm meridional (northward) mean wind

W(U10) wind speed factor as a function of surface wind speed

x longitude, height, or log pressure

x vector position

x′ trajectory position

y latitude, pressure, density, or temperature parameter

ym monthly mean value

z geopotential altitude

zo surface roughness

zu zonal-mean value of the eastward wind

zy zonal-mean value

α a constant used in the computation of surface roughness over water, 0.015 or 

interpolation constant

β interpolation constant

γ temperature gradient

γc the ratio of specific heats of a gas at a constant pressure to a gas at a constant volume

δh horizontal step

δt time step

δz vertical step

θ longitude

λ local vertical wavelength

λz vertical wavelength number

μ normalized variant

ξ stability category

ρ density

ρ monthly mean density

ρl large scale density

σ local standard deviation (small-scale perturbation)
xiii

NOMENCLATURE (Continued)

σ2 total variance of small-scale perturbation

σcos standard deviation of the cosine function

σL standard deviation of large scale

σP standard deviation of pressure

σS standard deviation of wind speed or small-scale standard deviation

σT total standard deviation or standard deviation of temperature

σu standard deviation of west-to-east component of wind

σv standard deviation of south-to-north component of wind

σw standard deviation of the vertical wind component

σρ standard deviation of density

σρl standard deviation of large-scale density

τ time scale

φ latitude

φq random wave phase

ψ boundary layer wind function

ω Brunt-Vaisala frequency
xiv
1

TECHNICAL MEMORANDUM

THE NASA MARSHALL SPACE FLIGHT CENTER EARTH GLOBAL REFERENCE 

ATMOSPHERIC MODEL—2010 VERSION

1. INTRODUCTION

1.1 Background and Overview

Reference or standard atmospheric models have long been used for design and mission 

planning of various aerospace systems. The NASA Marshall Space Flight Center (MSFC) Global 

Reference Atmospheric Model (GRAM) was developed in response to the need for a design reference atmosphere that provides complete global geographical variability, complete altitude coverage 

(surface to orbital altitudes), and complete seasonal and monthly variability of the thermodynamic 

variables and wind components. A unique feature of GRAM is that, in addition to providing the 

geographical, height, and monthly variation of the mean atmospheric state, it includes the ability to 

simulate spatial and temporal perturbations in these atmospheric parameters (e.g., fluctuations due 

to turbulence and other atmospheric perturbation phenomena). A summary comparing GRAM 

features to characteristics and features of other reference or standard atmospheric models can be 

found in reference 1.

The original GRAM (found in ref. 2) has undergone a series of improvements over the years 

with recent additions and changes.3–9 The software program is called Earth-GRAM2010 to distinguish it from similar programs for other bodies (e.g., Mars, Venus, Neptune, and Titan). However, 

in order to make this Technical Memorandum (TM) more readable, the software will be referred to 

simply as GRAM2010 or GRAM unless additional clarity is needed. Section 1 gives an overview 

of the basic features of GRAM2010 including the newly added features. Section 2 provides a more 

detailed description of GRAM2010 and how the model output is generated. Section 3 presents 

sample results and section 4 gives specific user information. Appendix A describes the National 

Centers For Environmental Prediction (NCEP) Reanalysis Project Climatology Data. Appendix B 

provides instructions for compiling and running GRAM2010. Appendix C gives a description of 

the required NAMELIST input file. Appendix D gives sample output. Appendix E shows a list of 

available parameters to enable the user to generate special output. Appendix F gives an example 

and guidance on incorporating GRAM2010 as a subroutine in other programs such as trajectory 

codes. 

1.2 Basic Description of the Global Reference Atmospheric Model 2010

GRAM2010 is a mixture of empirically based models that represents different altitude 

ranges and the geographical and temporal variations within these altitude ranges. Figure 1 shows 
2

MET2007, MSIS, or JB2008 Thermosphere Model

MAP Data Bases

Thermosphere

Altitude (km)

Mesosphere

Stratosphere

Troposphere

Satellite Data

Rocket and Remote

Sensing Data

Balloon, Aircraft, and Satellite

Remote Sensing Data

NCEP

Fairing Between MAP and Thermosphere Model

Fairing Between MAP and NCEP Data

120

110

100

90

80

70

60

50

40

30

20

10

0

Figure 1. Summary of the atmospheric regions in the GRAM2010 program, 

sources for the model, and data on which the mean monthly 

GRAM2010 values are based.

how GRAM divides the atmosphere into three regions from which mean values of atmospheric 

parameters are provided. A perturbation model (see sec. 2.7) then computes variations about these 

means if dispersions are desired. Monthly mean values and standard deviations in the lower atmosphere come from the NCEP database. These are newly added for GRAM2010 and described more 

fully in the next section. 

Unlike the Global Upper Air Climatic Atlas (GUACA) data used by previous versions of 

GRAM that had to be ordered from the National Climatic Data Center (NCDC), the NCEP database is provided with the GRAM2010 software. The database read by GRAM is in binary form, 

but an American Standard Code for Information Interchange (ASCII) version is also provided. 

A program is available on the GRAM digital videodisc (DVD) that the user may run on their 

machine to convert the ASCII version to their machine-specific binary. 

The middle atmospheric region (20–120 km) data set is compiled from Middle Atmosphere 

Program (MAP) data10 and other sources referenced in the GRAM-90 and GRAM-95 reports.5,6

For the highest altitude region (above 90 km), the user has the choice of three thermosphere models (see sec. 2.1). Fairing techniques provide smooth transition between the altitude regions. Unlike 

interpolation (used to ‘fill in’ values across a gap in data), fairing is a process that provides a 

smooth transition from one set of data to another in overlapping regions (e.g., 20 km–10 mb level 

for NCEP and MAP data and 90–120 km for MAP data and the thermosphere models). Figure 1 

provides a graphical summary of the data sources and height regions. In addition to these databases, the user has the option of instructing GRAM to use the 2006 Range Reference Atmosphere 

(RRA) data set of specific sites or the user can provide an auxiliary profile of mean values and 

standard deviations.
3

Beginning with GRAM-95, the model provides estimates of atmospheric species concentrations for water vapor (H2O), ozone (O3), nitrous oxide (N2O), carbon monoxide (CO), methane 

(CH4), carbon dioxide (CO2), nitrogen (N2), molecular oxygen (O2), atomic oxygen (O), argon 

(Ar), helium (He), and hydrogen (H). The thermosphere models provide the species concentrations 

for N2, O2, O, Ar, He, and H above 90 km. Air Force Geophysics Laboratory (AFGL) atmospheric 

constituent profiles are also used extensively for the constituents to a 120-km altitude.11 The NASA 

Langley Research Center (LaRC) H2O climatology includes H2O values from a 6.5- to a 40.5-

km altitude.12 The MAP data include H2O data from the 100- to 0.01-mb pressure level.13 Other 

details of the species concentration model are given in sections 1.4 and 2.4 of reference 6.

1.3 Summary of Significant Changes and Features for Global Reference Atmospheric Model 2010

1.3.1 Programming Changes

For the 2010 version, GRAM has been converted to Fortran90. This allows the use of modules that can group related procedures and data together and make them available to other program 

units. In addition, interface blocks provide a vastly improved argument-passing mechanism, allowing them to be checked at compile time. The program was also converted to double precision.

1.3.2 New Database for the Lower Atmosphere With Diurnal Variation

The GUACA database previously used in GRAM has been replaced by the NCEP database 

for GRAM2010. Not only does this new database have a more contemporary period-of-record 

(POR), it also provides monthly means for four different times of day: 00Z, 06Z, 12Z, and 18Z. 

In addition, the new database is now provided with the GRAM software (all on a DVD) so there 

is no longer a requirement for the user to order it from a second party. The following description 

was adapted from reference 14.

The NCEP/NCAR Reanalysis Project is a joint project between the NCEP and the NCAR. 

The goal of this joint effort is to produce new atmospheric analyses using historical data (1948 

onwards) and to produce analyses of the current atmospheric state (Climate Data Assimilation 

System (CDAS)). Until recently, the meteorological community has had to use analyses that supported the real-time weather forecasting. These analyses are very inhomogeneous in time as there 

have been big improvements in the data assimilation systems. The quality and utility of the 

reanalyses should be superior to NCEP’s original analyses because of the following:

• A state-of-the-art data assimilation is used.

• More observations are used.

• Quality control has been improved.

• The model/data assimilation procedure remains unchanged during the project.

• Many more fields are being saved.
4

• Global coverage (some older analyses were hemispheric).

• Better vertical resolution (stratosphere).

More information about the reanalysis project and data are available from several sources, 

including reference 15 and at <http://www.cdc.noaa.gov/cdc/data.nmc.reanalysis.html>.

Data used in Earth-GRAM 2010 were downloaded from the National Oceanic and Atmospheric Administration (NOAA) Air Resources Lab (ARL) archives at <http://www.arl.noaa.gov/

archives.php>.

The NCEP data are provided with the GRAM software in both ASCII and personal computer (PC) binary formats. GRAM inputs the NCEP data as binary files. Files for each month 

are named Nby1y2mm.bin, where the POR is for years y1 through y2 (e.g., 9008 is for POR 1990 

through 2008), and month is mm. For a non-PC platform, the user may need to convert the ASCII 

data to binary on their specific machine. A utility program named NCEPbin is provided for the 

conversion. More details of the NCEP database can be found in appendix A.

1.3.3 Revised Model for the Vertical Wind

A new model computes standard deviation for boundary layer (BL) vertical wind as a function of surface type (water or various land types) and surface-horizontal wind (at 10-m height). 

Surface height (above mean sea level (MSL)) is interpolated from a 1°× 1° topographic database 

in the new ‘atmosdat’ file (see sec. 4.3) or from RRA surface altitude (if within the zone-ofinfluence of any RRA site). Boundary layer depth (d) (height of the top of the BL above the surface) is computed from a new time-of-day and stability-dependent model. Land cover type is taken 

from a 1° × 1° resolution data set also in the new ‘atmosdat’ file. Further details can be found 

in section 2.4.

1.3.4 New Input Parameters

Earth-GRAM 2010 has 10 new input parameters that are provided through the 

NAMELIST input file:

rralist: File name for list of RRA sites (optional).

y10: Solar X-Ray and Lya index scaled to F10 (for JB2008).

y10b: Solar X-Ray and Lya 81-day avg. centered index (for JB2008).

dstdtc: Temperature change computed from Dst index (for JB2008).

NCEPyr: Period-of-record (POR=y1y2) for NCEP climatology. POR includes years y1 

through y2 (e.g., NCEPyr=9008 for POR=1990 through 2008). NCEP monthly 

climatology is determined by input value of month (mn) in initial time input.

NCEPhr: Code for universal time (UT) hour of day for NCEP climatology: 1=00UT, 

2=06UT, 3=12UT, 4=18UT, 5=all times of day combined, or 0 to use NCEP timeof-day based on input UT coordinated (UTC) hour (ihro).
5

ruscale: Random perturbation scale for horizontal winds; nominal=1, maximum=2, minimum=0.1. 

rwscale: Random perturbation scale for vertical winds; nominal=1, maximum=2, minimum=0.1 .

z0in: Surface roughness (z0) for sigma-w model (<0 to use 1°× 1° lat-lon surface data, 

from new file atmosdat_E10.txt; =0 for speed-dependent z0 over water; or enter 

a value between 1×10–5 and 3 for user-specified z0 value).

ibltest: Unit number for boundary layer model output file (bltest.txt), or 0 for no BL model 

output (see description in sec. 4.6.4).

Two previous input parameters (iguayr and iyrrra) are no longer used and should not be 

included in the NAMELIST input file.

1.3.5 New Range Reference Atmosphere Input Parameter 

An option exists to use data (in the form of vertical profiles) from a set of RRAs at RRA 

site locations as an alternate to the usual GRAM climatology. RRA data includes information on 

both monthly means and standard deviations of the various parameters at the RRA site. Under 

the RRA option, when a given trajectory point is sufficiently close to an RRA site, the mean RRA 

data replace the mean values of the conventional GRAM climatology, and the RRA standard 

deviations replace the conventional GRAM standard deviations in the perturbation model computations. A new feature for GRAM2010 is that the user has the option to provide a file name for 

a list of available sites. Different RRA sites or combinations of sites can be made available by 

building various RRA lists, and the RRA set to use can be controlled at run time.

1.3.6 Updated Thermosphere Models

The JB2006 thermosphere model has been replaced with the new JB2008. Global climatology of chemical release winds was also used to revise wind perturbation standard deviations in the 

90–120-km altitude range. 

1.3.7 New Scaling Parameter for Standard Deviations

The user now has the option of independently changing the standard deviations of the 

horizontal wind, the vertical wind, and the thermodynamic variables (density, temperature, and 

pressure). 

1.3.8 New Option for Auxiliary Profiles

An option was added to input standard deviations (sigmas) in auxiliary profiles. If all 

zero values are entered, sigmas are taken from conventional climatology. An exception to this is 

for isolated zero values of sigma; in which case, the previous value along the profile or trajectory 

is used.
6

1.3.9 Additional Output Parameters

The mean sound speed and perturbed sound speed were added to the ‘print format’ and 

‘special format’ output files. Wind speed means and standard deviations, and cross-correlation 

(Ruv) between eastward and northward wind components were also added to the output. Ruv is 

used to compute the wave-like large-scale northward wind perturbation in such a way as to produce 

the appropriate degree of cross-correlation. See section 2.8 for further discussion of Ruv.

1.3.10 Moisture Corrections

The Elliott-Gaffen moisture corrections were revised to take advantage of all moisture variables available in the NCEP data. Revisions were also made in the calculation of standard deviation of relative humidity (RH), to account for correlation between vapor pressure and saturation 

vapor pressure (correlation evaluated empirically from study of NCEP RH data). 

1.4 Summary of Global Reference Atmospheric Model 2010 Characteristics

1.4.1 Output is Based on Atmospheric Measurements 

The lowest region of the model utilizes measurements from the NCEP or the RRA database that have been quality checked. Although other databases may exist, the NCEP dataset has 

global coverage; contains pressure, temperature, and winds; and also contains both means and 

standard deviations. The middle atmosphere of the model is based on the available (though limited) 

data from rocket and remote sensing programs. Finally, the upper atmosphere uses one of three 

thermospheric models that have been guided by data from satellite observations and space research.

1.4.2 Can be Driven by External Data 

If the user has atmospheric data that is believed more appropriate for their application than 

that contained within GRAM2010, it can be easily ingested into the model using the Auxiliary 

Profile option. The auxiliary profile need not be a vertical profile, but could also be data dependent 

on latitude, longitude, and height. Alternatively, the user could also provide model data by adding 

an RRA site to the database as described in section 2.10. 

1.4.3 Monte Carlo Runs of Global Reference Atmospheric Model 2010 Reproduce the Observed 

Means and Standard Deviations 

When a large number of dispersions are generated at any location, the mean and standard 

deviation of these data will match those of the observations. This is important in order for the 

model to be statistically equivalent to available measurements.
7

1.4.4 The Total (Large-Scale + Small-Scale) Dispersions of Global Reference Atmospheric Model 

2010 are Approximately Gaussian Distributed

The exception is pressure where most of the variance is due to the large scale since smallscale pressure variations equilibrate quickly. Because the large scale is modeled with a cosine wave, 

the probability distribution is influenced by that function to a larger degree. Newly introduced 

randomly varying amplitudes for large-scale wave perturbations make the total dispersions more 

Gaussian. Therefore, dispersions can be expected to have a more normal frequency than earlier.

1.4.5 The Small-Scale Dispersions Have a Dryden Power Spectrum 

Since the small-scale dispersions are modeled with a one step Markov technique having 

a correlation coefficient that decreases exponentially with distance (and time), the energy spectrum 

is inversely proportional to the square of the length (and time) scale. Thus, most of the observed 

variance occurs over large length (and time) scales.

1.4.6 The Computed Wind Shears are Consistent With Those Observed at the Kennedy Space Center 

Structure function analysis of wind shears observed at Kennedy Space Center (KSC) from 

balloon and tower data resulted in improvements in the perturbation model. See reference 16 for 

a comparison of the model to measured data. In addition, data for the cross-correlation of the 

horizontal wind component data in NCEP have been utilized.
8

2. TECHNICAL DESCRIPTION OF THE MODEL

2. 1 The Upper Atmosphere Section (Above 90 km)

GRAM2010 has the option of three different thermosphere models for use above 90 km. 

The Marshall Engineering Thermosphere (MET) 07 (MET-07) constitutes the default upper 

atmosphere model. 17–23 The Jacchia model in MET-07 for the thermosphere and exosphere was 

originally implemented to compute atmospheric density and temperature at satellite altitudes. 24

It represents total atmospheric density by summing the densities of six, separately modeled, atmospheric constituents (N2, O2, O, Ar, He, and H). The Jacchia model accounts for temperature and 

density variations due to solar and geomagnetic activity and diurnal, seasonal, and latitude-longitude (lat-lon) variations throughout the height range above 90 km. The Jacchia model assumes 

a uniformly mixed composition below 105 km, with diffusive equilibrium among the constituents 

above 105 km. Fixed (time-independent) boundary values for temperature and density are assumed 

at 90 km. Alterations described in reference 2 were made to allow atmospheric pressure to be computed from the density and temperature. Geostrophic wind components, modified by the effects 

of molecular viscosity,5 are evaluated in the Jacchia section by using the Jacchia model to estimate 

horizontal pressure gradients. This wind model has been used in GRAM since the 1990 version.5

Between 90 and 120 km, a fairing process described in section 2.6.4 ensures smooth transition 

between the MET model values and the middle atmosphere data. 

As an alternative to MET, an option is provided to use the 2000 version Naval Research 

Laboratory (NRL) Mass Spectrometer, Incoherent Scatter Radar Extended (NRLMSISE) model, 

NRLMSISE-00, for thermospheric conditions. If this option is selected, thermospheric winds are 

evaluated using the NRL 1993 Harmonic Wind Model (HWM), HWM-93. Information on the 

Mass Spectrometer, Incoherent Scatter (MSIS) and HWM models is available at the following 

uniform resource locators (urls):

• <http://www.nrl.navy.mil/content.php?P=03REVIEW105>.

• <http://modelweb.gsfc.nasa.gov/atmos/nrlmsise00.html>.

• <http://www.answers.com/topic/nrlmsise-00>.

• <http://fact-archive.com/encyclopedia/NRLMSISE-00>.

• <http://www.eiscat.rl.ac.uk/svn/guisdap.svn/trunk/dist/g85/models/nrlmsise00/readme.txt>.

• <http://modelweb.gsfc.nasa.gov/atmos/hwm.html>.

• <http://adsabs.harvard.edu/abs/2006AGUFMSA11A..07D>.

• <http://nssdcftp.gsfc.nasa.gov/models/atmospheric/hwm07/readme.txt>.
9

Minor corrections in MSIS and HWM have been made. Therefore, MSIS/HWM output 

from GRAM will not agree totally with output from the original NRLMSISE-00 version.

Another thermosphere option is the JB2008 model that replaces JB2006 used in the previous version of GRAM.25 The model was developed using the Committee on Space Research 

(COSPAR) International Reference Atmosphere (CIRA) 72 (CIRA-72) Jacchia 71 model as the 

basis for the diffusion equations. If JB2008 is selected for calculation of thermospheric density and 

temperature, winds are computed with the HWM-93, used in conjunction with the MSIS model. 

Other information and references to developmental papers for JB2008 are given at the JB2008 Web 

sites at the following urls:

• <http://sol.spacenvironment.net/~JB2008/>.

• <http://sol.spacenvironment.net/~JB2008/code.html>.

• <http://adsabs.harvard.edu/abs/2008cosp...37..367B>.

These sites have links to solar indices required by JB2008 (s10 and xm10), JB2008 source 

code, publications, contacts, figures, and the Space Environment Technologies Space Weather site.

2.2 The Middle Atmosphere Section (20–120 km)

The MAP data in GRAM characterizes the monthly mean middle atmosphere (20–120 km) 

by two gridded data sets, one representing the zonal mean atmospheric values (gridded by height 

and latitude) and the other the monthly mean stationary wave patterns (i.e., stationary perturbations about the monthly mean gridded by height, latitude, and longitude). The zonal mean data set 

was merged from six separate data sets covering the 20–120-km altitude range. The zonal monthly 

mean data set (pressure, density, temperature, and mean eastward wind component) is gridded in 

10° latitude and 5-km height increments (–80° to +80° and 20–120 km). Zonal mean values at ±90°

are computed by an across-the-pole interpolation scheme discussed in section 2.6. Zonal mean 

values between the gridded data set values are interpolated vertically by hydrostatic and perfect gas 

law assumptions and horizontally by two-dimensional (lat-lon) interpolation methods.

The stationary perturbation data set (standing wave perturbations in pressure, density, 

temperature, and eastward and northward wind components) was merged from three sources of 

data on planetary scale standing wave patterns.5 This data set is gridded in 10° latitude increments 

(–80° to +80°), 20° longitude increments (180° W., 160° W., 140° W.,..., 140° E., 160° E.), and 5-km 

height intervals (20–90 km). Stationary perturbations are identically zero at the poles. Stationary 

perturbation values are linearly interpolated in the vertical dimension and horizontally by twodimensional (lat-lon) interpolation methods.
10

2.3 The Lower Atmosphere Section (Surface to 10 mb)

2.3.1 The National Centers for Environmental Prediction Database

For the lower atmosphere, GRAM2010 uses climatological data derived from an NCEP 

global reanalysis database. The NCEP data consist of means and standard deviations (at a global 

lat-lon resolution of 2.5° × 2.5°) at 4 specific times of day (00, 06, 12, and 18 UTC) and for all 4 

times-of-day combined at the surface and at each of 17 pressure levels. Averages and standard deviations are by month over a POR from 1990 through 2008. More information about the reanalysis 

project and data are available from several sources, including reference 15. As part of validation 

studies conducted for GRAM2010, NCEP hourly and daily averages of surface winds and temperatures were compared with statistics from more directly observed surface winds and temperatures. 

During these studies, it was found that NCEP average surface winds and temperatures did not 

have nearly as much variation with hour-of-day as did observed surface winds and temperatures. 

Consequently, a more detailed study of surface and near-surface NCEP data and observed winds 

and temperatures were undertaken. 

2.3.2 National Centers for Environmental Prediction Versus 2006 Range Reference Atmospheres 

(Daily Data) 

For 21 selected locations (mostly NASA or Air Force test ranges), GRAM2010 provides 

an alternative to NCEP climatology in the form of RRA profiles. These data contain only monthly 

average ‘daily’ averages and standard deviations (i.e., no information from individual hours of 

the day, as with NCEP). Temperature and wind speed data from NCEP daily averages for various months were compared with monthly average profiles from 17 of the RRA sites. Excluded 

from this analysis were four ‘island’ RRA sites (Ascension, Barking Sands, Kwajalein, and Taguac 

islands), because of possible cross-contamination between water-surface and land-surface characteristics. Analysis indicated that over the available altitude range, there is no significant bias error 

between NCEP and RRA values for either temperature or wind speed (except near the surface).

Surface altitude at a given RRA site is the altitude (above MSL) of the actual local topographic surface. This may differ significantly from the surface altitude in GRAM which uses 

a 1° × 1° topographic database, as given by Gates and Nelson.26 For this reason, a more detailed 

comparison was made between monthly-average, near-surface RRA values of wind speed and 

temperature, and monthly-average GRAM values interpolated to RRA surface altitude from the 

NCEP data. Ratios of RRA to NCEP monthly surface wind speed values were averaged over 

several months, and the results for average wind speed ratio are plotted in figure 2. The stations 

included China Lake, El Paso, White Sands Missile Range (WSMR), Edwards Air Force Base 

(AFB) (EAFB), and other sites. This figure indicates a significant tendency of the NCEP surface 

winds to overestimate the true (RRA) surface winds. 

The solid trend line in figure 2 is given by,

SR = 0.634 + 0.205ER ⎡

⎣ ⎤⎦ SN , (1)
11

Surface Wind Magnitude Factor

Station Altitude (km)

1.2

1

0.8

0.6

0.4

0.2

0

0 0.2 0.4 0.6 0.8 1 1.2 1.4

EAFB

China Lake

WSMR

El Paso

Figure 2. Average ratio of RRA surface wind speed to NCEP wind speed evaluated 

at the RRA surface altitude.

where SR is the RRA surface wind speed in m/s, ER is the site elevation in km, and SN is the NCEP 

wind speed in m/s. This suggests that a multiplication factor could be applied to the NCEP winds 

in order to make it agree more closely with the RRA winds.

For consistency between means and standard deviations of the wind components and the 

mean and standard deviation for wind speed, the factor given by the term in brackets in equation 

(1) must be applied to all of these statistics. That a common factor on all the wind statistics preserves consistency is easily seen from the fact that a given wind speed value (S) is related to wind 

components u and v by, 

S2 = u

2 + v2 , (2)

and taking an average of equation (2) yields a relationship between the average wind speed, its 

components, and their standard deviations.

S 2+ σ S

2 = u

2

+ σ u

2 + v

2

+ σ v

2 , (3)

where the brackets indicate an average value. Any common factor applied to all the means and 

standard deviations in equation (3) leaves this equation unchanged.

In figure 2, the wind speed factor for China Lake is seen to be significantly lower than the 

factor for nearby EAFB. This might be due to the fact that China Lake could be significantly 

more affected by local topography than EAFB. It is also likely that the NCEP POR (1990–2008) 

yields significantly different results than the China Lake RRA POR (1948–2000). Some instrumental problems are known to exist in pre-1990 data, which may adversely influence the China Lake 
12

RRA data. An analogous situation exists for the different results between nearby sites El Paso 

and WSMR in figure 2. WSMR RRA has a POR 1949–1993, but WSMR may be more affected 

by local topography than nearby El Paso. A similar analysis was performed for temperature but, 

unlike wind speed, there was no significant bias between surface RRA temperature and NCEP 

surface temperature. 

2.3.3 Land-Surface Diurnal Data 

Since the land-surface RRA data examined earlier did not include diurnal variations of 

hourly mean wind speed or temperature, these factors for near-surface data had to be examined by 

using specially collected data. To this end, multiyear, POR hourly wind and temperature data were 

assembled from Cape Canaveral, EAFB, and WSMR. Two data sets were used from Cape Canaveral—one from a small tower at the Shuttle Landing Facility (SLF) site and one from the 16.5-m 

(54-ft) height on KSC tower 313. 

From each of these four data sets and for each month, ratios of POR average monthly average hourly mean values and daily mean values were evaluated. Ratios of hourly average to daily 

average, by local hour of the day, were averaged across the data sets to produce a ‘universal diurnal 

factor’ (UDF) curve. Standard deviations about the UDF averages give a sense of the variability of 

UDF values among the four data sets and 12 months examined. UDF data values for wind speed 

are shown in figure 3 and for temperature are given in figure 4. Speed Ratio

Local Time (hr)

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0 2 4 6 8 10 12 14 16 18 20 22 24

Figure 3. Multisite average of surface wind speed ratio of hourly average wind speed 

to daily average wind speed.
13

Temperature Ratio

Local Time (hr)

1.04

1.03

1.02

1.01

1

0.99

0.98

0.97

0.96

0 2 4 6 8 10 12 14 16 18 20 22 24

Figure 4. Multisite average of surface temperature ratio of hourly average temperature 

to daily average temperature.

The solid curves in figures 3 and 4 show least squares fits to these UDF data points, with 

both diurnal and semidiurnal harmonics represented in the UDF analytical curves. The UDF curve 

for wind speed as a function of local time (hour, (H)) is given by,

FS (H) = 1.0 + 0.3525•Cos((H/12) – 3.727) + 0.09447•Cos((H/6)–0.5930) , (4)

while the UDF for temperature is given by, 

FT (H) = 1.0 + 0.01745•Cos((H/12) – 3.715) + 0.004083•Cos((H/6)–0.2043) . (5)

By definition, the leading term in both UDF equations is 1.0, since averaging over all hours 

should leave the daily average unchanged. A similar analysis was performed comparing the NCEP 

surface data over water to data sets for 23 buoys. Based on these results, no need for NCEP adjustment is perceived to be required for either daily averages or hourly averages for either wind speed 

or air temperature at water-surface NCEP grid locations.

2.3.4 Methodology for ‘Fixing’ Near-Surface National Center for Environmental Prediction Data 

Based on study results described in the previous section, the following methodology is used 

to ‘fix’ near-surface values of hourly average and daily average NCEP wind and temperature data. 

The methodology is applied (as necessary) at each 2.5° × 2.5° NCEP grid point, for each of the 

12 monthly data sets. The 1° × 1° global surface-type data set of DeFries and Townshend is used 
14

to determine if the NCEP grid point has a water surface or land surface.27 For water-surface grid 

points, no adjustment is applied to the NCEP data for either wind or temperature. For land-surface 

locations, topographic altitude (h) at the NCEP grid point is determined from the 1° × 1° global 

topography,26 and a surface wind adjustment factor, F(h) = 0.634 + 0.205h, is computed. For large 

h, F(h) is limited to be ≤1. If the geopotential altitude (z) above the surface is ≤0 (i.e., below sea 

level) for a given NCEP pressure level, then F(h) is used as a multiplier on the hourly averages and 

standard deviations and daily averages and standard deviations for wind speed and for both horizontal wind components. If z>0 and z ≤ 500 m, then F is linearly interpolated between F= F(h) at 

z=0 and F=1 (no adjustment) at z=500 m. The factor F is then used as an adjustment multiplier 

on all wind statistics. If z>500 m, no adjustment is applied to wind statistics. 

Local time (H) is computed based on longitude of the NCEP grid point and on UTC time 

for the NCEP hourly average. Values of UDFs, (FS(H) for speed and FT(H) for temperature) are 

computed from equations (4) and (5). As for wind adjustment factor F, values of F are interpolated 

on height above the surface, z, until UDF= 1 (no diurnal adjustment) at z≥500 m. Then the factor 

FT(H) is used to adjust hourly average and standard deviation of temperature if the data does 

not show sufficient variability. Atmospheric density and moisture variables are also adjusted to 

preserve the perfect gas law relation, based on the given hourly average RH. Factor FS(H) is also 

used to adjust hourly averages and standard deviations of wind speed and both horizontal wind 

components if there is insufficient variability in the NCEP data.

2.3.4.1 Summary. No adjustments are made to any NCEP data over the oceans or to any 

data above 500 m over land. Furthermore, no corrections are made to the monthly mean temperature data anywhere. If hourly average NCEP temperature <T(H)> deviates from the daily average 

by less than the amount expected from FT(H), then <T(H)> is adjusted until the deviation from the 

daily average is as expected. If <T(H)> deviates from the daily average by more than the amount 

expected from FT(H), the value of <T(H)> is assumed to be valid and is left unchanged. To ensure 

consistency with adjusted hourly NCEP values, the daily NCEP average value <Tday> is recomputed from the adjusted hourly values after the hourly adjustment has been completed. Since the 

NCEP data is provided on pressure levels, the pressure data is also unchanged and the density is 

calculated from the gas law and corrected NCEP temperature.

The UDF for wind speed (FS(H)) is used in a similar fashion to adjust surface wind statistics. For wind adjustment, R(H) is the ratio <S(H)>/<Sday>, where <S(H)> is hourly average 

surface wind speed and <Sday> is daily average surface wind speed. Once an adjustment factor 

FS(H)/R(H) (other than 1) is determined, this factor is used to multiply both hourly average speed 

and standard deviation of speed, and to multiply hourly averages and standard deviations for 

both horizontal wind components. The factor F makes no adjustment to daily average wind statistics. These adjustments are made once to create a fixed NCEP database that is supplied with the 

GRAM software.

2.3.5 Example Results and Validation 

Figure 5 compares the observed POR average, monthly average, hourly mean surface 

wind speed at the KSC. The POR for the observed data is similar to the POR for NCEP data 
15

Speed (m/s)

Local Time (hr)

10

9

8

7

6

5

4

3

2

1

0

0 2 4 6 8 10 12 14 16 18 20 22 24

SLF Data

Tower 54 ft

GRAM With Fixed NCEP

Original NCEP

Figure 5. Observed diurnal variation of January hourly average surface wind speed at KSC.

(1990–2008). GRAM2010 output values for hourly average surface-wind speed and standard 

deviation at the four NCEP UTC times (expressed as local time at each site) are shown by the data 

points and ‘error bars’ connected by a dashed line. For the GRAM output, near-surface NCEP 

data were employed after having been ‘fixed’ by the procedure discussed in the previous section. For 

comparison, original NCEP data values are also shown.

Figure 5 shows that the ‘fixed’ NCEP surface winds have about the right amplitude of 

diurnal variation, but the NCEP daily average wind speed is somewhat larger than observed. This 

results from the fact that one of the four NCEP grid point locations surrounding KSC is a watersurface site (in the Atlantic Ocean). NCEP winds at this grid location are not adjusted downward, 

as are the winds at the other three (land-surface) NCEP grid locations surrounding KSC. Even 

after GRAM does horizontal interpolation to the lat-lon of KSC, GRAM output winds at KSC 

are still ‘contaminated’ somewhat by this nearby water-surface grid point. Users should realize that 

adjustment of the NCEP data (particularly the dirurnal data) near the land surface is somewhat 

crude and may not be the best choice for their particular application. Alternative choices include 

site-specific data such as RRA data or site measurements that can be injested into GRAM using 

an auxiliary profile (see app. B.9).

2.4 The Boundary Layer Model for Vertical Velocity

2.4.1 Background

A small-scale vertical wind perturbation model has been part of the GRAM since its 1995 

release.6 Height-dependent standard deviations of vertical winds were taken from reference 28. 
16

This vertical wind model continued in GRAM through the 1999 release8 and version 1.1 of the 

2007 release.9 Recent strong interest in capsule parachute landing simulations led to including 

a vertical wind distribution as a function of horizontal wind and underlying surface characteristics 

(surface roughness). An earlier version vertical wind model, designed to address these issues, was 

released (in October 2008) as GRAM 2007 Version 1.2. That model incorporated many features of 

BL effects on vertical wind standard deviations. However, time-of-day effects were not addressed, 

atmospheric stability influence was represented in only an approximate fashion, and BL depth was 

assumed to be a constant value of 1,500 m. The revised vertical wind model discussed here, and 

being released in GRAM2010, incorporates effects of these additional factors. This new model 

computes standard deviation for BL vertical wind as a function of surface type (water or various 

land types), and surface horizontal wind (at 10-m height). Surface height (above MSL) is interpolated from the 1°×1° topographic database of reference 26 or from RRA surface altitude, if 

the GRAM RRA option is selected. Boundary layer depth is computed from a new time-of-day 

and stability-dependent model. Land cover type is given at 1° resolution from the database of 

reference 27.

Surface type codes are shown in table 1. Surface roughness (zo) values assumed for each surface type were computed as the geometric mean value from a variety of sources and are also given 

in table 1. To account, in an approximate way, for the influence of mountainous topography on zo, 

values from table 1 are increased linearly for surface altitudes above 1.5-km MSL up to either 

a maximum surface height of 4.5 km or to a maximum zo of 3 m, whichever is appropriate. Surface 

wind dependence is based on hourly average wind speed computed from wind components given 

by monthly mean wind at 10 m plus GRAM large-scale perturbed wind components at the surface. 

Since GRAM large-scale wind perturbations change from profile-to-profile in a Monte-Carlo run, 

surface wind speed changes from profile-to-profile. 

Table 1. Surface codes and associated zo values.

Code Land Cover Class

zo

(m)

0 Water u-dependent

1 Broadleaf evergreen forest 0.6

2 Coniferous evergreen forest and woodland 0.48

3 High-latitude deciduous forest and woodland 0.42

4 Tundra 0.0056

5 Mixed coniferous forest and woodland 0.45

6 Wooded grassland 0.12

7 Grassland 0.046

8 Bare ground 0.015

9 Shrubs and bare ground 0.042

10 Cultivated crops 0.065

11 Broadleaf deciduous forest and woodland 0.45

12 Data unavailable (reassigned to codes 4, 6, or 13, as appropriate) -.-

13 Ice 3.2 × 10–4
17

While the surface roughness over land is determined from table 1, zo over water is based 

on the formulation of Donelan et al. as,29

z

o = αu*

2

g , (6)

where g is the gravitational acceleration and u* is the friction velocity. The codependence of zo and 

u* is solved by a four-step iteration process. There is also an option whereby the user may supply 

any desired zo value (between 10–3 m and 3 m), to be used in place of these prescribed values. 

Friction velocity is computed from the standard logarithmic law-of-the-wall for neutral 

atmospheric stability, modified by a stability-dependent term (y),

u* = 0.4U10

ln

10

zo

⎛

⎝

⎜

⎞

⎠

⎟ −ψ

10

L

⎛

⎝

⎜

⎞

⎠

⎟

, (7)

where U10 is the wind speed at 10-m height and L is the Monin-Obukhov length. The BL wind 

profile function is given by,

= −50 L if 1 L > 0 (stable)

ψ (10 L) = 0.0 if 1 L = 0 (neutral)

= 1.0496(−10 L)

0.4591 if 1 L < 0 (unstable) . (8)

The unstable formulation for y is from reference 30 and is a simplification of an often used 

but more complicated expression derived by Paulson.31

The inverse of the Monin-Obukhov length (1/L) is calculated by a four-step process, based 

on information derived from table 4-7, table 4-8, and figure 4-9 of reference 32. First, a net radiation index (nr) is computed that depends on solar elevation angle and time-of day (or night), where 

nr ranges from –3.5 (strong outgoing net radiation) to + 4.5 (strong incoming net radiation). See 

table 4-7 in reference 32. Then a wind-speed factor W(U10) is computed from empirically derived 

functions,

= 1−U10 ( / 7.5) if U10 < 6m s

W U10 ( ) = 0.2 if U10 = 6m s

= 0.2Exp 12 − 2U10 ( ) if U10 > 6m s. (9)

A stability category x is computed as a function of W(U10) and nr by, 

ξ = 4.229 − nrW , (10)
18

which is an empirical fit to table 4-7 in reference 32. Values of x are limited to 0.5 on the low side 

(most unstable) and 7.5 on the high side (most stable). Finally, the inverse Monin-Obukhov length 

versus stability category x and surface roughness length is determined using,

1 L = (1 4)(−0.2161+ 0.0511ξ)Log10 10 z

o ( ) , (11)

which is an empirical fit to figure 4-9 of reference 32. These steps are similar to the methodology of 

Blackadar et al. for the estimation of L.

33

The standard deviation of vertical wind is now computed as a function of height above the 

surface and stability dependent Monin-Obukhov length by, 

= 1.25u*(1+ 0.2 z L) (stable:1 L > 0)

σ w = 1.25u* (neutral:1 L = 0)

= 1.25u*(1− 3z L)

1 3 (unstable:1 L < 0) , (12)

where the stable relation is from equation 1.33 of reference 34 and also found in reference 35, and 

the unstable relation is from equation (2) on page 161 of reference 36, a relation which has been 

widely used to represent this factor for the unstable atmospheric surface layer.34, 37–39 A variety 

of different formulations for σw in stable situations has been suggested, including a formula equivalent to the unstable relation in equation (12) (e.g., eq. (8) and table 1 of ref. 40). However, a simple 

linear relationship for the stable case, such as given in equation (12), has been more widely used.

As shown by references 41 and 42 and in the discussion of figure 7.2 of reference 36, equation (12) is not expected to apply above about z=0.1d, where d is the BL depth. Therefore, for 

stable and neutral cases, σw is limited to a value of 3.75u*, while for unstable cases, σw is limited 

by the magnitude of the convective velocity w* to a value of σw<0.62w*, where w* is given by,

w* = u* ⎡−d / (0.4L) ⎣ ⎤

⎦

1/3 , (13)

(eq. (4) of ref. 41). These limiting values account for transition from the surface layer to the 

convective layer (z/L<0) or to the stable BL (z/L>0).

The BL depth d is calculated from simplifications of methodologies given by references 43, 

44, and 45. For stable-to-neutral cases, the methodology of section 2.1 of reference 43 is used.

d = 2dN / 1+ 1+ 4dN ( / L) ⎡ 1/2

⎣

⎢ ⎤

⎦

⎥ , (14)

except that their form for the neutral BL depth (dN) is changed from,

dN = 0.2u* / f , (15)
19

to,

dN = u* 80 / ω2 f ( ) ⎡

⎣⎢ ⎤⎦⎥

1/3

, (16)

where f is the coriolis parameter and w is the Brunt-Vaisala frequency.

For the unstable BL, the time-dependent differential equation solution in reference 44, as 

expressed in reference 45, is converted to an algebraic equation by assuming that the time rate of 

change of d can be replaced by df/2. This operation yields an analytical equation for d,

d = dN (1− 0.1125d / L)

1/3 , (17)

whose solution can be found by iteration.

For time variation between sunrise (if applicable) and midday, a time-factor multiplier 

G(El), given by, 

G El ( ) = 0.3+ 0.7 El E

md , (18)

is applied, where El is solar elevation at the current time and Emd is midday solar elevation. This 

allows for time variation of d to be accounted for in an analytical fashion rather than the solution 

of a differential equation versus time.

Subject to the limiting values mentioned above, the height-dependent equations (12) are 

used to compute σw from the surface to the top of the BL. As part of its original vertical wind 

model, GRAM contains values of σw at 5-km intervals (above MSL). Between the top of the BL 

and the next height for which σw is available, linear interpolation is used to estimate σw. 

Calculation of the vertical wind perturbations in GRAM is not changed, only the methodology for computing standard deviation of vertical wind. Values of σw are constrained to 

be 0.1 m/s or greater, since the perturbation calculation methodology does not work properly 

if σw is 0. Calculation of mean vertical winds (typically a few cm/s or less) is still done by a 

Montgomery stream function approach, first implemented in GRAM-90 (sec. 2.7 of ref. 5), 

and the perturbations are determined from a 1-step Markov algorithm.

2.4.2 Example Model Output

The above equations are used to compute standard deviation of vertical wind as a function 

of height above the surface, the surface roughness, and the surface wind speed. These have been 

implemented as the revised vertical wind model in GRAM2010. In this model, values of U10 are 

computed from wind components given by GRAM lat-lon-dependent monthly mean wind at 

10-m height, plus GRAM large-scale perturbed wind components at the surface. For each randomly selected wind profile in a Monte-Carlo simulation sequence, different large-scale wind 

perturbations are produced, so U10 values used in the σw model vary from profile to profile.
20

Table 2 provides statistics for σw, computed from 600+ profile Monte Carlo runs of 

GRAM2010 at three different BL altitudes above the surface and at a variety of sites for specific 

months. Sites examined include EAFB (low surface roughness, zo=0.04 m), KSC land surface 

(moderate surface roughness, zo=0.45 m), KSC water surface, and ocean sites near San Clemente 

and in the North Atlantic (latitude 50° N. longitude 30° W.).

Table 2. Sample output statistics for vertical wind standard deviation (m/s) 

from GRAM2010.

KSC Feb Land KSC June Land

Height (m) 10 100 1,000 10 100 1,000

Average 0.60 0.87 1.05 0.45 0.71 0.85

Std.Dev. 0.25 0.38 0.49 0.21 0.42 0.54

Minimum 0.10 0.10 0.19 0.10 0.10 0.19

Maximum 1.29 1.75 2.38 1.10 1.92 2.69

KSC Feb Water EAFB Feb

Height (m) 10 100 1,000 10 100 1,000

Average 0.16 0.26 0.33 0.37 0.50 0.57

Std.Dev. 0.06 0.11 0.10 0.20 0.25 0.24

Minimum 0.10 0.10 0.19 0.10 0.10 0.20

Maximum 0.36 0.57 0.57 0.85 1.11 1.23

San Clemente Feb Water North Atlantic Ocean Feb

Height (m) 10 100 1,000 10 100 1,000

Average 0.26 0.31 0.37 0.59 0.61 0.63

Std.Dev. 0.12 0.12 0.10 0.32 0.30 0.28

Minimum 0.10 0.10 0.19 0.10 0.10 0.19

Maximum 0.58 0.58 0.58 1.79 1.79 1.79

As expected from equation (12), the average σw in table 2 increases with height at all sites. 

The increase in zo from EAFB to KSC land surface produces a significant increase in σw. A change 

from KSC land surface to KSC water surface, with resultant decrease in zo (by eq. (6)), causes 

a significant decrease in σw. With similar statistics for surface wind speed, KSC water results 

and San Clemente values are fairly similar. However, because of substantially higher surface wind 

speeds at the North Atlantic site, there is a substantial increase in σw over values for KSC (water) 

or San Clemente. Effects of stability are illustrated by comparison of σw values from KSC 

February with KSC June. Lighter winds (hence smaller u* values) in June make both the average 

σw and the range of variability of σw at 10-m height smaller for June than for February. While the 

average σw for June at KSC remains lower at all altitudes, effects of convection under more prevalent unstable conditions in June make the range of σw larger in June than in February, at both 

100-m and 1,000-m altitudes.
21

2.4.3 Boundary Layer Model Validation 

Vertical winds are roughly an order of magnitude smaller than horizontal winds and are 

correspondingly roughly an order of magnitude more difficult (and more expensive) to measure 

than horizontal winds. Consequently, availability of vertical wind measurements for model validation is fairly limited. For example, despite extensive meteorological instrumentation at KSC, 

vertical winds are not routinely measured. However, a limited amount of KSC vertical wind data, 

discussed below, provides some degree of model validation. The surface roughness value (zo=

0.45 m) used for KSC land surface results in table 2, comes directly from the GRAM 1° × 1° global 

database (discussed above). Nevertheless, this value is in good agreement with average zo values at 

KSC determined from wind profile analysis using the NASA 150-m meteorological tower.33,46

In 1992 and 1993, the KSC Applied Meteorology Unit (AMU) used a doppler and sound 

detection and ranging (SODAR) instrument (called a MiniSODARTM) to study horizontal and 

vertical winds near Space Launch Complex (SLC) 37 (SLC-37) at KSC.47 They report (in ref. 47 

fig. 14) that vertical wind standard deviation during June 17–30 reached a diurnal peak of 0.57 m/s 

at about 1800 hrs local time, at an altitude of 60 m. This MiniSODAR value is noticeably less than 

the maximum KSC σw between 10-m and 100-m altitude from table 2 for both February and June. 

Part of this discrepancy may be due to the limited sampling period (June 17–30) used by the AMU. 

It is also possible that the vertical winds are underestimated by the SODAR instrument, since the 

AMU report notes “...an underspecification of vertical velocity variations by the phased array 

scanning sequence and the mathematical form of retrieval algorithms required for estimating peak 

wind speeds.” This is referred to elsewhere in the report as a problem with “...undersampling of the 

vertical wind velocity over the profiler beams.” 47

High-resolution tracking of balloon trajectories has also been used to estimate vertical 

winds near KSC. Rider and Armendariz measured σw at KSC from high-resolution tracking of 

37 wintertime and 10 summertime Jimsphere flights.48 At altitudes between 100 and 1,200 m, this 

study found that “vertical wind components ranged from 10–25 cm/s in a stable atmosphere to 

55–100 cm/s under unstable conditions, depending on wind speed.” A maximum vertical wind of 

100 cm/s agrees fairly well with values at KSC (land surface) from table 2. Record et al., measured 

σw at KSC from high-resolution tracking of 10 overland and 5 overwater tetroon flights. 49 This 

study found (in their table 2-3) that in four of the overland cases (40% of observations) 10-min 

average σw values exceeded 1 m/s, and that one of the five overwater cases had a 10-min average 

σw of 0.97 m/s, also in fairly good agreement with values from table 2 of this TM.

Blackadar, et al., examined wind profiles observed from the KSC 150-m tower and used 

observed mean speed at z=18 m (U18) and BL theory to estimate surface roughness and surface 

friction velocity.33 Although estimates of the standard deviations of the horizontal wind components are given, there are no direct measurements or estimates for σw. However, Blackadar’s table 3 

gives u* values from which approximate values for σw can be calculated by σw=Factor(z/L)u* (e.g., 

as in equation (12)). Blackadar et al., give values of Richardson number (Ri) from which values of 

z/L can be calculated, namely (from their eq. (18) and (19)),33
22

z L = Ri (unstable conditions)

= 5Ri 1− 5Ri ( ) (stable conditions) . (19)

Table 3 gives a statistical summary computed from data given by Blackadar et al., for cases 

having estimated u* values.33 Both estimated average σw and maximum σw from this table are somewhat larger than the GRAM-estimated values from table 2 for heights up to 100 m. The fact that 

estimates of σw at KSC range from less than to greater than values given from GRAM estimates in 

table 2 is taken as an indication that the new GRAM vertical wind model is at least approximately 

correct, within the constraints and limitations of the present model. 

Table 3. Summary of KSC vertical wind estimates from data in table 3 of reference 33.

U18, m/s zo, m u

*

, m/s Factor(z/L) σw(m/s) =Factor(z/L)×u

*

Avg 4.88 0.46 0.67 1.58 1.04

Std. Dev 2.47 0.17 0.28 0.32 0.41

Min 1.40 0.27 0.20 1.25 0.27

Max 11.70 0.79 1.47 2.79 2.36

2.5 Water Vapor and Other Atmospheric Species Concentrations

Water vapor and other atmospheric species concentrations were introduced in GRAM-95, 

with values above 90 km from the MET model and via a new species concentration database 

discussed in section 4.3 of reference 6. Water vapor output from GRAM includes both monthly 

means and standard deviations. The H2O values vary with month, height, latitude, and longitude.

Means and standard deviations in H2O are represented in the form of vapor pressure 

(N/m2), vapor density (kg/m3), dewpoint temperature (K), and RH (%). Mean H2O values in the 

form of volume concentration (ppmv) and number density (molecules/m3) are also output. Only 

monthly mean concentration values are output for the species, other than H2O, and in the form 

of volume concentration and number density.

Interpolation of the dewpoint temperature for altitudes between the input pressure levels 

and for latitude and longitude between the input grid points is handled the same as the other variables. Height and latitude interpolation between input height-latitude grid points for H2O above 

the 10-mb level, and for the other species, is done by an adaptation of the two-dimensional 

interpolation discussed in the next section (to do height-latitude interpolation rather than lat-lon 

interpolation).

Species concentrations c(t) are assumed to change with year t according to the relation,

c(t) = c t

0 ( ) 1+ rt ( )

t−t

0 , (20)
23

where t0 is 1976 (the initial time) for the AFGL data and 1981 for the MAP concentration data and 

the concentration rate of change (rt) is 0.005 for CO2, 0.009 for CH4, 0.007 for CO, and 0.003 for 

N2O. For O3, rt varies linearly from 0.003 at the surface to 0 at 15 km, linearly from 0 at 30 km to 

–0.005 at 40 km, and again linearly from –0.005 to 0 at 120 km. The rate of change, rt, for H2O and 

the other constituents is assumed to be 0.

2.6 Interpolation and Fairing Techniques

2.6.1 Vertical Interpolation 

Pressure (p(z)), temperature (T(z)), and density (r(z)) obey the perfect gas law,

p = ρRT , (21)

where R is the gas constant. They also agree very closely with the hydrostatic assumption,

dp dz = −ρg , (22)

where g is the acceleration of gravity. If there exists grid-point pressure values p1 and p2 and temperature values T1 and T2 at heights z1 and z2, then vertical interpolation to any height z (between 

z1 and z2) is done by assuming a linear temperature variation,

T(z) = T1 + γ (z – z

1) , (23)

where g is the temperature gradient,

γ = (T2 – T1) / (z2 – z

1) . (24)

The hydrostatic relation with a constant g implies a power-law variation with pressure. 

Therefore, p(z) may be computed by,

p(z) = p1 T (z) T1 ⎡

⎣ ⎤⎦

−a , (25)

where the exponent a is given by,

a = g / (Rγ ) . (26)

In the NCEP height range, this vertical interpolation is complicated by the fact that the moisture varies with height and the gas constant for moist air depends on the moisture concentration. 

For the NCEP data, a variant of equation (25) uses an interpolated gas constant R.

The exponent a can be evaluated using two levels where temperature and pressure are 

known,
24

a = log p2 p1 ( ) log T1 T2 ( ) . (27)

For an isothermal layer where T1=T2, equation (25) becomes

p(z) = p1exp −g z − z

1 ( )

RT1

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

. (28)

The density, r(z), is found by solving the perfect gas law relation (eq. (21)).

The form of vertical interpolation given by equation (25) is used to fill in mean values of 

pressure, density, and temperature between the input pressure levels of the NCEP data (with z

the geopotential height) and the zonal mean values between the input height grids of the MAP 

database. Other variables that do not obey perfect gas law relationships (e.g., wind components, 

dewpoint temperature, and all standard deviations) are interpolated linearly in the vertical.

2.6.2 Two-Dimensional Interpolation 

Let V be a variable that is available on a two-dimensional grid array (x and y) and consider 

the grid point values V11=V(x1,y1), V12=V(x1,y2), V21=V(x2,y1) and V22=V(x2,y2). Then any 

value V(x,y) (for x between x1 and x2 and y between y1 and y2) may be found by the interpolation 

scheme,

V ( x, y) = α′β′V11 + α′βV12 + αβ′V21 + αβV22 , (29)

where a=(x–x1)/(x2 –x1), a′=1–a, b=(y–y1)/(y2 – y1), and b′=1–b. This interpolation relation is 

mathematically equivalent to that used (for lat-lon interpolation) in earlier GRAM versions but is 

expressed here in a more symmetric notation.

Equation (29) is used to interpolate between lat-lon grid points (x=longitude and 

y=latitude) for the NCEP grids and the stationary perturbation grids of the MAP data. For variables dependent on a height-latitude (or a pressure-latitude) grid (such as the species concentration 

data), then equation (29) is used with y=latitude and x=height (or x=log pressure). The variables 

actually interpolated for concentration data are the logarithms of the concentration values.

2.6.3 Interpolation Across the Poles 

Several GRAM height-latitude dependent databases lack values at or near the poles. These 

are filled in by an interpolation procedure that assumes a parabolic variation (across both sides of 

the pole) that fits the last and next-to-last available latitudes. The results are a weighted average of 

these last and next-to-last latitude values. For example, if values of a parameter are available at 

±70° and ±80°, but not at ±90°, then the missing polar values are supplied by,

y±90 = 4y±80 − y±70 ( ) 3. (30)
25

If values are available at ±60° and ±70° but not at ±80° or ±90°, then the missing values are 

supplied by,

y±90 = 9y±70 − 4y±60 ( ) 5 , (31)

and

y±80 = 8y±70 − 3y±60 ( ) 5 . (32)

For the species concentration data, this interpolation is done on the logarithm of the 

concentration values.

2.6.4 Fairing Between Two Data Sets 

If we have two data sets, A(z) and B(z), that overlap throughout the height range from 

z1 to z2 (with A valid below z2, B valid above z1, and z2>z1), then a fairing process,

C(z) = f (z) A(z) + 1− f (z) ⎡

⎣ ⎤⎦ B(z) , (33)

ensures a smooth transition for the faired variable C across the height interval from z1 to z2

if f(z1)=1 and f(z2)=0. Thus, A(z) is used below z1, B(z) above z2, and the faired variable, C(z) 

varies smoothly between A(z) and B(z) as z varies from z1 to z2. A linear form is used for f,

f (z) = z2 ( − z) z2 − z

1 ( ) , (34)

or, with variables for which continuity of vertical derivatives is important, f is taken as,

f (z) = cos2 (π 2) z − z

1 ( ) z2 − z1 ( ) ⎡

⎣ ⎤⎦ . (35)

Equation (35) is used in fairing between the NCEP and MAP data between 20 and 27 km, 

between the thermosphere model and MAP data between 90 and 120 km, and the helium number 

density in the MET model between 440 and 500 km. For fairing the species concentration data, 

equation (34) is used with the logarithm of the species concentration as the variable to fair.

2.6.5 Seasonal and Monthly Interpolation 

Some of the species concentration databases do not contain monthly data. For example, 

the AFGL concentrations are seasonal averages (summer and winter), the LaRC H2O data have 

four seasonal averages, and the MAP H2O data have only certain months of the year (November 

through May). The initialization routines in GRAM use an annual harmonic temporal variation 

model to estimate the concentration data for the specific month to be simulated. For the AFGL 

data, this is accomplished by applying precomputed weights to obtain a weighted average of the 

summer and winter values used to estimate the value for the specific month. For the LaRC H2O 

data, a weighted average of the two adjacent seasonal values is used to estimate the monthly value 
26

(i.e., Mar–April–May and Jun–July–August values are used to estimate the monthly values for 

May and June with different weights applied for month). For the MAP H2O data, a combination 

of annual harmonic Fourier fit and 6-month displacement from northern to southern hemisphere 

(and vice-versa) is used at initialization to establish the global values for each month from the 

monthly values of November through May in the database.

2.7 The Perturbation Model

2.7.1 Small Scale Perturbation Model 

GRAM2010 uses a simple, first-order, autoregressive model to compute a perturbation 

at each new position from the correlated perturbation value at the previous position. In addition 

to maintaining the correlation necessary between these successive perturbation values, the model 

accounts for the effects of variation in the mean values and the standard deviation from one position to another. Consider a normalized variate m(x) (i.e., m is the deviation of the value from the 

mean value divided by the standard deviation, all at the vector position x). The perturbation model 

computes m(x′) at the next trajectory position x′,

μ( x′) = rμ( x) + 1− r

2 ( )

1

2 q( x) , (36)

where q is a Gaussian-distributed random number with a mean of 0 and standard deviation of 1, 

and r is the autocorrelation between the successive values of the normalized variate,

r = < μ( x′)μ( x) > , (37)

where the angle brackets denote an average. The autocorrelation value (r) is obviously a function 

of the vector displacement, δx=x′–x.

Consider two normalized variates, m(x) and n(x) (each relative to its own mean value and 

each normalized by its own standard deviation) that have a cross-correlation (rc) between them 

(i.e., rc=<m(x)n(x)>). Variate v(x′) at the new position is computed from n(x) and m(x′) by,

v( x′) = r

v

v( x) + r

μμ ( x′) + rqq( x) , (38)

where the coefficients are given by,

r

v = r 1− rc

2 ( ) 1− rr

c ( ) ⎡ 2

⎣

⎢ ⎤

⎦

⎥ , (39)

r

μ = rc

1− r2 ( ) 1− rr

c ( ) ⎡ 2

⎣

⎢ ⎤

⎦

⎥ , (40)

and
27

r

q = 1− rv

2 − r

μ

2 − 2r

vrμrcr ( )

1 2

. (41)

Values of r are computed by assuming an exponential correlation function,

r(δ x) = exp −δh Lh ( )exp −δz Lz ( )exp(−δt τ ) , (42)

where δh and δz are the magnitudes of the horizontal and vertical components of δx=x′–x and 

Lh and Lz are horizontal and vertical scale parameters that are functions of height and latitude 

only. Time correlation (even in the special case when the user selects δh=0 and δz=0) is accounted 

for by the third exponential term in equation (42), where t is a time scale that varies with height 

and δt is the magnitude of the time step between data points. 

GRAM2010 computes the density and vertical velocity perturbations using only autocorrelation (using a form of equation (36) with the correlation coefficient from equation (42)). Pressure 

perturbations are computed with cross-correlation to density (using a form of equation (38), correlation coefficients from equations (39)–(42), and a Buell50,51 formulation for the pressure-density 

correlation). The temperature perturbation is computed from a first order version of the ideal gas 

law and Buell relations. The horizontal wind perturbations are also cross-correlated with density 

with the wind-density correlation given in the ‘atmosdat’ data file (see sec. 4.3). For additional 

discussion of the perturbation model, see sections 2.6 and 2.7 of reference 6.

Generation of GRAM perturbations starts with the observed (climatological) values of 

total standard deviation of observations about the monthly mean. Total variance (square of the 

standard deviation) is partitioned into variance contributed by two perturbation components: 

(1) A large-scale, wave-like perturbation and (2) a small-scale, stochastic (random) perturbation. 

Vertical shears from the large-scale, wave-like perturbations in GRAM are proportional 

to A/l, where A is the local wave amplitude and l is the local vertical wavelength. Vertical shears 

from the small-scale, stochastic perturbations in GRAM are proportional to s/L, where s is the 

local standard deviation of the small-scale perturbations, and L is the local vertical correlation 

scale for the small-scale perturbations. An increase in vertical wavelength l therefore yields smaller 

vertical shears from the large-scale, wave-like perturbations. A height-dependent factor on vertical and horizontal correlation scales increases L below ≈15 km, while decreasing L above ≈15 km. 

This effect decreases (increases) small-scale shears at heights below (above) 15 km, while leaving 

small-scale shears above 30 km unchanged. The addition of time dependence for the large-scale 

perturbations allows GRAM to simulate synoptic-scale variations in time and space. 

2.7.2 Patchy Severe Turbulence 

In order to approximate intermittency (‘patchiness’) in the perturbations, a variable scale 

model was introduced in GRAM-95 (sec. 2.6 of ref. 6) and also used in GRAM2010. The GRAM 

database (‘atmosdat’ data file described in sec. 4.3) includes (for both horizontal and vertical scales) 

values for average scale size (Lavg), minimum scale size (Lmin), and standard deviation of the 

variable scale size (sL). Periods of ‘severe’ perturbations are characterized as having a scale size 

of Lmin.
28

In the perturbation model, ‘nonsevere’ (i.e., light-to-moderate) perturbations are 

characterized as having a scale size of Lmax, such that,

L

avg = Psev

L

min + 1− Psev ( ) Lmax , (43)

where Psev is the probability of encountering severe perturbations given by,

Psev = Ptail Lavg − L ( min ) σ ( L ). (44)

where Ptail is the tail probability of a Gaussian distribution. From equation (43) the scale for 

nonsevere perturbations is given by,

Lmax = Lavg − PsevL ( min ) 1− Psev ( ) . (45)

When in severe turbulence, the length scales used in equation (42) are the minimum length 

scale read in (and height interpolated) from the ‘atmosdat’ file. When in nonsevere turbulence, the 

length scales in equation (42) are the maximum value computed from equation (45). The triggering 

of severe turbulence occurs by tracking an artificial horizontal scale that is autocorrelated (using 

a form of eq. (36)) and an artificial vertical scale that is cross-correlated with the horizontal scale 

(using a form of eq. (38)). If either of these scales goes below a minimum value, severe turbulence 

is initiated.

Furthermore, the variance of the severe perturbations is assumed to be fsev σ2, and the variance of the nonsevere perturbations is assumed to be fnon σ2, where σ2 is the total variance of the 

small-scale perturbations (s, the standard deviation of the small-scale perturbations is also given 

in the ‘atmosdat’ file data). Considering the probability of occurrence, σ2 is given by,

σ2 = P

sev fsevσ2 + 1− Psev ( ) fnonσ2 . (46)

From standard deviation data in reference 27, the factor fsev is approximated as varying with 

height z, having values ranging from 6 at z=0 km to 12 at z=10 km and back to 6 at z=16 km 

(and higher). With fsev thus specified, fnon is calculated from equation (46) by,

f

non = 1− fsev

P

sev ( ) 1− Psev ( ) . (47)

As GRAM simulates perturbations along a given trajectory, it uses a random number 

generator to decide when (with probability Psev) the perturbations are in the severe category. During this time, the variance is adjusted from its nonsevere magnitude (fnonσ2) to its severe magnitude 

(fsevσ2). Patchy severe turbulence is applied only to the small-scale perturbations and not the largescale perturbations and is enabled only when the parameter patchy (in the input file) has a nonzero 

value.
29

2.7.3 The Large-Scale Perturbation Model 

While the small-scale perturbations are modeled using a stochastic process that is approximately Gaussian distributed, the large-scale perturbations are modeled with a sinusoidal formulation to represent the atmospheric wave phenomena observed at this scale. The large-scale density 

(again normalized by its mean value) is given by,

ρl

σ ρl

= AQ

cos nθ + mφ + 2π

z

λz

+ 2π

t

T

+ φq

⎛

⎝

⎜

⎞

⎠

⎟

σ cos

, (48)

where ρl is the large-scale density, σρl is the large-scale standard deviation, AQ is an amplification 

factor, m is the number of waves in the north-south direction, n is the number of waves in the eastwest direction, z is height, lz is the vertical wavelength, t is the elapsed time, T is a randomized wave 

period, φq is a random wave phase, and σcos is the standard deviation of the cosine function and 

equal to 1 2 . AQ was added to this model in GRAM in order to provide exceedances beyond 2

sigma that would otherwise not occur. AQ was determined empirically (but constrained so that the 

standard deviation of density is unchanged) as,

AQ = 0.4808 + 0.96iQ , (49)

where Q is a uniformly distributed random number between 0 and 1. Therefore AQ varies from 

0.4808 to 1.4408 and thus allows for 2 sigma exceedances. The same value is used for both horizontal wave numbers n and m. They are determined randomly for a given Monte-Carlo run from

m = n = IntegerOf 4.0 + 0.833iQnm ⎡

⎣ ⎤⎦ , (50)

 where Qnm is a Gaussian-distributed random number with a mean of 0 and sigma of 1. This 

formulation is derived so that the horizontal wave numbers are between two and six waves. The vertical wavelength lz is computed as a function of height with parameters av (which is randomized) 

and bv which is equal to 0.045,

λz = av + bv z

3 . (51)

The large-scale pressure is similarly calculated except that an additional phase term is added 

to the cosine argument so that pressure and density are properly correlated. The large-scale temperature is then calculated from the Buell relation and rescaled so that it reproduces the observed 

variance. The large-scale horizontal wind components are also modeled with a cosine function 

and a phase shift is used for proper correlation. This correlation is taken from the RRA data or the 

NCEP data as appropriate. There is no model for large-scale vertical velocity, only small-scale values and mean (Montgomery stream function) values. Once the small- and large-scale perturbations 

are determined, they are added to the mean for the total atmospheric value.
30

2.8 Perturbation Model Initialization

Initial values for the perturbation model may be selected by user input, as described in the 

next section, or they may be random values, automatically selected by the program, as described 

here. Because large-scale perturbations (sec. 2.7.3) are wave-like and small-scale perturbations 

(sec. 2.7.1) are Gaussian-distributed random values, two different processes are used for their 

initialization.

2.8.1 Small-Scale Perturbations

Initial values for small-scale perturbations in all three components of wind and in density 

and pressure are selected randomly from Gaussian distributions having the appropriate standard 

deviation for each of these quantities (at the initial position to be simulated). The first-order perfect 

gas law from the initial small-scale pressure and density perturbations is then used to compute the 

initial small-scale temperature perturbation. This initial small-scale temperature perturbation is 

then rescaled so that it reproduces the appropriate small-scale temperature variance.

2.8.2 Large-Scale Perturbations

Initial values for large-scale perturbations are computed from a randomly selected-wave 

amplitude (AQ in eq. (48)) and a randomly selected phase for density perturbation (φq in eq. (48)). 

Phases for other large-scale perturbations are selected to produce appropriate phase differences 

among all the large-scale perturbations. Once these initial wave phase values have been selected 

for a particular program run, variations of wave phases progress in time and space according 

to prescribed wave numbers and period (n, m, and T in eq. (48)).

Initial density wave phase φq is randomly selected from a uniform distribution with values ranging between 0 and 2p. Wave phase for pressure is shifted by an amount required to yield 

appropriate pressure-density cross-correlation, and wave phase for large-scale perturbation in an 

eastward wind is shifted by an amount required to yield appropriate density-velocity correlation. 

Wave phase difference between northward and eastward wind components is selected to produce 

observed amount of cross-correlation (Ruv) between these components. Note that Ruv is observed 

cross-correlation between total (large- plus small-scale) perturbations. Required phase shift for the 

large-scale northward component is computed from Ruv/(0.02+0.98fL), where fL is the large-scale 

fractional variance (0–1) discussed in section 4.3.4.

The first-order perfect gas law is used to compute the initial large-scale temperature perturbation from the initial large-scale pressure and density perturbations. This initial large-scale temperature perturbation is then rescaled so that it reproduces the appropriate large-scale temperature 

variance. Finally, large-scale pressure perturbation is recomputed from the second-order perfect gas 

law.
31

2.9 Optional User-Selected Initial Perturbations

Like the previous version of GRAM, GRAM2010 allows, as a user-controlled option, the 

input of user-selected initial perturbation values. This option is controlled by the input parameter, 

initpert. When initpert=0 (the default value), then GRAM selects the random initial values. When 

initpert=1, the user selects values for the initial perturbations.

The following is an example application for user-selected initial perturbations.

Suppose a measured profile (e.g., a day-of-launch atmospheric sounding) is to be used as an 

actual (perturbed) profile to the highest measured altitude and a GRAM perturbed profile (or profiles) is desired for higher altitudes. Actual atmospheric values from a measured profile are used to 

compute perturbed values to initialize GRAM (by methods discussed more fully in the next paragraph). With these initial perturbation values, GRAM perturbed profile(s) for the higher altitude 

region have complete continuity with the measured profile from the lower altitude region.

In this example, suppose the measured profile extends to an altitude of 25 km. Also suppose 

the measured values at 25 km are density=0.044 kg/m3 and eastward wind=14 m/s (along with 

other measured values). To use the user-selected initial perturbation option, first perform a GRAM 

run starting at 25 km in this example with the same latitude, longitude, and month as the measured 

profile. Suppose this GRAM run gives a mean density of 0.04 kg/m3 and mean eastward wind 

of 20 m/s. The values of user-selected initial density and eastward wind perturbations to use 

in subsequent GRAM runs are as follows:

• Initial density perturbation (%)=100×(measured density –GRAM mean)/GRAM mean 

 =100×(0.044 –0.04)/0.04=10(%).

• Initial east-west wind perturbation (m/s)=measured eastward wind–GRAM mean eastward 

 wind=14 m/s–20 m/s=–6 m/s.

Similar calculations apply to the density, temperature, and other wind components. The 

pressure perturbation is calculated internally from the density and temperature pertubations.

For subsequent GRAM runs (in this example), start at 25 km using initpert=1, rdinit=10, 

and ruinit = –6 (and whatever values apply to the other initial perturbation components). These 

values ensure that the highest altitude (25 km) data point in the measured profile is consistent with 

the starting value (at 25 km) of the perturbed profile from GRAM. If multiple perturbed profiles 

are desired for a Monte Carlo application, each is initialized with the same values (rdinit=10, 

ruinit=–6, etc.).

2.10 Optional Range Reference Atmosphere Data

An option exists to use data (in the form of vertical profiles) from a set of RRA as an 

alternate to the usual GRAM climatology at a set of RRA site locations. With this feature for 

example, it is possible to simulate a flight profile that takes off from the location of one RRA site 
32

(e.g., EAFB, using the EAFB RRA atmospheric data) to smoothly transition into an atmosphere 

characterized by the GRAM climatology, then smoothly transition into an atmosphere characterized by a different RRA site (e.g., White Sands, NM) to be used as the landing site in the 

simulation.

RRA data include information on both monthly means and standard deviations of the 

various parameters at the RRA site (see description below). Under the RRA option, when a given 

trajectory point is sufficiently close to an RRA site (lat-lon radius from site less than sitenear, see 

below), the mean RRA data replace the mean values of the conventional GRAM climatology, and 

the RRA standard deviations replace the conventional GRAM standard deviations in the perturbation model computations. In Earth-GRAM 2007, a feature was introduced to replace GRAM 

surface data with surface data from the appropriate RRA site when the RRA option is used.

A total of 21 sites are available for 2006 RRA data (1983 RRA data available in EarthGRAM 2007 are no longer provided for Earth-GRAM 2010). After discovery of an error in 

standard deviations of pressure and density in RRA data from the Roosevelt Roads Puerto Rico 

site (code rrd), data from this RRA site are no longer included. The 2006 RRA data POR varies from site to site, but is generally 1990–2002. Exceptions are El Paso (1990–1995), Great Falls 

(1990–1994), Taguac (1990–1999), China Lake (1948–2000), and White Sands (1949–1993). El Paso 

RRA data (0–30 km) are augmented with White Sands rocket-sonde data from 30–70 km. White 

Sands RRA file includes only 0–30 km data. The user can also prepare (in the appropriate format 

as described below) data for any other site desired for use in the RRA mode. Another mode to 

use alternatives for the conventional GRAM climatology is the ‘Auxiliary Profile’ option. Auxiliary profiles also allow substitution of alternate data for both means and standard deviations. The 

format for preparing auxiliary profiles is much simpler than the required formatting for additional 

RRA data files (see app. B.9).

In addition to the RRA data files, a file called rras2006.txt is provided. This file gives filecode identifier, year, geodetic and geocentric latitude, longitude, surface altitude, maximum altitude, World Meteorological Organization (WMO) site number, and site name for each of 

the available 2006 RRA sites. The user may prepare alternate lists of RRA files if new sites or 

a different set of sites are desired. The RRA site list file to be used by Earth-GRAM 2010 for 

a specific program run is specified by input parameter rralist. Table 4 is a list of RRA site data.

Use of the RRA data option in Earth-GRAM 2010 is controlled by several input parameters: (1) rrapath gives the name of the directory containing the RRA data, (2) rralist gives the name 

of the file containing the list of RRA sites to be used, (3) iurra is the unit number to be used by 

the program for reading the RRA data, and (4) sitelim and sitenear control the size of the lat-lon 

region in the vicinity of any RRA site for which data from that RRA site is to be used (the RRA 

zone of influence). For any location having a radial distance (in lat-lon terms) of less than the 

value given by sitenear, the RRA data (with a full weight of 1) is used. For any location outside 

a lat-lon radius given by sitelim, the GRAM climatology data is used (i.e., a weight of 0 for the 

RRA data). Between radial distances of sitenear and sitelim, a weighted average of RRA and 

GRAM climatology data is used, ensuring a smooth transition from RRA data to GRAM data.
33

Table 4. List of RRA site data provided, file ‘rras2006.txt.’

Code Year GdLat GcLat Lon (E+) Hgt (m) Zmax WMO # Site Name

anf 2006 47.62 47.43 –52.73 140. 30. 718010 Argentia, Newfoundland (St. Johns Airport)

asc 2006 –7.93 –7.88 –14.42 79. 70. 619020 Ascension Island, Atlantic

bar 2006 21.98 21.85 –159.34 31. 30. 911650 Barking Sands, Hawaii (Lihue)

cap 2006 28.47 28.31 –80.55 3. 70. 747940 Cape Canaveral, Florida

chl 2006 35.68 35.50 –117.68 665. 30. 746120 China Lake Naval Air Weapons Center, CA

dug 2006 40.77 40.58 –111.97 1,288. 30. 725720 Dugway Proving Ground (Salt Lake City), UT

eaf 2006 34.92 34.74 –117.90 724. 30. 723810 Edwards Air Force Base, California

egl 2006 30.48 30.31 –86.52 20. 30. 722210 Eglin AFB, Florida

elp 2006 31.81 31.64 –106.38 1,199. 70. 722700 El Paso, Texas

fad 2006 64.80 64.65 –147.88 135. 30. 702610 Fairbanks, Alaska

fha 2006 32.12 31.95 –110.93 787. 30. 722740 Ft. Huachuca Elec Prvng Grnd (Tucson), AZ

gtf 2006 47.47 47.28 –111.38 1,118. 30. 727750 Great Falls, MT

kmr 2006 8.73 8.67 167.75 2. 70. 913660 Kwajalein Missile Range, Pacific

ncf 2006 43.87 43.68 4.40 62. 30. 076450 Nimes-Courbessac, France (STS TAL Site)

nel 2006 36.62 36.44 –116.02 1,007. 30. 723870 Nellis AFB, Nevada (Mercury)

ptu 2006 34.12 33.94 –119.12 2. 70. 723910 Point Mugu Naval Air Weapons Center, CA

tag 2006 13.55 13.46 144.85 78. 30. 912170 Taguac, Guam (Anderson AFB)

vaf 2006 34.75 34.57 –120.57 121. 30. 723930 Vandenberg AFB, California

wal 2006 37.85 37.66 –75.48 13. 30. 724020 Wallops Island, Virginia (NASA)

wsm 2006 32.38 32.21 –106.48 1,207. 30. 722690 White Sands Missile Range, New Mexico

ysd 2006 32.87 32.69 –117.14 134. 30. 722930 Yuma Proving Ground, AZ (San Diego, CA)

Notes: 

• Latitudes in the RRA data files are geodetic. In the rras2006.txt file, latitudes GdLat are geodetic and latitudes GcLat are geocentric. Earth-GRAM input 

latitudes are geocentric. Internally, Earth-GRAM works with geocentric RRA site latitudes if the RRA data option is used. The Earth-GRAM output file lists 

both geodetic and geocentric RRA site latitudes.

• For the Kwajalein Missile Range (kmr), data are available above 30 km for the annual mean case only. None of the individual months have sufficient data 

(number must be greater than 10) to be used, so all months have missing data codes (e.g., 99.99) between 30 and 70 km.

Nominal (default) values are sitenear=0.5° and sitelim=2.5°. For these values then, 

any lat-lon within a radius of 0.5° from any of the RRA sites will use data from that RRA site. 

Any location beyond a radius of 2.5° would use the GRAM data. Between 0.5° and 2.5° radius, 

a weighted average of RRA data and GRAM data would be used, with the RRA data weight 

smoothly changing from 1 at a radius of 0.5° to a weight of 0 at a radius of 2.5°.

Depending on the value of sitelim and the proximity of the various RRA sites used, it may 

be possible that a given trajectory location is in the vicinity of more than one RRA site (e.g., for 

locations near Point Mugu, EAFB, and Vandenberg AFB). If a given trajectory location could 

be influenced by more than one RRA site, only data from the nearest (highest weight) site is used. 

Note, that if in such a situation, the user desires to always use a specific RRA site (e.g., EAFB) 

and never use a nearby RRA site (e.g., Point Mugu), then the name and information for the 

undesired nearby RRA site should be removed from the file list, and the modified site list used 

as specified by input parameter rralist.
34

RRA data apply from 0 km to a maximum of 70 km (above MSL). There is also a smooth 

interpolation process used to transition from the RRA data to GRAM data as the top of the RRA 

data is approached. This transition takes place between the next-to-highest RRA altitude (where 

the RRA weight=1) and the highest RRA altitude (where the RRA weight becomes 0).

RRA date files for a given site consist of three data files: T1sssyy.txt, T2sssyy.txt, and 

T3sssyy.txt, where sss is the three-character site code from the list of sites given in table 4, and 

yy=06 for the 2006 RRA data. The RRA data files are in the format given in the series of RRA 

reports (e.g., see ref. 52). Files Txsssyy.txt correspond to table x (x=1–3) in the RRA reports.

Each Txsssyy.txt file contains an annual average data set and 12 monthly data sets. GRAM 

uses only the RRA data for the desired month, and the annual average data are always ignored 

on read-in. For 2006 RRA data, the annual average data must follow the 12 monthly data sets. 

Annual data preceded the 12 monthly data sets in the 1983 RRA data files (no longer used in 

Earth-GRAM2010). 

RRA table-1 data contain wind statistical parameters: Height, mean eastward wind, 

standard deviation of eastward wind, correlation between eastward and northward wind, mean 

northward wind, standard deviation of northward wind, mean wind speed, standard deviation of 

wind speed, skewness of wind speed(*), and number of observations(*). Asterisks denote parameters that are not used or output by GRAM, although any RRA data having fewer than 10 

observations are ignored by the RRA read routines.

RRA table-2 data contain thermodynamic statistical parameters: Height, mean pressure, 

standard deviation of pressure, skewness of pressure(*), mean temperature, standard deviation of 

temperature, skewness of temperature(*), mean density, standard deviation of density, skewness of 

density(*), number of pressure observations(*), number of temperature observations(*), and number of density observations(*). Asterisks denote parameters that are not used or output by GRAM, 

although any RRA data having fewer than 10 observations are ignored by the RRA read routines. 

RRA table-3 data contain moisture related statistical parameters: Height, mean vapor pressure, standard deviation of vapor pressure, skewness of vapor pressure(*), mean virtual temperature(*), standard deviation of virtual temperature(*), skewness of virtual temperature(*), mean 

dewpoint temperature, standard deviation of dewpoint temperature, skewness of dewpoint temperature(*), number of observations of vapor pressure and dewpoint temperature(*), and number 

of observations of virtual temperature(*). Asterisks denote parameters that are not used or output 

by GRAM. RRA table-4 data are not used in GRAM.

User-provided RRA data can also be used if the following conditions are adhered to. Each 

new RRA site must be entered into the ‘rralist’ file (maximum total number of sites allowed is 99). 

The site code can be any three-character code not already being used. Heights for any new RRA 

data must be in the range from 0 to altitude Zmax (km), as given in the ‘rralist’ file. Heights should 

be given in ascending order in the Txsssyy.txt files with 300 or fewer heights entered (height increments can be any value and fixed height increments do not have to be used). The first data line of 

each Txsssyy.txt may have descriptive information (such as site name). However, the first data line 
35

of each file MUST contain the site geodetic latitude and longitude. Latitude is given as xx.xxN. 

or xx.xxS.; longitude is given as xxx.xxE. or xxx.xxW., in format (17X,F5.2,A1,2X,F6.2,A1). 

Latitude and longitude values from the first data line are compared with the latitude and longitude 

in the ‘rralist’ file to ensure that the appropriate site data are being used. In the ‘rralist’ file, north 

latitudes are positive and south latitudes are negative, while east longitudes are positive and west 

longitudes are negative. Each file T1sssyy.txt or T2sssyy.txt must have five ‘header’ lines preceding 

each monthly set of data values. Each file T3sssyy.txt must have six ‘header’ lines preceding each 

monthly set of data values. Monthly data values for all 12 months must be provided. The data 

lines may be in free-field (list-directed) format but must contain a numerical value for each of the 

parameters expected, depending on the table type. Parameters not used by GRAM (those indicated 

by asterisks) may be input as zero values (except for number of observations, which can be any 

number greater than 10). Missing values (i.e., those that will be ignored) may be indicated by using 

99.99 or 999.99.

2.11 Speed of Sound Calculation

Many users have a need to determine the local speed of sound (cs) for determining the 

Mach number. To facilitate this, GRAM2010 performs the calculation and makes it available 

for output. The cs is computed from the total temperature (monthly mean temperature plus 

perturbations) TTot as,

c

s = γ c

RTTot , (52)

where γc is the ratio of specific heats of air at a constant pressure to air at a constant volume and is 

equal to 1.4 . Because the gas constant R can vary with molecular weight, it is calculated from the 

ideal gas equation of state based on monthly mean values (which vary with height),

R = p

ρT . (53)

Thus, in the GRAM code, cs (coded as csp) is computed as

cs = 1.4 p

ρ

TTot

T . (54)

If the user desires the monthly mean speed of sound cs (coded as csp0), then equation (54) 

becomes,

cs = 1.4 p

ρ . (55)
36

3. SAMPLE RESULTS

3.1 Large-Scale Perturbations

Figure 6 illustrates an example of the large-scale wave perturbation model. Amplitudes 

of the wave perturbations are randomly selected within reasonable bounds. Wavelengths are also 

established from a stochastic process in the GRAM code. Phase of the wave perturbation is initialized randomly from the starting random number seed. Thus, in a Monte Carlo run using various 

seed values, different phases of the wave perturbations are sampled. Height (km)

Large-Scale Wave Perturbations

80

70

60

50

40

30

20

10

0

–20 –10 0 10 20 30 40 50

Density (% of Mean)

Temperature (% of Mean)

EW Wind (m/s)

NS Wind (m/s)

Figure 6. Sample vertical profile of large-scale wave perturbations using 

a large-scale wave perturbation model output.

Because the amplitudes and wavelengths of the wave perturbations depend on altitude, 

the waves are not purely sinusoidal in shape. Generally, the amplitude and wavelength increase 

as the altitude increases. The model systematically controls relative phases of the various wave 

perturbations. Temperature and density wave perturbations tend to be roughly 180° out of phase.

3.2 Density Perturbations

The perturbation model provides a realistic dispersion set. Figure 7 shows the results of 

a 1,000 profile Monte Carlo run of density perturbation versus height at the KSC. Also shown are 

the 2- and 3-sigma envelopes. Evident from this plot is that the dispersions (driven by the standard 

deviations) reach a local maximum at jet stream altitudes (≈15 km) and then diminish before 

trending upward at higher altitudes. The significant number of 2-sigma exceedances and a few 

exceedances beyond 3 sigma are also apparent.
37

Height (km)

Density Pertubation (% of Mean)

80

70

60

50

40

30

20

10

0

–25 –20 –15 –10 –5 0 5 10 15 20 25

+3 Sigma

+2 Sigma

Density

–2 Sigma

–3 Sigma

Figure 7. A plot of a 1,000 profile Monte Carlo run of density perturbation (in percent

of the mean value) as a function of height. The 2- and 3-sigma envelopes are 

also shown.

3.3 Revised Boundary Layer Model for Vertical Velocity

As described in section 2.4, the calculation of standard deviation of the veritcal velocity 

(σw) has been modified from the previous GRAM. The σw increases with the horizontal wind, site 

elevation, surface roughness, and solar elevation. Once determined, σw is used to drive the perturbation model of the veritcal velocity. Figure 8 shows a global plot for a particular case in September at 00Z. Panel (a) of figure 8 shows a number of structures in the σw field (e.g., relatively higher 

values in the Rockies of the United States (U.S.), Canada, Iceland, Asia, parts of west central 

South America, Antarctica, and structures in the southern hemisphere ocean). A detailed explanation will not be presented here, but panel (b) shows a correlation of many of these features with the 

surface roughness. Furthermore, panel (c) suggests that the local elevation in these regions contributes to this roughness by grossly modeling the influence of mountainous regions. The wave structure of the southern hemisphere ocean, while of uniform elevation, correlates well with the wave 

structure of the horizontal wind shown in panel (d).
38

Latitude

Longitude

Hgt

50

0

–50

8

7.5

7

6.5

6

5.5

5

4.5

4

3.5

3

2.5

2

1.5

1

0.5

0

 –100 0 100

Latitude

(a) Longitude (b)

(c) (d)

σw

Zo

50

0

–50

5

4.5

4

3.5

3

2.5

2

1.5

1

0.5

0

 –100 0 100

Latitude

Longitude

Wind

50

0

–50

18

16

15

13.5

12

10.5

9

7.5

6

4.5

3

1.5

0

 –100 0 100

Latitude

Longitude

50

0

–50

2.8

2.6

2.4

2.3

2.1

1.9

1.7

1.5

1.3

1.1

0.9

0.9

0.6

0.4

0.2

 –100 0 100

Figure 8. An example realization of the global distribution of: (a) The standard deviation 

of the vertical velocity in m/s, (b) the surface roughness in m, (c) the surface 

elevation in km, and (d) the mean horizontal surface wind in m/s.

3.4 Range Reference Atmosphere Data Option

Section 2.10 describes the RRA data option for GRAM2010. A simplified example is illustrated in figures 9 and 10. For this example, a parabolic trajectory is assumed, with take-off from 

EAFB, flying to an apogee at 100-km altitude, followed by a landing at WSMR. Default values are 

used in this example. Hence, RRA values are used when the trajectory is within a lat-lon radius 

of 0.5 km from either of the RRA sites, GRAM climatology is used when the trajectory is beyond 

a lat-lon radius of 2.5° from either RRA site, and a smooth transition is assumed between RRA 

data and GRAM data between 0.5° and 2.5° lat-lon radius.

Figure 9 illustrates the temperature profile between takeoff and landing for a pure GRAM 

climatology trajectory (solid line) and the RRA/GRAM option (dotted line). Percentage differences between pure GRAM values and RRA/GRAM values of less than ±4% are shown in 

figure 10.
39

Temperature (K)

Longitude (Deg)

280

270

260

250

240

230

220

210

200

 –118 –116 –114 –112 –110 –108 –106

Gram Data

RRA Data

Parabolic Trajectory (Apogee = 100 km)

Takeoff = EAFB

Landing = WSMR

Figure 9. GRAM2010 (solid line) or RRA/GRAM2010 (dotted line) profiles 

of temperature along hypothetical parabolic trajectory between EAFB 

and WSMR with 100-km apogee.

Difference (% of mean)

Longitude (Deg)

4

3

2

1

0

–1

–2

–3

–4

 –118 –116 –114 –112 –110 –108 –106

Density

Temperature

Parabolic Trajectory (Apogee = 100 km, January POR)

Takeoff = EAFB

Landing = WSMR

Figure 10. Differences in density (solid line) and temperature (dotted line) between 

GRAM2010 and RRA/GRAM2010 values for the hypothetical trajectory 

used in figure 9.
40

4. GLOBAL REFERENCE ATMOSPHERIC MODEL 2010 USERS GUIDE

4.1 General Program Review

Like its predecessors, GRAM2010, is designed to produce atmospheric parameter values 

either along a linear path (a profile) or along any set of related time-position data (a trajectory). 

Based on user-selected input values, the program can step automatically in height, latitude, longitude, and time along any desired linear profile. For the trajectory evaluation option, times and 

positions are provided to the program as a separate input (trajectory) file. Optionally GRAM2010 

can also be incorporated as a subroutine in the users trajectory (or orbit propagation) code for 

evaluation along trajectory or orbital positions.

GRAM2010 uses two required input files and up to five other input files, depending on 

user-selected options. Required files are the NAMELIST-formatted input file (app. C) and ‘atmosdat’ file (sec. 4.3). An optional input file for the lower atmosphere (0 km to the 10 mb level) is the 

NCEP database (app. A). Optional RRA data input are described in section 2.10. Optional trajectory input file format is described in section 4.4. An optional auxiliary profile input is described in 

appendix B.9. Note that RRA data cannot be used if an auxiliary profile is being employed. For 

use in Monte-Carlo analysis, with a number of identical profiles or trajectories using different 

random number seeds, a file of such seed numbers is described in section 4.5.

Output of GRAM2010 consists of four files. For cases in which GRAM was incorporated 

as a subroutine in a user-provided trajectory code, an option exists to suppress all output from 

GRAM. The primary output file is the standard formatted output described in section 4.6.1 and 

appendix D.1. An optional species concentration output file (sec. 4.6.2 and app. D.2) can be produced. An optional special formatted output file (sec. 4.6.3 and app. D.3) is designed to make it 

easy for the user to select from a wide range of output variables and to output them in an easily modified format. Lastly, there is an optional BL file that provides information about specific 

parameters in this region (sec. 4.6.4 and app. D.4).

Path names for the input and output files (except the NAMELIST input file) are provided 

via input from the NAMELIST input file. Options selected in the NAMELIST input file determine 

which of the optional input and output files are actually used for a given program run.

4.2 Units, Coordinates, and Conventions

The coordinate system used by GRAM is that of geocentric latitude, longitude, and geocentric height above sea level for a reference ellipsoid. Note that the latitudes in the RRA files are 

geodetic and GRAM converts these internally to geocentric. The equatorial and polar Earth radii 

for the sea-level reference ellipsoid have been updated to World Geodetic System (WGS) 84 (WGS 

84) values. The equatorial radius used is 6,378.137 km and the polar radius is 6,356.752314 km. 

WGS 84 values are used by the Global Positioning System (GPS) navigation system. These are 
41

also equivalent (to 10 significant figures) to the Geodetic Reference System (GRS) 80 (GRS 80) 

values. In Earth-GRAM 2010, input values of altitude greater than 6,000 km are treated as geocentric radius values, rather than heights. Both radius and height are now given in the output file. 

Although all input latitudes are geocentric, GRAM now gives both geocentric and geodetic values 

in the output file. 

GRAM input and output uses the International Standard (SI) for units (i.e., metric). Users 

who desire nonstandard units must perform the conversions for their application. Time is measured 

in seconds except where noted in the input file that specifically requests year, hour, and minutes. 

Lengths are in km except as noted in the optional BL output file. Latitude and longitude are in 

degrees. Pressure is in N/m2 (pascals), density in kg/m3, and temperature in K. The u-component 

of wind is in m/s and is positive when blowing from west to east. The v-component is also in m/s 

and is positive when blowing from south to north. The w-component is in m/s and positive when 

blowing vertically upward. Relative humidity is in percent. Species concentrations that output as 

mole fraction (volume mixing ratio) are given in ppm while output as number density is given as 

number/m3. Additional details can be found in comments in the subroutine atmod_e10 within 

models_E10.f90.

4.3 The ‘atmosdat’ Input File

The ‘atmosdat’ file consists of several types of data in several formats easily readable 

as ASCII characters. The file requires a little more than 4 Mb of disk storage. 

4.3.1 Zonal-Mean Data 

The zonal-mean data consists of 12 monthly sets of zonal-mean values for pressure, density, temperature, and zonal wind tabulated at 10° latitude intervals from –90° to +90° and 5-km 

height increments from 20 km to 120 km. Prefix codes, ZP, ZD, ZT, and ZU indicate pressure, 

density, temperature, and zonal wind, respectively. Each record contains the code, month, height 

in km, and –90°, –80°, ..., 80°, 90° latitude values of the parameter expressed as a four-digit integer 

with an exponent common to all values in the field appearing at the end of the record. Thus, a 

value of 2,761 with an exponent at the end of the record of –6 would be the same as 2,761×10–6

or 2.761×10–3. Pressure data are in units of N/m2, density values kg/m3, temperatures in K, and 

zonal winds in m/s. The zonal-mean data set contains 1,008 Fortran readable records, the code, 

and 22 integer values in each record (format A2, I4, I5, 19I6, I4).

4.3.2 Stationary Perturbations 

The stationary perturbations are lat-lon dependent (relative perturbations) to be applied 

to the zonal-mean values. Data for each of 12 months are given for the northern and southern 

hemisphere latitudes. Prefix codes SP, SD, ST, SU, and SV indicate stationary perturbation values 

for pressure, density, temperature, zonal (eastward), or meridional (northward) wind components, 

respectively. Each record contains the code, month, height in km, latitude (–80° to +80°) and 18 

values of stationary perturbations in per mil (%/10) for thermodynamic variables, and 0.1 m/s for 

winds at longitudes of 180° W., 160° W., 140° W., ..., 140° E., and 160° E. The monthly mean value 

(ym) for parameter y (pressure, density, or temperature) at any latitude and longitude is computed 
42

from the zonal-mean value (zy) at the latitude and stationary perturbation (sy) (in per mil) at the 

latitude and longitude by the relation,

ym =zy(1+sy/1,000). (56)

For zonal (eastward) wind components, the monthly mean is um =zu+su/10, while meridional (northward) mean winds are equal to the stationary northward wind perturbation value (i.e., 

vm =sv /10), where su and sv are zonal and meridional stationary wind perturbations (in 0.1 m/s). 

Note that the 90° latitude stationary perturbation values are always 0. The stationary perturbation 

data consists of 15 300 Fortran readable records with a code and 21 integer values in each record 

(format A2, 21I5).

4.3.3 Random Perturbations 

Random perturbation magnitudes (standard deviations) are dependent only on latitude. 

Prefix codes RP, RD, RT, RU, and RV indicate random perturbation magnitudes in pressure, density, temperature, zonal (northward) wind, and meridional (eastward) wind components, respectively. Each random perturbation record has the code, month, and height in km, followed by 19 

values of random perturbation magnitude at 10° latitude increments from –90° to +90° followed 

by a common exponent value. These data give the relative standard deviations σp/p, σρ/r, and σT/T

(in %) for use in the random perturbation model. The code RU and RV data are similar, except the 

wind perturbations are absolute deviations in m/s and cover the height range 0 to 200 km, whereas 

the RP, RD, and RT data cover 20–200 km. Random perturbation magnitudes for 0 km to the 10 

mb level altitudes are provided by the NCEP database for both the thermodynamic and wind variables. The random perturbation data consist of 1,596 Fortran readable records with code and 22 

integer values in each record (format A2, I4, I5, 19I6, I4).

4.3.4 Large-Scale Fraction Data 

From daily difference analysis described in section 2 of reference 3, the fraction of the total 

variance (σ2 from the random perturbation data) contained in the large-scale perturbations was 

determined as a function of height and latitude. The ‘atmosdat’ file contains the annual average 

fraction (expressed as per mil) of total variance contained in the large scale. Large- and smallscale magnitudes (sL and σS) are computed from the fractional data (fL) in per mil (code PT for 

pressure, density, and temperature or code PW for winds), by the relations,

σ L = f

L ( / 1,000)

1 2

σT , (57)

and

σ S = 1− f

L ( ( / 1,000))

1 2

σ T , (58)

where σT is the total perturbation magnitude. The code PT and PW data sets contain 25 Fortran 

readable records with code word PT or PW, followed by 17 integer values in each record (format 

A2, 17I7) for code PT and 12 integer values (format A2, 12I7) for PW code records.
43

4.3.5 Density-Velocity Correlations 

Daily difference analysis was also used to evaluate the cross-correlations for use in the velocity perturbation model described in section 2 of reference 6 and in references 3 and 4. Both largescale and small-scale values of the density-velocity correlations were evaluated and are given in the 

‘atmosdat’ database (codes CL and CS) in per mil (i.e., divide by 1,000 to get correlations in the 

range –1 to +1). The code CL and CS data consist of 50 Fortran readable records with code word 

CL or CS followed by 12 integer values in each record (format A2, 12I7).

All foregoing data values in the ‘atmosdat’ database are ingested into the GRAM program 

through the subroutine setup in the initial_E10.f90 file.

4.3.6 Variable-Scale Random Perturbation Model Data 

Variable-scale random perturbation model data appear next in the ‘atmosdat’ database. 

They consist of 29 Fortran readable records containing a code RS and 10 real (floating-point) 

values each (1 height and 9 associated parameters (sec. 2.6)), which are ingested into the GRAM 

program through the subroutine scalinit found in the initial_E10.f90 file. See page 12 of reference 6 

for a description of these parameters. The format is A2, F5.0, 2F7.1, F7.2, F7.1, 5F7.2.

4.3.7 Langley Research Center Data 

The next segment of data in the ‘atmosdat’ database is the NASA LaRC concentration 

data for the atmospheric constituent H2O.12 The data consist of 4 groups of 35 Fortran readable 

records of a code and 9 data values each (1 height and 8 associated array values at latitudes –70°

through +70°) and are ingested into the GRAM program through the subroutine concinit in the 

speconc_E10.f90 file. The four record groups present seasonal data at latitudes –70° through +70°

for heights 6.5 through 40.5 km. Codes are LDJF for December-January-February, LMAM for 

March-April-May, LJJA for June-July-August, and LSON for September-October-November.

4.3.8 Air Force Geophysics Lab Data 

The next segment of data in the ‘atmosdat’ database is the AFGL concentration data for 

the atmospheric constituents H2O, O3, N2O, CO, and CH4.

11 The data consist of 5 groups of 50 

Fortran readable records of 6 values each (1 height and 5 associated array values for each of the 5 

constituents) and are ingested into the GRAM program through the subroutine concinit. The five 

record groups present tropical (Air Force Tropical (AFTR)), midlatitude summer (Air Force Midlatitude Summer (AFMS)), midlatitude winter (Air Force Midlatitude Winter (AFMW)), subarctic 

summer (Air Force Subarctic Summer (AFSS)), and subarctic winter (Air Force Subarctic Winter 

(AFSW)) data. Tropical data are for latitudes of ±15°, midlatitude data are for ±45°, and subarctic 

data are for ±60°. As necessary, a 6-month displacement is used to estimate southern hemisphere 

values from northern hemisphere values.
44

4.3.9 Middle Atmosphere Program Data 

The next-to-last segment of data in the ‘atmosdat’ database is the MAP concentration data 

for the years 1979–1983.13 The code O3 data are for O3 at 24 pressure levels (0.003–20 mb) for 12 

months. Each of the 288 records consists of the code, month, pressure level (mb), and data values 

for 17 latitudes (–80° to +80°) and a common exponent value. The code H2O data are for H2O at 

11 pressure levels (1.5 to 100 mb) for 12 months, followed by 8 annual values (denoted by month 

13) for the pressure levels 0.01–1 mb. There are a total of 140 H2O records. Each record contains 

the code, month, pressure level (mb), and five mean values at latitudes –60°, –45°, ±15°, +45° and 

+60° (with –60° estimated by 6-month displacement of +60° data), followed by five standard deviation values at these latitudes. The code N2O data are for MAP N2O (code CH4 data for CH4). 

The N2O and CH4 data consist of 204 records each. Each record contains the code, month (1–12), 

pressure level (17 levels, 0.1–20 mb), data at 15 latitudes (–70° to +70°) and a common exponent. 

The code OX data is for atomic oxygen (O) at 19 altitudes (130–40 km) for each month. There are 

228 total records, each containing the code, month, height (km), data values at 17 latitudes (–80°

to +80°), and a common exponent. Units of the MAP code OX data are atoms/cm3. The MAP 

code O3, H2O, and CH4 species data values are volume concentrations in units of ppmv while 

the code N2O data are in ppbv.

4.3.10 Topographic and Land Code Data

The last group of data in the ‘atmosdat’ data file contains global information used for the 

BL model. The first column and second column contain longitude and latitude, respectively, in 

degrees. The third column is the land code as shown in table 1 of section 2.4. The fourth column 

is the elevation of the surface in meters above sea level.

4.4 The Trajectory Input File

The trajectory file is required only when a trajectory rather than an automatically determined profile is desired. The file may contain an unlimited number of individual list-directed (freefield) records (i.e., lines) consisting of four real values: Time (real seconds), height (km), latitude 

(±90°, with southern latitudes being negative), and longitude (±360°, with west longitudes being 

negative). Using the values in the first record of the trajectory file, the program evaluates the atmospheric parameters and continues looping back to read a new trajectory position until a position 

below the surface (height <0) or the end of the file is reached.

4.5 Random Number Seed Input File

If a number of Monte-Carlo simulations are to be computed in one program run, subsequent starting random number seed values are input via a special optional input file. The file 

contains one random seed number per line. Each random number seed value is an integer, ranging 

from 1 to 900,000,000. Random seed values do not have to be randomly generated numbers, but 

values should not repeat in the list. Thus, any convenient sequence of consecutive integers may 

serve as valid random seed values.
45

4.6 Output Data Files

4.6.1 The Standard Formatted Output File 

The standard output file (example in app. D.1) has header information consisting of the 

principal input data values and the Julian date required by the thermosphere section of the 

program, and it is calculated internally by the program. Positions and times, generated by the 

automatic linear profile feature or as input by the trajectory input data, are listed on the output 

with the associated calculated values of the atmospheric variables. If a latitude greater than 90°

in absolute magnitude is generated (or input), the following transformation is made, 

lat = (180° − lat )(lat lat ) , (59)

and

lon = lon − 180° . (60)

All longitudes are converted to the range –180° to +180° before being output. The ‘mean’ 

line shows the current height above the reference ellipsoid (i.e., sea level), geocentric latitude, and 

the longitude.

The ‘mean’ line also provides values of pressure, density, temperature, and wind components 

consisting of one of the following:

(1) Values calculated from the NCEP database input if the height is 20 km or below.

(2) The sum of middle atmosphere zonal-mean plus stationary perturbation values if the 

height is between the 10-mb pressure level and 90 km.

(3) A value faired between the NCEP data and zonal-mean plus stationary perturbations 

if the height is between 20-km and the 10-mb level.

(4) Thermosphere model values if the height is above 120 km. 

(5) Faired values between middle atmosphere and the thermosphere model values if the 

height is between 90 and 120 km.

Standard atmosphere values computed by the subroutine stdatm in the gramsubs_E10.f90 

file are used to evaluate the percent deviations from the 1976 U.S. Standard Atmosphere on the 

‘M-76’ line. The percent deviations are evaluated by the relations 100(T–Ts)/Ts, 100(r–rs)/rs, and 

100(p – ps)/ps, where the subscript s refers to the U.S. Standard Atmosphere values. This subroutine 

accurately reproduces the tabulated 1976 U.S. Standard Atmosphere values within an accuracy 

of better than 0.2% above 90 km and even more accurately in the height region below 90 km, 

where the molecular weight is constant. Since the 1976 U.S. Standard Atmosphere is not defined 

above 1,000 km, the percent deviations output for heights above 1,000 km are 0. Because the 
46

thermosphere models are sensitive to solar activity conditions, large deviations from U.S. Standard 

Atmosphere values can be produced in this height range for certain ranges of F10.7 and ap values. 

The ‘M-76’ line also gives the current radius from the Earth’s center and the geodetic latitude.

The values on the ‘ranS,’ ‘ranL,’ and ‘ranT’ lines are the small-scale, large-scale, and total 

random perturbations evaluated at the output time and place. The values on the ‘sigS,’ ‘sigL,’ and 

‘sigT’ lines are standard deviations of the small-scale, large-scale, and total random components 

at the output time and place. According to the Gaussian distribution on which the random perturbations are based, the perturbation values should be within the range ±s 68 % of the time and 

outside the range ±s 32 % of the time. Similarly, the perturbation values should be within the range 

±2s 95 % of the time and outside the range ±2s 5 %. The values of the foregoing parameters are 

derived from the variable-scale perturbation model discussed in section 2.7. Also on the ‘ranS’ line 

is the elapsed time and an identifier denoting what data source was used. If GRAM climatology 

was used, ‘GRM’ will appear in that slot. If an RRA site was used, the site identifier will be shown, 

such as ‘cap06’ to indicate KSC 2006 RRA. On the other hand, ‘profl’ will appear if an auxiliary 

profile was used. The weight also appears on this line indicating how much of the RRA or 

auxiliary profile is used.

The parameter values output on the ‘Tot.’ line are the mean values defined above plus the 

random and wave model perturbations. These mean-plus-perturbation values represent typical 

‘instantaneous’ evaluations of the pressure, density, temperature, and winds. The percent deviations 

from the U.S. Standard Atmosphere on the ‘T-76’ line are computed in the same way as the percent 

deviations of the monthly mean values from the U.S. Standard Atmosphere.

Values on the ‘H2O’ line are the mean H2O values expressed as vapor pressure (N/m2), 

vapor density (kg/m3), dewpoint temperature (K), and RH (%). Mean H2O values are computed 

from the NCEP, LaRC, MAP, or AFGL data according to altitude. Fairing is used for a smooth 

transition between these data sources. Values on the ‘sigH’ line are standard deviations in H2O in 

the same units as the mean H2O values.

New for GRAM2010 is a table showing the correlation between the horizontal wind 

components (Ruv), the average wind speed (SpdAv), the standard deviation of the wind speed 

(SpdSd), the monthly average speed of sound (SoSav), and the speed of sound for the perturbed 

environment (SoSpt).

4.6.2 The Species Concentration Output File 

The species concentration output file (example in app. D.2) is also optional and controlled 

similarly to the special format output file by the value of an input parameter iuc and the pathname 

parameter conpath. 

4.6.3 The ‘Special’ Format Output File 

The ‘special’ output file is optional and is controlled by the input value of the iopp parameter switch and special output file pathname nprpath (app. D.3). As incorporated in the standard 
47

distributed code, this output file is configured at two separate locations. The file’s header definition is found in the init subroutine of the initial_E10.f90 file in the section near line number 

INIT603, while the file’s parameter output definition is found in the atmod subroutine of 

the models_E10.f90 file in the section near line ATMD880. The code at both locations may 

be modified to fit the requirements of the user.

As a further aid to the user in constructing special output files, appendix E gives tables listing the standard variables available for output. The tables are also given in the code in the atmod 

subroutine of the models_E10.f90 file near line ATMD779.

4.6.4 The ‘BLTest.txt’ Output File

The ‘BLTest.text’ output file is optional and controlled by the input parameter ibltest. It lists 

the parameters used to compute σw in the BL model. A description of the output parameters is 

provided in table 5.

Table 5. Boundary layer output parameters.

Header Description

Day: Day of month (including fractional part)

LST: Local solar time (hours)

Hgt: Height above MSL (MSL, km)

Lat: Geocentric latitude (degrees)

Lon: East longitude (degrees)

hsrf: Surface height (MSL, km)

spdsrf: Surface (10 m) wind speed (from mean-plus-large-scale-perturbation, m/s)

LC: Land surface type code (see table 1, section 2.4.1)

z0: Surface roughness length (m) 

Elmn: Solar elevation at midnight (degrees)

El: Current solar elevation angle (degrees)

Elmd: Solar elevation at midday (degrees)

sha: Current solar hour angle (degrees)

blfct: Height factor for unstable BL during early daytime (unitless)

nri: Net radiation index (unitless), for stability calculation

S: Atmospheric stability category (unitless)

ool: Inverse of Monin-Obukhov scale length (1/m)

ustar: Surface friction velocity (u*, m/s)

BVfsq: Square of Brunt-Vaisala frequency (s–2)

hN: Depth of neutral boundary layer (m)

hbl: Current depth of boundary layer (m)

chb: Current height above surface (m) or height to top of boundary layer 

(for evaluating height variation of standard deviation of vertical wind)

sigrat: Ratio of sigma-w to ustar at current height

swb: Vertical wind standard deviation at top of boundary layer (m/s)
48

Header Description

swh: Current standard deviation of vertical winds (m/s)

spdavsrf: Monthly average wind speed at surface (10 m) (m/s)

spdsdsrf: Standard deviation of surface wind speed (m/s)

tsrf: Monthly average surface temperature (K)

stsrf: Standard deviation of surface temperature (K)

4.7 Description of Program Files and Subroutines

There are 14 source code files for the basic GRAM2010 program (Cfiles_E10_C.f90, gram_

E10.f90, gramsubs_E10.f90, HWMsubs_E10.f90, Ifile_E10_I.f90, initial_E10.f90, JB2008_E10.

f90, MET07prg_E10.f90, models_E10.f90, MSISsubs_E10.f90, NCEPsubs_E10.f90, random_E10.

f90, rramods_E10.f90, and speconc_E10.f90). In addition to these programs required to run 

GRAM2010, there are a number of utility codes that accompany the software. Brief descriptions 

of these GRAM2010 program source code files and auxiliary source code files are:

Cfiles_E10_C.f90 Module file for all common block variables.

gram_E10.f90 Main Earth-GRAM 2010 program.

gramsubs_E10.f90 General Earth-GRAM 2010 subroutines.

HWMsubs_E10.f90 Harmonic Wind Model (used with MSIS thermosphere model).

Ifile_E10_I.f90 Interface module file for all subroutines.

initial_E10.f90 Reads atmosdat file and initializes data.

JB2008_E10.f90 Jacchia-Bowman 2008 model.

MET07prg_E10.f90 The Marshall Engineering Thermosphere (MET-07) model.

models_E10.f90 Other Earth-GRAM 2010 subroutines, not in gramsubs.

MSISsubs_E10.f90 Naval Research Labs MSIS (00) thermosphere model.

NCEPsubs_E10.f90 Reads and prepares NCEP climatology data.

random_E10.f90 Random number generators.

rramods_E10.f90 Reads the Range Reference Atmosphere (RRA) data.

speconc_E10.f90 Species concentration subroutines.

trajcalc_E10.f90 Subroutines used in trajectory demonstration programs.

gramtraj_E10.f90 Subroutine for use in user-provided trajectory program.

trajdemo_E10.f90 Main driver (replaces gram_E10.f90) in simple trajectory demonstration 

program.

trajopts_E10.f90 Main driver (replaces gram_E10.f90) in example trajectory program that 

demonstrates several special options.

multtraj_E10.f90 Main driver (replaces gram_E10.f90) program illustrating how to call 

Earth-GRAM 2010 to evaluate several different (multiple) trajectories in 

one program run.

corrtraj_E10.f90 Main driver (replaces gram_E10.f90) program illustrating how to call 

Earth-GRAM 2010 to evaluate multiple profiles in one program run, with 

small-scale and large-scale correlations preserved between the profiles.

Table 5. Boundary layer output parameters (continued).
49

multbody_E10.f90 Main driver illustrating how to call GRAM to evaluate perturbations 

along trajectories of multiple bodies which start out together and at various times separate from each other. The perturbations for each body start 

out the same, and then remain correlated over both position and time 

along the body trajectories, and across the spatial separation between the 

bodies.

4.8 Setup of Global Reference Atmospheric Model 2010 

Before running GRAM10, all files must be available in the proper configuration and location. Following is a discussion of how to set up the files. The first example is for a PC and the 

second is for a UNIX system.

4.8.1 Manual Setup on a Personal Computer

The following example of manual setup on a PC assumes that the user wants to set up 

Earth-GRAM 2010 in a directory called EarthGRAM2010 on the C: drive. The distribution DVD 

is assumed to be on the E: drive. This example is as follows:

(1) Copy the E:\AuxProfiles folder to C:\EarthGRAM2010\AuxProfiles.

(2) Copy the E:\DOCUMENTATION folder to C:\EarthGRAM2010\

DOCUMENTATION.

(3) Copy the E:\GRAM_code folder to C:\EarthGRAM2010\GRAM_code.

(4) Copy the E:\NCEPdata folder to C:\EarthGRAM2010\NCEPdata.

(5) Copy the E:\PC_Executables folder to C:\EarthGRAM2010\PC_Executables.

(6) Copy the E:\IOfiles folder to C:\EarthGRAM2010\PC_IOfiles.

(7) Copy the E:\RRAdata folder to C:\EarthGRAM2010\RRAdata.

(8) Copy the E:\Utilities_Code folder to C:\EarthGRAM2010\Utilities_Code.

In Windows Explorer, all of these operations can be done at one time by creating a folder C:\

EarthGRAM2010 then highlighting all folders on the E: drive (AuxProfiles, DOCUMENTATION, 

GRAM_code, NCEPdata, PC_Executables, IOfiles, RRAdata, and Utilities_Code), then dragging 

and dropping these folders to folder C:\EarthGRAM2010.

Note: Personal computer executable files are provided. Unless the user wishes to make 

code changes (e.g., to modify the ‘special-formatted’ output), it is not necessary to compile the 

GRAM code. The user can run the executable program gram_E10.exe located in the subdirectory 

PC_Executables. The program will then prompt the user for the Namelist input file. This input file 
50

gives GRAM the instructions for the type of run and the location of files that it needs. Details of 

the input file can be found in appendix C. If the user wants to edit the source code, then GRAM 

must be compiled and linked. A description of the source code can be found in section 4.7. Details 

about compiling GRAM can be found in appendix B. See appendix F for integrating GRAM into 

another program.

If the user makes changes to GRAM, it is recommended that the output be compared to 

output from the provided program gram_E10.exe. For example, the user should run the example 

input file NameRef.txt located in the subdirectory IOfiles and ensure that files generated are the 

same as output files OutputRef.txt, SpecialRef.txt, and SpeciesRef.txt located in the same folder. 

Alternatively, the user could take an input file and run it in gram_E10.exe to compare with its 

output. Lastly, if the user has imbedded GRAM into a trajectory program, the user could create 

a trajectory file (see app. B.7) and run that in gram_E10.exe to compare outputs. More details 

about testing can be found in appendix B.6.

Note: NCEP binary data files are provided. These should work as-is with the PC executable 

programs provided. If the user changes any of the source code provided and recompile, then it 

is possible that the user may need to rebuild the NCEP binary files from the NCEP ASCII files 

provided. In that case, proceed as follows:

(1) Copy the E:\EarthGRAM2010\NCEPdata\ASCIIdata folder-to-folder C:\EarthGRAM2010\NCEPdata\ASCIIdata.

(2) Compile and run utility program NCEPbinF.f90 to generate binary format NCEP 

data file.

4.8.2 Manual Setup on a UNIX Platform

If the user has access to a UNIX machine with a DVD drive called /DVDROM for example, 

then a setup procedure similar to that for PC installation, given above, can be used. Note that 

source code and other text files may still have PC end-of-line markers rather than UNIX end-ofline markers when copied directly from the DVD. The following assumes that the user wants to set 

up Earth-GRAM 2010 in a directory /usr/EarthGRAM2010 on the UNIX machine:

(1) Copy the /DVDROM/AuxProfiles folder to /usr/EarthGRAM2010/AuxProfiles.

(2) Copy the /DVDROM/DOCUMENTATION folder to /usr/EarthGRAM2010/

DOCUMENTATION.

(3) Copy the /DVDROM/GRAM_code folder to /usr/EarthGRAM2010/GRAM_code.

(4) Copy the /DVDROM/NCEPdata/ASCIIdata folder to folder /usr/EarthGRAM2010/

NCEPdata/ASCIIdata; Compile and run utility program NCEPbinF.f90 to generate binary format 

NCEP data file. See further details in README4.txt and README8.txt.
51

(5) Copy the /DVDROM/RRAdata folder to /usr/EarthGRAM2010/RRAdata.

(6) Copy the /DVDROM/IOfiles folder to /usr/EarthGRAM2010/UNIX_IOfiles.

(7) Copy the /DVDROM/Utilities_Code folder to /usr/EarthGRAM2010/Utilities_Code.

Note: UNIX executable files are not provided. Executable files must be compiled on UNIX

platforms. Details for this procedure can be found in appendix B. For setup on UNIX machines for 

which a DVD drive is not easily accessible, the distribution DVD may be loaded on a PC, and File 

Transfer Protocol (FTP) software may be used to transfer files, rather than using the copy commands as outlined above. If files are transferred to a UNIX platform from a PC platform by using 

ASCII-mode FTP, conversion of end-of-line markers is handled automatically.

4.8.3 Setup on Other Platforms

MSFC Natural Environments Group does not have adequate resources to provide program 

versions and installation setups for all possible user platforms. Hopefully, the guidance provided 

above will be adequate to allow users to set up Earth-GRAM 2010 on whatever platform they 

desire to use. For example, the setup process on a Linux machine would be similar to that on 

a UNIX platform.
52
APPENDIX A—NATIONAL CENTERS FOR ENVIRONMENTAL PREDICTION 

REANALYSIS PROJECT CLIMATOLOGY DATA 

(Adapted from NCEP/NCAR Reanalysis Data Archive Description Version Revised: 26 

September 2003) 

A.1 General Description 

A subset of the full NCEP data is available from ARL in a format suitable for many 

applications, by selecting "Reanalysis" in the meteorological data set selection pull-down menu. 

 Data Period Availability: 1948 ==> 2008 

The directory contains data files with the following syntax: 

R{S|P}{YEAR}{MONTH}.{gbl|tbd} 

where R indicates "Reanalysis," S or P indicates that the data are on Sigma or Pressure surfaces, 

YEAR is a four digit year, and MONTH is a two digit month. The "RP" (pressure level data) is 

used in Earth-GRAM 2010. The file suffix identifies the projection as either the 2.5 degree 

global latitude -longitude projection (gbl, as used in Earth-GRAM 2010), or a regional conformal 

map projection. 

The sigma level data were obtained from NCEP's internal spectral coefficient archive, 

and are not used by Earth-GRAM 2010. The pressure level data were obtained from the NOAACIRES Climate Diagnostics Center, Boulder, Colorado, USA. 

A.2 Additional Data Set Details 

 A.2.1 Pressure Level Data 

2.5 degree latitude-longitude global grid 

144 X 73 points from 90N-90S, 0E-357.5E 

1/1/1948 - present with output every 6 hours 

Levels (hPa): 1000, 925, 850, 700, 600, 500, 400, 300, 250, 200, 150, 100, 70, 50, 30, 20, 10 

Surface or near the surface (.995 sigma level) winds and temperature 

Precipitation 

Model Type: LAT-LON

Vert Coord: 2 

Numb X pt: 144 

Numb Y pt: 73 

Numb Levels: 18 

53
Sfc Variables: 5 PRSS T02M U10M V10M TPP6 

Upper Levels: 6 HGTS TEMP UWND VWND WWND RELH 

A.2.2 Example Header 

92 1 1 0 0 099INDX 0 .0000000E+00 .0000000E+00CDC1 0 0 90.00 357.50 2.50 2.50

.00 .00 .00 1.00 1.00 -90.00 .00 .00144 73 18 2 996.00000 5PRSS199 T02M232

U10M 77 V10M176 TPP6195 1000.0 6HGTS 60 TEMP183 UWND212 VWND 49 WWND 42 RELH149 925.00 6HGTS

16 TEMP110 UWND215 VWND 88 WWND131 RELH 3 850.00 6HGTS247 TEMP185 UWND234 VWND100 WWND182 

RELH 52 700.00 6HGTS161 TEMP 20 UWND123 VWND 72 WWND187 RELH 96 600.00 6HGTS152 TEMP 60 

UWND211 VWND148 WWND137 RELH 38 500.00 6HGTS136 TEMP193 UWND144 VWND 99 WWND130 RELH161

400.00 6HGTS107 TEMP212 UWND159 VWND117 WWND136 RELH139 300.00 6HGTS 80 TEMP127 UWND131

VWND 6 WWND198 RELH255 250.00 5HGTS 25 TEMP 66 UWND101 VWND247 WWND 57 200.00 5HGTS188

TEMP153 UWND169 VWND 92 WWND 23 150.00 5HGTS 86 TEMP 3 UWND133 VWND 98 WWND149 100.00

5HGTS201 TEMP 71 UWND135 VWND136 WWND 12 70.000 4HGTS 46 TEMP 82 UWND153 VWND208 50.000 

4HGTS122 TEMP 4 UWND230 VWND162 30.000 4HGTS 20 TEMP132 UWND117 VWND211 20.000 4HGTS 37 

TEMP119 UWND212 VWND165 10.000 4HGTS108 TEMP157 UWND101 VWND159

A.2.3 Data Packing Format 

NCEP typically saves their model output in GRIB format. However, at ARL the data are 

reprocessed and stored in a 1-byte packing algorithm. This 1-byte packing is a bit more compact 

than GRIB and can be directly used on a variety of computing platforms with direct access I/O. 

The data array is packed and stored into one byte characters. To preserve as much data precision 

as possible the difference between the values at grid points is saved and packed rather than the 

actual values. The grid is then reconstructed by adding the differences between grid values 

starting with the first value, which is stored in unpacked ASCII form in the header record. To 

illustrate the process, assume that a grid of real data, R, of dimensions i,j is given by the below 

example. 

 1,j 2,j .... i-1,j i,j

 1,j-1 2,j-1 .... i-1,j-1 i,j-1 

 .... .... .... .... ....

 1,2 2,2 .... i-1,2 i,2

 1,1 2,1 .... i-1,1 i,1

The packed value, P, is then given by 

 Pi,j = (Ri,j - Ri-1,j)* (2**(7-N)),

where the scaling exponent 

 N = ln dRmax / ln 2 .

The value of dRmax is the maximum difference between any two adjacent grid points for the 

entire array. It is computed from the differences along each i index holding j constant. The 

54
difference at index (1,j) is computed from index (1,j-1), and at 1,1 the difference is always zero. 

The packed values are one byte unsigned integers, where values from 0 to 126 represent -127 

to -1, 127 represents zero, and values of 128 to 254 represent 1 to 127. Each record length is then 

equal in bytes to the number of array elements plus 50 bytes for the header label information. 

The 50 byte label field precedes each packed data field and contains the following ASCII data: 

Field Format Description 

Year I2 Greenwich date for which data valid 

Month I2 " 

Day I2 " 

Hour I2 " 

Forecast* I2 Hours forecast, zero for analysis 

Level I2 Level from the surface up 

Grid I2 Grid identification 

Variable A4 Variable label 

Exponent I4 Scaling exponent needed for unpacking 

Precision E14.7 Precision of unpacked data 

Value 1,1 E14.7 Unpacked data value at grid point 1,1 

*Forecast hour is -1 for missing data. 

Example: 2 1 1 0 0 099PRSS 8 .1007874E+01 .6867000E+03 

ARL provides a Fortran-90 program that can be used to unpack and read the first few elements 

of the data array for each record of an ARL packed meteorological file. This file, called 

CHK_DATA.F, was adapted for reading and processing the ARL data files for use in EarthGRAM 2010. Additional information can be found in Kalnay et al.15

A.2.4 NCEP Data in Earth-GRAM 2010 

 

NCEP climatology is provided in ASCII format in folder NCEPdata\FixedASCII. Files 

for each month are named Nfy1y2mm.txt, where the period of record (POR) covers years y1 

through y2 (e.g. 9008 is for POR 1990 through 2008), and month is mm. Surface and nearsurface NCEP data in these files have been adjusted according to procedures described in file 

NCEPmods.pdf, in the DOCUMENTATION folder, and in Section 2.3.4, above. ASCII data in 

these files have been prepared in a compact format, with decimals removed, and some spaces 

removed. An example file header and first few data lines is given by: 

h L J I N Hav Hsd Uav Us Vav Vs Tav Ts Dav Dsn RHaRHs TdaTds eTa eTsn Sav Ss Ruv

1 1 1 1 589 6828 56 12 27 -20 302467 3696401321 4572742355107357627202 42 21 12

1 2 1 1 589 16 597 8 23 -30 262656 381310 190 7451692615 51270910241 42 20 -89

1 3 1 1 589 6111 573 7 23 -29 262617 371231 180 7451692576 501989 7611 41 19 -91

1 4 1 1 589 12621 562 7 22 -29 262576 371149 160 7451692538 491439 5571 41 19 -80

1 5 1 1 589 27172 591 14 25 -32 282483 3398181311 7451692448 46645624912 46 22-137

1 6 1 1 589 38380 651 22 42 -29 442455 278512 951 4562732344 96295619212 62 33-230

1 7 1 1 589 51290 745 10 48 -19 512381 287314 861 4392272282 761417 8292 65 35-240

1 8 1 1 589 66535 869 6 58 3 632286 256097 661 3352162164 84418830893 75 42-265

1 9 1 1 589 85419 967 1 65 25 692220 214708 441 941321996 67533373864 84 50-314

55
110 1 1 589 97290 952 -3 61 33 642232 303903 531 861182003 62535966994 81 50-350

111 1 1 589111984 932 -7 53 38 572264 333078 451 791042025 62721790274 73 45-326

112 1 1 589131199 962 -8 44 37 482291 262281 261 72 902042 59 87310453 65 37-244

113 1 1 589158571 1021 -8 34 32 432320 171502 111 64 762061 54105511593 55 32-182

114 1 1 589182933 1012 -11 31 29 392343 151041 71 57 622074 49119711983 51 30-180

115 1 1 589206107 978 -11 28 28 332359 177383 542 50 472082 44126411293 45 27-128

116 1 1 589241563 948 -11 25 20 292384 214383 392 43 332096 38142310613 38 23 -38

117 1 1 589270016 990 -13 24 13 262409 222892 262 37 202107 301557 8273 35 20 -6 

118 1 1 589319695 1189 -9 24 21 242500 211392 122 31 202166 183065 7283 36 19 -12

where 

 h = UT hour of day: 1=00 UT, 2=06UT, 3=12UT, 4=18UT. Statistics for all 

 hours of day combined (h=5) are added in the conversion from ASCII 

 format to binary format, by utility program NCEPbinF.f90. 

 L = Pressure levels 1-18. In mb, these are surface,1000,925,850,700,600, 

 500,400,300,250,200,150,100,70,50,30,20, and 10. Data for sea-level 

 are computed in the conversion from ASCII format to binary format, 

 by utility program NCEPbinF.f90. 

 J = Latitude index (1-73) 

 I = East longitude index (1-144). 

 N = Number of data in the period of record (e.g. if there are no missing 

 data, POR 1990-2008 has 589 values for a 31-day month) 

 Hav = Monthly average geopotential altitude for given UT hour (m times 10). 

 For level 1, Hav is average surface pressure (mb times 10) 

 Hsd = Standard deviation for geopotential altitude (m times 10). For level 

 1, Hsd is standard deviation of surface pressure (mb times 10) 

 Uav = Monthly average Eastward wind for given UT hour (m/s times 10) 

 Us = Standard deviation for Eastward wind (m/s times 10) 

 Vav = Monthly average Northward wind for given UT hour (m/s times 10) 

 Vs = Standard deviation for Northward wind (m/s times 10) 

 Tav = Monthly average temperature for given UT hour (K times 10) 

 Ts = Standard deviation for temperature (K times 10) 

 Dav = Monthly average density for given UT hour 

 Ds = Standard deviation for density 

 n = Density exponent. Densities in kg/m**3 are given by Dav*10**(-(3+n)) 

 and Ds*10**(-(3+n)) 

 RHa = Monthly average relative humidity for given UT hour (percent times 10) 

 RHs = Standard deviation for relative humidity (percent times 10) 

 Tda = Monthly average dewpoint temperature for given UT hour (K times 10) 

 Tds = Standard deviation for dewpoint temperature (K times 10) 

 eTa = Monthly average vapor pressure for given UT hour 

 eTs = Standard deviation for vapor pressure 

 n = Vapor pressure exponent. Vapor pressures in N/m**2 are given by 

 eTa*10**(-n) and eTs*10**(-n) 

 Sav = Monthly average wind speed (m/s times 10) 

 Ss = Monthly standard deviation of wind speed (m/s times 10) 

 Ruv = Cross-correlation between Eastward and Northward wind components (times 1000) 

 

56
NCEP ASCII data format is (I1,2I2,I3,I4,I6,I5,4(I4,I3),I1,2(I4,I3),2I4,I1,I4,I3,I4). 

Binary format NCEP data are provided in PC form. Files for each month are named 

Nby1y2mm.bin, where the period of record is for years y1 through y2 (e.g. 9008 is for POR 

1990 through 2008), and month is mm. Utility program NCEPbinF is used to generate similar 

binary format files on any non-PC platform. In addition to building binary format versions of the 

NCEP data, utility program NCEPbinF can also be used at any time to output easily-readable 

vertical profile data and horizontal grids ("maps") of NCEP data values. The NCEPbinF utility 

program MUST be used to generate binary version NCEP data for use by Earth-GRAM 2010 on 

non-PC computer platforms. 

57
APPENDIX B—COMPILING AND RUNNING GLOBAL REFERENCE 

ATMOSPHERIC MODEL 2010 

B.1 General Introduction 

Earth-GRAM 2010 can be run in stand-alone mode (i.e. as an independent program), or 

as a set of subroutines in a user-provided program, such as a trajectory code. The following 

material gives several examples of how to compile and run Earth-GRAM 2010 in each of these 

modes. Examples are given for both PC and UNIX machines. If you wish to run stand-alone 

GRAM on a PC, and do not need to make any code changes, you can use PC executable files 

provided on the distribution DVD. It is necessary to compile the Earth-GRAM 2010 source code 

if you: 

1) wish to run on a UNIX or other non-PC platform, 

2) make changes in the code (e.g. by selecting other/additional parameters for output, as 

described in Appendix E), or 

3) want to incorporate Earth-GRAM 2010 as subroutines in your own code, such as a 

trajectory program. 

Unless otherwise noted below, it is assumed in the following material that all files from the 

distribution DVD have been copied to folders as named in the instructions for how to setup 

Earth-GRAM 2010, given in Section 4.8. 

B.2 Command-Line Compiling on a PC 

One example of how to compile Earth-GRAM 2010 on a PC is to use command line 

mode. Command line mode is initiated by clicking on "Start," then "Run," then entering 

"CMD.EXE" (without the quotes) in the run window. For the GNU PC Fortran complier 

(gfortran), stand-alone Earth-GRAM can be compiled (to an executable file named 

gram_E10.exe) by entering the following commands: 

gfortran -c Cfiles_E10_C.F90 

gfortran -c Ifiles_E10_I.F90 

gfortran -c GRAMSUBS_E10.F90 

gfortran -c INITIAL_E10.F90 

gfortran -c MET07PRG_E10.F90 

gfortran -c MODELS_E10.F90 

gfortran -c RANDOM_E10.F90 

gfortran -c SPECONC_E10.F90 

gfortran -c RRAmods_E10.F90 

gfortran -c MSISsubs_E10.F90 

gfortran -c HWMsubs_E10.F90 

gfortran -c JB2008_E10.F90 

gfortran -c NCEPsubs_E10.F90 

gfortran GRAM_E10.F90 Cfiles_E10_C.o Ifiles_E10_I.o GRAMSUBS_E10.o INITIAL_E10.o 

 MET07PRG_E10.o MODELS_E10.o RANDOM_E10.o SPECONC_E10.o RRAmods_E10.o 

58
 MSISsubs_E10.o HWMsubs_E10.o JB2008_E10.o NCEPsubs_E10.o -o gram_E10.exe 

Note - For some compilers Cfiles_E10.F90 and Ifiles_E10.F90 must appear first in the list as in 

the above example. 

Alternatively, these commands may be put into an executable batch (.bat) file, in which 

case it is advisable to include a pause statement at the end of the batch file, so the temporary 

command window remains open after compilation has completed, allowing the user to view any 

compilation error messages that may have been produced. Optionally, the last gfortran call may 

include any of several switches to get various run-time error messages, such as 

gfortran -fbacktrace -std=f95 -Wextra -Wall -pedantic -fbounds-check ... 

Other compilers will have different commands and compile switches for doing command-line 

compile operations. Compilers also generally provide a "Programmer's Workbench" or similar 

graphical-user-interface mode for doing program compile-and-link operations. 

Subroutines trajcalc_E10.f90 and gramtraj_E10.f90 and a dummy main driver 

(trajdemo_E10.f90) are provided, to give an example of how to incorporate and use EarthGRAM 2010 as subroutines in your own code. To compile this example "trajectory" code (using 

gfortran), enter each of the following command lines (or incorporate them into an executable 

batch file) - 

To compile trajdemo, enter the following commands: 

gfortran -c Cfiles_E10_C.F90 

gfortran -c Ifiles_E10_I.F90 

gfortran -c gramtraj_E10.F90 

gfortran -c trajcalc_E10.F90 

gfortran -c GRAMSUBS_E10.F90 

gfortran -c INITIAL_E10.F90 

gfortran -c MET07PRG_E10.F90 

gfortran -c MODELS_E10.F90 

gfortran -c RANDOM_E10.F90 

gfortran -c SPECONC_E10.F90 

gfortran -c RRAmods_E10.F90 

gfortran -c MSISsubs_E10.F90 

gfortran -c HWMsubs_E10.F90 

gfortran -c JB2008_E10.F90 

gfortran -c NCEPsubs_E10.F90 

gfortran trajdemo_E10.F90 gramtraj_E10.o trajcalc_E10.o Cfiles_E10_C.o 

 Ifiles_E10_I.o GRAMSUBS_E10.o INITIAL_E10.o MET07PRG_E10.o MODELS_E10.o 

 RANDOM_E10.o SPECONC_E10.o RRAmods_E10.o MSISsubs_E10.o HWMsubs_E10.o 

 JB2008_E10.o NCEPsubs_E10.o -o trajdemo_E10.exe 

59
NOTE - After successful compilation to executable programs, all object files and module files 

can be deleted, such as by the commands: 

erase *.o 

erase *.mod 

These commands may also be incorporated into the executable compile batch files. 

Program trajdemo illustrates a basic trajectory program implementation. Other example 

trajectory driver programs, offering special options and features, are available upon approved 

request. These include: (1) Program trajopts, which shows how to implement various trajectory 

options, (2) Program multtraj, which illustrates implementation for calculating multiple 

trajectories in one program run (without cross-correlation between perturbations on the separate 

trajectories), (3) Program corrtraj, which evaluates multiple profiles in one program run, with 

time cross-correlations preserved between the profiles, and (4) Program multbody (including 

associated subroutines), which provides as an example of how to use GRAM in a trajectory code 

to compute space and time-correlated perturbations influencing multiple spacecraft bodies. 

Extensive comments in these example trajectory program driver routines provide more details. 

B.3 Compiling on a UNIX Machine 

The UNIX f90 command can be used to compile Earth-GRAM 2010, to an executable 

named gram_E10.x, by entering the followingf90 Cfiles_E10_C.f90 Ifiles_E10_I.f90 gram_E10.f90 gramsubs_E10.f90 / 

 NCEPsubs_E10.f90 initial_E10.f90 MET07prg_E10.f90 models_E10.f90 / 

 random_E10.f90 speconc_E10.f90 rramods_E10.f90 MSISsubs_E10.f90 / 

 HWMsubs_E10.f90 JB2008_E10.f90 

mv a.out gram_E10.x 

Similarly, the f90 command may also be used to compile the trajdemo program that provides an 

example of how to incorporate Earth-GRAM 2010 in user codef90 Cfiles_E10_C.f90 Ifiles_E10_I.f90 trajdemo_E10.f90 trajcalc_E10.f90 / 

 gramtraj_E10.f90 gramsubs_E10.f90 NCEPsubs_E10.f90 initial_E10.f90 / 

 MET07prg_E10.f90 models_E10.f90 random_E10.f90 speconc_E10.f90 / 

 rramods_E10.f90 MSISsubs_E10.f90 HWMsubs_E10.f90 JB2008_E10.f90 

mv a.out trajdemo_E10.x 

It should be noted that the forward slash character indicates a continuation line. After successful 

compilation to executable programs, all object files and module files can be deleted, such as by 

the commands: 

rm -f *.o 

rm -f *.mod 

60
The above compilation commands and rm commands may also be incorporated into an 

executable batch file. 

Note: If the fullwarn compile option is used on the UNIX f90 compiler, several 

CAUTION or NOTE messages may result. Specifically, there may be several CAUTIONS about 

the VAST_KIND_PARAM module having "already been directly or indirectly use associated 

into" the current scope. These CAUTION and NOTE messages can safely be ignored. However, 

no Error or Warning messages should be produced by the compilation process. 

 B.4 Running in Command-Line Mode on a PC 

With PC executable files placed in folder C:\EarthGRAM10\PC_Executables, and 

example input/output files placed in folder C:\EarthGRAM10\PC_IOfiles, GRAM 2010 can 

easily be run from any directory. For example, to run from a directory named C:\MyTest, do the 

following: 

1) Copy (and edit and/or rename, if desired) the file 

C:\EarthGRAM10\PC_IOfiles\NameRef.txt to the C:\MyTest folder. Note that 

NAMELIST input file names are limited to 99 characters. 

2) Open a PC command-line window by Clicking Start and Run and entering the command 

CMD.EXE 

3) Change directory by entering the commands C: and CD \MyTest 

4) Execute Earth-GRAM 2010 by entering the command 

C:\EarthGRAM10\PC_Executables\gram_E10.exe 

5) Enter the name of the input file (from step 1) when prompted 

6) Output files will appear in the C:\MyTest folder 

If file open errors are encountered, make sure that file pathnames are properly set in the 

NAMELIST input file. For files residing in folders as described in Section 4.8.2, set the 

following path names in the NAMELIST input file: 

o atmpath = 'C:\EarthGRAM10\PC_IOfiles\atmosdat_E10.txt' 

o NCEPpath 

• = 'C:\EarthGRAM10\NCEPdata\' if the NCEP data are to be read from the C: drive, or 

• = 'E:\NCEPdata\' if the NCEP data are to be read from the DVD on the E: drive. 

 

For test or demonstration purposes, it is also possible to run Earth-GRAM 2010 directly 

from the distribution DVD. To do this, from the C:\MyTest directory, as above, simply replace 

"C:\EarthGRAM10\" with "E:\" (assuming that E: is the DVD drive) in the command and input 

pathnames for the executable file, the atmosdat_E10.txt file, and the NCEP path name. See later 

discussion on how to set file path names if using the input trajectory option, the Range Reference 

Atmosphere input option, the auxiliary profile input option, and/or the multiple-profile Monte 

Carlo option. Output file path names can be any name specified by the user. All path names are 

limited to 99 characters in length. 

B.5 Running in Command-Line Mode on a UNIX Machine 

61
UNIX executable files must be compiled and created, as discussed above. For example, 

suppose the Earth-GRAM 2010 UNIX executable is created and named gram_E10.x in directory 

/usr/EarthGRAM10/UNIX_Executables. If the setup procedure discussed in Section 4.8.3 is 

used, example input/output files are placed in folder /usr/EarthGRAM10/UNIX_IOfiles. EarthGRAM 2010 can easily be run from any directory. For example, to run from a directory named 

/usr/MyTest, do the following1) Copy (and edit and/or rename, if desired) the file 

/usr/EarthGRAM10/UNIX_IOfiles/NameRef.txt to the /usr/MyTest folder. Note that 

NAMELIST input file names are limited to 99 characters. 

2) Change directory by entering the command cd /usr/MyTest 

3) Execute Earth-GRAM 2010 by entering the command 

/usrEarthGRAM10/UNIX_Executables/gram_E10.x 

4) Enter the name of the input file (from step 1) when prompted 

5) Output files will appear in the /usr/MyTest folder 

If file open errors are encountered, make sure that file pathnames are properly set in the 

NAMELIST input file. For files residing in folders as described in Section 4.8.3, set the 

following path names in the NAMELIST input file: 

o atmpath = '/usr/EarthGRAM10/UNIX_IOfiles/atmosdat_E10.txt' 

o NCEPpath 

• = '/usr/EarthGRAM10/NCEPdata/' if the NCEP data are to be read from the 

/usr/EarthGRAM10 area, or 

• = '/DVDROM/NCEPdata/' if NCEP data are to be read from the DVD on the 

/DVDROM/ drive 

See later discussion on how to set file path names if using the input trajectory option, the Range 

Reference Atmosphere input option, the auxiliary profile input option, and/or the multiple-profile 

Monte Carlo option. Output file path names can be any name specified by the user. All path 

names are limited to 99 characters in length. 

B.6 Reference Input/Output Files for Testing 

To facilitate runtime testing, a NAMELIST-formatted reference input file, called 

NameRef.txt, is provided on the distribution DVD (in folder EarthGRAM10\IOfiles on the 

distribution DVD). Reference output files are also provided (OutputRef.txt and SpeciesRef.txt 

on the distribution DVD). If a test run (as described in the above sections) is done using input 

file NameRef.txt, to produce output files named output.txt and species.txt, these output files can 

be tested against the reference output files provided. On a PC (from the directory where the test 

output files reside), to compare against reference files on the DVD (E: drive), enter PC 

commands 

 fc output.txt E:\PC_IOfiles\OutputRef.txt 

 

 fc special.txt E:\PC_IOfiles\SpecialRef.txt 

62
 fc species.txt E:\PC_IOfiles\SpeciesRef.txt 

and 

 fc BLTest.txt E:\PC_IOfiles\BLTestRef.txt 

Any file differences will be noted in the output from the fc (file compare) command. To do the 

same tests on a UNIX machine, the commands are 

 diff output.txt /DVDROM/UNIX_IOfiles/OutputRef.txt 

 diff special.txt /DVDROM/UNIX_IOfiles/SpecialRef.txt 

 diff species.txt /DVDROM/UNIX_IOfiles/SpeciesRef.txt 

and 

 diff BLTest.txt /DVDROM/UNIX_IOfiles/BLTestRef.txt 

 

Be sure to compare against files from the appropriate directory on the distribution DVD, 

since there are small differences in the PC and UNIX version reference output files. In UNIX 

format, numbers that are less than 1 (in magnitude) are written (0.xxx -0.xxx etc.). For some 

compilers in the PC environment, such numbers are written without the leading zeroes (i.e., as 

.xxx -.xxx etc.). Because of variations in handling of round-off by different operating systems 

and/or compilers, a few numbers in the reference output files may differ from those in the usergenerated test output files. Such differences should be no larger than about 1 in the last 

significant digit of the output. 

B.7 Running with an Input Trajectory File 

To run the stand-alone Earth-GRAM 2010 program with a pre-computed input trajectory 

file of positions and times, set the trajectory file pathname (trapath) in the NAMELIST input file 

to whatever file name is desired, set the number of computed positions (nmax) to zero, and set 

the trajectory file unit number (iopt) to any non-conflicting value. The trajectory file contains 

one time and position per line, having values for elapsed time (seconds), height (km), geocentric 

latitude (degrees, North positive), and longitude (degrees, East positive). Trajectory input heights 

greater than 6000 km are treated as geocentric radius values, rather than as altitudes above 

reference ellipsoid. Example programs illustrating how to drop Earth-GRAM into trajectory code 

cannot be run with trajectory file input, since trajectory positions are generated "on the fly" in 

these programs. For additional discussion of input options, see Appendix C. 

Multiple profiles or trajectories can be computed in one run of the program, in a MonteCarlo simulation of various perturbation profiles, by providing input for any number of random 

seed values. Input random seeds are provided, with one seed value per line, in a file whose path 

name is specified by input parameter rndpath, the file unit number for which is specified by input 

parameter iun. Integer random seed values must be in the range 0 seed 900,000,000. Other 

aspects of the perturbation model can be controlled by input parameters such as rpscale, initpert, 

patchy, rdinit, rtinit, ruinit, rvinit, rwinit, etc. For additional discussion of input options, see 

Appendix C. 

63
B.8 Running with Range Reference Atmosphere (RRA) Input 

A major feature is the (optional) ability to use data (in the form of vertical profiles) from 

a set of Range Reference Atmospheres (RRA), as an alternate to the usual GRAM climatology, 

at a set of RRA site locations. With this feature it is possible, for example, to simulate a flight 

profile that takes off from the location of one RRA site (e.g., Edwards AFB, using the Edwards 

RRA data), to smoothly transition into an atmosphere characterized by the GRAM climatology, 

then smoothly transition into an atmosphere characterized by a different RRA site (e.g., White 

Sands, NM), to be used as the landing site in the simulation. Use of the RRA option is controlled 

by setting input parameters rrapath, rralist, iurra, sitelim, and sitenear. For further discussion of 

input options, see Appendix C. For further discussion of RRA data, see Section 3.4.

B.9 Running with Auxiliary Profile Input 

As an option, data read from an auxiliary profile may be used to replace data from the 

conventional (NCEP/MAP/etc.) climatology. This option is controlled by setting parameters 

profile, sitenear, and sitelim in the NAMELIST input file. Each line of the auxiliary profile input 

file consists of: (1) height, in km [height values greater than 6,000 km are interpreted as radius 

values, in km], (2) geocentric latitude, in degrees, (3) longitude, in degrees (East positive), (4) 

mean temperature, in K, (5) mean pressure, in N/m**2, (6) mean density, in kg/m**3, (7) mean 

Eastward wind, in m/s, (8) mean Northward wind, in m/s, (9) standard deviation (sigma) 

temperature, in K, (10) sigma pressure, in N/m**2, (11) sigma density, in kg/m**3, (12) sigma 

Eastward wind, in m/s, (13) sigma Northward wind, in m/s. Heights are relative to the reference 

ellipsoid, except that values greater than 6,000 km are interpreted as radius values, rather than 

altitudes. Latitudes are geocentric. Regular climatological values (NCEP/MAP data etc.) are used 

if any of the three values for temperature, pressure, or density data are input as zero in the 

auxiliary profile. Regular climatological values of wind components are used if BOTH wind 

components are zero in the auxiliary profile file. Note that RRA input option and auxiliary 

profile input option cannot be used simultaneously. Example auxiliary profiles are provided with 

the software. 

B.10 Compiling and Running on Other Platforms 

MSFC Natural Environments Group does not have adequate resources to provide 

program versions and installation setups for all possible user platforms. Hopefully, the guidance 

provided above will be adequate to allow users to set up, compile and run Earth-GRAM 2010 on 

whatever platform they desire to use. For questions on compiling or running Earth-GRAM 2010, 

see contact information below. 

If you have any questions or problems, please contact: 

Fred Leslie 

e-mail: Fred.W.Leslie@nasa.gov 

phone: (256)-544-1633 

64
fax: (256)-544-5754 

Mail Code EV44 

NASA Marshall Space Flight Center 

Huntsville, AL 35812 

OR

C. G. (Jere) Justus 

e-mail: Carl.G.Justus@nasa.gov 

phone: (256)-544-3260 

fax: (256)-544-5754 

Mail Code EV44/Dynbetics Technical Services 

NASA Marshall Space Flight Center 

Huntsville, AL 35812 

PDF versions of the background GRAM-95 and GRAM-99 reports [NASA Technical 

Memorandum 4715, "The NASA/MSFC Global Reference Atmospheric Model - 1995 Version 

(GRAM-95)," August, 1995 and NASA/TM-1999-209630 "The NASA/MSFC Global Reference 

Atmospheric Model - 1999 Version (GRAM-99)," May 1999] are on the Earth-GRAM 2010 

distribution DVD. 

65
APPENDIX C—DESCRIPTION OF NAMELIST FORMAT INPUT FILE

Following is a sample NAMELIST format input file (NameRef.txt) for use by EarthGRAM 2010. Note that some compilers use different formats for the beginning and ending lines 

of the file. This sample file contains values required to produce the reference output data (file 

OutputRef.txt). These input values are also the default values, set if none are provided. Only 

values that differ from these default values actually need to be input in the NAMELIST file. 

Definitions and discussion of Earth-GRAM 2010 input parameters that are the same as GRAM99 input parameters are given in Appendix D of NASA/TM-1999-209630. 

 $namein_e10

 atmpath = 'D:\GRAMs\EarthGRAM2010Ver1.0\PC_IOfiles\atmosdat_E10.txt'

 NCEPpath = 'D:\GRAMs\EarthGRAM2010Ver1.0\NCEPdata\BinData\' 

 trapath = 'null'

 prtpath = 'output.txt'

 nprpath = 'special.txt'

 conpath = 'species.txt'

 rndpath = 'null'

 rrapath = 'D:\GRAMs\EarthGRAM2010Ver1.0\RRAdata\' 

 rralist = 'rras2006.txt'

 profile = 'null'

 h1 = 140.

 phi1 = 0.45

 thet1 = -164.53

 f10 = 230.

 f10b = 230.

 ap = 20.3

 s10 = 0. 

 s10b = 0.

 xm10 = 0.

 xm10b = 0.

 y10 = 0.

 y10b = 0.

 dstdtc = 0.

 mn = 1

 ida = 1

 iyr = 2010

 ihro = 0

 mino = 0

 seco = 0.0

 dphi = 0.4

 dthet = 1.2

 dhgt = -2.0

 nmax = 71

 delt = 60.0

 iopt = 0

 iopp = 17

 iu0 = 0

 iup = 6

 ius = 3

66
 iuc = 4

 iug = 22

 NCEPyr = 9008

 NCEPhr = 5

 iopr = 1

 nr1 = 1234

 iun = 0

 rpscale = 1.0

 ruscale = 1.0

 rwscale = 1.0

 iurra = 35

 sitelim = 2.5

 sitenear = 0.5

 initpert = 0

 rdinit = 0.

 rtinit = 0.

 ruinit = 0.

 rvinit = 0.

 rwinit = 0.

 patchy = 0.

 itherm = 1

 z0in = -1.

 ibltest = 99

 $End

Parameter Descriptions:

atmpath = path name for "atmosdat" atmospheric data file

NCEPpath = path name for NCEP data files

trapath = path name for trajectory input file ('null' if none)

prtpath = path name for standard formatted output file ('null' if none)

nprpath = path name for the "special" format output file ('null' if none)

conpath = path name for species concentration output file ('null' if none)

rndpath = path name for file containing more random number seeds (optional)

rrapath = DIRECTORY for Range Reference Atmosphere (RRA) data (optional)

rralist = File name for list of RRA sites (optional)

profile = path name for auxiliary profile data ('null' if none)

h1 = initial height (km). Heights > 6000 km are interpreted as radius.

phi1 = initial geocentric latitude (degrees, N positive)

thet1 = initial longitude (degrees, East positive)

f10 = daily 10.7-cm flux

f10b = mean 10.7-cm flux

ap = geomagnetic index (Note: Valid ap must be used if JB2008 selected,

 for use in HWM wind model)

s10 = EUV index (26-34 nm) scaled to F10 units (0.0 -> s10=f10)

s10b = EUV 81-day center-averaged index (0.0 -> s10b = f10b)

xm10 = MG2 index scaled to F10 units (0.0 -> xm10 = f10)

xm10b = MG2 81-day center-averaged index (0.0 -> xm10b = f10b)

y10 = Solar X-Ray & Lya index scaled to F10 (0.0 -> y10=f10)

y10b = Solar X-Ray & Lya 81-day avg. centered index (0.0 -> y10b=f10b)

dstdtc = Temperature change computed from Dst index (for JB2008)

mn = month (1-12)

ida = day of month

iyr = 4-digit year, or 2-digit year: >56=19xx <57=20XX

ihro = initial UTC (Greenwich) time hour (0-23)

mino = initial UTC (Greenwich) time minutes (0-59)

seco = initial UTC (Greenwich) time seconds (0.0-60.0)

dphi = geocentric latitude increment (degrees, Northward positive)

dthet = longitude increment (degrees, Eastward positive)

67
dhgt = height increment (km, upward positive). If radius input is used,

 dhgt is interpreted as a radius increment.

nmax = maximum number of positions (including initial one; 0 means read

 trajectory input file)

delt = time increment between positions (real seconds)

iopt = trajectory option (0 = no trajectory data; otherwise unit number

 for trajectory input file)

iopp = "special" output option (0 = no "special" output; otherwise unit

 number of "special" output file)

iu0 = unit number for screen output (normally 6 or 0)

iup = unit number for standard formatted output file (0 for none)

ius = unit number for atmosdat data

iuc = unit number for concentrations output (0 for none)

iug = unit for NCEP data files

NCEPyr = y1y2 to use NCEP climatology for period-of-record (POR) from year 

 y1 through year y2 (e.g. NCEPyr=9008 for POR = 1990 through 

 2008). NCEP monthly climatology is determined by input value 

 of month (mn) in initial time input

NCEPhr = Code for UT hour of day if NCEP climatology is used: 1=00 UT, 

 2=06UT, 3=12UT, 4=18UT, 5=all times of day combined, or 0 to 

 use NCEP time-of-day based on input UTC hour (ihro)

iopr = random output option (1 = random output, 2 = none)

nr1 = first starting random number (1 to 9 * 10**8)

iun = unit number for more starting random numbers (0 for none)

rpscale = random perturbation scale for density, temperature and pressure; 

 nominal=1.0, max=2.0, min=0.1

ruscale = random perturbation scale for horizontal winds; nominal=1.0, 

 maximum=2.0, minimum=0.1

rwscale = random perturbation scale for vertical winds; nominal=1.0, 

 maximum=2.0, minimum=0.1

iurra = unit number for Range Reference Atmosphere (RRA) data (0 if none)

sitelim = lat-lon radius (deg) from RRA site, outside which RRA data are

 NOT used. Also used, with a similar meaning, for auxiliary

 profile input. Note that RRA and auxiliary profile input

 cannot be used simultaneously.

sitenear = lat-lon radius (deg) from RRA site, inside which RRA data is

 used with full weight of 1 (smooth transition of weight factor

 from 1 to 0 between sitenear and sitelim). Also used, with a 

 similar meaning, for auxiliary profile input.

initpert = Use 1 for user-selected initial perturbations or 0 (default) for

 GRAM-derived, random initial perturbation values

rdinit = initial density perturbation value (% of mean)

rtinit = initial temperature perturbation value (% of mean). Note - initial

 pressure perturbation is computed from rdinit and rtinit.

ruinit = initial eastward velocity perturbation (m/s)

rvinit = initial northward velocity perturbation (m/s)

rwinit = initial upward velocity perturbation (m/s)

patchy = not equal 0 for patchiness; 0 to suppress patchiness in 

 perturbation model

itherm = 1 for MET (Jacchia), 2 for MSIS, or 3 for JB2008 thermosphere 

z0in = surface roughness (z0) for sigma-w model [ < 0 to use 1-by-1 deg 

 lat-lon surface data, from file atmosdat_E10.txt; = 0 for

 speed-dependent z0 over water; or enter a value between 1.0e-5 

 and 3 for user-specified z0 value ]. For more information, 

 see file README7.txt.

ibltest = unit number for BL model output file (bltest.txt), or 0 for no 

 BL model output

68
APPENDIX D—SAMPLE OUTPUT PF GLOBAL REFERENCE 

ATMOSPHERIC MODEL 2010 

D.1 Sample Standard Formatted Output Produced by Input File of Appendix C 

  Earth Global Reference Atmospheric Model - 2010 (Earth-GRAM-2010) ** **

 Version 1.0, Released Jul, 2010

 MM/DD/YYYY = 1/ 1/2010 HH:MM:SS(UTC) = 0: 0: 0.0 Julian Day = 2455197.500

 F10.7 = 230.00 Mean F10.7 = 230.00 ap Index = 20.30

 Max of 71 positions, generated automatically.

 Range Reference Atmosphere (RRA) sites available

 No Code Yr GdLat GcLat Lon(E+) Hgt(m) Zmax WMO # Site Name

-- ---- -- ------ ------ ------- ------ ---- ------ ---------------------------

 1 anf 06 47.62 47.43 -52.73 140. 30. 718010 Argentia, Newfoundland (St. Johns Airport) 

 2 asc 06 -7.93 -7.88 -14.42 79. 70. 619020 Ascension Island, Atlantic 

 3 bar 06 21.98 21.85 -159.34 31. 30. 911650 Barking Sands, Hawaii (Lihue) 

 4 cap 06 28.47 28.31 -80.55 3. 70. 747940 Cape Canaveral, Florida 

 5 chl 06 35.68 35.50 -117.68 665. 30. 746120 China Lake Naval Air Weapons Center, CA 

 6 dug 06 40.77 40.58 -111.97 1288. 30. 725720 Dugway Proving Ground (Salt Lake City), UT 

 7 eaf 06 34.92 34.74 -117.90 724. 30. 723810 Edwards Air Force Base, California 

 8 egl 06 30.48 30.31 -86.52 20. 30. 722210 Eglin AFB, Florida 

 9 elp 06 31.81 31.64 -106.38 1199. 70. 722700 El Paso, Texas 

 10 fad 06 64.80 64.65 -147.88 135. 30. 702610 Fairbanks, Alaska 

 11 fha 06 32.12 31.95 -110.93 787. 30. 722740 Ft. Huachuca Elec Prvng Grnd (Tucson), AZ 

 12 gtf 06 47.47 47.28 -111.38 1118. 30. 727750 Great Falls, MT 

 13 kmr 06 8.73 8.67 167.75 2. 70. 913660 Kwajalein Missile Range, Pacific 

 14 ncf 06 43.87 43.68 4.40 62. 30. 076450 Nimes-Courbessac, France (STS TAL Site) 

 15 nel 06 36.62 36.44 -116.02 1007. 30. 723870 Nellis AFB, Nevada (Mercury) 

 16 ptu 06 34.12 33.94 -119.12 2. 70. 723910 Point Mugu Naval Air Weapons Center, CA 

 17 tag 06 13.55 13.46 144.85 78. 30. 912170 Taguac, Guam (Anderson AFB) 

 18 vaf 06 34.75 34.57 -120.57 121. 30. 723930 Vandenberg AFB, California 

 19 wal 06 37.85 37.66 -75.48 13. 30. 724020 Wallops Island, Virginia (NASA) 

 20 wsm 06 32.38 32.21 -106.48 1207. 30. 722690 White Sands Missile Range, New Mexico 

 21 ysd 06 32.87 32.69 -117.14 134. 30. 722930 Yuma Proving Ground, AZ (San Diego, CA) 

 NCEP Global Climatology Data: POR = 9008 NCEPhr = 5

 Path = D:\GRAMs\EarthGRAM2010Ver1.0\NCEPdata\FixedBin\ 

 Thermospheric conditions from MET model

 Random Option = 1 1st Random No. = 1234 Random Scale Factors = 1.00 1.00 1.00

 Patchy Turbulence Option = Off

 Mean-76 and Total-76 are percent deviations from 1976 US Standard Atmosphere.

 Other deviations in percent are with respect to mean values. RH is relative

 humidity in percent. Zeroes for H2O indicate no estimate available.

 E-W wind positive toward East; N-S wind positive toward North.

 Height/ GcLat Long. Tempera- Vert.

 Radius GdLat [E+W-] Pressure Density/ ture/ E-W N-S Wind

 (km) (deg) (deg) /Vap.Pr. Vap.Dens. Dewpt. Wind Wind (m/s)

 Time_sec /RRA /Weight (Nt/m**2) (kg/m**3) (K) (m/s) (m/s) RH(%)

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 140.000 0.450 -164.530 9.966E-04 4.406E-09 690.2 20.4 0.3 -0.000 Mean

 6518.136 0.453 38.36% 15.00% 23.34% M-76

 0.0 GRM 0.0000 -0.88% 3.90% -8.64% 83.9 -8.9 ranS

 2.90% 6.19% 12.54% 45.0 45.0 sigS

 Wind and SoS -4.55% 4.32% -3.97% -12.9 -60.8 ranL

------------ 12.16% 3.69% 7.47% 52.3 52.3 sigL

 Ruv = 0.014 -5.43% 8.21% -12.61% 71.0 -69.7 -3.45 ranT

 SpdAv= 78.6 12.50% 7.20% 14.60% 69.0 69.0 8.33 sigT

 SpdSd= 61.3 9.424E-04 4.768E-09 603.2 91.5 -69.4 -3.45 Tot.

 SoSav= 562.7 30.84% 24.45% 7.78% T-76

 SoSpt= 526.0 0.000E+00 0.000E+00 0.0 0.0% H2O

 0.000E+00 0.000E+00 0.0 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 138.000 0.850 -163.330 1.085E-03 5.022E-09 662.0 17.5 0.5 -0.000 Mean

69
 6516.132 0.856 36.08% 14.26% 21.94% M-76

 60.0 GRM 0.0000 -2.70% 0.70% -6.27% 64.4 14.5 ranS

 3.05% 6.22% 13.15% 43.1 43.0 sigS

 Wind and SoS -4.79% 4.27% -5.59% -21.1 -56.2 ranL

------------ 12.84% 3.77% 7.97% 50.5 50.4 sigL

 Ruv = 0.014 -7.48% 4.97% -11.87% 43.4 -41.7 -4.10 ranT

 SpdAv= 75.0 13.20% 7.27% 15.37% 66.4 66.2 8.16 sigT

 SpdSd= 58.9 1.004E-03 5.272E-09 583.5 60.8 -41.2 -4.10 Tot.

 SoSav= 550.0 25.90% 19.94% 7.47% T-76

 SoSpt= 516.3 0.000E+00 0.000E+00 0.0 0.0% H2O

 0.000E+00 0.000E+00 0.0 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 136.000 1.250 -162.130 1.186E-03 5.764E-09 633.2 14.0 0.6 -0.000 Mean

 6514.127 1.258 33.85% 13.60% 20.49% M-76

 120.0 GRM 0.0000 -3.55% -4.43% 1.67% 50.8 13.0 ranS

 3.18% 6.25% 13.72% 41.1 40.9 sigS

 Wind and SoS -2.25% 4.13% -7.18% -28.1 -50.4 ranL

------------ 13.49% 3.85% 8.45% 48.6 48.3 sigL

 Ruv = 0.013 -5.80% -0.31% -5.51% 22.7 -37.5 8.50 ranT

 SpdAv= 71.2 13.86% 7.35% 16.11% 63.6 63.3 7.99 sigT

 SpdSd= 56.4 1.117E-03 5.746E-09 598.3 36.8 -36.9 8.50 Tot.

 SoSav= 536.8 26.09% 13.25% 13.85% T-76

 SoSpt= 521.8 0.000E+00 0.000E+00 0.0 0.0% H2O

 0.000E+00 0.000E+00 0.0 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 134.000 1.650 -160.930 1.303E-03 6.667E-09 603.8 10.1 0.6 0.000 Mean

 6512.119 1.661 31.73% 13.08% 18.98% M-76

 180.0 GRM 0.0000 -3.59% -4.86% 2.43% 54.9 0.5 ranS

 3.30% 6.29% 14.25% 39.1 38.8 sigS

 Wind and SoS -3.58% 3.87% -8.68% -33.8 -43.8 ranL

------------ 14.11% 3.94% 8.93% 46.6 46.2 sigL

 Ruv = 0.013 -7.17% -0.98% -6.25% 21.1 -43.3 9.04 ranT

 SpdAv= 67.4 14.49% 7.42% 16.82% 60.8 60.3 7.82 sigT

 SpdSd= 53.8 1.209E-03 6.602E-09 566.1 31.1 -42.7 9.04 Tot.

 SoSav= 523.0 22.28% 11.97% 11.54% T-76

 SoSpt= 506.4 0.000E+00 0.000E+00 0.0 0.0% H2O

 0.000E+00 0.000E+00 0.0 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 132.000 2.050 -159.730 1.438E-03 7.778E-09 573.9 5.7 0.5 0.000 Mean

 6510.109 2.064 29.67% 12.65% 17.43% M-76

 240.0 GRM 0.0000 -2.74% -5.07% 4.53% 49.9 49.5 ranS

 3.41% 6.32% 14.76% 37.0 36.6 sigS

 Wind and SoS -4.23% 3.52% -10.04% -38.1 -36.6 ranL

------------ 14.70% 4.02% 9.39% 44.5 44.0 sigL

 Ruv = 0.013 -6.97% -1.55% -5.51% 11.8 12.9 9.05 ranT 

 SpdAv= 63.6 15.09% 7.49% 17.49% 57.9 57.2 7.65 sigT

 SpdSd= 51.1 1.338E-03 7.658E-09 542.3 17.5 13.4 9.05 Tot.

 SoSav= 508.8 20.63% 10.91% 10.96% T-76

 SoSpt= 494.6 0.000E+00 0.000E+00 0.0 0.0% H2O

 0.000E+00 0.000E+00 0.0 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 130.000 2.450 -158.530 1.597E-03 9.159E-09 543.6 1.0 0.4 0.000 Mean

 6508.098 2.466 27.71% 12.34% 15.85% M-76

 300.0 GRM 0.0000 -1.38% -1.66% 0.56% 22.0 48.8 ranS

 3.52% 6.35% 15.23% 34.9 34.3 sigS

 Wind and SoS -7.99% 3.08% -11.19% -40.9 -29.1 ranL

------------ 15.27% 4.11% 9.85% 42.3 41.6 sigL

 Ruv = 0.013 -9.37% 1.42% -10.63% -18.9 19.8 7.72 ranT

 SpdAv= 59.8 15.67% 7.56% 18.14% 54.9 53.9 7.48 sigT

 SpdSd= 48.3 1.448E-03 9.288E-09 485.8 -17.9 20.2 7.72 Tot.

 SoSav= 494.1 15.75% 13.93% 3.53% T-76

 SoSpt= 467.1 0.000E+00 0.000E+00 0.0 0.0% H2O

 0.000E+00 0.000E+00 0.0 0.0% sigH

70
-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 128.000 2.850 -157.330 1.785E-03 1.090E-08 513.1 -4.0 0.3 0.000 Mean

 6506.084 2.869 25.90% 12.17% 14.26% M-76

 360.0 GRM 0.0000 2.28% -3.75% 12.05% 37.8 43.7 ranS

 3.63% 6.37% 15.69% 32.7 32.0 sigS

 Wind and SoS -3.54% 2.54% -12.09% -42.2 -21.5 ranL

------------ 15.82% 4.19% 10.31% 40.0 39.1 sigL

 Ruv = 0.012 -1.25% -1.21% -0.04% -4.4 22.1 7.13 ranT

 SpdAv= 56.3 16.23% 7.63% 18.77% 51.7 50.5 7.31 sigT

 SpdSd= 45.4 1.763E-03 1.077E-08 512.9 -8.4 22.4 7.13 Tot. 

 SoSav= 478.9 24.32% 10.81% 14.21% T-76

 SoSpt= 478.8 0.000E+00 0.000E+00 0.0 0.0% H2O

 0.000E+00 0.000E+00 0.0 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 126.000 3.250 -156.130 2.011E-03 1.312E-08 482.3 -9.1 0.1 0.000 Mean

 6504.068 3.271 24.15% 12.04% 12.68% M-76

 420.0 GRM 0.0000 1.71% -8.30% 20.15% 22.6 5.9 ranS

 3.75% 6.40% 16.12% 30.4 29.5 sigS

 Wind and SoS -1.10% 1.93% -12.71% -42.1 -14.2 ranL

------------ 16.35% 4.27% 10.76% 37.5 36.4 sigL

 Ruv = 0.012 0.60% -6.36% 7.44% -19.5 -8.3 6.55 ranT

 SpdAv= 53.1 16.77% 7.70% 19.38% 48.3 46.8 7.14 sigT

 SpdSd= 42.3 2.023E-03 1.228E-08 518.2 -28.7 -8.2 6.55 Tot.

 SoSav= 463.2 24.90% 4.91% 21.07% T-76

 SoSpt= 480.2 0.000E+00 0.000E+00 0.0 0.0% H2O

 0.000E+00 0.000E+00 0.0 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 124.000 3.650 -154.930 2.284E-03 1.599E-08 451.5 -14.2 -0.0 0.000 Mean

 6502.050 3.674 22.59% 12.05% 11.15% M-76

 480.0 GRM 0.0000 1.81% -12.96% 30.01% 52.9 18.7 ranS

 3.87% 6.43% 16.53% 28.0 26.9 sigS

 Wind and SoS 1.50% 1.26% -13.00% -40.5 -7.5 ranL

------------ 16.86% 4.36% 11.20% 34.8 33.5 sigL

 Ruv = 0.012 3.32% -11.70% 17.00% 12.4 11.2 3.45 ranT

 SpdAv= 50.3 17.30% 7.77% 19.97% 44.7 42.9 6.97 sigT

 SpdSd= 39.0 2.359E-03 1.412E-08 528.3 -1.8 11.1 3.45 Tot.

 SoSav= 447.1 26.66% -1.06% 30.05% T-76

 SoSpt= 483.6 0.000E+00 0.000E+00 0.0 0.0% H2O

 0.000E+00 0.000E+00 0.0 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 122.000 4.050 -153.730 2.619E-03 1.978E-08 421.0 -19.0 -0.2 0.000 Mean

 6500.030 4.077 21.09% 11.96% 9.75% M-76

 540.0 GRM 0.0000 -1.04% 0.45% -3.05% 19.5 -2.2 ranS

 3.98% 6.45% 16.92% 25.5 24.1 sigS

 Wind and SoS -14.13% 0.54% -12.96% -37.7 -1.7 ranL

------------ 17.35% 4.44% 11.65% 31.9 30.3 sigL

 Ruv = 0.011 -15.17% 0.99% -16.00% -18.2 -3.9 3.04 ranT

 SpdAv= 47.7 17.81% 7.83% 20.54% 40.8 38.7 6.80 sigT

 SpdSd= 35.4 2.222E-03 1.997E-08 353.6 -37.1 -4.0 3.04 Tot.

 SoSav= 430.6 2.72% 13.07% -7.81% T-76

 SoSpt= 394.7 0.000E+00 0.000E+00 0.0 0.0% H2O

 0.000E+00 0.000E+00 0.0 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 120.000 4.450 -152.530 3.038E-03 2.481E-08 391.1 -23.3 -0.3 -0.000 Mean

 6498.008 4.479 19.69% 11.66% 8.65% M-76

 600.0 GRM 0.0000 -0.68% -3.30% 5.39% 28.5 -15.2 ranS

 4.09% 6.48% 17.30% 22.7 21.1 sigS

 Wind and SoS -9.76% -0.22% -12.56% -33.7 3.1 ranL

------------ 17.84% 4.52% 12.08% 28.7 26.7 sigL

 Ruv = 0.011 -10.44% -3.51% -7.17% -5.2 -12.1 -0.92 ranT

 SpdAv= 45.3 18.30% 7.90% 21.10% 36.6 34.0 6.63 sigT

 SpdSd= 31.4 2.721E-03 2.394E-08 363.1 -28.4 -12.4 -0.92 Tot.

 SoSav= 414.0 7.20% 7.74% 0.86% T-76

71
 SoSpt= 398.9 0.000E+00 0.000E+00 0.0 0.0% H2O

 0.000E+00 0.000E+00 0.0 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 118.000 4.850 -151.330 3.559E-03 3.154E-08 362.3 -26.5 -0.3 -0.000 Mean

 6495.983 4.882 18.07% 10.82% 7.82% M-76

 660.0 GRM 0.0000 2.68% -10.05% 25.25% 6.0 13.2 ranS

 3.98% 7.11% 16.16% 22.3 23.2 sigS

 Wind and SoS -2.12% -1.09% -12.10% -32.5 8.3 ranL

------------ 17.34% 5.04% 11.46% 28.5 29.5 sigL

 Ruv = 0.011 0.56% -11.13% 13.16% -26.5 21.5 5.68 ranT

 SpdAv= 48.4 17.79% 8.71% 19.81% 36.2 37.5 6.49 sigT

 SpdSd= 32.8 3.578E-03 2.803E-08 409.9 -53.0 21.1 5.68 Tot.

 SoSav= 397.4 18.73% -1.52% 22.01% T-76

 SoSpt= 422.8 1.135E-09 7.362E-15 186.1 0.0% H2O

 4.085E-10 2.650E-15 0.0 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 116.000 5.250 -150.130 4.207E-03 4.063E-08 334.3 -28.1 -0.5 -0.000 Mean

 6493.957 5.285 15.83% 9.17% 7.14% M-76

 720.0 GRM 0.0000 2.94% -13.17% 30.55% 23.4 42.0 ranS

 3.86% 7.67% 14.96% 21.9 24.9 sigS

 Wind and SoS -1.95% -2.08% -11.40% -30.7 14.1 ranL

------------ 16.83% 5.52% 10.76% 28.2 32.0 sigL

 Ruv = 0.011 0.98% -15.25% 19.15% -7.3 56.2 -1.85 ranT

 SpdAv= 50.6 17.27% 9.45% 18.43% 35.7 40.6 6.36 sigT

 SpdSd= 34.0 4.249E-03 3.443E-08 398.3 -35.5 55.7 -1.85 Tot.

 SoSav= 380.8 16.97% -7.48% 27.66% T-76

 SoSpt= 415.6 1.450E-09 1.015E-14 180.0 0.0% H2O

 5.222E-10 3.653E-15 0.0 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 114.000 5.650 -148.930 5.037E-03 5.320E-08 307.3 -27.9 -0.6 -0.000 Mean

 6491.929 5.687 13.27% 6.92% 6.70% M-76

 780.0 GRM 0.0000 3.03% -7.38% 18.60% 26.0 5.1 ranS

 3.75% 8.25% 13.79% 22.7 25.7 sigS

 Wind and SoS -6.45% -3.19% -10.60% -29.8 19.7 ranL 

------------ 16.34% 6.02% 10.07% 29.4 33.3 sigL

 Ruv = 0.010 -3.42% -10.57% 8.00% -3.8 24.8 2.10 ranT

 SpdAv= 51.8 16.77% 10.21% 17.07% 37.1 42.0 6.22 sigT

 SpdSd= 35.2 4.865E-03 4.758E-08 331.9 -31.7 24.2 2.10 Tot.

 SoSav= 364.1 9.39% -4.38% 15.23% T-76

 SoSpt= 378.4 1.868E-09 1.413E-14 173.2 0.0% H2O

 6.723E-10 5.088E-15 0.0 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 112.000 6.050 -147.730 6.134E-03 7.115E-08 281.5 -26.0 -0.9 -0.000 Mean

 6489.898 6.090 10.43% 4.05% 6.62% M-76

 840.0 GRM 0.0000 -0.82% -11.95% 18.42% 20.4 8.2 ranS

 3.64% 8.82% 12.66% 24.3 25.7 sigS

 Wind and SoS -8.26% -4.38% -9.76% -29.2 24.4 ranL

------------ 15.88% 6.53% 9.37% 31.7 33.6 sigL

 Ruv = 0.010 -9.08% -16.33% 8.66% -8.8 32.7 -2.25 ranT

 SpdAv= 52.2 16.29% 10.98% 15.75% 39.9 42.3 6.09 sigT

 SpdSd= 36.6 5.577E-03 5.953E-08 305.9 -34.8 31.8 -2.25 Tot.

 SoSav= 347.4 0.40% -12.94% 15.85% T-76

 SoSpt= 362.2 2.433E-09 1.999E-14 166.0 0.0% H2O

 8.759E-10 7.195E-15 0.0 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 110.000 6.450 -146.530 7.637E-03 9.791E-08 256.3 -22.7 -1.3 -0.000 Mean

 6487.866 6.492 7.50% 0.85% 6.80% M-76

 900.0 GRM 0.0000 -4.08% -15.90% 17.83% 4.0 68.1 ranS

 3.53% 9.36% 11.44% 25.6 25.8 sigS

 Wind and SoS -10.41% -5.60% -8.91% -27.3 28.8 ranL

------------ 15.40% 7.02% 8.59% 33.7 34.0 sigL

 Ruv = 0.010 -14.49% -21.50% 8.92% -23.3 97.0 0.22 ranT 

 SpdAv= 52.0 15.80% 11.70% 14.30% 42.3 42.7 5.95 sigT

72
 SpdSd= 37.8 6.530E-03 7.686E-08 279.2 -46.0 95.7 0.22 Tot.

 SoSav= 330.5 -8.08% -20.83% 16.33% T-76

 SoSpt= 344.9 3.243E-09 2.906E-14 158.2 0.0% H2O

 1.167E-09 1.046E-14 0.0 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 108.000 6.850 -145.330 9.758E-03 1.367E-07 236.1 -18.0 -1.8 -0.000 Mean

 6485.831 6.895 4.71% -1.04% 5.73% M-76

 960.0 GRM 0.0000 -2.57% -1.57% -1.35% 7.5 40.5 ranS

 3.42% 9.91% 10.38% 23.5 25.2 sigS

 Wind and SoS -14.47% -6.85% -8.07% -21.4 31.8 ranL

------------ 14.91% 7.54% 7.90% 31.2 33.4 sigL

 Ruv = 0.010 -17.05% -8.42% -9.42% -14.0 72.3 1.48 ranT

 SpdAv= 48.1 15.29% 12.45% 13.05% 39.0 41.9 5.81 sigT

 SpdSd= 36.0 8.094E-03 1.252E-07 213.8 -32.0 70.5 1.48 Tot.

 SoSav= 316.1 -13.14% -9.38% -4.23% T-76

 SoSpt= 300.9 4.507E-09 4.357E-14 151.3 0.0% H2O

 1.623E-09 1.569E-14 0.0 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 106.000 7.250 -144.130 1.281E-02 1.955E-07 218.1 -12.7 -2.4 -0.000 Mean

 6483.795 7.298 2.84% 0.09% 2.46% M-76

 1020.0 GRM 0.0000 -2.94% -10.35% 8.77% 16.4 17.7 ranS

 3.30% 10.42% 9.23% 21.4 24.6 sigS

 Wind and SoS -14.33% -8.05% -7.37% -15.8 34.1 ranL

------------ 14.40% 8.04% 7.13% 28.7 32.9 sigL

 Ruv = 0.010 -17.26% -18.40% 1.40% 0.6 51.8 0.95 ranT

 SpdAv= 44.3 14.77% 13.16% 11.66% 35.8 41.1 5.68 sigT

 SpdSd= 34.2 1.060E-02 1.595E-07 221.2 -12.1 49.4 0.95 Tot.

 SoSav= 302.8 -14.91% -18.33% 3.89% T-76

 SoSpt= 304.9 6.438E-09 6.690E-14 144.7 0.0% H2O

 2.318E-09 2.408E-14 0.0 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 104.000 7.650 -142.930 1.728E-02 2.839E-07 204.1 -8.1 -3.2 -0.000 Mean

 6481.756 7.700 2.37% 2.56% -0.59% M-76

 1080.0 GRM 0.0000 -2.30% -5.18% 2.91% 21.0 -21.6 ranS

 3.19% 10.95% 8.12% 22.1 24.1 sigS

 Wind and SoS -15.58% -9.21% -7.00% -12.2 35.9 ranL

------------ 13.89% 8.57% 6.36% 29.8 32.6 sigL

 Ruv = 0.009 -17.89% -14.39% -4.09% 8.8 14.3 0.69 ranT

 SpdAv= 43.6 14.25% 13.90% 10.31% 37.1 40.5 5.54 sigT

 SpdSd= 34.5 1.419E-02 2.431E-07 195.8 0.7 11.1 0.69 Tot.

 SoSav= 291.9 -15.94% -12.20% -4.65% T-76

 SoSpt= 285.9 9.394E-09 1.036E-13 139.2 0.0% H2O

 3.382E-09 3.730E-14 0.0 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 102.000 8.050 -141.730 2.385E-02 4.139E-07 194.5 -4.8 -4.1 -0.000 Mean

 6479.716 8.103 3.12% 5.26% -2.51% M-76

 1140.0 GRM 0.0000 -3.42% -12.71% 7.80% 21.0 -13.7 ranS

 3.07% 11.49% 7.06% 25.1 23.8 sigS

 Wind and SoS -18.49% -10.30% -6.36% -9.0 37.2 ranL

------------ 13.39% 9.12% 5.60% 34.2 32.4 sigL

 Ruv = 0.009 -21.91% -23.02% 1.44% 12.0 23.6 1.36 ranT

 SpdAv= 45.9 13.73% 14.67% 9.02% 42.4 40.2 5.40 sigT

 SpdSd= 36.7 1.862E-02 3.186E-07 197.3 7.2 19.4 1.35 Tot.

 SoSav= 284.0 -19.47% -18.97% -1.10% T-76

 SoSpt= 286.1 1.393E-08 1.601E-13 135.4 0.0% H2O

 5.014E-09 5.762E-14 0.1 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 100.000 8.450 -140.530 3.351E-02 6.094E-07 186.9 -2.7 -5.2 -0.000 Mean

 6477.673 8.505 4.69% 8.75% -4.19% M-76

 1200.0 GRM 0.0000 -4.93% -19.68% 9.53% 9.6 35.5 ranS

 2.95% 12.00% 5.84% 27.7 23.5 sigS

 Wind and SoS -23.21% -11.25% -5.49% -4.3 38.0 ranL

------------ 12.87% 9.65% 4.70% 38.0 32.3 sigL

73
 Ruv = 0.009 -28.14% -30.93% 4.04% 5.3 73.5 -4.01 ranT

 SpdAv= 48.4 13.20% 15.40% 7.50% 47.0 40.0 5.26 sigT

 SpdSd= 38.8 2.408E-02 4.209E-07 194.5 2.6 68.3 -4.01 Tot.

 SoSav= 277.5 -24.77% -24.89% -0.32% T-76

 SoSpt= 283.0 2.103E-08 2.498E-13 132.2 0.0% H2O

 7.571E-09 8.994E-14 0.3 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 98.000 8.850 -139.330 4.775E-02 8.875E-07 183.9 -2.1 -6.0 -0.001 Mean

 6475.628 8.908 6.08% 10.07% -4.09% M-76

 1260.0 GRM 0.0000 -1.83% 0.47% -1.64% 2.6 16.8 ranS

 3.05% 11.33% 5.91% 26.9 21.4 sigS

 Wind and SoS -15.54% -11.17% -5.83% 1.0 35.7 ranL

------------ 13.32% 9.46% 4.94% 37.8 30.2 sigL

 Ruv = 0.009 -17.37% -10.70% -7.48% 3.7 52.4 -9.67 ranT

 SpdAv= 46.6 13.66% 14.76% 7.70% 46.4 37.0 5.16 sigT

 SpdSd= 37.3 3.946E-02 7.926E-07 170.1 1.6 46.4 -9.67 Tot.

 SoSav= 274.5 -12.35% -1.70% -11.26% T-76

 SoSpt= 264.0 3.397E-08 4.080E-13 131.1 0.0% H2O

 1.223E-08 1.469E-13 0.6 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 96.000 9.250 -138.130 6.841E-02 1.291E-06 182.1 -2.3 -6.5 -0.001 Mean

 6473.582 9.310 7.28% 11.07% -3.81% M-76

 1320.0 GRM 0.0000 -1.19% -2.06% 0.69% 19.5 -1.2 ranS

 3.17% 10.66% 5.97% 26.0 19.1 sigS

 Wind and SoS -16.44% -10.87% -6.09% 6.2 32.2 ranL

------------ 13.80% 9.23% 5.17% 37.5 27.5 sigL

 Ruv = 0.008 -17.63% -12.93% -5.40% 25.7 31.0 -5.43 ranT

 SpdAv= 44.6 14.16% 14.10% 7.90% 45.7 33.5 5.06 sigT

 SpdSd= 35.6 5.635E-02 1.124E-06 172.3 23.3 24.5 -5.43 Tot.

 SoSav= 272.4 -11.63% -3.29% -9.00% T-76

 SoSpt= 265.0 5.516E-08 6.655E-13 131.9 0.0% H2O

 1.986E-08 2.396E-13 0.8 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 94.000 9.650 -136.930 9.907E-02 1.872E-06 182.6 -3.6 -6.8 -0.001 Mean

 6471.533 9.713 9.39% 12.10% -2.74% M-76

 1380.0 GRM 0.0000 -0.50% -0.13% -0.33% 7.8 7.5 ranS

 3.29% 10.01% 6.04% 26.4 18.0 sigS

 Wind and SoS -15.94% -10.40% -6.27% 11.6 30.5 ranL

------------ 14.33% 8.99% 5.43% 38.9 26.6 sigL

 Ruv = 0.008 -16.44% -10.54% -6.60% 19.4 38.0 -1.64 ranT

 SpdAv= 45.0 14.71% 13.45% 8.12% 47.0 32.1 4.96 sigT

 SpdSd= 35.8 8.278E-02 1.675E-06 170.5 15.8 31.1 -1.64 Tot.

 SoSav= 272.2 -8.59% 0.28% -9.16% T-76

 SoSpt= 263.1 9.327E-08 1.118E-12 133.2 0.0% H2O

 3.358E-08 4.024E-13 0.8 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 92.000 10.050 -135.730 1.441E-01 2.695E-06 185.1 -5.5 -7.0 0.003 Mean

 6469.483 10.115 11.85% 12.64% -0.99% M-76

 1440.0 GRM 0.0000 0.21% 1.46% -1.28% -23.4 -1.7 ranS

 3.42% 9.38% 6.12% 27.5 18.5 sigS

 Wind and SoS -15.54% -9.78% -6.36% 17.6 30.9 ranL

------------ 14.90% 8.73% 5.70% 41.6 28.0 sigL

 Ruv = 0.008 -15.33% -8.32% -7.64% -5.7 29.3 -1.38 ranT

 SpdAv= 47.6 15.29% 12.81% 8.36% 49.9 33.5 4.85 sigT 

 SpdSd= 37.8 1.220E-01 2.471E-06 171.0 -11.3 22.2 -1.38 Tot.

 SoSav= 273.6 -5.30% 3.27% -8.56% T-76

 SoSpt= 263.0 1.632E-07 1.923E-12 134.8 0.0% H2O

 5.876E-08 6.924E-13 0.9 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 90.000 10.450 -134.530 2.082E-01 3.845E-06 188.0 -6.6 -6.7 0.004 Mean

 6467.430 10.518 13.38% 12.54% 0.61% M-76

 1500.0 GRM 0.0000 -0.33% -1.31% 1.16% -24.2 12.8 ranS

 3.52% 8.74% 6.18% 28.3 18.8 sigS

74
 Wind and SoS -14.64% -9.01% -6.34% 23.9 30.9 ranL

------------ 15.36% 8.43% 5.96% 44.0 29.3 sigL

 Ruv = 0.008 -14.96% -10.32% -5.18% -0.3 43.6 -3.17 ranT

 SpdAv= 49.8 15.76% 12.14% 8.58% 52.3 34.8 4.75 sigT

 SpdSd= 39.5 1.770E-01 3.448E-06 178.3 -6.9 36.9 -3.17 Tot.

 SoSav= 275.3 -3.59% 0.92% -4.60% T-76

 SoSpt= 268.1 2.845E-07 3.278E-12 136.4 0.0% H2O

 1.024E-07 1.180E-12 0.9 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 88.000 10.850 -133.330 2.957E-01 5.367E-06 191.5 -3.8 -5.1 0.003 Mean

 6465.376 10.920 12.97% 10.09% 2.48% M-76

 1560.0 GRM 0.0000 -2.85% -8.88% 7.16% -40.0 -2.4 ranS

 2.93% 7.20% 5.16% 27.1 19.4 sigS

 Wind and SoS -10.18% -7.23% -3.48% 28.2 30.6 ranL

------------ 12.78% 7.19% 5.16% 43.2 30.9 sigL

 Ruv = 0.009 -13.03% -16.12% 3.68% -11.8 28.2 -0.30 ranT

 SpdAv= 49.1 13.11% 10.18% 7.29% 50.9 36.4 4.49 sigT

 SpdSd= 39.4 2.571E-01 4.502E-06 198.5 -15.6 23.1 -0.30 Tot.

 SoSav= 277.7 -1.75% -7.65% 6.25% T-76 

 SoSpt= 282.8 4.789E-07 5.419E-12 138.0 0.0% H2O

 1.724E-07 1.951E-12 0.9 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 86.000 11.250 -132.130 4.174E-01 7.449E-06 195.0 -0.9 -3.6 0.002 Mean

 6463.319 11.323 11.80% 7.07% 4.36% M-76

 1620.0 GRM 0.0000 -2.42% -5.01% 3.09% 4.9 2.9 ranS

 2.20% 5.36% 3.99% 26.0 19.7 sigS

 Wind and SoS -5.84% -5.16% -0.97% 32.1 29.7 ranL

------------ 9.59% 5.55% 4.13% 42.6 32.3 sigL

 Ruv = 0.011 -8.26% -10.17% 2.12% 37.0 32.5 5.63 ranT

 SpdAv= 48.8 9.84% 7.71% 5.74% 49.9 37.8 4.22 sigT

 SpdSd= 39.3 3.829E-01 6.692E-06 199.2 36.1 28.9 5.64 Tot.

 SoSav= 280.1 2.56% -3.82% 6.57% T-76

 SoSpt= 283.0 8.014E-07 8.904E-12 139.7 0.0% H2O

 2.885E-07 3.206E-12 1.0 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 84.000 11.650 -130.930 5.844E-01 1.027E-05 198.2 1.6 -2.9 0.001 Mean

 6461.261 11.725 10.04% 5.90% 3.86% M-76

 1680.0 GRM 0.0000 -0.50% 0.85% -1.62% 22.4 -45.9 ranS

 1.64% 4.00% 3.14% 24.3 18.5 sigS

 Wind and SoS -3.18% -3.63% 0.69% 34.5 26.2 ranL

------------ 7.14% 4.29% 3.37% 40.9 31.2 sigL

 Ruv = 0.012 -3.69% -2.78% -0.94% 56.9 -19.6 -2.79 ranT

 SpdAv= 46.7 7.33% 5.86% 4.61% 47.6 36.3 3.93 sigT

 SpdSd= 37.6 5.628E-01 9.981E-06 196.4 58.5 -22.5 -2.79 Tot.

 SoSav= 282.3 5.98% 2.96% 2.89% T-76

 SoSpt= 281.0 1.344E-06 1.470E-11 141.4 0.0% H2O

 4.840E-07 5.292E-12 1.0 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 82.000 12.050 -129.730 8.121E-01 1.407E-05 201.0 4.1 -3.0 0.001 Mean

 6459.200 12.128 8.26% 4.84% 3.23% M-76

 1740.0 GRM 0.0000 -0.37% -1.00% 0.74% 19.8 -27.0 ranS

 1.45% 3.57% 2.83% 21.8 16.0 sigS

 Wind and SoS -1.49% -3.00% 1.49% 34.7 20.8 ranL

------------ 6.34% 3.97% 3.15% 37.7 27.6 sigL

 Ruv = 0.013 -1.86% -4.00% 2.23% 54.5 -6.1 -3.99 ranT

 SpdAv= 42.3 6.51% 5.34% 4.23% 43.5 31.9 3.62 sigT

 SpdSd= 33.9 7.970E-01 1.350E-05 205.5 58.7 -9.1 -3.99 Tot.

 SoSav= 284.3 6.25% 0.65% 5.54% T-76

 SoSpt= 287.4 2.263E-06 2.439E-11 143.1 0.0% H2O

 8.148E-07 8.783E-12 1.0 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 80.000 12.450 -128.530 1.123E+00 1.920E-05 203.8 7.1 -3.2 0.001 Mean

 6457.138 12.530 6.74% 4.04% 2.58% M-76

75
 1800.0 GRM 0.0000 0.01% 0.24% -0.26% 13.0 -27.8 ranS

 1.25% 3.12% 2.51% 19.2 13.2 sigS

 Wind and SoS -0.32% -2.37% 2.13% 33.7 15.6 ranL

------------ 5.44% 3.60% 2.89% 34.1 23.5 sigL

 Ruv = 0.014 -0.31% -2.14% 1.87% 46.7 -12.2 -4.87 ranT

 SpdAv= 37.7 5.58% 4.76% 3.82% 39.1 26.9 3.30 sigT

 SpdSd= 29.8 1.120E+00 1.879E-05 207.6 53.8 -15.4 -4.87 Tot.

 SoSav= 286.2 6.41% 1.81% 4.50% T-76

 SoSpt= 288.9 3.458E-06 3.677E-11 144.6 0.0% H2O

 1.084E-06 1.153E-11 0.9 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 78.000 12.850 -127.330 1.549E+00 2.618E-05 206.0 13.6 -1.1 0.000 Mean

 6455.074 12.933 5.54% 3.73% 1.72% M-76

 1860.0 GRM 0.0000 0.72% 1.87% -1.34% -23.8 -23.0 ranS

 1.24% 3.00% 2.44% 18.2 12.3 sigS 

 Wind and SoS 0.26% -2.01% 2.47% 34.9 12.9 ranL

------------ 5.40% 3.59% 2.92% 33.4 22.6 sigL

 Ruv = 0.016 0.98% -0.14% 1.13% 11.1 -10.1 -4.08 ranT

 SpdAv= 38.2 5.54% 4.68% 3.80% 38.0 25.8 2.98 sigT

 SpdSd= 28.9 1.564E+00 2.614E-05 208.3 24.7 -11.1 -4.08 Tot.

 SoSav= 287.8 6.58% 3.58% 2.87% T-76

 SoSpt= 289.4 4.018E-06 4.225E-11 145.0 0.0% H2O

 1.494E-06 1.571E-11 1.1 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 76.000 13.250 -126.130 2.128E+00 3.559E-05 208.3 20.1 0.8 -0.000 Mean

 6453.008 13.335 4.68% 3.72% 0.89% M-76

 1920.0 GRM 0.0000 1.18% 4.01% -3.35% -33.8 -12.0 ranS

 1.23% 2.88% 2.37% 17.2 11.5 sigS

 Wind and SoS 0.57% -1.65% 2.75% 35.5 10.4 ranL

------------ 5.37% 3.57% 2.94% 32.6 21.7 sigL

 Ruv = 0.017 1.75% 2.36% -0.60% 1.7 -1.7 0.86 ranT

 SpdAv= 39.9 5.51% 4.59% 3.78% 36.9 24.6 2.67 sigT

 SpdSd= 27.8 2.166E+00 3.643E-05 207.0 21.7 -0.8 0.86 Tot.

 SoSav= 289.4 6.51% 6.17% 0.28% T-76

 SoSpt= 288.5 6.122E-06 6.369E-11 146.4 0.0% H2O

 2.053E-06 2.136E-11 1.1 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 74.000 13.650 -124.930 2.919E+00 4.805E-05 211.6 25.4 1.5 -0.000 Mean

 6450.940 13.737 4.20% 3.58% 0.58% M-76

 1980.0 GRM 0.0000 2.86% 5.83% -3.48% -31.3 -4.5 ranS

 1.18% 2.72% 2.22% 17.0 10.8 sigS

 Wind and SoS 1.10% -1.27% 2.90% 35.1 7.2 ranL

------------ 5.13% 3.49% 2.85% 31.2 19.7 sigL 

 Ruv = 0.004 3.95% 4.56% -0.58% 3.8 2.6 -0.18 ranT

 SpdAv= 41.4 5.26% 4.43% 3.61% 35.5 22.4 2.39 sigT

 SpdSd= 26.4 3.034E+00 5.024E-05 210.3 29.2 4.1 -0.18 Tot.

 SoSav= 291.6 8.32% 8.31% -0.01% T-76

 SoSpt= 290.8 9.302E-06 9.526E-11 148.2 0.0% H2O

 2.816E-06 2.884E-11 0.9 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 72.000 14.050 -123.730 3.983E+00 6.428E-05 215.9 29.7 1.1 -0.000 Mean

 6448.871 14.140 3.83% 3.07% 0.75% M-76

 2040.0 GRM 0.0000 1.79% 1.34% 0.51% -32.3 4.1 ranS

 1.06% 2.51% 1.97% 17.5 9.7 sigS

 Wind and SoS 2.04% -0.89% 2.86% 33.8 3.7 ranL

------------ 4.61% 3.33% 2.61% 29.4 16.3 sigL

 Ruv = -0.024 3.83% 0.45% 3.37% 1.5 7.8 1.47 ranT

 SpdAv= 42.5 4.73% 4.17% 3.26% 34.2 19.0 2.15 sigT

 SpdSd= 24.6 4.136E+00 6.457E-05 223.1 31.2 9.0 1.47 Tot.

 SoSav= 294.5 7.81% 3.53% 4.14% T-76

 SoSpt= 299.5 1.691E-05 1.698E-10 151.2 0.0% H2O

 4.812E-06 4.831E-11 0.7 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

76
 70.000 14.450 -122.530 5.404E+00 8.555E-05 220.1 34.1 0.8 -0.000 Mean

 6446.799 14.542 3.50% 3.28% 0.24% M-76

 2100.0 GRM 0.0000 1.68% 2.70% -1.07% -20.7 2.5 ranS

 0.92% 2.29% 1.70% 17.8 8.0 sigS

 Wind and SoS 2.15% -0.54% 2.70% 32.2 1.1 ranL

------------ 4.02% 3.13% 2.33% 27.6 12.4 sigL

 Ruv = -0.052 3.83% 2.16% 1.63% 11.5 3.6 1.70 ranT

 SpdAv= 44.1 4.13% 3.88% 2.88% 32.8 14.7 1.91 sigT 

 SpdSd= 22.6 5.611E+00 8.740E-05 223.7 45.6 4.4 1.70 Tot.

 SoSav= 297.4 7.46% 5.51% 1.87% T-76

 SoSpt= 299.8 3.004E-05 2.957E-10 154.1 0.0% H2O

 7.602E-06 7.484E-11 0.6 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 68.000 14.850 -121.330 7.281E+00 1.121E-04 226.4 35.1 0.6 -0.000 Mean

 6444.726 14.945 3.22% 2.67% 0.58% M-76

 2160.0 GRM 0.0000 0.84% -1.36% 2.15% -5.8 -7.5 ranS

 0.90% 2.31% 1.61% 17.3 8.5 sigS

 Wind and SoS 2.27% -0.28% 2.68% 29.4 0.9 ranL

------------ 3.94% 3.26% 2.28% 25.0 12.3 sigL

 Ruv = -0.008 3.11% -1.64% 4.83% 23.6 -6.6 -0.26 ranT

 SpdAv= 43.9 4.04% 4.00% 2.79% 30.4 15.0 1.76 sigT

 SpdSd= 21.3 7.508E+00 1.102E-04 237.3 58.7 -6.0 -0.26 Tot.

 SoSav= 301.6 6.43% 0.98% 5.44% T-76

 SoSpt= 308.8 4.839E-05 4.632E-10 157.6 0.0% H2O

 9.194E-06 8.800E-11 0.3 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 66.000 15.250 -120.130 9.730E+00 1.458E-04 232.5 36.3 0.4 -0.000 Mean

 6442.651 15.347 2.84% 2.00% 0.86% M-76

 2220.0 GRM 0.0000 0.51% 0.14% 0.35% 6.5 -11.3 ranS

 0.88% 2.30% 1.52% 16.5 9.1 sigS

 Wind and SoS 2.58% -0.01% 2.62% 26.4 0.9 ranL

------------ 3.83% 3.36% 2.22% 22.3 12.3 sigL

 Ruv = 0.037 3.09% 0.12% 2.96% 32.9 -10.4 0.56 ranT

 SpdAv= 43.9 3.93% 4.07% 2.69% 27.8 15.3 1.61 sigT

 SpdSd= 19.9 1.003E+01 1.460E-04 239.4 69.2 -10.0 0.56 Tot.

 SoSav= 305.6 6.02% 2.13% 3.85% T-76

 SoSpt= 310.1 7.695E-05 7.170E-10 161.0 0.0% H2O

 1.106E-05 1.031E-10 0.2 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 64.000 15.650 -118.930 1.292E+01 1.890E-04 238.2 36.3 0.4 0.001 Mean

 6440.574 15.749 2.49% 1.60% 0.90% M-76

 2280.0 GRM 0.0000 -0.07% 0.32% -0.34% -0.3 -12.5 ranS

 0.92% 2.40% 1.47% 16.4 9.5 sigS

 Wind and SoS 2.80% 0.25% 2.50% 23.9 0.6 ranL

------------ 3.99% 3.44% 2.12% 20.2 11.7 sigL

 Ruv = 0.059 2.73% 0.56% 2.16% 23.6 -11.9 -1.11 ranT

 SpdAv= 43.2 4.10% 4.20% 2.58% 26.0 15.0 1.55 sigT

 SpdSd= 18.9 1.327E+01 1.901E-04 243.3 59.9 -11.5 -1.11 Tot.

 SoSav= 309.3 5.28% 2.17% 3.07% T-76

 SoSpt= 312.7 1.111E-04 1.011E-09 163.8 0.0% H2O

 1.659E-05 1.509E-10 0.1 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 62.000 16.050 -117.730 1.707E+01 2.444E-04 243.3 35.1 0.5 0.001 Mean

 6438.495 16.152 2.28% 1.53% 0.74% M-76

 2340.0 GRM 0.0000 -1.04% -3.57% 2.12% -21.9 -3.2 ranS

 1.01% 2.63% 1.45% 17.0 9.5 sigS

 Wind and SoS 2.20% 0.49% 2.24% 22.0 0.0 ranL

------------ 4.42% 3.54% 1.95% 18.7 10.5 sigL

 Ruv = 0.061 1.16% -3.08% 4.37% 0.1 -3.2 0.91 ranT

 SpdAv= 41.7 4.54% 4.41% 2.43% 25.3 14.2 1.58 sigT

 SpdSd= 18.2 1.727E+01 2.369E-04 253.9 35.2 -2.7 0.91 Tot.

 SoSav= 312.7 3.46% -1.60% 5.14% T-76

 SoSpt= 319.5 1.580E-04 1.407E-09 166.3 0.0% H2O

77
 2.530E-05 2.253E-10 0.1 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 60.000 16.450 -116.530 2.243E+01 3.144E-04 248.4 34.0 0.6 0.001 Mean

 6436.414 16.554 2.12% 1.53% 0.57% M-76

 2400.0 GRM 0.0000 -2.06% -5.15% 2.44% -3.3 2.6 ranS

 1.10% 2.86% 1.41% 17.4 9.4 sigS

 Wind and SoS 1.41% 0.72% 1.51% 20.1 -0.3 ranL

------------ 4.81% 3.61% 1.78% 17.2 9.3 sigL

 Ruv = 0.063 -0.65% -4.43% 3.95% 16.8 2.3 -0.69 ranT

 SpdAv= 40.3 4.94% 4.61% 2.27% 24.4 13.2 1.61 sigT

 SpdSd= 17.5 2.228E+01 3.005E-04 258.2 50.8 2.9 -0.69 Tot.

 SoSav= 316.0 1.46% -2.96% 4.55% T-76

 SoSpt= 322.2 2.140E-04 1.866E-09 168.7 0.0% H2O

 3.383E-05 2.950E-10 0.1 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 58.000 16.850 -115.330 2.929E+01 4.026E-04 253.5 29.5 0.2 0.000 Mean

 6434.332 16.956 1.96% 1.59% 0.38% M-76

 2460.0 GRM 0.0000 -0.73% 0.19% -0.72% 12.4 0.1 ranS

 1.06% 2.84% 1.40% 17.9 9.4 sigS

 Wind and SoS 1.49% 0.85% 0.45% 19.1 -0.4 ranL

------------ 4.62% 3.37% 1.66% 16.4 8.6 sigL

 Ruv = 0.073 0.76% 1.03% -0.27% 31.4 -0.3 1.49 ranT

 SpdAv= 36.4 4.74% 4.40% 2.18% 24.3 12.7 1.53 sigT

 SpdSd= 17.3 2.951E+01 4.068E-04 252.8 60.9 -0.1 1.49 Tot.

 SoSav= 319.1 2.73% 2.64% 0.11% T-76

 SoSpt= 318.7 2.725E-04 2.329E-09 170.6 0.0% H2O

 3.807E-05 3.254E-10 0.1 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 56.000 17.250 -114.130 3.805E+01 5.129E-04 258.6 25.0 -0.3 -0.000 Mean

 6432.248 17.358 1.84% 1.67% 0.22% M-76

 2520.0 GRM 0.0000 0.93% 4.02% -2.41% 18.3 -8.0 ranS

 1.02% 2.80% 1.39% 18.5 9.3 sigS 

 Wind and SoS 1.99% 0.92% 0.49% 18.0 -0.4 ranL

------------ 4.43% 3.13% 1.55% 15.7 7.9 sigL

 Ruv = 0.081 2.92% 4.94% -1.93% 36.3 -8.3 2.80 ranT

 SpdAv= 32.8 4.55% 4.20% 2.09% 24.3 12.2 1.46 sigT

 SpdSd= 17.1 3.916E+01 5.383E-04 253.6 61.3 -8.6 2.80 Tot.

 SoSav= 322.3 4.81% 6.70% -1.71% T-76

 SoSpt= 319.2 3.453E-04 2.893E-09 172.6 0.0% H2O

 4.274E-05 3.581E-10 0.1 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 54.000 17.650 -112.930 4.920E+01 6.535E-04 262.4 21.0 -0.5 -0.000 Mean

 6430.162 17.761 1.78% 2.26% -0.42% M-76

 2580.0 GRM 0.0000 2.01% 5.55% -2.79% -6.1 -14.0 ranS

 0.98% 2.71% 1.36% 18.9 9.3 sigS

 Wind and SoS 2.09% 0.97% 0.51% 17.5 -0.6 ranL

------------ 4.26% 2.96% 1.49% 15.4 7.5 sigL

 Ruv = 0.080 4.10% 6.52% -2.27% 11.5 -14.6 -0.52 ranT

 SpdAv= 29.8 4.37% 4.01% 2.02% 24.4 11.9 1.37 sigT

 SpdSd= 17.0 5.122E+01 6.961E-04 256.5 32.5 -15.1 -0.52 Tot.

 SoSav= 324.7 5.95% 8.94% -2.68% T-76

 SoSpt= 320.9 4.357E-04 3.598E-09 174.0 0.0% H2O

 4.789E-05 3.954E-10 0.1 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 52.000 18.050 -111.730 6.343E+01 8.341E-04 265.0 17.3 -0.6 -0.000 Mean

 6428.075 18.163 1.95% 3.53% -1.50% M-76

 2640.0 GRM 0.0000 1.00% 0.76% 0.19% -1.4 4.2 ranS

 0.94% 2.56% 1.31% 19.1 9.2 sigS

 Wind and SoS 1.51% 1.00% 0.54% 17.6 -1.1 ranL

------------ 4.08% 2.83% 1.45% 15.6 7.5 sigL

 Ruv = 0.071 2.51% 1.77% 0.73% 16.3 3.1 -2.14 ranT

 SpdAv= 27.4 4.19% 3.82% 1.95% 24.7 11.9 1.26 sigT

 SpdSd= 17.2 6.502E+01 8.488E-04 266.9 33.6 2.5 -2.14 Tot. 

78
 SoSav= 326.3 4.50% 5.36% -0.78% T-76

 SoSpt= 327.5 5.609E-04 4.586E-09 175.1 0.0% H2O

 5.379E-05 4.398E-10 0.1 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 50.000 18.450 -110.530 8.158E+01 1.062E-03 267.7 13.5 -0.6 -0.000 Mean

 6425.985 18.565 2.26% 3.41% -1.10% M-76

 2700.0 GRM 0.0000 1.08% 2.24% -0.96% -15.1 4.6 ranS

 0.89% 2.40% 1.24% 19.3 9.1 sigS

 Wind and SoS 1.73% 1.00% 0.54% 17.8 -1.4 ranL

------------ 3.90% 2.70% 1.40% 15.8 7.5 sigL

 Ruv = 0.063 2.81% 3.24% -0.42% 2.7 3.2 -0.61 ranT

 SpdAv= 25.4 4.00% 3.62% 1.87% 25.0 11.8 1.15 sigT

 SpdSd= 17.4 8.387E+01 1.096E-03 266.5 16.2 2.6 -0.61 Tot.

 SoSav= 328.0 5.13% 6.76% -1.52% T-76

 SoSpt= 327.3 6.984E-04 5.653E-09 175.9 0.0% H2O

 5.267E-05 4.264E-10 0.0 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 48.000 18.850 -109.330 1.048E+02 1.368E-03 266.8 13.6 -0.7 -0.000 Mean

 6423.895 18.967 2.41% 3.91% -1.44% M-76

 2760.0 GRM 0.0000 1.53% 3.65% -1.79% 6.2 -8.1 ranS

 0.85% 2.30% 1.24% 18.7 8.5 sigS

 Wind and SoS 2.72% 1.00% 1.40% 17.7 -1.5 ranL

------------ 3.71% 2.67% 1.44% 15.7 7.1 sigL

 Ruv = 0.061 4.25% 4.65% -0.39% 23.8 -9.6 -0.64 ranT

 SpdAv= 24.9 3.81% 3.53% 1.91% 24.4 11.1 1.05 sigT

 SpdSd= 16.8 1.092E+02 1.432E-03 265.7 37.5 -10.3 -0.64 Tot.

 SoSav= 327.4 6.76% 8.75% -1.82% T-76

 SoSpt= 326.8 8.568E-04 6.959E-09 175.3 0.0% H2O

 5.117E-05 4.156E-10 0.0 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 46.000 19.250 -108.130 1.346E+02 1.764E-03 265.9 13.6 -0.7 0.000 Mean

 6421.802 19.369 2.50% 2.89% -0.38% M-76

 2820.0 GRM 0.0000 1.06% 1.46% -0.35% -24.9 -5.8 ranS

 0.81% 2.20% 1.25% 18.0 7.8 sigS

 Wind and SoS 2.79% 0.98% 1.72% 17.6 -1.4 ranL

------------ 3.51% 2.65% 1.50% 15.6 6.8 sigL

 Ruv = 0.059 3.84% 2.44% 1.37% -7.3 -7.3 0.25 ranT

 SpdAv= 24.4 3.61% 3.44% 1.95% 23.8 10.3 0.94 sigT

 SpdSd= 16.3 1.398E+02 1.807E-03 269.5 6.3 -8.0 0.25 Tot.

 SoSav= 326.9 6.44% 5.40% 0.98% T-76

 SoSpt= 329.1 1.086E-03 8.847E-09 174.9 0.0% H2O

 7.047E-05 5.743E-10 0.1 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 44.000 19.650 -106.930 1.733E+02 2.291E-03 263.5 13.9 -0.8 0.000 Mean

 6419.708 19.771 2.23% 1.43% 0.79% M-76

 2880.0 GRM 0.0000 0.90% 1.60% -0.61% 5.5 -5.9 ranS

 0.76% 2.07% 1.23% 17.3 7.1 sigS

 Wind and SoS 2.82% 0.90% 1.80% 17.2 -1.3 ranL

------------ 3.32% 2.56% 1.53% 15.3 6.2 sigL

 Ruv = 0.063 3.72% 2.50% 1.19% 22.7 -7.1 0.20 ranT

 SpdAv= 23.9 3.41% 3.29% 1.97% 23.1 9.4 0.86 sigT

 SpdSd= 15.7 1.797E+02 2.348E-03 266.6 36.7 -7.9 0.20 Tot.

 SoSav= 325.4 6.04% 3.96% 1.99% T-76

 SoSpt= 327.3 1.360E-03 1.119E-08 173.8 0.0% H2O

 8.185E-05 6.731E-10 0.1 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 42.000 20.050 -105.730 2.239E+02 3.007E-03 259.4 14.7 -0.8 -0.000 Mean

 6417.612 20.173 1.77% 0.39% 1.37% M-76

 2940.0 GRM 0.0000 1.09% 2.45% -1.26% 3.9 -7.4 ranS

 0.72% 1.89% 1.20% 16.5 6.3 sigS

 Wind and SoS 2.70% 0.78% 1.81% 16.5 -1.0 ranL

------------ 3.13% 2.41% 1.53% 14.7 5.6 sigL

 Ruv = 0.072 3.79% 3.23% 0.54% 20.4 -8.4 -0.37 ranT

79
 SpdAv= 23.6 3.21% 3.06% 1.94% 22.1 8.4 0.81 sigT

 SpdSd= 14.9 2.324E+02 3.104E-03 260.8 35.1 -9.2 -0.37 Tot.

 SoSav= 322.9 5.64% 3.64% 1.92% T-76

 SoSpt= 323.8 1.696E-03 1.417E-08 172.0 0.0% H2O

 8.753E-05 7.313E-10 0.2 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 40.000 20.450 -104.530 2.902E+02 3.961E-03 255.2 14.9 -0.9 -0.000 Mean

 6415.515 20.576 1.06% -0.86% 1.94% M-76

 3000.0 GRM 0.0000 1.24% 2.02% -0.77% -13.7 -0.5 ranS

 0.68% 1.71% 1.17% 15.6 5.5 sigS

 Wind and SoS 2.49% 0.64% 1.81% 15.8 -0.7 ranL

------------ 2.95% 2.25% 1.54% 14.0 4.9 sigL

 Ruv = 0.080 3.73% 2.66% 1.05% 2.1 -1.2 0.91 ranT

 SpdAv= 22.9 3.03% 2.83% 1.93% 21.0 7.4 0.75 sigT

 SpdSd= 14.0 3.010E+02 4.067E-03 257.9 17.0 -2.1 0.91 Tot.

 SoSav= 320.3 4.84% 1.78% 3.00% T-76

 SoSpt= 321.9 2.381E-03 2.021E-08 170.7 0.0% H2O

 9.956E-05 8.457E-10 0.2 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 38.000 20.850 -103.330 3.787E+02 5.287E-03 249.5 13.9 -1.0 -0.000 Mean

 6413.416 20.978 0.42% -1.47% 1.92% M-76

 3060.0 GRM 0.0000 0.86% 0.41% 0.47% 15.3 7.4 ranS

 0.63% 1.64% 1.22% 14.8 5.3 sigS

 Wind and SoS 2.36% 0.48% 1.84% 15.1 -0.5 ranL 

------------ 2.76% 2.10% 1.57% 13.2 4.7 sigL

 Ruv = 0.083 3.22% 0.89% 2.31% 30.4 6.9 0.38 ranT

 SpdAv= 21.5 2.83% 2.67% 1.99% 19.9 7.1 0.70 sigT

 SpdSd= 13.3 3.909E+02 5.335E-03 255.3 44.4 5.9 0.38 Tot.

 SoSav= 316.7 3.65% -0.60% 4.27% T-76

 SoSpt= 320.3 3.389E-03 2.943E-08 171.7 0.0% H2O

 1.163E-04 1.011E-09 0.2 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 36.000 21.250 -102.130 4.973E+02 7.106E-03 243.8 12.8 -1.0 -0.000 Mean

 6411.316 21.380 -0.24% -2.10% 1.89% M-76

 3120.0 GRM 0.0000 0.67% 0.60% 0.08% -9.0 1.5 ranS

 0.58% 1.55% 1.26% 13.9 5.1 sigS

 Wind and SoS 2.19% 0.31% 1.85% 14.3 -0.2 ranL

------------ 2.54% 1.95% 1.59% 12.4 4.5 sigL

 Ruv = 0.086 2.87% 0.91% 1.93% 5.3 1.3 0.54 ranT

 SpdAv= 20.1 2.60% 2.49% 2.03% 18.6 6.8 0.65 sigT

 SpdSd= 12.5 5.116E+02 7.171E-03 248.5 18.1 0.3 0.53 Tot.

 SoSav= 313.0 2.62% -1.20% 3.86% T-76

 SoSpt= 316.0 4.381E-03 3.894E-08 172.6 0.0% H2O

 1.370E-04 1.219E-09 0.2 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 34.000 21.650 -100.930 6.575E+02 9.614E-03 238.3 12.1 -0.9 -0.000 Mean

 6409.214 21.782 -0.89% -2.77% 1.95% M-76

 3180.0 GRM 0.0000 0.43% 1.02% -0.66% -13.6 -4.3 ranS

 0.53% 1.45% 1.25% 12.7 4.7 sigS

 Wind and SoS 1.90% 0.14% 1.81% 13.4 0.1 ranL

------------ 2.32% 1.79% 1.55% 11.5 4.2 sigL

 Ruv = 0.076 2.33% 1.16% 1.16% -0.2 -4.1 -0.30 ranT 

 SpdAv= 18.7 2.38% 2.30% 2.00% 17.1 6.3 0.61 sigT

 SpdSd= 11.5 6.728E+02 9.725E-03 241.1 11.8 -5.0 -0.30 Tot.

 SoSav= 309.4 1.42% -1.64% 3.13% T-76

 SoSpt= 311.2 5.653E-03 5.140E-08 173.7 0.0% H2O

 1.742E-04 1.586E-09 0.2 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 32.000 22.050 -99.730 8.751E+02 1.309E-02 233.0 11.8 -0.5 -0.000 Mean

 6407.110 22.184 -1.57% -3.43% 1.99% M-76

 3240.0 GRM 0.0000 0.29% -0.86% 1.30% 11.0 1.0 ranS

 0.48% 1.31% 1.19% 11.3 4.1 sigS

 Wind and SoS 1.81% -0.04% 1.72% 12.2 0.4 ranL

80
------------ 2.10% 1.62% 1.47% 10.3 3.8 sigL

 Ruv = 0.052 2.10% -0.90% 3.02% 23.2 1.4 -0.09 ranT

 SpdAv= 17.3 2.16% 2.08% 1.89% 15.3 5.6 0.57 sigT

 SpdSd= 10.2 8.935E+02 1.297E-02 240.1 35.0 0.9 -0.09 Tot.

 SoSav= 305.9 0.49% -4.29% 5.07% T-76

 SoSpt= 310.5 7.334E-03 6.819E-08 174.9 0.0% H2O

 2.126E-04 1.979E-09 0.2 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 30.000 22.450 -98.530 1.172E+03 1.794E-02 227.8 11.3 -0.2 -0.000 Mean

 6405.005 22.586 -2.11% -2.57% 0.58% M-76

 3300.0 GRM 0.0000 0.11% -0.68% 0.92% 1.3 -0.1 ranS

 0.41% 1.13% 1.09% 9.5 3.5 sigS

 Wind and SoS 1.50% -0.19% 1.58% 10.4 1.1 ranL

------------ 1.81% 1.39% 1.34% 8.9 3.3 sigL

 Ruv = 0.088 1.60% -0.87% 2.49% 11.7 1.0 0.48 ranT

 SpdAv= 15.7 1.86% 1.79% 1.73% 13.0 4.8 0.53 sigT

 SpdSd= 8.5 1.191E+03 1.778E-02 233.5 23.0 0.8 0.48 Tot. 

 SoSav= 302.4 -0.54% -3.42% 3.08% T-76

 SoSpt= 306.2 9.662E-03 9.190E-08 176.3 0.1% H2O

 2.613E-04 2.487E-09 0.2 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 28.000 22.850 -97.330 1.581E+03 2.476E-02 222.5 8.8 0.7 -0.000 Mean

 6402.899 22.987 -2.17% -1.25% -0.90% M-76

 3360.0 GRM 0.0000 0.20% -0.66% 0.95% 0.0 -0.7 ranS

 0.31% 0.90% 0.85% 7.4 3.2 sigS

 Wind and SoS 1.06% -0.32% 1.31% 8.2 2.3 ranL

------------ 1.34% 1.19% 1.12% 7.1 3.1 sigL

 Ruv = 0.214 1.25% -0.98% 2.26% 8.3 1.5 0.22 ranT

 SpdAv= 12.4 1.37% 1.49% 1.40% 10.3 4.4 0.50 sigT

 SpdSd= 6.5 1.601E+03 2.452E-02 227.5 17.0 2.2 0.22 Tot.

 SoSav= 299.0 -0.95% -2.23% 1.34% T-76

 SoSpt= 302.3 1.294E-02 1.260E-07 177.8 0.1% H2O

 3.280E-04 3.197E-09 0.2 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 26.000 23.250 -96.130 2.143E+03 3.430E-02 217.7 5.9 2.1 -0.000 Mean

 6400.791 23.389 -2.05% 0.14% -2.17% M-76

 3420.0 GRM 0.0000 0.15% -0.26% 0.45% 0.1 4.0 ranS

 0.23% 0.76% 0.76% 5.9 2.7 sigS

 Wind and SoS 0.81% -0.45% 1.23% 6.4 2.6 ranL

------------ 1.00% 1.08% 1.08% 5.8 2.7 sigL

 Ruv = 0.300 0.96% -0.71% 1.68% 6.5 6.7 0.71 ranT

 SpdAv= 9.6 1.02% 1.32% 1.32% 8.3 3.8 0.47 sigT

 SpdSd= 5.5 2.164E+03 3.406E-02 221.4 12.4 8.8 0.71 Tot.

 SoSav= 295.8 -1.11% -0.57% -0.53% T-76

 SoSpt= 298.2 1.723E-02 1.715E-07 179.3 0.3% H2O

 4.658E-04 4.640E-09 0.2 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 24.000 23.650 -94.930 2.930E+03 4.763E-02 214.3 5.0 2.4 0.000 Mean

 6398.681 23.791 -1.42% 1.48% -2.86% M-76

 3480.0 GRM 0.0000 0.39% 0.71% -0.35% -6.6 4.9 ranS

 0.19% 0.65% 0.65% 4.6 2.8 sigS

 Wind and SoS 0.54% -0.54% 1.11% 4.8 2.7 ranL

------------ 0.83% 0.95% 0.96% 4.6 2.8 sigL

 Ruv = 0.227 0.93% 0.17% 0.76% -1.8 7.5 0.54 ranT

 SpdAv= 8.1 0.85% 1.16% 1.16% 6.5 3.9 0.44 sigT

 SpdSd= 4.8 2.957E+03 4.771E-02 215.9 3.2 9.9 0.54 Tot.

 SoSav= 293.4 -0.50% 1.65% -2.11% T-76

 SoSpt= 294.6 2.241E-02 2.266E-07 180.7 0.6% H2O

 6.709E-04 6.792E-09 0.2 0.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 22.000 24.050 -93.730 4.035E+03 6.716E-02 209.3 6.1 2.7 -0.000 Mean

 6396.570 24.193 -0.30% 4.12% -4.24% M-76

 3540.0 GRM 0.0000 0.27% 0.90% -0.66% -1.1 -0.8 ranS

81
 0.17% 0.69% 0.67% 3.9 2.6 sigS

 Wind and SoS 0.37% -0.70% 1.10% 3.8 2.6 ranL

------------ 0.72% 0.97% 0.94% 3.9 2.6 sigL

 Ruv = 0.189 0.64% 0.20% 0.44% 2.7 1.7 0.74 ranT

 SpdAv= 8.4 0.74% 1.19% 1.15% 5.5 3.7 0.43 sigT

 SpdSd= 4.5 4.061E+03 6.730E-02 210.2 8.8 4.5 0.74 Tot.

 SoSav= 290.0 0.33% 4.33% -3.82% T-76

 SoSpt= 290.6 2.822E-02 2.921E-07 182.0 1.5% H2O

 1.010E-03 1.047E-08 0.3 0.1% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 20.000 24.450 -92.530 5.586E+03 9.537E-02 204.1 9.0 3.0 -0.000 Mean

 6394.458 24.595 1.02% 7.26% -5.81% M-76

 3600.0 GRM 0.0000 0.24% 0.50% -0.27% -3.5 -0.3 ranS

 0.16% 0.73% 0.71% 3.7 2.7 sigS

 Wind and SoS 0.26% -0.86% 1.13% 3.2 2.9 ranL

------------ 0.68% 0.99% 0.96% 3.8 2.8 sigL

 Ruv = 0.167 0.49% -0.36% 0.86% -0.2 2.6 0.75 ranT

 SpdAv= 10.5 0.69% 1.23% 1.19% 5.3 3.9 0.42 sigT

 SpdSd= 4.9 5.614E+03 9.502E-02 205.8 8.8 5.6 0.75 Tot.

 SoSav= 286.4 1.52% 6.88% -5.00% T-76

 SoSpt= 287.6 3.446E-02 3.659E-07 183.1 3.6% H2O

 1.762E-03 1.873E-08 0.4 0.2% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 18.000 24.850 -91.330 7.819E+03 1.360E-01 200.3 16.2 4.0 -0.020 Mean

 6392.345 24.997 3.35% 11.79% -7.53% M-76

 3660.0 GRM 0.0000 -0.05% 1.57% -1.71% 5.1 -4.7 ranS

 0.18% 0.76% 0.76% 4.9 3.7 sigS

 Wind and SoS 0.03% -1.00% 1.13% 3.5 4.1 ranL

------------ 0.78% 0.99% 0.99% 5.0 3.7 sigL

 Ruv = 0.129 -0.01% 0.58% -0.58% 8.5 -0.5 -0.57 ranT

 SpdAv= 17.6 0.80% 1.25% 1.24% 7.0 5.2 0.46 sigT

 SpdSd= 6.8 7.818E+03 1.368E-01 199.2 24.7 3.5 -0.59 Tot.

 SoSav= 283.7 3.34% 12.43% -8.07% T-76

 SoSpt= 282.9 3.908E-02 4.227E-07 183.8 7.0% H2O

 4.167E-03 4.512E-08 0.9 0.7% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 16.000 25.250 -90.130 1.096E+04 1.884E-01 202.6 25.5 5.5 -0.125 Mean

 6390.230 25.398 5.85% 13.20% -6.46% M-76

 3720.0 GRM 0.0000 0.32% 1.17% -0.94% 12.8 6.5 ranS

 0.22% 0.71% 0.70% 6.4 5.1 sigS

 Wind and SoS -0.34% -1.00% 0.74% 3.3 6.3 ranL 

------------ 0.96% 0.90% 0.88% 6.7 5.3 sigL

 Ruv = 0.167 -0.02% 0.17% -0.19% 16.0 12.8 0.28 ranT

 SpdAv= 27.1 0.99% 1.15% 1.12% 9.3 7.4 0.49 sigT

 SpdSd= 9.3 1.096E+04 1.888E-01 202.3 41.5 18.3 0.15 Tot.

 SoSav= 285.3 5.83% 13.39% -6.64% T-76

 SoSpt= 285.1 4.913E-02 5.253E-07 185.1 6.3% H2O

 2.845E-02 3.046E-07 5.2 3.7% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 14.000 25.650 -88.930 1.524E+04 2.523E-01 210.5 33.1 7.1 -0.153 Mean

 6388.114 25.800 7.56% 10.74% -2.86% M-76

 3780.0 GRM 0.0000 0.35% 1.06% -0.81% 14.7 8.1 ranS

 0.25% 0.74% 0.74% 7.8 6.8 sigS

 Wind and SoS -0.61% -1.15% 0.63% 2.1 8.2 ranL

------------ 1.07% 0.98% 0.98% 8.2 7.2 sigL

 Ruv = 0.244 -0.26% -0.08% -0.18% 16.8 16.3 -1.32 ranT

 SpdAv= 35.2 1.10% 1.23% 1.23% 11.3 9.9 0.53 sigT

 SpdSd= 11.6 1.520E+04 2.521E-01 210.1 49.9 23.4 -1.48 Tot.

 SoSav= 290.8 7.27% 10.65% -3.03% T-76

 SoSpt= 290.5 1.138E-01 1.171E-06 190.1 5.1% H2O

 6.670E-02 6.876E-07 5.6 3.0% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 12.000 26.050 -87.730 2.086E+04 3.305E-01 219.9 34.4 6.2 0.036 Mean

82
 6385.996 26.202 7.54% 5.97% 1.50% M-76

 3840.0 GRM 0.0000 0.23% -0.15% 0.43% 1.3 -5.3 ranS

 0.25% 0.73% 0.74% 8.9 8.4 sigS

 Wind and SoS -0.68% -1.31% 0.59% -0.2 9.7 ranL

------------ 1.10% 1.11% 1.13% 9.6 9.0 sigL

 Ruv = 0.212 -0.45% -1.46% 1.03% 1.1 4.5 -0.47 ranT

 SpdAv= 37.0 1.12% 1.33% 1.35% 13.1 12.3 0.58 sigT

 SpdSd= 13.3 2.077E+04 3.257E-01 222.2 35.5 10.7 -0.43 Tot.

 SoSav= 297.3 7.06% 4.42% 2.55% T-76 

 SoSpt= 298.8 5.286E-01 5.208E-06 200.1 7.4% H2O

 2.997E-01 2.957E-06 6.2 4.2% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 10.000 26.450 -86.530 2.816E+04 4.221E-01 232.4 29.7 4.9 0.136 Mean

 6383.877 26.604 6.27% 2.07% 4.12% M-76

 3900.0 GRM 0.0000 0.09% -0.59% 0.82% 13.2 1.9 ranS

 0.24% 0.47% 0.47% 8.5 7.9 sigS

 Wind and SoS -0.87% -0.94% -0.07% -2.8 8.4 ranL

------------ 1.03% 0.85% 0.85% 9.3 8.7 sigL

 Ruv = 0.187 -0.78% -1.53% 0.75% 10.4 10.3 -0.48 ranT

 SpdAv= 32.3 1.06% 0.97% 0.97% 12.6 11.7 0.63 sigT

 SpdSd= 12.6 2.794E+04 4.156E-01 234.2 40.1 15.3 -0.35 Tot.

 SoSav= 305.6 5.44% 0.51% 4.90% T-76

 SoSpt= 306.8 9.835E+00 9.168E-05 222.7 34.5% H2O

 4.883E+00 4.561E-05 6.9 17.1% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 8.000 26.850 -85.330 3.735E+04 5.271E-01 246.8 23.5 4.0 0.151 Mean

 6381.757 27.005 4.75% 0.25% 4.48% M-76

 3960.0 GRM 0.0000 -0.01% -0.62% 0.69% 21.4 5.1 ranS

 0.20% 0.44% 0.44% 7.1 6.7 sigS

 Wind and SoS -0.86% -0.79% -0.15% -4.6 6.4 ranL

------------ 0.86% 0.83% 0.82% 7.9 7.5 sigL

 Ruv = 0.139 -0.87% -1.40% 0.55% 16.8 11.5 0.21 ranT

 SpdAv= 25.9 0.89% 0.94% 0.93% 10.7 10.1 0.63 sigT

 SpdSd= 10.6 3.702E+04 5.197E-01 248.1 40.3 15.5 0.36 Tot.

 SoSav= 315.0 3.84% -1.16% 5.05% T-76

 SoSpt= 315.8 2.627E+01 2.307E-04 233.3 37.0% H2O

 2.121E+01 1.864E-04 8.9 25.3% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 6.000 27.250 -84.130 4.883E+04 6.526E-01 260.6 17.4 3.0 0.072 Mean

 6379.636 27.407 3.42% -1.14% 4.56% M-76

 4020.0 GRM 0.0000 -0.02% -0.11% 0.10% 12.0 -9.2 ranS

 0.16% 0.44% 0.43% 6.0 5.7 sigS

 Wind and SoS -0.80% -0.60% -0.21% -5.7 4.6 ranL

------------ 0.70% 0.83% 0.82% 6.8 6.4 sigL

 Ruv = 0.082 -0.82% -0.71% -0.11% 6.3 -4.6 0.88 ranT

 SpdAv= 19.8 0.72% 0.94% 0.92% 9.1 8.6 0.63 sigT

 SpdSd= 8.9 4.844E+04 6.480E-01 260.3 23.8 -1.7 0.95 Tot.

 SoSav= 323.7 2.58% -1.84% 4.45% T-76

 SoSpt= 323.5 6.657E+01 5.536E-04 242.8 28.5% H2O

 5.088E+01 4.236E-04 9.3 21.3% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 4.000 27.650 -82.930 6.299E+04 8.038E-01 272.7 11.7 1.9 0.075 Mean

 6377.513 27.808 2.15% -1.90% 4.02% M-76

 4080.0 cap06 0.0536 0.17% 0.24% -0.08% -1.7 -3.1 ranS

 0.13% 0.40% 0.40% 5.1 4.6 sigS

 Wind and SoS -0.67% -0.33% -0.33% -6.1 2.8 ranL

------------ 0.56% 0.81% 0.80% 5.9 5.3 sigL

 Ruv = 0.019 -0.50% -0.09% -0.41% -7.8 -0.3 -0.27 ranT

 SpdAv= 14.1 0.58% 0.90% 0.90% 7.8 7.1 0.62 sigT

 SpdSd= 7.4 6.267E+04 8.031E-01 271.6 3.9 1.6 -0.20 Tot.

 SoSav= 331.2 1.64% -1.98% 3.59% T-76

 SoSpt= 330.5 1.710E+02 1.358E-03 253.5 29.2% H2O

 1.309E+02 1.041E-03 9.9 21.3% sigH

83
-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 2.000 28.050 -81.730 8.045E+04 9.927E-01 281.6 6.3 1.7 0.081 Mean

 6375.390 28.210 1.19% -1.37% 2.35% M-76

 4140.0 cap06 0.8115 0.03% -0.10% 0.13% -0.6 -0.8 ranS

 0.11% 0.47% 0.47% 4.6 3.9 sigS

 Wind and SoS -0.57% -0.06% -0.51% -6.2 1.2 ranL

------------ 0.49% 1.10% 1.09% 5.3 4.6 sigL

 Ruv = -0.011 -0.54% -0.16% -0.38% -6.8 0.5 0.18 ranT

 SpdAv= 9.7 0.51% 1.20% 1.19% 7.0 6.0 0.50 sigT

 SpdSd= 5.8 8.002E+04 9.912E-01 280.5 -0.5 2.1 0.26 Tot.

 SoSav= 336.8 0.65% -1.53% 1.96% T-76

 SoSpt= 336.2 5.594E+02 4.304E-03 268.6 50.2% H2O

 3.611E+02 2.783E-03 10.8 21.7% sigH

-------- ------- -------- --------- ---------- ------ ------ ------ ------ ----

 0.000 28.450 -80.530 1.020E+05 1.220E+00 289.6 0.1 -0.2 0.000 Mean

 6373.265 28.611 0.66% -0.39% 0.49% M-76

 4200.0 cap06 1.0000 0.07% 0.24% -0.16% -0.5 -1.4 ranS

 0.11% 0.85% 0.70% 1.9 2.2 sigS

 Wind and SoS -0.17% 0.63% -0.81% -2.6 1.1 ranL

------------ 0.46% 2.01% 1.67% 2.2 2.6 sigL

 Ruv = -0.258 -0.10% 0.87% -0.96% -3.1 -0.3 -0.53 ranT

 SpdAv= 3.3 0.47% 2.18% 1.81% 2.9 3.4 0.34 sigT

 SpdSd= 3.0 1.019E+05 1.231E+00 286.8 -2.9 -0.5 -0.53 Tot.

 SoSav= 342.1 0.55% 0.47% -0.48% T-76

 SoSpt= 340.4 1.607E+03 1.202E-02 286.1 85.8% H2O

 5.767E+02 4.324E-03 6.6 21.9% sigH

84
D.2 Sample Species Concentration Output File Produced by Input File of Appendix C 

  Earth Global Reference Atmospheric Model - 2010 (Earth-GRAM-2010) ** **

 Version 1.0, Released Jul, 2010

 Species Concentration Data

 MM/DD/YYYY = 1/ 1/2010 HH:MM:SS(UTC) = 0: 0: 0.0 Julian Day = 2455197.500

 F10.7 = 230.00 Mean F10.7 = 230.00 ap Index = 20.30

 Standard deviations of concentration variation may be a substantial fraction

 (50% or more) of the mean value. Zero concentration values indicate no

 estimate available.

 Thermospheric constituents from MET model

 Height/

 Radius GcLat Long. Concen- Number | Concen- Number

 (km) GdLat [E+W-] tration Density | tration Density Species

 Time_sec (deg) (deg) (ppmv) (#/m**3) | (ppmv) (#/m**3)

-------- ------- -------- --------- --------- + --------- --------- ----+----

 140.000 0.450 -164.530 0.000E+00 0.000E+00 | 0.000E+00 0.000E+00 H2O | O3

 6518.136 0.453 0.000E+00 0.000E+00 | 0.000E+00 0.000E+00 N2O | CO

 0.0 0.000E+00 0.000E+00 | 0.000E+00 0.000E+00 CH4 | CO2

 6.532E+05 6.830E+16 | 9.206E+04 9.627E+15 N2 | O2

 2.523E+05 2.638E+16 | 2.324E+03 2.430E+14 O | Ar

 1.894E+02 1.980E+13 | 9.563E-06 1.000E+06 He | H

 0.000E+00 0.000E+00 | MW=25.373 1.046E+17 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 138.000 0.850 -163.330 0.000E+00 0.000E+00 | 0.000E+00 0.000E+00 H2O | O3

 6516.132 0.856 0.000E+00 0.000E+00 | 0.000E+00 0.000E+00 N2O | CO

 60.0 0.000E+00 0.000E+00 | 0.000E+00 0.000E+00 CH4 | CO2

 6.588E+05 7.821E+16 | 9.411E+04 1.117E+16 N2 | O2

 2.444E+05 2.902E+16 | 2.440E+03 2.896E+14 O | Ar

 1.735E+02 2.060E+13 | 8.424E-06 1.000E+06 He | H

 0.000E+00 0.000E+00 | MW=25.477 1.187E+17 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 136.000 1.250 -162.130 0.000E+00 0.000E+00 | 0.000E+00 0.000E+00 H2O | O3

 6514.127 1.258 0.000E+00 0.000E+00 | 0.000E+00 0.000E+00 N2O | CO

 120.0 0.000E+00 0.000E+00 | 0.000E+00 0.000E+00 CH4 | CO2

 6.646E+05 9.017E+16 | 9.626E+04 1.306E+16 N2 | O2

 2.364E+05 3.208E+16 | 2.566E+03 3.481E+14 O | Ar

 1.582E+02 2.147E+13 | 7.370E-06 1.000E+06 He | H

 0.000E+00 0.000E+00 | MW=25.583 1.357E+17 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 134.000 1.650 -160.930 0.000E+00 0.000E+00 | 0.000E+00 0.000E+00 H2O | O3

 6512.119 1.661 0.000E+00 0.000E+00 | 0.000E+00 0.000E+00 N2O | CO

 180.0 0.000E+00 0.000E+00 | 0.000E+00 0.000E+00 CH4 | CO2

 6.704E+05 1.048E+17 | 9.852E+04 1.540E+16 N2 | O2

 2.283E+05 3.567E+16 | 2.703E+03 4.225E+14 O | Ar

 1.436E+02 2.244E+13 | 6.399E-06 1.000E+06 He | H

 0.000E+00 0.000E+00 | MW=25.693 1.563E+17 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 132.000 2.050 -159.730 0.000E+00 0.000E+00 | 0.000E+00 0.000E+00 H2O | O3

 6510.109 2.064 0.000E+00 0.000E+00 | 0.000E+00 0.000E+00 N2O | CO

 240.0 0.000E+00 0.000E+00 | 0.000E+00 0.000E+00 CH4 | CO2

 6.762E+05 1.227E+17 | 1.009E+05 1.832E+16 N2 | O2

 2.199E+05 3.991E+16 | 2.855E+03 5.182E+14 O | Ar

 1.296E+02 2.352E+13 | 5.510E-06 1.000E+06 He | H

 0.000E+00 0.000E+00 | MW=25.805 1.815E+17 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

85
 130.000 2.450 -158.530 0.000E+00 0.000E+00 | 0.000E+00 0.000E+00 H2O | O3

 6508.098 2.466 0.000E+00 0.000E+00 | 0.000E+00 0.000E+00 N2O | CO

 300.0 0.000E+00 0.000E+00 | 0.000E+00 0.000E+00 CH4 | CO2

 6.821E+05 1.451E+17 | 1.034E+05 2.201E+16 N2 | O2

 2.113E+05 4.495E+16 | 3.022E+03 6.431E+14 O | Ar

 1.162E+02 2.472E+13 | 4.701E-06 1.000E+06 He | H

 0.000E+00 0.000E+00 | MW=25.921 2.128E+17 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 128.000 2.850 -157.330 0.000E+00 0.000E+00 | 0.000E+00 0.000E+00 H2O | O3

 6506.084 2.869 0.000E+00 0.000E+00 | 0.000E+00 0.000E+00 N2O | CO

 360.0 0.000E+00 0.000E+00 | 0.000E+00 0.000E+00 CH4 | CO2

 6.881E+05 1.734E+17 | 1.061E+05 2.675E+16 N2 | O2

 2.024E+05 5.102E+16 | 3.208E+03 8.086E+14 O | Ar

 1.035E+02 2.607E+13 | 3.970E-06 1.000E+06 He | H

 0.000E+00 0.000E+00 | MW=26.040 2.520E+17 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 126.000 3.250 -156.130 0.000E+00 0.000E+00 | 0.000E+00 0.000E+00 H2O | O3

 6504.068 3.271 0.000E+00 0.000E+00 | 0.000E+00 0.000E+00 N2O | CO

 420.0 0.000E+00 0.000E+00 | 0.000E+00 0.000E+00 CH4 | CO2

 6.941E+05 2.096E+17 | 1.090E+05 3.292E+16 N2 | O2

 1.934E+05 5.838E+16 | 3.417E+03 1.032E+15 O | Ar

 9.140E+01 2.759E+13 | 3.314E-06 1.001E+06 He | H

 0.000E+00 0.000E+00 | MW=26.164 3.019E+17 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 124.000 3.650 -154.930 0.000E+00 0.000E+00 | 0.000E+00 0.000E+00 H2O | O3

 6502.050 3.674 0.000E+00 0.000E+00 | 0.000E+00 0.000E+00 N2O | CO

 480.0 0.000E+00 0.000E+00 | 0.000E+00 0.000E+00 CH4 | CO2

 7.001E+05 2.565E+17 | 1.121E+05 4.108E+16 N2 | O2

 1.840E+05 6.741E+16 | 3.652E+03 1.338E+15 O | Ar

 8.003E+01 2.932E+13 | 2.732E-06 1.001E+06 He | H

 0.000E+00 0.000E+00 | MW=26.291 3.663E+17 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 122.000 4.050 -153.730 0.000E+00 0.000E+00 | 0.000E+00 0.000E+00 H2O | O3

 6500.030 4.077 0.000E+00 0.000E+00 | 0.000E+00 0.000E+00 N2O | CO

 540.0 0.000E+00 0.000E+00 | 0.000E+00 0.000E+00 CH4 | CO2

 7.062E+05 3.183E+17 | 1.155E+05 5.204E+16 N2 | O2

 1.744E+05 7.859E+16 | 3.919E+03 1.766E+15 O | Ar

 6.939E+01 3.127E+13 | 2.222E-06 1.001E+06 He | H

 0.000E+00 0.000E+00 | MW=26.424 4.507E+17 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 120.000 4.450 -152.530 0.000E+00 0.000E+00 | 0.000E+00 0.000E+00 H2O | O3

 6498.008 4.479 0.000E+00 0.000E+00 | 0.000E+00 0.000E+00 N2O | CO

 600.0 0.000E+00 0.000E+00 | 0.000E+00 0.000E+00 CH4 | CO2

 7.122E+05 4.007E+17 | 1.191E+05 6.698E+16 N2 | O2

 1.645E+05 9.252E+16 | 4.224E+03 2.376E+15 O | Ar

 5.952E+01 3.348E+13 | 1.781E-06 1.002E+06 He | H

 0.000E+00 0.000E+00 | MW=26.561 5.626E+17 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 118.000 4.850 -151.330 2.151E-01 1.531E+11 | 1.248E-03 8.879E+08 H2O | O3

 6495.983 4.882 2.158E-04 1.536E+08 | 5.871E+01 4.177E+13 N2O | CO

 660.0 5.357E-02 3.811E+10 | 4.365E+01 3.106E+13 CH4 | CO2

 7.209E+05 5.129E+17 | 1.201E+05 8.546E+16 N2 | O2

 1.542E+05 1.097E+17 | 4.576E+03 3.256E+15 O | Ar

 5.046E+01 3.590E+13 | 1.406E-06 1.000E+06 He | H

 0.000E+00 0.000E+00 | MW=26.693 7.115E+17 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 116.000 5.250 -150.130 2.314E-01 2.109E+11 | 3.108E-03 2.834E+09 H2O | O3

 6493.957 5.285 2.270E-04 2.069E+08 | 5.426E+01 4.946E+13 N2O | CO

 720.0 7.039E-02 6.417E+10 | 4.585E+01 4.180E+13 CH4 | CO2

 7.289E+05 6.644E+17 | 1.221E+05 1.113E+17 N2 | O2

 1.439E+05 1.311E+17 | 4.988E+03 4.547E+15 O | Ar

 4.226E+01 3.853E+13 | 1.093E-06 9.966E+05 He | H

 0.000E+00 0.000E+00 | MW=26.831 9.116E+17 N | Tot

86
-------- ------- -------- --------- --------- + --------- --------- ----+----

 114.000 5.650 -148.930 2.475E-01 2.939E+11 | 7.748E-03 9.199E+09 H2O | O3

 6491.929 5.687 2.391E-04 2.838E+08 | 4.994E+01 5.929E+13 N2O | CO

 780.0 8.833E-02 1.049E+11 | 5.089E+01 6.043E+13 CH4 | CO2

 7.359E+05 8.738E+17 | 1.251E+05 1.486E+17 N2 | O2

 1.333E+05 1.583E+17 | 5.470E+03 6.495E+15 O | Ar

 3.494E+01 4.148E+13 | 8.370E-07 9.937E+05 He | H

 0.000E+00 0.000E+00 | MW=26.976 1.187E+18 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 112.000 6.050 -147.730 2.633E-01 4.156E+11 | 1.938E-02 3.059E+10 H2O | O3

 6489.898 6.090 2.529E-04 3.992E+08 | 4.590E+01 7.245E+13 N2O | CO

 840.0 1.062E-01 1.676E+11 | 5.986E+01 9.449E+13 CH4 | CO2

 7.421E+05 1.171E+18 | 1.292E+05 2.040E+17 N2 | O2

 1.225E+05 1.934E+17 | 6.033E+03 9.523E+15 O | Ar

 2.845E+01 4.491E+13 | 6.300E-07 9.945E+05 He | H

 0.000E+00 0.000E+00 | MW=27.129 1.579E+18 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 110.000 6.450 -146.530 2.800E-01 6.043E+11 | 4.887E-02 1.055E+11 H2O | O3

 6487.866 6.492 2.697E-04 5.820E+08 | 4.252E+01 9.176E+13 N2O | CO

 900.0 1.286E-01 2.776E+11 | 7.097E+01 1.532E+14 CH4 | CO2

 7.475E+05 1.613E+18 | 1.345E+05 2.903E+17 N2 | O2

 1.112E+05 2.400E+17 | 6.669E+03 1.439E+16 O | Ar

 2.273E+01 4.906E+13 | 4.648E-07 1.003E+06 He | H

 0.000E+00 0.000E+00 | MW=27.294 2.158E+18 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 108.000 6.850 -145.330 3.026E-01 9.059E+11 | 8.533E-02 2.554E+11 H2O | O3

 6485.831 6.895 2.886E-04 8.641E+08 | 3.787E+01 1.134E+14 N2O | CO

 960.0 1.374E-01 4.112E+11 | 9.109E+01 2.727E+14 CH4 | CO2

 7.528E+05 2.254E+18 | 1.396E+05 4.178E+17 N2 | O2

 1.000E+05 2.995E+17 | 7.419E+03 2.221E+16 O | Ar

 1.789E+01 5.357E+13 | 3.377E-07 1.011E+06 He | H

 0.000E+00 0.000E+00 | MW=27.457 2.994E+18 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 106.000 7.250 -144.130 3.271E-01 1.391E+12 | 1.496E-01 6.360E+11 H2O | O3

 6483.795 7.298 3.101E-04 1.319E+09 | 3.385E+01 1.439E+14 N2O | CO

 1020.0 1.473E-01 6.262E+11 | 1.174E+02 4.991E+14 CH4 | CO2

 7.576E+05 3.222E+18 | 1.453E+05 6.181E+17 N2 | O2

 8.867E+04 3.771E+17 | 8.257E+03 3.512E+16 O | Ar

 1.379E+01 5.866E+13 | 2.404E-07 1.022E+06 He | H

 0.000E+00 0.000E+00 | MW=27.627 4.253E+18 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 104.000 7.650 -142.930 3.512E-01 2.154E+12 | 2.280E-01 1.398E+12 H2O | O3

 6481.756 7.700 3.331E-04 2.043E+09 | 2.987E+01 1.832E+14 N2O | CO

 1080.0 1.558E-01 9.558E+11 | 1.500E+02 9.202E+14 CH4 | CO2

 7.627E+05 4.678E+18 | 1.516E+05 9.300E+17 N2 | O2

 7.678E+04 4.709E+17 | 8.678E+03 5.322E+16 O | Ar

 1.197E+01 7.342E+13 | 1.684E-07 1.033E+06 He | H

 0.000E+00 0.000E+00 | MW=27.801 6.133E+18 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 102.000 8.050 -141.730 3.748E-01 3.328E+12 | 3.011E-01 2.673E+12 H2O | O3

 6479.716 8.103 3.564E-04 3.164E+09 | 2.591E+01 2.301E+14 N2O | CO

 1140.0 1.622E-01 1.440E+12 | 1.896E+02 1.684E+15 CH4 | CO2

 7.684E+05 6.822E+18 | 1.583E+05 1.405E+18 N2 | O2

 6.450E+04 5.726E+17 | 8.613E+03 7.647E+16 O | Ar

 1.188E+01 1.055E+14 | 1.170E-07 1.038E+06 He | H

 0.000E+00 0.000E+00 | MW=27.975 8.879E+18 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 100.000 8.450 -140.530 4.000E-01 5.195E+12 | 3.970E-01 5.155E+12 H2O | O3

 6477.673 8.505 3.807E-04 4.944E+09 | 2.245E+01 2.915E+14 N2O | CO

 1200.0 1.685E-01 2.189E+12 | 2.393E+02 3.107E+15 CH4 | CO2

 7.736E+05 1.005E+19 | 1.654E+05 2.148E+18 N2 | O2

 5.228E+04 6.789E+17 | 8.510E+03 1.105E+17 O | Ar

 1.174E+01 1.525E+14 | 8.023E-08 1.042E+06 He | H

87
 0.000E+00 0.000E+00 | MW=28.149 1.299E+19 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 98.000 8.850 -139.330 4.510E-01 8.484E+12 | 4.330E-01 8.145E+12 H2O | O3

 6475.628 8.908 4.080E-04 7.674E+09 | 1.843E+01 3.467E+14 N2O | CO

 1260.0 1.743E-01 3.279E+12 | 2.730E+02 5.135E+15 CH4 | CO2

 7.815E+05 1.470E+19 | 1.731E+05 3.255E+18 N2 | O2

 3.659E+04 6.883E+17 | 8.513E+03 1.601E+17 O | Ar

 1.174E+01 2.209E+14 | 5.546E-08 1.043E+06 He | H

 0.000E+00 0.000E+00 | MW=28.369 1.881E+19 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 96.000 9.250 -138.130 5.085E-01 1.384E+13 | 4.705E-01 1.280E+13 H2O | O3

 6473.582 9.310 4.356E-04 1.185E+10 | 1.508E+01 4.103E+14 N2O | CO

 1320.0 1.797E-01 4.888E+12 | 3.104E+02 8.445E+15 CH4 | CO2

 7.873E+05 2.142E+19 | 1.808E+05 4.920E+18 N2 | O2

 2.301E+04 6.262E+17 | 8.511E+03 2.316E+17 O | Ar

 1.174E+01 3.195E+14 | 3.824E-08 1.040E+06 He | H

 0.000E+00 0.000E+00 | MW=28.564 2.721E+19 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 94.000 9.650 -136.930 5.913E-01 2.324E+13 | 4.922E-01 1.934E+13 H2O | O3

 6471.533 9.713 4.657E-04 1.830E+10 | 1.242E+01 4.881E+14 N2O | CO

 1380.0 1.847E-01 7.258E+12 | 3.394E+02 1.334E+16 CH4 | CO2

 7.918E+05 3.112E+19 | 1.869E+05 7.344E+18 N2 | O2

 1.243E+04 4.886E+17 | 8.503E+03 3.342E+17 O | Ar

 1.173E+01 4.610E+14 | 2.636E-08 1.036E+06 He | H

 0.000E+00 0.000E+00 | MW=28.715 3.930E+19 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 92.000 10.050 -135.730 7.089E-01 3.998E+13 | 4.955E-01 2.794E+13 H2O | O3

 6469.483 10.115 4.983E-04 2.810E+10 | 1.030E+01 5.809E+14 N2O | CO

 1440.0 1.893E-01 1.068E+13 | 3.570E+02 2.013E+16 CH4 | CO2

 7.949E+05 4.483E+19 | 1.906E+05 1.075E+19 N2 | O2

 5.558E+03 3.134E+17 | 8.514E+03 4.802E+17 O | Ar

 1.175E+01 6.625E+14 | 1.825E-08 1.029E+06 He | H

 0.000E+00 0.000E+00 | MW=28.813 5.640E+19 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 90.000 10.450 -134.530 8.500E-01 6.816E+13 | 4.968E-01 3.984E+13 H2O | O3

 6467.430 10.518 5.311E-04 4.259E+10 | 8.507E+00 6.822E+14 N2O | CO

 1500.0 1.933E-01 1.550E+13 | 3.740E+02 2.999E+16 CH4 | CO2

 7.943E+05 6.370E+19 | 1.935E+05 1.552E+19 N2 | O2

 2.299E+03 1.843E+17 | 9.511E+03 7.627E+17 O | Ar

 5.295E+00 4.247E+14 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.876 8.019E+19 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 88.000 10.850 -133.330 1.007E+00 1.127E+14 | 4.856E-01 5.430E+13 H2O | O3

 6465.376 10.920 5.723E-04 6.400E+10 | 6.841E+00 7.650E+14 N2O | CO

 1560.0 1.982E-01 2.216E+13 | 3.777E+02 4.224E+16 CH4 | CO2

 7.923E+05 8.860E+19 | 1.969E+05 2.202E+19 N2 | O2

 8.944E+02 1.000E+17 | 9.483E+03 1.060E+18 O | Ar

 5.280E+00 5.904E+14 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.907 1.118E+20 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 86.000 11.250 -132.130 1.194E+00 1.851E+14 | 4.010E-01 6.217E+13 H2O | O3

 6463.319 11.323 6.162E-04 9.553E+10 | 5.496E+00 8.521E+14 N2O | CO

 1620.0 2.029E-01 3.146E+13 | 3.810E+02 5.908E+16 CH4 | CO2

 7.896E+05 1.224E+20 | 2.002E+05 3.104E+19 N2 | O2

 3.505E+02 5.434E+16 | 9.447E+03 1.465E+18 O | Ar

 5.259E+00 8.154E+14 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.926 1.550E+20 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 84.000 11.650 -130.930 1.431E+00 3.055E+14 | 3.478E-01 7.426E+13 H2O | O3

 6461.261 11.725 6.655E-04 1.421E+11 | 4.099E+00 8.753E+14 N2O | CO

 1680.0 2.049E-01 4.376E+13 | 3.839E+02 8.197E+16 CH4 | CO2

 7.867E+05 1.680E+20 | 2.034E+05 4.343E+19 N2 | O2

 1.685E+02 3.599E+16 | 9.410E+03 2.009E+18 O | Ar

88
 5.239E+00 1.119E+15 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.940 2.135E+20 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 82.000 12.050 -129.730 1.733E+00 5.072E+14 | 3.272E-01 9.572E+13 H2O | O3

 6459.200 12.128 7.213E-04 2.110E+11 | 2.838E+00 8.303E+14 N2O | CO

 1740.0 2.042E-01 5.974E+13 | 3.862E+02 1.130E+17 CH4 | CO2

 7.837E+05 2.293E+20 | 2.064E+05 6.039E+19 N2 | O2

 9.898E+01 2.896E+16 | 9.375E+03 2.743E+18 O | Ar

 5.219E+00 1.527E+15 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.953 2.926E+20 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 80.000 12.450 -128.530 1.915E+00 7.645E+14 | 2.828E-01 1.129E+14 H2O | O3

 6457.138 12.530 7.816E-04 3.121E+11 | 1.965E+00 7.846E+14 N2O | CO

 1800.0 2.034E-01 8.123E+13 | 3.886E+02 1.552E+17 CH4 | CO2

 7.808E+05 3.118E+20 | 2.094E+05 8.364E+19 N2 | O2

 5.821E+01 2.324E+16 | 9.339E+03 3.730E+18 O | Ar

 5.199E+00 2.076E+15 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.965 3.993E+20 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 78.000 12.850 -127.330 1.614E+00 8.785E+14 | 2.161E-01 1.176E+14 H2O | O3

 6455.074 12.933 8.571E-04 4.667E+11 | 1.316E+00 7.164E+14 N2O | CO

 1860.0 2.034E-01 1.107E+14 | 3.895E+02 2.121E+17 CH4 | CO2

 7.808E+05 4.251E+20 | 2.095E+05 1.140E+20 N2 | O2

 2.498E+01 1.360E+16 | 9.339E+03 5.085E+18 O | Ar

 5.200E+00 2.831E+15 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.965 5.444E+20 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 76.000 13.250 -126.130 1.789E+00 1.324E+15 | 1.653E-01 1.223E+14 H2O | O3

 6453.008 13.335 9.399E-04 6.957E+11 | 8.813E-01 6.523E+14 N2O | CO

 1920.0 2.034E-01 1.506E+14 | 3.905E+02 2.890E+17 CH4 | CO2

 7.808E+05 5.779E+20 | 2.095E+05 1.550E+20 N2 | O2

 1.081E+01 8.001E+15 | 9.340E+03 6.913E+18 O | Ar

 5.200E+00 3.849E+15 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.966 7.402E+20 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 74.000 13.650 -124.930 1.982E+00 1.981E+15 | 1.517E-01 1.515E+14 H2O | O3

 6450.940 13.737 1.036E-03 1.035E+12 | 5.816E-01 5.811E+14 N2O | CO

 1980.0 2.034E-01 2.032E+14 | 3.910E+02 3.907E+17 CH4 | CO2

 7.808E+05 7.802E+20 | 2.095E+05 2.093E+20 N2 | O2

 5.821E+00 5.817E+15 | 9.340E+03 9.332E+18 O | Ar

 5.200E+00 5.196E+15 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.966 9.992E+20 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 72.000 14.050 -123.730 2.641E+00 3.530E+15 | 1.831E-01 2.447E+14 H2O | O3

 6448.871 14.140 1.149E-03 1.535E+12 | 3.782E-01 5.055E+14 N2O | CO

 2040.0 2.034E-01 2.719E+14 | 3.910E+02 5.225E+17 CH4 | CO2

 7.808E+05 1.044E+21 | 2.095E+05 2.800E+20 N2 | O2

 3.875E+00 5.180E+15 | 9.340E+03 1.248E+19 O | Ar

 5.200E+00 6.950E+15 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.966 1.337E+21 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 70.000 14.450 -122.530 3.457E+00 6.148E+15 | 2.314E-01 4.116E+14 H2O | O3

 6446.799 14.542 1.273E-03 2.264E+12 | 2.459E-01 4.373E+14 N2O | CO

 2100.0 2.034E-01 3.617E+14 | 3.910E+02 6.952E+17 CH4 | CO2

 7.808E+05 1.388E+21 | 2.095E+05 3.725E+20 N2 | O2

 2.579E+00 4.586E+15 | 9.340E+03 1.661E+19 O | Ar

 5.200E+00 9.246E+15 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.966 1.778E+21 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 68.000 14.850 -121.330 4.134E+00 9.631E+15 | 3.121E-01 7.272E+14 H2O | O3

 6444.726 14.945 1.420E-03 3.308E+12 | 1.824E-01 4.249E+14 N2O | CO

 2160.0 2.034E-01 4.739E+14 | 3.910E+02 9.108E+17 CH4 | CO2

 7.808E+05 1.819E+21 | 2.095E+05 4.880E+20 N2 | O2

89
 2.164E+00 5.042E+15 | 9.340E+03 2.176E+19 O | Ar

 5.200E+00 1.211E+16 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.966 2.330E+21 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 66.000 15.250 -120.130 4.919E+00 1.491E+16 | 4.192E-01 1.271E+15 H2O | O3

 6442.651 15.347 1.582E-03 4.794E+12 | 1.374E-01 4.163E+14 N2O | CO

 2220.0 2.034E-01 6.165E+14 | 3.910E+02 1.185E+18 CH4 | CO2

 7.808E+05 2.366E+21 | 2.095E+05 6.348E+20 N2 | O2

 1.827E+00 5.536E+15 | 9.340E+03 2.831E+19 O | Ar

 5.200E+00 1.576E+16 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.966 3.031E+21 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 64.000 15.650 -118.930 5.349E+00 2.102E+16 | 5.418E-01 2.129E+15 H2O | O3

 6440.574 15.749 1.092E-03 4.290E+12 | 1.145E-01 4.500E+14 N2O | CO

 2280.0 1.681E-01 6.604E+14 | 3.910E+02 1.536E+18 CH4 | CO2

 7.808E+05 3.068E+21 | 2.095E+05 8.231E+20 N2 | O2

 1.520E+00 5.973E+15 | 9.340E+03 3.670E+19 O | Ar

 5.200E+00 2.043E+16 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.966 3.929E+21 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 62.000 16.050 -117.730 5.755E+00 2.924E+16 | 7.003E-01 3.559E+15 H2O | O3

 6438.495 16.152 1.208E-03 6.141E+12 | 1.044E-01 5.305E+14 N2O | CO

 2340.0 1.820E-01 9.249E+14 | 3.910E+02 1.987E+18 CH4 | CO2

 7.808E+05 3.968E+21 | 2.095E+05 1.064E+21 N2 | O2

 1.246E+00 6.334E+15 | 9.340E+03 4.746E+19 O | Ar

 5.200E+00 2.642E+16 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.966 5.081E+21 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 60.000 16.450 -116.530 5.935E+00 3.881E+16 | 9.036E-01 5.908E+15 H2O | O3

 6436.414 16.554 1.386E-03 9.063E+12 | 9.478E-02 6.197E+14 N2O | CO

 2400.0 1.980E-01 1.295E+15 | 3.910E+02 2.556E+18 CH4 | CO2

 7.808E+05 5.105E+21 | 2.095E+05 1.370E+21 N2 | O2

 1.026E+00 6.706E+15 | 9.340E+03 6.107E+19 O | Ar

 5.200E+00 3.400E+16 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.966 6.538E+21 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 58.000 16.850 -115.330 5.787E+00 4.842E+16 | 1.146E+00 9.591E+15 H2O | O3

 6434.332 16.956 1.627E-03 1.361E+13 | 8.984E-02 7.518E+14 N2O | CO

 2460.0 2.185E-01 1.829E+15 | 3.910E+02 3.272E+18 CH4 | CO2

 7.808E+05 6.534E+21 | 2.095E+05 1.753E+21 N2 | O2

 7.801E-01 6.528E+15 | 9.340E+03 7.816E+19 O | Ar

 5.200E+00 4.351E+16 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.966 8.368E+21 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 56.000 17.250 -114.130 5.644E+00 6.016E+16 | 1.378E+00 1.468E+16 H2O | O3

 6432.248 17.358 2.019E-03 2.152E+13 | 8.467E-02 9.024E+14 N2O | CO

 2520.0 2.625E-01 2.798E+15 | 3.910E+02 4.167E+18 CH4 | CO2

 7.808E+05 8.322E+21 | 2.095E+05 2.232E+21 N2 | O2

 5.963E-01 6.355E+15 | 9.340E+03 9.954E+19 O | Ar

 5.200E+00 5.542E+16 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.966 1.066E+22 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 54.000 17.650 -112.930 5.508E+00 7.480E+16 | 1.641E+00 2.228E+16 H2O | O3

 6430.162 17.761 2.639E-03 3.584E+13 | 7.889E-02 1.071E+15 N2O | CO

 2580.0 3.228E-01 4.384E+15 | 3.910E+02 5.309E+18 CH4 | CO2

 7.808E+05 1.060E+22 | 2.095E+05 2.844E+21 N2 | O2

 4.312E-01 5.855E+15 | 9.340E+03 1.268E+20 O | Ar

 5.200E+00 7.061E+16 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.966 1.358E+22 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 52.000 18.050 -111.730 5.500E+00 9.535E+16 | 1.917E+00 3.324E+16 H2O | O3

 6428.075 18.163 3.428E-03 5.943E+13 | 7.256E-02 1.258E+15 N2O | CO

 2640.0 3.745E-01 6.492E+15 | 3.910E+02 6.778E+18 CH4 | CO2

90
 7.808E+05 1.354E+22 | 2.095E+05 3.631E+21 N2 | O2

 2.943E-01 5.103E+15 | 9.340E+03 1.619E+20 O | Ar

 5.200E+00 9.014E+16 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.966 1.734E+22 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 50.000 18.450 -110.530 5.325E+00 1.175E+17 | 2.304E+00 5.085E+16 H2O | O3

 6425.985 18.565 4.240E-03 9.360E+13 | 6.624E-02 1.462E+15 N2O | CO

 2700.0 4.170E-01 9.205E+15 | 3.910E+02 8.630E+18 CH4 | CO2

 7.808E+05 1.724E+22 | 2.095E+05 4.624E+21 N2 | O2

 2.013E-01 4.444E+15 | 9.340E+03 2.062E+20 O | Ar

 5.200E+00 1.148E+17 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.966 2.207E+22 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 48.000 18.850 -109.330 5.087E+00 1.447E+17 | 2.827E+00 8.041E+16 H2O | O3

 6423.895 18.967 5.164E-03 1.469E+14 | 5.764E-02 1.640E+15 N2O | CO

 2760.0 4.551E-01 1.295E+16 | 3.910E+02 1.112E+19 CH4 | CO2

 7.808E+05 2.221E+22 | 2.095E+05 5.958E+21 N2 | O2

 1.136E-01 3.231E+15 | 9.340E+03 2.657E+20 O | Ar

 5.200E+00 1.479E+17 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.966 2.844E+22 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 46.000 19.250 -108.130 5.016E+00 1.839E+17 | 3.508E+00 1.286E+17 H2O | O3

 6421.802 19.369 6.730E-03 2.468E+14 | 5.131E-02 1.882E+15 N2O | CO

 2820.0 5.016E-01 1.840E+16 | 3.910E+02 1.434E+19 CH4 | CO2

 7.808E+05 2.863E+22 | 2.095E+05 7.682E+21 N2 | O2

 6.410E-02 2.351E+15 | 9.340E+03 3.425E+20 O | Ar

 5.200E+00 1.907E+17 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.966 3.667E+22 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 44.000 19.650 -106.930 4.883E+00 2.326E+17 | 4.331E+00 2.063E+17 H2O | O3

 6419.708 19.771 9.316E-03 4.438E+14 | 4.598E-02 2.191E+15 N2O | CO

 2880.0 5.653E-01 2.693E+16 | 3.910E+02 1.863E+19 CH4 | CO2

 7.808E+05 3.720E+22 | 2.095E+05 9.978E+21 N2 | O2

 3.176E-02 1.513E+15 | 9.340E+03 4.449E+20 O | Ar

 5.200E+00 2.477E+17 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.966 4.764E+22 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 42.000 20.050 -105.730 4.712E+00 2.946E+17 | 5.227E+00 3.267E+17 H2O | O3

 6417.612 20.173 1.298E-02 8.117E+14 | 4.124E-02 2.578E+15 N2O | CO

 2940.0 6.329E-01 3.957E+16 | 3.910E+02 2.444E+19 CH4 | CO2

 7.808E+05 4.881E+22 | 2.095E+05 1.309E+22 N2 | O2

 1.375E-02 8.593E+14 | 9.340E+03 5.839E+20 O | Ar

 5.200E+00 3.251E+17 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.966 6.252E+22 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 40.000 20.450 -104.530 5.102E+00 4.203E+17 | 6.152E+00 5.067E+17 H2O | O3

 6415.515 20.576 1.728E-02 1.423E+15 | 3.721E-02 3.065E+15 N2O | CO

 3000.0 6.879E-01 5.666E+16 | 3.910E+02 3.220E+19 CH4 | CO2

 7.808E+05 6.431E+22 | 2.095E+05 1.725E+22 N2 | O2

 5.895E-03 4.856E+14 | 9.340E+03 7.693E+20 O | Ar

 5.200E+00 4.283E+17 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.966 8.237E+22 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 38.000 20.850 -103.330 5.566E+00 6.120E+17 | 6.866E+00 7.548E+17 H2O | O3

 6413.416 20.978 2.553E-02 2.807E+15 | 3.380E-02 3.716E+15 N2O | CO

 3060.0 7.647E-01 8.407E+16 | 3.910E+02 4.298E+19 CH4 | CO2

 7.808E+05 8.584E+22 | 2.095E+05 2.303E+22 N2 | O2

 0.000E+00 0.000E+00 | 9.340E+03 1.027E+21 O | Ar

 5.200E+00 5.716E+17 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.966 1.099E+23 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 36.000 21.250 -102.130 5.479E+00 8.095E+17 | 7.561E+00 1.117E+18 H2O | O3

 6411.316 21.380 4.250E-02 6.279E+15 | 3.118E-02 4.606E+15 N2O | CO

91
 3120.0 8.928E-01 1.319E+17 | 3.910E+02 5.776E+19 CH4 | CO2

 7.808E+05 1.154E+23 | 2.095E+05 3.095E+22 N2 | O2

 0.000E+00 0.000E+00 | 9.340E+03 1.380E+21 O | Ar

 5.200E+00 7.682E+17 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.966 1.477E+23 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 34.000 21.650 -100.930 5.347E+00 1.069E+18 | 7.760E+00 1.551E+18 H2O | O3

 6409.214 21.782 8.116E-02 1.622E+16 | 2.893E-02 5.781E+15 N2O | CO

 3180.0 1.088E+00 2.174E+17 | 3.910E+02 7.813E+19 CH4 | CO2

 7.808E+05 1.560E+23 | 2.095E+05 4.186E+22 N2 | O2

 0.000E+00 0.000E+00 | 9.340E+03 1.867E+21 O | Ar

 5.200E+00 1.039E+18 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.966 1.999E+23 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 32.000 22.050 -99.730 5.213E+00 1.418E+18 | 7.703E+00 2.095E+18 H2O | O3

 6407.110 22.184 1.087E-01 2.957E+16 | 2.672E-02 7.268E+15 N2O | CO

 3240.0 1.214E+00 3.303E+17 | 3.910E+02 1.063E+20 CH4 | CO2

 7.808E+05 2.124E+23 | 2.095E+05 5.697E+22 N2 | O2

 0.000E+00 0.000E+00 | 9.340E+03 2.540E+21 O | Ar

 5.200E+00 1.414E+18 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.966 2.720E+23 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 30.000 22.450 -98.530 5.129E+00 1.911E+18 | 7.356E+00 2.740E+18 H2O | O3

 6405.005 22.586 1.390E-01 5.177E+16 | 2.433E-02 9.063E+15 N2O | CO

 3300.0 1.353E+00 5.041E+17 | 3.910E+02 1.457E+20 CH4 | CO2

 7.808E+05 2.909E+23 | 2.095E+05 7.804E+22 N2 | O2

 0.000E+00 0.000E+00 | 9.340E+03 3.479E+21 O | Ar

 5.200E+00 1.937E+18 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.966 3.726E+23 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 28.000 22.850 -97.330 5.092E+00 2.621E+18 | 6.740E+00 3.469E+18 H2O | O3

 6402.899 22.987 1.832E-01 9.430E+16 | 2.192E-02 1.128E+16 N2O | CO

 3360.0 1.495E+00 7.696E+17 | 3.910E+02 2.012E+20 CH4 | CO2

 7.808E+05 4.018E+23 | 2.095E+05 1.078E+23 N2 | O2

 0.000E+00 0.000E+00 | 9.340E+03 4.807E+21 O | Ar

 5.200E+00 2.676E+18 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.966 5.147E+23 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 26.000 23.250 -96.130 5.000E+00 3.566E+18 | 5.975E+00 4.261E+18 H2O | O3

 6400.791 23.389 1.588E-01 1.132E+17 | 2.003E-02 1.428E+16 N2O | CO

 3420.0 1.285E+00 9.163E+17 | 3.910E+02 2.788E+20 CH4 | CO2

 7.808E+05 5.568E+23 | 2.095E+05 1.494E+23 N2 | O2

 0.000E+00 0.000E+00 | 9.340E+03 6.660E+21 O | Ar

 5.200E+00 3.708E+18 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.966 7.131E+23 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 24.000 23.650 -94.930 4.757E+00 4.711E+18 | 4.422E+00 4.379E+18 H2O | O3

 6398.681 23.791 1.762E-01 1.745E+17 | 1.775E-02 1.757E+16 N2O | CO

 3480.0 1.417E+00 1.403E+18 | 3.910E+02 3.872E+20 CH4 | CO2

 7.808E+05 7.732E+23 | 2.095E+05 2.074E+23 N2 | O2

 0.000E+00 0.000E+00 | 9.340E+03 9.249E+21 O | Ar

 5.200E+00 5.149E+18 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.966 9.903E+23 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 22.000 24.050 -93.730 4.350E+00 6.073E+18 | 2.790E+00 3.896E+18 H2O | O3

 6396.570 24.193 1.948E-01 2.719E+17 | 1.559E-02 2.177E+16 N2O | CO

 3540.0 1.635E+00 2.283E+18 | 3.910E+02 5.459E+20 CH4 | CO2

 7.808E+05 1.090E+24 | 2.095E+05 2.925E+23 N2 | O2

 0.000E+00 0.000E+00 | 9.340E+03 1.304E+22 O | Ar

 5.200E+00 7.260E+18 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.966 1.396E+24 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 20.000 24.450 -92.530 3.837E+00 7.608E+18 | 1.770E+00 3.510E+18 H2O | O3

92
 6394.458 24.595 2.328E-01 4.615E+17 | 1.686E-02 3.342E+16 N2O | CO

 3600.0 1.836E+00 3.639E+18 | 3.910E+02 7.751E+20 CH4 | CO2

 7.808E+05 1.548E+24 | 2.095E+05 4.153E+23 N2 | O2

 0.000E+00 0.000E+00 | 9.340E+03 1.852E+22 O | Ar

 5.200E+00 1.031E+19 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.966 1.983E+24 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 18.000 24.850 -91.330 3.109E+00 8.788E+18 | 7.675E-01 2.170E+18 H2O | O3

 6392.345 24.997 2.762E-01 7.807E+17 | 2.497E-02 7.059E+16 N2O | CO

 3660.0 1.968E+00 5.563E+18 | 3.910E+02 1.105E+21 CH4 | CO2

 7.808E+05 2.207E+24 | 2.095E+05 5.921E+23 N2 | O2

 0.000E+00 0.000E+00 | 9.340E+03 2.640E+22 O | Ar

 5.200E+00 1.470E+19 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.966 2.827E+24 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 16.000 25.250 -90.130 2.788E+00 1.092E+19 | 2.909E-01 1.139E+18 H2O | O3

 6390.230 25.398 3.083E-01 1.208E+18 | 3.892E-02 1.524E+17 N2O | CO

 3720.0 2.051E+00 8.033E+18 | 3.910E+02 1.531E+21 CH4 | CO2

 7.808E+05 3.058E+24 | 2.095E+05 8.204E+23 N2 | O2

 0.000E+00 0.000E+00 | 9.340E+03 3.658E+22 O | Ar

 5.200E+00 2.037E+19 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.966 3.917E+24 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 14.000 25.650 -88.930 4.643E+00 2.435E+19 | 2.189E-01 1.148E+18 H2O | O3

 6388.114 25.800 3.241E-01 1.700E+18 | 6.376E-02 3.344E+17 N2O | CO

 3780.0 2.120E+00 1.112E+19 | 3.910E+02 2.051E+21 CH4 | CO2

 7.808E+05 4.095E+24 | 2.095E+05 1.099E+24 N2 | O2

 0.000E+00 0.000E+00 | 9.340E+03 4.899E+22 O | Ar

 5.200E+00 2.727E+19 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.966 5.245E+24 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 12.000 26.050 -87.730 1.576E+01 1.083E+20 | 1.618E-01 1.112E+18 H2O | O3

 6385.996 26.202 3.366E-01 2.313E+18 | 9.900E-02 6.803E+17 N2O | CO

 3840.0 2.174E+00 1.494E+19 | 3.910E+02 2.686E+21 CH4 | CO2

 7.808E+05 5.365E+24 | 2.095E+05 1.439E+24 N2 | O2

 0.000E+00 0.000E+00 | 9.339E+03 6.417E+22 O | Ar

 5.200E+00 3.573E+19 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.966 6.871E+24 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 10.000 26.450 -86.530 2.173E+02 1.907E+21 | 1.006E-01 8.829E+17 H2O | O3

 6383.877 26.604 3.486E-01 3.059E+18 | 1.262E-01 1.108E+18 N2O | CO

 3900.0 2.233E+00 1.960E+19 | 3.909E+02 3.430E+21 CH4 | CO2

 7.806E+05 6.850E+24 | 2.094E+05 1.838E+24 N2 | O2

 0.000E+00 0.000E+00 | 9.338E+03 8.194E+22 O | Ar

 5.199E+00 4.562E+19 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.963 8.775E+24 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 8.000 26.850 -85.330 7.040E+02 7.716E+21 | 6.484E-02 7.107E+17 H2O | O3

 6381.757 27.005 3.540E-01 3.881E+18 | 1.507E-01 1.652E+18 N2O | CO

 3960.0 2.266E+00 2.483E+19 | 3.907E+02 4.282E+21 CH4 | CO2

 7.802E+05 8.552E+24 | 2.093E+05 2.294E+24 N2 | O2

 0.000E+00 0.000E+00 | 9.333E+03 1.023E+23 O | Ar

 5.196E+00 5.695E+19 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.958 1.096E+25 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 6.000 27.250 -84.130 1.365E+03 1.853E+22 | 4.868E-02 6.608E+17 H2O | O3

 6379.636 27.407 3.538E-01 4.803E+18 | 1.633E-01 2.217E+18 N2O | CO

 4020.0 2.285E+00 3.103E+19 | 3.904E+02 5.300E+21 CH4 | CO2

 7.797E+05 1.058E+25 | 2.092E+05 2.840E+24 N2 | O2

 0.000E+00 0.000E+00 | 9.327E+03 1.266E+23 O | Ar

 5.193E+00 7.049E+19 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.951 1.357E+25 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

93
 4.000 27.650 -82.930 2.722E+03 4.553E+22 | 3.733E-02 6.245E+17 H2O | O3

 6377.513 27.808 3.533E-01 5.911E+18 | 1.656E-01 2.771E+18 N2O | CO

 4080.0 2.299E+00 3.846E+19 | 3.899E+02 6.523E+21 CH4 | CO2

 7.787E+05 1.303E+25 | 2.089E+05 3.495E+24 N2 | O2

 0.000E+00 0.000E+00 | 9.314E+03 1.558E+23 O | Ar

 5.186E+00 8.675E+19 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.936 1.673E+25 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 2.000 28.050 -81.730 7.002E+03 1.449E+23 | 3.288E-02 6.804E+17 H2O | O3

 6375.390 28.210 3.518E-01 7.279E+18 | 1.762E-01 3.646E+18 N2O | CO

 4140.0 2.289E+00 4.737E+19 | 3.882E+02 8.033E+21 CH4 | CO2

 7.753E+05 1.604E+25 | 2.080E+05 4.304E+24 N2 | O2

 0.000E+00 0.000E+00 | 9.274E+03 1.919E+23 O | Ar

 5.163E+00 1.068E+20 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.889 2.069E+25 N | Tot

-------- ------- -------- --------- --------- + --------- --------- ----+----

 0.000 28.450 -80.530 1.601E+04 4.084E+23 | 3.004E-02 7.663E+17 H2O | O3

 6373.265 28.611 3.486E-01 8.894E+18 | 1.871E-01 4.773E+18 N2O | CO

 4200.0 2.268E+00 5.787E+19 | 3.847E+02 9.815E+21 CH4 | CO2

 7.683E+05 1.960E+25 | 2.061E+05 5.258E+24 N2 | O2

 0.000E+00 0.000E+00 | 9.190E+03 2.345E+23 O | Ar

 5.117E+00 1.305E+20 | 0.000E+00 0.000E+00 He | H

 0.000E+00 0.000E+00 | MW=28.790 2.551E+25 N | Tot

94
D.3 Sample Special Output File Produced by Input File of Appendix 

Time Hgtkm GeocenLat Lon(East) DensMean PresMean Tmean EWmean NSmean DensPert PresPert Tpert EWpert NSpert Dpert% Ppert% SDden% SDprs% SDtemK SDuwnd SDvwnd SDwwnd Wpert SpdAvg 

0 140 0.45 -164.53 4.41E-09 9.97E-04 690.23 20.45 0.31 4.77E-09 9.42E-04 603.18 91.47 -69.41 8.21 -5.43 7.2 12.5 100.77 69 69 8.33 -3.45 78.61 

60 138 0.85 -163.33 5.02E-09 1.09E-03 662.03 17.48 0.51 5.27E-09 1.00E-03 583.48 60.84 -41.21 4.97 -7.48 7.27 13.2 101.78 66.36 66.2 8.16 -4.1 74.98 

120 136 1.25 -162.13 5.76E-09 1.19E-03 633.2 14.02 0.59 5.75E-09 1.12E-03 598.32 36.76 -36.88 -0.31 -5.8 7.35 13.86 102.02 63.64 63.3 7.99 8.5 71.22 

180 134 1.65 -160.93 6.67E-09 1.30E-03 603.8 10.08 0.59 6.60E-09 1.21E-03 566.05 31.14 -42.72 -0.98 -7.17 7.42 14.49 101.53 60.83 60.31 7.82 9.04 67.38 

240 132 2.05 -159.73 7.78E-09 1.44E-03 573.92 5.7 0.52 7.66E-09 1.34E-03 542.28 17.52 13.41 -1.55 -6.97 7.49 15.09 100.39 57.9 57.19 7.65 9.05 63.56 

300 130 2.45 -158.53 9.16E-09 1.60E-03 543.64 0.96 0.4 9.29E-09 1.45E-03 485.84 -17.91 20.16 1.42 -9.37 7.56 15.67 98.64 54.85 53.92 7.48 7.72 59.84 

360 128 2.85 -157.33 1.09E-08 1.79E-03 513.08 -4.04 0.26 1.08E-08 1.76E-03 512.85 -8.45 22.39 -1.21 -1.25 7.63 16.23 96.32 51.66 50.49 7.31 7.13 56.33 

420 126 3.25 -156.13 1.31E-08 2.01E-03 482.33 -9.15 0.11 1.23E-08 2.02E-03 518.22 -28.67 -8.22 -6.36 0.6 7.7 16.77 93.48 48.28 46.85 7.14 6.55 53.12 

480 124 3.65 -154.93 1.60E-08 2.28E-03 451.51 -14.19 -0.03 1.41E-08 2.36E-03 528.29 -1.8 11.13 -11.7 3.32 7.77 17.3 90.17 44.69 42.94 6.97 3.45 50.25 

540 122 4.05 -153.73 1.98E-08 2.62E-03 420.96 -18.96 -0.15 2.00E-08 2.22E-03 353.6 -37.12 -4.03 0.99 -15.17 7.83 17.81 86.48 40.83 38.7 6.8 3.04 47.69 

600 120 4.45 -152.53 2.48E-08 3.04E-03 391.14 -23.26 -0.25 2.39E-08 2.72E-03 363.08 -28.42 -12.38 -3.51 -10.44 7.9 18.3 82.53 36.6 33.99 6.63 -0.92 45.28 

660 118 4.85 -151.33 3.15E-08 3.56E-03 362.27 -26.54 -0.34 2.80E-08 3.58E-03 409.94 -53.03 21.14 -11.13 0.56 8.71 17.79 71.77 36.17 37.51 6.49 5.68 48.45 

720 116 5.25 -150.13 4.06E-08 4.21E-03 334.29 -28.14 -0.46 3.44E-08 4.25E-03 398.31 -35.46 55.69 -15.25 0.98 9.45 17.27 61.61 35.71 40.57 6.36 -1.85 50.59 

780 114 5.65 -148.93 5.32E-08 5.04E-03 307.3 -27.95 -0.64 4.76E-08 4.87E-03 331.87 -31.72 24.16 -10.57 -3.42 10.21 16.77 52.47 37.08 42.05 6.22 2.1 51.8 

840 112 6.05 -147.73 7.11E-08 6.13E-03 281.47 -26.01 -0.89 5.95E-08 5.58E-03 305.85 -34.79 31.77 -16.33 -9.08 10.98 16.29 44.33 39.91 42.33 6.09 -2.25 52.2 

900 110 6.45 -146.53 9.79E-08 7.64E-03 256.31 -22.71 -1.27 7.69E-08 6.53E-03 279.18 -46.05 95.69 -21.5 -14.49 11.7 15.8 36.65 42.33 42.72 5.95 0.22 52.02 

960 108 6.85 -145.33 1.37E-07 9.76E-03 236.08 -17.99 -1.78 1.25E-07 8.09E-03 213.84 -31.99 70.5 -8.42 -17.05 12.45 15.29 30.8 39.05 41.86 5.81 1.48 48.06 

1020 106 7.25 -144.13 1.96E-07 1.28E-02 218.13 -12.73 -2.43 1.60E-07 1.06E-02 221.18 -12.13 49.41 -18.4 -17.26 13.16 14.77 25.43 35.77 41.08 5.68 0.95 44.3 

1080 104 7.65 -142.93 2.84E-07 1.73E-02 204.1 -8.09 -3.23 2.43E-07 1.42E-02 195.76 0.72 11.11 -14.39 -17.89 13.9 14.25 21.04 37.13 40.52 5.54 0.69 43.62 

1140 102 8.05 -141.73 4.14E-07 2.38E-02 194.53 -4.8 -4.15 3.19E-07 1.86E-02 197.33 7.19 19.42 -23.02 -21.91 14.67 13.73 17.54 42.42 40.2 5.4 1.35 45.89 

1200 100 8.45 -140.53 6.09E-07 3.35E-02 186.92 -2.74 -5.16 4.21E-07 2.41E-02 194.46 2.57 68.33 -30.93 -28.14 15.4 13.2 14.02 47.02 40 5.26 -4.01 48.37 

1260 98 8.85 -139.33 8.88E-07 4.78E-02 183.88 -2.12 -5.96 7.93E-07 3.95E-02 170.13 1.56 46.45 -10.7 -17.37 14.76 13.66 14.17 46.38 37.01 5.16 -9.67 46.58 

1320 96 9.25 -138.13 1.29E-06 6.84E-02 182.1 -2.32 -6.47 1.12E-06 5.63E-02 172.27 23.34 24.54 -12.93 -17.63 14.1 14.16 14.39 45.69 33.46 5.06 -5.43 44.58 

1380 94 9.65 -136.93 1.87E-06 9.91E-02 182.59 -3.63 -6.84 1.67E-06 8.28E-02 170.54 15.79 31.13 -10.54 -16.44 13.45 14.71 14.83 47.01 32.13 4.96 -1.64 44.96 

1440 92 10.05 -135.73 2.70E-06 1.44E-01 185.12 -5.52 -7.01 2.47E-06 1.22E-01 170.96 -11.26 22.25 -8.32 -15.33 12.81 15.29 15.48 49.9 33.5 4.85 -1.38 47.59 

1500 90 10.45 -134.53 3.84E-06 2.08E-01 188 -6.55 -6.73 3.45E-06 1.77E-01 178.27 -6.86 36.91 -10.32 -14.96 12.14 15.76 16.14 52.32 34.8 4.75 -3.17 49.77 

1560 88 10.85 -133.33 5.37E-06 2.96E-01 191.5 -3.75 -5.1 4.50E-06 2.57E-01 198.54 -15.59 23.15 -16.12 -13.03 10.18 13.11 13.97 50.95 36.45 4.49 -0.3 49.13 

1620 86 11.25 -132.13 7.45E-06 4.17E-01 195.01 -0.93 -3.61 6.69E-06 3.83E-01 199.15 36.07 28.93 -10.17 -8.26 7.71 9.84 11.2 49.9 37.79 4.22 5.64 48.83 

1680 84 11.65 -130.93 1.03E-05 5.84E-01 198.22 1.6 -2.9 9.98E-06 5.63E-01 196.35 58.46 -22.51 -2.78 -3.69 5.86 7.33 9.13 47.59 36.31 3.93 -2.79 46.68 

1740 82 12.05 -129.73 1.41E-05 8.12E-01 201.03 4.13 -2.98 1.35E-05 7.97E-01 205.53 58.65 -9.1 -4 -1.86 5.34 6.51 8.5 43.52 31.92 3.62 -3.99 42.29 

1800 80 12.45 -128.53 1.92E-05 1.12E+00 203.76 7.07 -3.19 1.88E-05 1.12E+00 207.57 53.78 -15.42 -2.14 -0.31 4.76 5.58 7.79 39.1 26.93 3.3 -4.87 37.73 

1860 78 12.85 -127.33 2.62E-05 1.55E+00 206.03 13.56 -1.05 2.61E-05 1.56E+00 208.35 24.69 -11.15 -0.14 0.98 4.68 5.54 7.83 38.03 25.76 2.98 -4.08 38.23 

1920 76 13.25 -126.13 3.56E-05 2.13E+00 208.28 20.06 0.84 3.64E-05 2.17E+00 207.03 21.75 -0.81 2.36 1.75 4.59 5.51 7.87 36.86 24.57 2.67 0.86 39.88 

1980 74 13.65 -124.93 4.80E-05 2.92E+00 211.57 25.43 1.51 5.02E-05 3.03E+00 210.33 29.2 4.13 4.56 3.95 4.43 5.26 7.63 35.54 22.44 2.39 -0.18 41.45 

2040 72 14.05 -123.73 6.43E-05 3.98E+00 215.86 29.72 1.14 6.46E-05 4.14E+00 223.14 31.22 8.97 0.45 3.83 4.17 4.73 7.05 34.17 18.99 2.15 1.47 42.53 

2100 70 14.45 -122.53 8.56E-05 5.40E+00 220.11 34.07 0.81 8.74E-05 5.61E+00 223.7 45.55 4.4 2.16 3.83 3.88 4.13 6.35 32.8 14.74 1.91 1.7 44.09 

2160 68 14.85 -121.33 1.12E-04 7.28E+00 226.37 35.1 0.59 1.10E-04 7.51E+00 237.3 58.74 -5.98 -1.64 3.11 4 4.04 6.31 30.37 15.01 1.76 -0.26 43.9 

2220 66 15.25 -120.13 1.46E-04 9.73E+00 232.53 36.27 0.39 1.46E-04 1.00E+01 239.42 69.16 -10.03 0.12 3.09 4.07 3.93 6.26 27.77 15.31 1.61 0.56 43.86 

2280 64 15.65 -118.93 1.89E-04 1.29E+01 238.16 36.26 0.43 1.90E-04 1.33E+01 243.29 59.89 -11.48 0.56 2.73 4.2 4.1 6.14 26.03 15.04 1.55 -1.11 43.15 

2340 62 16.05 -117.73 2.44E-04 1.71E+01 243.32 35.09 0.53 2.37E-04 1.73E+01 253.95 35.19 -2.68 -3.08 1.16 4.41 4.54 5.92 25.28 14.16 1.58 0.91 41.7 

2400 60 16.45 -116.53 3.14E-04 2.24E+01 248.43 34.01 0.61 3.01E-04 2.23E+01 258.25 50.82 2.87 -4.43 -0.65 4.61 4.94 5.63 24.44 13.2 1.61 -0.69 40.29 

2460 58 16.85 -115.33 4.03E-04 2.93E+01 253.49 29.51 0.18 4.07E-04 2.95E+01 252.8 60.94 -0.11 1.03 0.76 4.4 4.74 5.51 24.33 12.73 1.53 1.49 36.43 

2520 56 17.25 -114.13 5.13E-04 3.81E+01 258.59 25.04 -0.25 5.38E-04 3.92E+01 253.61 61.34 -8.57 4.94 2.92 4.2 4.55 5.4 24.25 12.24 1.46 2.8 32.76 

2580 54 17.65 -112.93 6.53E-04 4.92E+01 262.42 20.98 -0.5 6.96E-04 5.12E+01 256.46 32.47 -15.07 6.52 4.1 4.01 4.37 5.3 24.36 11.93 1.37 -0.52 29.76 

2640 52 18.05 -111.73 8.34E-04 6.34E+01 265 17.28 -0.58 8.49E-04 6.50E+01 266.94 33.55 2.53 1.77 2.51 3.82 4.19 5.18 24.66 11.85 1.26 -2.14 27.42 

2700 50 18.45 -110.53 1.06E-03 8.16E+01 267.67 13.52 -0.62 1.10E-03 8.39E+01 266.54 16.23 2.58 3.24 2.81 3.62 4 5.01 24.98 11.78 1.15 -0.61 25.39 

2760 48 18.85 -109.33 1.37E-03 1.05E+02 266.76 13.65 -0.7 1.43E-03 1.09E+02 265.73 37.49 -10.25 4.65 4.25 3.53 3.81 5.09 24.41 11.06 1.05 -0.64 24.92 

2820 46 19.25 -108.13 1.76E-03 1.35E+02 265.9 13.59 -0.74 1.81E-03 1.40E+02 269.55 6.27 -8.02 2.44 3.84 3.44 3.61 5.19 23.83 10.29 0.94 0.25 24.35 

2880 44 19.65 -106.93 2.29E-03 1.73E+02 263.47 13.94 -0.79 2.35E-03 1.80E+02 266.61 36.66 -7.91 2.5 3.72 3.29 3.41 5.18 23.08 9.43 0.86 0.2 23.9 

2940 42 20.05 -105.73 3.01E-03 2.24E+02 259.38 14.66 -0.84 3.10E-03 2.32E+02 260.8 35.06 -9.22 3.23 3.79 3.06 3.21 5.04 22.11 8.45 0.81 -0.37 23.55 

3000 40 20.45 -104.53 3.96E-03 2.90E+02 255.19 14.94 -0.92 4.07E-03 3.01E+02 257.87 17 -2.1 2.66 3.73 2.83 3.03 4.93 20.97 7.41 0.75 0.91 22.87 

3060 38 20.85 -103.33 5.29E-03 3.79E+02 249.51 13.94 -0.97 5.33E-03 3.91E+02 255.27 44.36 5.94 0.89 3.22 2.67 2.83 4.96 19.85 7.11 0.7 0.38 21.54 

3120 36 21.25 -102.13 7.11E-03 4.97E+02 243.81 12.82 -1.04 7.17E-03 5.12E+02 248.52 18.14 0.26 0.91 2.87 2.49 2.6 4.95 18.64 6.76 0.65 0.53 20.08 

3180 34 21.65 -100.93 9.61E-03 6.58E+02 238.3 12.08 -0.87 9.72E-03 6.73E+02 241.06 11.85 -5.02 1.16 2.33 2.3 2.38 4.76 17.13 6.26 0.61 -0.3 18.66 

95
3240 32 22.05 -99.73 1.31E-02 8.75E+02 233.04 11.81 -0.53 1.30E-02 8.93E+02 240.08 35 0.86 -0.9 2.1 2.08 2.16 4.41 15.31 5.55 0.57 -0.09 17.32 

3300 30 22.45 -98.53 1.79E-02 1.17E+03 227.81 11.34 -0.24 1.78E-02 1.19E+03 233.5 23.05 0.8 -0.87 1.6 1.79 1.86 3.94 12.99 4.79 0.53 0.48 15.65 

3360 28 22.85 -97.33 2.48E-02 1.58E+03 222.51 8.77 0.72 2.45E-02 1.60E+03 227.54 17.02 2.25 -0.98 1.25 1.49 1.37 3.12 10.32 4.44 0.5 0.22 12.43 

3420 26 23.25 -96.13 3.43E-02 2.14E+03 217.72 5.86 2.14 3.41E-02 2.16E+03 221.37 12.36 8.8 -0.71 0.96 1.32 1.02 2.87 8.27 3.81 0.47 0.71 9.62 

3480 24 23.65 -94.93 4.76E-02 2.93E+03 214.26 5.05 2.41 4.77E-02 2.96E+03 215.9 3.2 9.93 0.17 0.93 1.16 0.85 2.48 6.46 3.93 0.44 0.54 8.13 

3540 22 24.05 -93.73 6.72E-02 4.04E+03 209.32 6.11 2.74 6.73E-02 4.06E+03 210.23 8.83 4.47 0.2 0.64 1.19 0.74 2.41 5.53 3.68 0.43 0.74 8.41 

3600 20 24.45 -92.53 9.54E-02 5.59E+03 204.07 9.04 3 9.50E-02 5.61E+03 205.82 8.8 5.62 -0.36 0.49 1.23 0.69 2.43 5.31 3.87 0.42 0.75 10.54 

3660 18 24.85 -91.33 1.36E-01 7.82E+03 200.34 16.18 4.01 1.37E-01 7.82E+03 199.17 24.71 3.47 0.58 -0.01 1.25 0.8 2.49 6.98 5.23 0.46 -0.59 17.57 

3720 16 25.25 -90.13 1.88E-01 1.10E+04 202.65 25.47 5.54 1.89E-01 1.10E+04 202.26 41.51 18.3 0.17 -0.02 1.15 0.99 2.27 9.26 7.4 0.49 0.15 27.08 

3780 14 25.65 -88.93 2.52E-01 1.52E+04 210.46 33.12 7.1 2.52E-01 1.52E+04 210.08 49.88 23.38 -0.08 -0.26 1.23 1.1 2.59 11.31 9.88 0.53 -1.48 35.2 

3840 12 26.05 -87.73 3.31E-01 2.09E+04 219.91 34.37 6.18 3.26E-01 2.08E+04 222.16 35.51 10.67 -1.46 -0.45 1.33 1.12 2.98 13.11 12.27 0.58 -0.43 36.97 

3900 10 26.45 -86.53 4.22E-01 2.82E+04 232.44 29.68 4.95 4.16E-01 2.79E+04 234.2 40.08 15.26 -1.53 -0.78 0.97 1.06 2.25 12.63 11.74 0.63 -0.35 32.33 

3960 8 26.85 -85.33 5.27E-01 3.73E+04 246.79 23.53 3.98 5.20E-01 3.70E+04 248.14 40.32 15.5 -1.4 -0.87 0.94 0.89 2.29 10.67 10.07 0.63 0.36 25.94 

4020 6 27.25 -84.13 6.53E-01 4.88E+04 260.56 17.43 2.97 6.48E-01 4.84E+04 260.27 23.75 -1.67 -0.71 -0.82 0.94 0.72 2.4 9.11 8.62 0.63 0.95 19.77 

4080 4 27.65 -82.93 8.04E-01 6.30E+04 272.69 11.72 1.93 8.03E-01 6.27E+04 271.57 3.92 1.64 -0.09 -0.5 0.9 0.58 2.44 7.83 7.06 0.62 -0.2 14.07 

4140 2 28.05 -81.73 9.93E-01 8.04E+04 281.61 6.27 1.68 9.91E-01 8.00E+04 280.54 -0.52 2.14 -0.16 -0.54 1.2 0.51 3.34 7.03 6.03 0.5 0.26 9.73 

4200 0 28.45 -80.53 1.22E+00 1.02E+05 289.55 0.14 -0.16 1.23E+00 1.02E+05 286.77 -2.94 -0.47 0.87 -0.1 2.18 0.47 5.25 2.9 3.35 0.34 -0.53 3.27 

1 

96
D.4 Sample Boundary Layer Output File Produced by Input File of Appendix C 

 Day LST Hgt Lat Lon hsrf spdsrf LC z0 Elmn El Elmd sha blfct nri S ool ustar BVfsq hN hbl chb sigrat swb 

1.815 19.55 4.000 27.650 -82.930 0.000 3.84 6 0.12000 -85.4 -30.2 39.3 113.24 1.000 -1.27 4.85 0.01527 0.296 0.00011 651. 200. 200. 2.013 0.60 

1.819 19.65 2.000 28.050 -81.730 0.012 2.47 6 0.12000 -85.0 -31.5 38.9 114.69 1.000 -1.35 5.13 0.02216 0.179 0.00011 390. 200. 200. 2.358 0.42 

1.823 19.74 0.000 28.450 -80.530 0.003 2.63 5 0.45000 -84.6 -32.9 38.5 116.14 1.000 -1.42 5.15 0.01584 0.270 0.00011 587. 200. 0. 1.250 0.34 

97
APPENDIX E—PARAMETERS AVAILABLE FOR SPECIAL OUTPUT

Following is a listing of the section of GRAM where the "Special Output" can be 

prepared and generated. This identifies logical places to do computations of special variables or 

to do units conversions (e.g., multiplying by conversion factors). Comments in this code section 

also provide lists of the names of the variables that are available for writing to the Special 

Output. An example of a write statement and user-provided format for writing to the Special 

Output is given on lines ATMD880 through ATMD884. Another feature is the capability to 

write surface data values to the special output file. Surface data parameter identifiers are 

discussed on lines ATMD845 - ATMD861. 

!-----"Special" output option section !ATMD748

 if (iopp /= 0) then !ATMD749

! EXAMPLES OF SPECIALLY COMPUTED OUTPUT: !ATMD750

!----- Wind speed (m/s) and direction (meteorological convention) from !ATMD751

! mean winds !ATMD752

 wndspd = dsqrt(ugh**2 + vgh**2) !ATMD753

 wnddir = 180.0D0 !ATMD754

 if (dabs(ugh)>0.0D0 .and. dabs(vgh)>0.0D0) wnddir = 180.0D0*(1.0D0 + & !ATMD755

 datan2(ugh,vgh)/pi) !ATMD756

!----- Pressure scale height (m), density scale height (m) !ATMD757

 hgtp = pgh/(dgh*g) !ATMD758

 if (ch <= hj1) then !ATMD759

 hgtd = hgtp/(1.0D0 + hgtp*dtz/tgh) !ATMD760

 else !ATMD761

 hgtd = hgtp/(1.0D0 + hgtp*dtz/tgh - hgtp*dmdz/wtmol) !ATMD762

 endif !ATMD763

!----- Mean free path (m) (assume mean values of pressure and temp.) !ATMD764

 mfpath = 7.071D17/(0.424D0*totnd) !ATMD765

!----- Other variables that are functions of pressure, density, !ATMD766

! temperature, wind and/or moisture, can be calculated here. !ATMD767

! Some such variables are: coefficient of viscosity, kinematic !ATMD768

! viscosity, thermal conduction coefficient, potential !ATMD769

! temperature, equivalent potential temperature, etc. !ATMD770

! !ATMD771

!---- **** To print out header information, refer to the section !ATMD772

!   near format label 200 in init subroutine of initial_E10.f. !ATMD773

!...................................................................... !ATMD774

! !ATMD775

! As an aid to the user, the following tables give the names of !ATMD776

! the variables that are available for output: !ATMD777

! !ATMD778

!---- Position and time parameters !ATMD779

! ---------------------------- !ATMD780

! ch - Geocentric Height (km) above WGS84 Reference Ellipsoid !ATMD781

! Rlocal - Radius from Earth center (km) (Earth radius plus ch) !ATMD782

! phi - Geocentric Latitude (deg) !ATMD783

! GdLat - Geodetic Latitude (deg) !ATMD784

! thet - Longitude (deg), East(+) West(-) !ATMD785

! elt - Elapsed Time (sec) !ATMD786

! !ATMD787

!---- Thermodynamic, wind and moisture parameters (on standard output) !ATMD788

! ---------------------------------------------------------------- !ATMD789

! !ATMD790

! Vert. !ATMD791

! Pressure Density/ Temperature E-W N-S Wind !ATMD792

! /Vap.Pr. Vap.Dens. /Dewpt. Wind Wind (m/s) !ATMD793

! (Nt/m** 2) (kg/m**3) (K) (m/s) (m/s) RH(%) !ATMD794

! --------- --------- ----------- ----- ----- ----- !ATMD795

!*Mean pgh dgh tgh ugh vgh wgh !ATMD796

! !ATMD797

!*Mean-76 pghp (%) dghp (%) tghp (%) n/a n/a n/a !ATMD798

! !ATMD799

!*Small-Scale !ATMD800

98
! Perturbation prhs (%) drhs (%) trhs (%) urhs vrhs n/a !ATMD801

! !ATMD802

!*Small-Scale !ATMD803

! Stand. Dev. sphs (%) sdhs (%) sths (%) suhs svhs n/a !ATMD804

! !ATMD805

!*Large-Scale !ATMD806

! Perturbation prhl (%) drhl (%) trhl (%) urhl vrhl n/a !ATMD807

! !ATMD808

!*Large-Scale !ATMD809

! Stand. Dev. sphl (%) sdhl (%) sthl (%) suhl svhl n/a !ATMD810

! !ATMD811

!*Total !ATMD812

! Perturbation prh (%) drh (%) trh (%) urh vrh wrh !ATMD813

! !ATMD814

!*Total Stand. !ATMD815

! Deviation sph (%) sdh (%) sth (%) suh svh swh !ATMD816

! !ATMD817

!*Total=Mean+ !ATMD818

! Perturbation ph dh th uh vh wh !ATMD819

! !ATMD820

!*Total-US76 php (%) dhp (%) thp (%) n/a n/a n/a !ATMD821

! !ATMD822

!*Mean H2O eofT rhov tdgh n/a n/a rhp !ATMD823

! !ATMD824

!*Stand. Dev. !ATMD825

! H2O seofT srhov stdgh n/a n/a srhp !ATMD826

! !ATMD826a

!---- Wind and Speed-of-Sound Statistics (on standard output) !ATMD826b

! ------------------------------------------------------- !ATMD826c

! !ATMD826d

!*Ruv = uvt2 (U-V cross correlation coefficient) !ATMD826e

! !ATMD826f

!*SpdAv, SpdSd = spdgh, sdsph (wind speed average and standard deviation, m/s) !ATMD826g

! !ATMD826h

!*SoSav, SoSpt = csp0, csp (average and perturbed speed-of-sound , m/s) !ATMD826i

! !ATMD826j

! !ATMD827k

!---- Species concentration parameters (on species output) !ATMD828

! ---------------------------------------------------- !ATMD829

! !ATMD830

! H2O O3 N2O CO CH4 CO2 N2 O2 O Ar He H N !ATMD831

! --- -- --- -- --- --- -- -- - -- -- - - !ATMD832

! Concen- ppmh2o ppmn2o ppmch4 ppmn2 ppmo ppmhe ppmn !ATMD833

! tration ppmo3 ppmco ppmco2 ppmo2 ppmar ppmh !ATMD834

! ----------------------------------------------------------------- !ATMD835

! Number h2ond n2ond ch4nd n2nd ond hend nnd !ATMD836

! Density o3nd cond co2nd o2nd arnd hnd !ATMD837

! !ATMD838

! Mean molecular weight=mwnd total number densty=totnd !ATMD839

! !ATMD840

! !ATMD841

!---- Surface data (passed from Subroutine NCEPmod, via Common !ATMD842

! Block srfdat) !ATMD843

! ------------------------------------------------------- !ATMD844

! psrf = average surface pressure (N/m**2) !ATMD845

! dsrf = average surface density (kg/m**3) !ATMD846

! tsrf = average surface temperature (K) !ATMD847

! usrf = average surface Eastward wind component (m/s) !ATMD848

! vsrf = average surface Northward wind component (m/s) !ATMD849

! hsrf = height of surface (km, above sea level) !ATMD850

! tdsrf = average surface dewpoint temperature (K) !ATMD851

! spsrf = standard deviation of surface pressure (N/m**2) !ATMD852

! sdsrf = standard deviation of surface density (kg/m**3) !ATMD853

! stsrf = standard deviation of surface temperature (K) !ATMD854

! susrf = standard deviation of surface Eastward wind (m/s) !ATMD855

! svsrf = standard deviation of surface Northward wind (m/s) !ATMD856

! shsrf = std. dev. (uncertainty) of surf. hgt (m, from spsrf) !ATMD857

! stdsrf = standard deviation of surface dewpoint temp. (K) !ATMD858

! spdavsrf = average wind speed at surface (m/s) !ATMD859

! spdsdsrf = standard deviation of surface wind speed (m/s) !ATMD860

! uvtsrf = U-V cross correlation at surface (unitless) !ATMD861

99
! !ATMD862

!... Surface roughness information (passed from Subroutine pertrb, !ATMD863

! via Common Block vert) for sigma-w model !ATMD864

! ------------------------------------------------------------- !ATMD865

! lc = land surface code (0-13 if from 1-by-1 deg data base !ATMD866

! or 99 if z0 is from user input) !ATMD867

! z0 = surface roughness (m), determined from 1-by-1 deg !ATMD868

! land surface type, or as specified by user via z0in) !ATMD869

! !ATMD870

!-----At this point, the user is invited to insert whatever output !ATMD871

! parameters (in whatever format) are desired for the "special" !ATMD872

! output instead of the Write and Format statements below. Any new !ATMD873

! variables introduced must be declared at the beginning of the !ATMD874

! atmod subroutine. !ATMD875

! !ATMD876

 isev = 0 !ATMD877

 if (densfact > 1.0D0) isev = 1 !ATMD878

!--- Release code version of write to special output file !ATMD879

 write (iopp, 9000) elt, ch, phi, thet, dgh, pgh, tgh, ugh, vgh, dh, & !ATMD880

 ph, th, uh, vh, drh, prh, sdh, sph, 0.01D0*sth*tgh, suh, svh, & !ATMD881

 swh, wh, spdgh,sdsph,csp0, csp, isev, lc, z0 !ATMD882

 9000 format(f10.2,f9.3,f10.5,f11.5,1p,2e11.4,0p,f8.2,2f8.2,1p,2e11.4,0p, & !ATMD883

 f8.2,2f8.2,9f7.2,4f8.2,i3,i4,f8.5) !ATMD884

! !ATMD885

!----- Any change of units for writing to "special" output file can !ATMD886

! be done here [e.g. International Standard (SI) to English !ATMD887

! units, etc.] !ATMD888

! !ATMD889

!--- Samples of how to change units: !ATMD890

! !ATMD891

! Change pressure and standard deviation to millibars !ATMD892

! pgh = pgh/100.0d0 !ATMD893

! sph = pgh*sph/100.0d0 !ATMD894

! ph = ph/100.0d0 !ATMD895

!--- Change density and standard deviation to gm/m**3 !ATMD896

! dgh = dgh*1000.0d0 !ATMD897

! sdh = dgh*sdh/100. !ATMD898

! dh = dh*1000.0d0 !ATMD899

!--- Change temperature and standard deviation to deg C !ATMD900

! sth = tgh*sth/100.0d0 !ATMD901

! tgh = tgh - 273.15d0 !ATMD902

! th = th - 273.15d0 !ATMD903

! !ATMD904

!--- Samples of some other write statements and formats for special !ATMD905

! output file, including some changes of units (e.g. dividing !ATMD906

! height by 0.3048 to convert to k-feet), dividing mission !ATMD907

! elapsed time by 3600. to convert to hours) !ATMD908

! !ATMD909

! Write(iopp,9000)ch,mfpath,dgh,tgh !ATMD910

!9000 Format(F6.1,1p,2E11.3,0p,F7.1) !ATMD911

! Write(iopp,9000)ch,suh,svh,sdh,urh,vrh,drh !ATMD912

!9000 Format(F6.2,6F8.2) !ATMD913

!--- Write(iopp,9000)elt/3600.,ch/0.3048,prhs,prhl,prh,drhs,drhl,drh, & !ATMD914

!--- trhs,trhl,trh,prhs/sphs,drhs/sdhs,trhs/sths !ATMD915

!9000 Format(2F8.1,12F8.3) !ATMD916

!--- Write(iopp,9000)elt/3600.,ch/0.3048,pgh,sph,ph,dgh,sdh,dh,tgh, & !ATMD917

!--- sth,th,prhs/sphs,drhs/sdhs,trhs/sths !ATMD918

!9000 Format(2F8.1,1p,6E10.3,0p,3F10.2,3F8.3) !ATMD919

!--- Write(iopp,9000)ch,sphs/sph,sdhs/sdh,sths/sth,suhs/suh,svhs/svh & !ATMD920

!--- sphl/sph,sdhl/sdh,sthl/sth,suhl/suh,svhl/svh,sph,sdh,sth,suh, & !ATMD921

!--- svh,suhs !ATMD922

!9000 Format(F7.2,10F6.4,3F7.3,F6.2,2F7.2) !ATMD923

!--- Write(iopp,9000)elt/3600.,ch,uh,vh !ATMD924

!9000 Format(F8.1,F8.3,2F8.2) !ATMD925

!--- Write(iopp,9000)elt,ch,phi,thet,dgh,dghp,sdh,drh,tgh,sth,trh,ugh, & !ATMD926

! suh,urh,vgh,svh,vrh !ATMD927

!9000 Format(F9.1,F9.3,F8.3,F9.3,1p,E10.3,0p,3F6.1,F7.1,2F6.1,6F7.1) !ATMD928

! !ATMD929

!----- The "special" output option Write and Format section ends here. !ATMD930

 endif !ATMD931

!...................................................................... !ATMD932

100
! !ATMD933

 return !ATMD934

 end subroutine atmod_e10 !ATMD935

 !ATMD936

!-------------------------------------------------------------------------------- !ATMD937

Note that the header for the special output is written in the subroutine initial_E10.f90. The 

following code section shows the header that is written for the sample special output list above. 

2

!----- This is the header for the "special" output file. The user !INIT595

! should insure that the 200 format is compatible with the output !INIT596

! format in subroutine atmod near label number 9000 in the !INIT597

! models_E10.f90 file. !INIT598

 write (iopp, 200) !INIT599

! !INIT600

!--- Header format for write statement in normal release code !INIT601

! !INIT602

 200 format(' Time Hgtkm GeocenLat Lon(East) DensMean', & !INIT603

 ' PresMean Tmean EWmean NSmean DensPert PresPert ', & !INIT604

 ' Tpert EWpert NSpert Dpert% Ppert% SDden% SDprs%', & !INIT605

 ' SDtemK SDuwnd SDvwnd SDwwnd Wpert SpdAvg SpdStd SoSmean ', & !INIT606

 'SoSpert Sev LC z0(m)') !INIT607

!--- Header formats corresponding to other example write statements !INIT608

! given in file models_E10.f90 !INIT609

! !INIT610

! 200 Format(' Hgtkm SigmaU SigmaV SigmaD Upert Vpert Dpert') !INIT611

! 200 Format(' Timehrs Hgtkft PAvgmb PStdmb Ppertmb', & !INIT612

! ' DAvggm3 DStdgm3 Dpertgm3 TAvgdegC TstddegC TpertdegC' & !INIT613

! ' dPsmn% dDsmn% dTsmn%') !INIT614

! 200 Format(' Timehrs Hgtkft dPsml% dPlrg% dPtot% dDsml%', & !INIT615

! ' dDlrg% dDtot% dTsml% dTlrg% dTtot% dPsmn% dDsmn%', & !INIT616

! ' dTsmn%') !INIT617

! 200 Format(' Hgtkm spS sdS stS suS svS spL sdL', & !INIT618

! ' stL suL svL spT sdT stT suT svT ') !INIT619

! 200 Format(' Timehrs Hgtkm Uwndmps Vwndmps') !INIT620

! 200 Format(' Time_sec Hgt_km Lat LonE Dens_kgm3 D-76%', & !INIT621

! ' sigD% dDen% Temp_K sigT% dTem% Uwnm/s sigUms dU_m/s', & !INIT622

! ' Vwnm/s sigVms dV_m/s') !INIT623

 endif !INIT624

!----- The "special" output header Write and Format section ends here. !INIT625

!........................................................................... !INIT626

101
APPENDIX F—EXAMPLE APPLICATION OF GLOBAL REFERENCE 

ATMOSPHERIC MODEL 2010 AS SUBROUTINES IN 

ANOTHER MAIN DRIVER 

F.1 General Description 

 

For many applications, it is desirable to use GRAM2010 in the form of subroutines in 

another program. For example, the main driver program may be a trajectory calculating program, 

for which GRAM2010 provides the atmospheric density and winds used to update the trajectory 

positions (or to provide the densities and temperatures to compute heat loads, etc.). Several code 

files are provided that illustrate how to use GRAM as a subroutine in a user-provided trajectory 

program, and how to implement these new features of the perturbation model. These files 

include: 

 gramtraj_E10.f90 A subroutine for use in user-provided trajectory programs 

 trajdemo_E10.f90 A main driver (replaces gram_E10.f) for use in a simple 

 trajectory demonstration program 

 trajopts_E10.f90 A main driver (replaces gram_E10.f) for use in an example 

 trajectory program that demonstrates several special options 

 of the perturbation model.

 multtraj_E10.f90 A main driver (replaces gram_E10.f) program that illustrates 

 how to call Earth-GRAM 2010 to evaluate multiple trajectories 

 in one program run, with independent (un-correlated) small- 

 scale correlations between trajectories. 

 trajcalc_E10.f90 Subroutines used in these trajectory demonstration programs, 

 illustrating how the user's trajectory program should 

 calculate and provide position and velocity information 

 to GRAM. 

 corrtraj_E10.f90 A main driver (replaces gram_E10.f) program illustrating 

 how to call Earth-GRAM 2010 to evaluate multiple profiles 

 in one program run, with small-scale correlations preserved 

 between the profiles. 

 multbody_E10.f90 Main driver illustrating how to call GRAM to evaluate 

 perturbations along trajectories of multiple bodies which 

 start out together and at various times separate from 

 each other. The perturbations for each body start out the 

 same, and then remain correlated over both position and 

 time along the body trajectories, and across the spatial 

 separation between the bodies. 

 

 As an example of how one might use GRAM2010 in a user-provided trajectory code, 

trajdemo_E10.f90 will be discussed and this program is shown below. As provided, trajdemo is a 

simple driver, not exercising any of several available GRAM calling options. Programs 

trajopts_E10.f90 and multtraj_E10.f90 illustrate how to call GRAM using these options and 

could be substituted for trajdemo_E10.f90 if the additional features are desired. To utilize 

trajdemo_E10.f90 in the user’s code, it must be compiled and linked with the GRAM routines: 

102
CFiles_E10.f90, IFiles_E10.f90, gramtraj_E10.f90, gramsubs_E10.f90, NCEPsubs_E10.f90, 

initial_E10.f90, MET07prg_E10.f90, models_E10.f90, random_E10.f90, speconc_E10.f90, 

RRAmods_E10.f90, MSISsubs_E10.f90, HWMsubs_E10.f90, and JB2008_E10.f90. Certain 

output parameters are currently passed through the argument list of gramtraj (e.g., mean and 

perturbed values of density, pressure, temperature and winds; U.S. standard atmosphere values of 

density, pressure, and temperature). The user can add other atmospheric variables to the 

argument list. See Appendix E for a description of the output variable names available. 

 Following is a simplified description of the functions required to be performed in the 

main driver program, as given in the “uncommented” lines of code in trajdemo_E10. Note that 

comment lines preceded with “!” are not executable and the syntax is case insensitive. 

1. TRJD66: Call to a dummy routine (setipos_E90 found in trajcalc_E10.f90) that should be 

replaced with the user’s code to provide the initial (starting) time (seconds), initial height 

(kilometers) above mean sea level or radius if above 6,000 kilometers, initial geocentric latitude 

(degrees), and initial longitude (degrees). 

 

2. TRJD68 – 71: Sets “previous” values (used later in the code) to the above initial values. 

3. TRJD82: The parameter ifirst is set equal to 1 which will subsequently trigger gramtraj_E10 

to initialize the GRAM model. 

4. TRJD84 – 89: Initial perturbations are set to zero unless over-ridden by values supplied by 

the user in the input file parameters initpert, rdinit, rtinit, ruinit, rvinit, and rwinit. 

5. TRJD92 – 96: The first call to gramtraj_E10 which will initialize the code. The inputs used 

by the code are ifirst (= 1 at this point), initial time ctime, initial height chgt, initial latitude clat, 

initial longitude clon, and the initial user perturbations if any (see Section 2.9 above) ppert, 

dpert, tpert, upert, vpert, and wpert. 

6. TRJD101 – 102: Call to a routine (exemplified by dummy routine newpos_E10 in 

trajcalc_E10.f90) that allows trajdemo_E10 to compute changes in time and position that it will 

use later. The call to newpos_E10 here, simply initializes the time and position values. 

7. TRJD107: In preparation for the next call to gramtraj_E10, the parameter ifirst is set to zero. 

This will prohibit a reinitialization of GRAM since that was accomplished in step 5 above. This 

line (label 20) also begins the loop over calculated positions and corresponding calculated 

atmospheric values. 

8. TRJD112 – 113: This is where newpos_E10 (or its functional equivalent in the user’s 

trajectory code) is called to compute the next time and position along the trajectory. 

9. TRJD118 – 122: This is the second call to gramtraj_E10. Since ifirst is now zero, GRAM 

will take the previous and current time and position and evaluate new mean and perturbed 

103
atmospheric values for the new position. This process continues (by looping back to label 20) 

until ifirst is set to a nonzero value by gramtraj_E10. 

10. TRJD123: As long as ifirst is equal to zero, the code will continue along the trajectory. In 

this example, the new positions are provided by the call to newpos_E10 at TRJD129, but should 

be replaced by the user’s new positions. The corresponding atmospheric values at these points 

are determined by the call to gramtraj_E10 at TRJD135. This looping continues until the end of 

the trajectory is reached. At the point, the user should change the value of ifirst to trigger a 

different action. If the user no longer requires additional GRAM values, then setting ifirst less 

than one (or any integer other than 0 or -1) will send the program to TRJD172 where the user can 

end the program or perform additional tasks at his discretion. If the user is performing a Monte 

Carlo run, then ifirst should be set to -1. 

11. TRJD 145: If ifirst has been set to -1 by gramtraj_E10, for another iteration of a Monte 

Carlo run, then the user perturbations and time are set to zero again (TRJD149 – 155). 

12. TRJD158 – 162: This is a call to gramtraj_E10 which will utilize the next random number 

seed and reinitialize GRAM. 

13. TRJD164: A call to dummy routine newpos_E10 to reset the initial position, and should be 

replaced by the user’s initial position data. 

14. TRJD166: The program is directed back to label 20 to start at the beginning of the trajectory 

for the next Monte Carlo cycle. 

F.2 Listing of Example Main Driver Program (trajdemo_E10.f90) Using 

gramtraj_E10.f90 as Subroutines 

 PROGRAM TRAJDEMO_E10 !TRJD 1

!----------------------------------------------- !TRJD 2

! M O D U L E S !TRJD 3

!----------------------------------------------- !TRJD 4

 USE VAST_KIND_PARAM, ONLY: DOUBLE !TRJD 5

! EXAMPLE GRAM DRIVER DEMONSTRATING HOW TO USE GRAMTRAJ SUBROUTINE !TRJD 6

! !TRJD 7

! THIS EXAMPLE DRIVER SHOULD BE COMPILED AND LINKED WITH; !TRJD 8

! GRAMTRAJ_E10.F90 - A SUBROUTINE THAT CAN BE USED TO CALL GRAM !TRJD 9

! FROM WITHIN IN THE USERS TRAJECTORY CODE !TRJD 10

! TRAJCALC_E10.F90 - A FILE CONTAINING SIMPLE EXAMPLES OF ROUTINES !TRJD 11

! TO INITIALIZE TRAJECTORY POSITION (SETIPOS) AND !TRJD 12

! UPDATE THE TRAJECTORY VELOCITY AND POSITION !TRJD 13

! (NEWPOS) !TRJD 14

! ALL THE OTHER GRAM ROUTINES (CFILES_E10.F90, IFILES_E10.F90, !TRJD 15

! GRAMSUBS_E10.F90, NCEPSUBS_E10.F90,INITIAL_E10.F90, MET07PRG_E10.F90, !TRJD 16

! MODELS_E10.F90, RANDOM_E10.F90,SPECONC_E10.F90, RRAMODS_E10.F90, !TRJD 17

! MSISSUBS_E10.F90, HWMSUBS_E10.F90, AND JB2008_E10.F90) !TRJD 18 

! !TRJD 19

! AS PROVIDED, TRAJDEMO IS A "PLAIN VANILLA" DRIVER, NOT EXERCISING !TRJD 20

! ANY OF SEVERAL AVAILABLE GRAM CALLING OPTIONS. PROGRAMS !TRJD 21

! TRAJOPTS_E10.F90 AND MULTTRAJ_E10.F90 ILLUSTRATE HOW TO CALL GRAM !TRJD 22

! USING THESE OPTIONS. !TRJD 23

! !TRJD 24

! CERTAIN OUTPUT PARAMETERS ARE CURRENTLY PASSED THROUGH THE !TRJD 25

! ARGUMENT LIST OF GRAMTRAJ (E.G. MEAN AND PERTURBED VALUES OF !TRJD 26

104
! DENSITY, PRESSURE, TEMPERATURE AND WINDS; US STANDARD !TRJD 27

! ATMOSPHERE VALUES OF DENSITY, PRESSURE, AND TEMPERATURE). !TRJD 28

! OTHER ATMOSPHERIC VARIABLES CAN BE ADDED TO THE ARGUMENT LIST !TRJD 29

! BY THE USER. SEE README FILES FOR A DESCRIPTION OF THE OUTPUT !TRJD 30

! VARIABLE NAMES AVAILABLE . !TRJD 31

! !TRJD 32

! AS AN EXAMPLE OF HOW A DOUBLE PRECISION TRAJECTORY CODE WOULD !TRJD 33

! BE CONFIGURED, THE CURRENT ARGUMENT LIST VARIABLES IN GRAMTRAJ !TRJD 34

! HAVE BEEN MADE DOUBLE PRECISION (REAL*8). IF ONLY SINGLE !TRJD 35

! PRECISION IS DESIRED, THESE DECLARATIONS (AND THE DBLE !TRJD 36

! ASSIGNMENT STATEMENTS OF THE ARGUMENT LIST VARIABLES IN !TRJD 37

! GRAMTRAJ) MAY BE MODIFIED ACCORDINGLY. !TRJD 38

! !TRJD 39

!----------------------------------------------- !TRJD 40

! I N T E R F A C E B L O C K S !TRJD 41

!----------------------------------------------- !TRJD 42

 USE SETIPOS_E10_I !TRJD 43

 USE GRAMTRAJ_E10_I !TRJD 44

 USE NEWPOS_E10_I !TRJD 45

 IMPLICIT NONE !TRJD 46

!----------------------------------------------- !TRJD 47

! L O C A L V A R I A B L E S !TRJD 48

!----------------------------------------------- !TRJD 49

 INTEGER :: IFIRST !TRJD 50

 REAL(DOUBLE) :: DSMALL, PSMALL, WAVERAND, PHIDENS, AMPFACT, WSMALL, & !TRJD 51

 VSMALL, USMALL, TSMALL, CTIME, CHGT, CLAT, CLON, DCTIME, DCHGT, DCLAT & !TRJD 52

 , DCLON, DMEAN, PMEAN, TMEAN, UMEAN, VMEAN, WMEAN, DPERT, PPERT, TPERT & !TRJD 53

 , UPERT, VPERT, WPERT, DSTAND, PSTAND, TSTAND, SOSMEAN, SOSPERT, PTIME & !TRJD 54

 , PHGT, PLAT, PLON !TRJD 55

 !TRJD 56

 SAVE IFIRST, DSMALL, PSMALL, WAVERAND, PHIDENS, AMPFACT, WSMALL, & !TRJD 57

 VSMALL, USMALL, TSMALL, CTIME, CHGT, CLAT, CLON, DCTIME, DCHGT, & !TRJD 58

 DCLAT, DCLON, DMEAN, PMEAN, TMEAN, UMEAN, VMEAN, WMEAN, DPERT, & !TRJD 59

 PPERT, TPERT, UPERT, VPERT, WPERT, DSTAND, PSTAND, TSTAND, & !TRJD 60

 SOSMEAN, SOSPERT, PTIME, PHGT, PLAT, PLON !TRJD 61

!----------------------------------------------- !TRJD 62

! !TRJD 63

!--- INITIALIZE THE TIME (SEC) AND POSITION (HEIGHT OR RADIUS, KM; !TRJD 64

! LATITUDE, DEG N; LONGITUDE, DEG E) !TRJD 65

 CALL SETIPOS_E10 (CTIME, CHGT, CLAT, CLON) !TRJD 66

!--- SAVE CURRENT TIME, POSITION AS PREVIOUS TIME, POSITION !TRJD 67

 PTIME = CTIME !TRJD 68

 PHGT = CHGT !TRJD 69

 PLAT = CLAT !TRJD 70

 PLON = CLON !TRJD 71

! !TRJD 72

! IFIRST IS USED AS A PARAMETER TO TRIGGER GRAM INITIALIZATION !TRJD 73

! (IFIRST = 1), AND TO BE USED AS A RETURN CODE TO TRIGGER ANY !TRJD 74

! DESIRED ACTIONS BY THE MAIN PROGRAM. IN THIS EXAMPLE, IFIRST !TRJD 75

! = 0 CAUSES RECYCLE TO NEXT POSITION; IFIRST = -1 CAUSES !TRJD 76

! RE-INITIALIZATION OF POSITION (AND VELOCITY) VALUES; !TRJD 77

! IFIRST < -1 CAUSES THE PROGRAM TO TERMINATE !TRJD 78

! !TRJD 79

! INITIALIZE THE ATMOSPHERIC VARIABLES WITH THE GRAMTRAJ ROUTINE !TRJD 80

! !TRJD 81

 IFIRST = 1 !TRJD 82

! !TRJD 83

 PPERT = 0.0D0 !TRJD 84

 DPERT = 0.0D0 !TRJD 85

 TPERT = 0.0D0 !TRJD 86

 UPERT = 0.0D0 !TRJD 87

 VPERT = 0.0D0 !TRJD 88

 WPERT = 0.0D0 !TRJD 89

!--- CALL TO GRAMTRAJ FOR SETTING INITIAL VALUES, INCLUDING READING OF !TRJD 90

! NAMELIST INPUT FILE, NCEP DATA AND ATMOSDAT FILES !TRJD 91

 CALL GRAMTRAJ_E10 (IFIRST, CTIME, CHGT, CLAT, CLON, DMEAN, PMEAN, TMEAN, & !TRJD 92

 UMEAN, VMEAN, WMEAN, DPERT, PPERT, TPERT, UPERT, VPERT, WPERT, DSTAND & !TRJD 93

 , PSTAND, TSTAND, 0, CTIME, CHGT, CLAT, CLON, 1, 1, 1, PHIDENS, & !TRJD 94 

 WAVERAND, PSMALL, DSMALL, TSMALL, USMALL, VSMALL, WSMALL, AMPFACT, & !TRJD 95

 SOSMEAN, SOSPERT) !TRJD 96

! !TRJD 97

105
! INITIALIZE THE TRAJECTORY VELOCITY (OR POSITION DISPLACEMENT) !TRJD 98

! VALUES (IF INITIALIZATION IS NECESSARY) !TRJD 99

! !TRJD100

 CALL NEWPOS_E10 (IFIRST, PTIME, PHGT, PLAT, PLON, CTIME, CHGT, CLAT, CLON & !TRJD101

 , DCTIME, DCHGT, DCLAT, DCLON, 0) !TRJD102

! !TRJD103

! BEGIN CYCLE OF POSITIONS AND ATMOSPHERIC VALUES !TRJD104

! !TRJD105

 20 CONTINUE !TRJD106

 IFIRST = 0 !TRJD107

! !TRJD108

! UPDATE THE VELOCITY (OR POSITION DISPLACEMENT) VALUES AND THE !TRJD109

! TIME AND POSITION VALUES !TRJD110

! !TRJD111

 CALL NEWPOS_E10 (IFIRST, PTIME, PHGT, PLAT, PLON, CTIME, CHGT, CLAT, CLON & !TRJD112

 , DCTIME, DCHGT, DCLAT, DCLON, 0) !TRJD113

! !TRJD114

! EVALUATE THE ATMOSPHERIC PARAMETERS AT THE NEW POSITION !TRJD115

! !TRJD116

!--- CALL TO GRAMTRAJ FOR NEXT TRAJECTORY POSITION !TRJD117

 CALL GRAMTRAJ_E10 (IFIRST, CTIME, CHGT, CLAT, CLON, DMEAN, PMEAN, TMEAN, & !TRJD118

 UMEAN, VMEAN, WMEAN, DPERT, PPERT, TPERT, UPERT, VPERT, WPERT, DSTAND & !TRJD119

 , PSTAND, TSTAND, 0, PTIME, PHGT, PLAT, PLON, 1, 1, 1, PHIDENS, & !TRJD120

 WAVERAND, PSMALL, DSMALL, TSMALL, USMALL, VSMALL, WSMALL, AMPFACT, & !TRJD121

 SOSMEAN, SOSPERT) !TRJD122

 DO WHILE(IFIRST == 0) !TRJD123

 IFIRST = 0 !TRJD124

! !TRJD125

! UPDATE THE VELOCITY (OR POSITION DISPLACEMENT) VALUES AND THE !TRJD126

! TIME AND POSITION VALUES !TRJD127

! !TRJD128

 CALL NEWPOS_E10 (IFIRST, PTIME, PHGT, PLAT, PLON, CTIME, CHGT, CLAT, & !TRJD129

 CLON, DCTIME, DCHGT, DCLAT, DCLON, 0) !TRJD130

! !TRJD131

! EVALUATE THE ATMOSPHERIC PARAMETERS AT THE NEW POSITION !TRJD132

! !TRJD133

!--- CALL TO GRAMTRAJ FOR NEXT TRAJECTORY POSITION !TRJD134

 CALL GRAMTRAJ_E10 (IFIRST, CTIME, CHGT, CLAT, CLON, DMEAN, PMEAN, & !TRJD135

 TMEAN, UMEAN, VMEAN, WMEAN, DPERT, PPERT, TPERT, UPERT, VPERT, & !TRJD136

 WPERT, DSTAND, PSTAND, TSTAND, 0, PTIME, PHGT, PLAT, PLON, 1, 1, 1 & !TRJD137

 , PHIDENS, WAVERAND, PSMALL, DSMALL, TSMALL, USMALL, VSMALL, WSMALL & !TRJD138

 , AMPFACT, SOSMEAN, SOSPERT) !TRJD139

! !TRJD140

! REPEAT THE CYCLE OR TERMINATE, DEPENDING ON THE RETURN VALUE !TRJD141

! OF THE PARAMETER IFIRST !TRJD142

! !TRJD143

 END DO !TRJD144

 IF (IFIRST == (-1)) THEN !TRJD145

! !TRJD146

!--- RE-INITIALIZE THE VELOCITY OR POSITION DISPLACEMENT VALUES !TRJD147

! (IF NECESSARY) !TRJD148

 PPERT = 0.0D0 !TRJD149

 DPERT = 0.0D0 !TRJD150

 TPERT = 0.0D0 !TRJD151

 UPERT = 0.0D0 !TRJD152

 VPERT = 0.0D0 !TRJD153

 WPERT = 0.0D0 !TRJD154

 CTIME = 0.0D0 !TRJD155

!--- CALL TO GRAMTRAJ FOR RE-INITIALIZING AT BEGINNING OF NEXT !TRJD156

! MONTE-CARLO PROFILE !TRJD157

 CALL GRAMTRAJ_E10 (IFIRST, CTIME, CHGT, CLAT, CLON, DMEAN, PMEAN, & !TRJD158

 TMEAN, UMEAN, VMEAN, WMEAN, DPERT, PPERT, TPERT, UPERT, VPERT, & !TRJD159

 WPERT, DSTAND, PSTAND, TSTAND, 0, PTIME, PHGT, PLAT, PLON, 1, 1, 1 & !TRJD160

 , PHIDENS, WAVERAND, PSMALL, DSMALL, TSMALL, USMALL, VSMALL, WSMALL & !TRJD161

 , AMPFACT, SOSMEAN, SOSPERT) !TRJD162

!--- RE-SET INITIAL TRAJECTORY POSITION FOR NEXT MONTE-CARLO PROFILE !TRJD163

 CALL NEWPOS_E10 (IFIRST, PTIME, PHGT, PLAT, PLON, CTIME, CHGT, CLAT, & !TRJD164

 CLON, DCTIME, DCHGT, DCLAT, DCLON, 0) !TRJD165

 GO TO 20 !TRJD166

 ENDIF !TRJD167

 STOP !TRJD168

106
! !TRJD169

! TERMINATE FOR ANY OTHER VALUES OF IFIRST !TRJD170

! !TRJD171

 END PROGRAM TRAJDEMO_E10 !TRJD172

!---------------------------------------------------------------------- !TRJD173

107

109

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The NASA Marshall Space Flight Center Earth Global 

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NASA/TM—2011–216467

Global Reference Atmospheric Model, atmospheric temperature, density, winds, thermosphere, atmospheric 

models, atmospheric perturbations

01–06–2011

UU 128

NASA

U U U

Reference or standard atmospheric models have long been used for design and mission planning of various aerospace systems. The NASA Marshall Space Flight Center Global Reference Atmospheric Model 

was developed in response to the need for a design reference atmosphere that provides complete global 

geographical variability and complete altitude coverage (surface to orbital altitudes), as well as complete 

seasonal and monthly variability of the thermodynamic variables and wind components. In addition to 

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