Reproduced From
Best Available Copy
384
AD-A185
AFGL-TR-87-0220
SSI-TR-124
OTI• FILE COPY
MODTRAN:
A MODERATE RESOLUTION MODEL FOR LOWTRAN
A. Berk, L. S. Bernstein, and D. C. Robertson
Spectral Sciences. Inc.
i11 S. Bedford Street
Burlington, MA 01803-5128
OTIC"
1
08 July 1987D
Scientific Report No. 1
-
Approved for public release;
distribution unlimited
AIR FORCE GEOPHYSICS LABORATORY
AIR FORCE SYSTEMS COMMAND
UNITED STATES AIR FORCE
HANSCOM AIR FORCE BASE,
MASSACHUSETTS
01731
81i'
10 8
03(
"This technical report has been reviewed and is
/n
approved for publication'
,_
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GEORGE A.
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Branch Chief
VANASSE
FOR THE COMMANDER
(Signature)
R. EARL GOOD
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10. SOURCE OF FUNDING NUMBERS
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62101F'
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ELEMENT NO.
I. TITLE (Include Security Claslfication)
MODTRAN: A Moderate
2. PERSONAL AUTHOR(S)
Alexander Berk,
]a. TYPE OF REPORT
Scientific
#l
Resolution Model for LOWTRAN
(U)
Lawrence S. Bernstein. and David C. Robertson
13b. TIME COVERED
14. DATE OF REPORT (Year,Month. Day)
FROM86Mv 12 TO 87Mav 1
87 July 08
5. PAGE COUNT
40
16. SUPPLEMENTARY NOTATION
17.
COSATI CODES
FIELD
GBOUP
]\.\
18. SUBJECT TERMS (Continue on reverse if necessay and identify by block number)
.
SUB-GROUP
,'
Transmission,
/I[Atmospheric,
Radiation,
Infrared,
Transmittance,
Band Model
and LOWTRAN
19. ABSTRACT (CucI/on reverse if necesay and Identify by block number)
This
interim
for the LOWTRAN 6
model parameters
using
from
the
0
-
1986
6.
HITRAN
model
The
report
atmospheric
for H2 0,
17,900/cm
transmittance
LOWTRAN
technical
C02,
line
and
at
a
new band model
transmittance/radiation
03,
N20,
atlas.
and
spectral
describes
CO,
They
five
associated
resolution
CH4-,
were
subroutines
this
computer
and N2
calculated
temperatures
of
02,
new
from
have
to
been
option
code.
I /Xm-F
300K.
is
better
A preliminary version of the code has been delivered
for testing.
Validation against
this
20. DISTRIBUTION IAVAILABIUTY OF ABSTRACT
0"UNCLASSIFIED/UNLIMITED Q' SAME AS RPT.
22a. NAME OF RESPON5IBLE INDIVIDUAL
Leonard Abreu
DD FORM 1473, 4 MAR
. . . . ...,. . .
FASCOD2
calculations
,
.-..
.•.
be
the
into
than
r
5
to AFGL
emphasis
effort.
'
'
121. ABSTRACT SECURITY CLASSIFICATION-b
UNCLASSIFIED
0]OTIC US'EtS
22b. TELEPHONE (Include Area Code) 22c. OFFICE SYMBOL
(617) 3
7
AFGL/OPI
83 APR edition may be used until exhausted.
All other editions are obsolete.
..
will
ins
This
integrated
cm'-t(FWHM).
for the remainder of
Band
were calculated
for
200
formulation
.~,,.ww•d
.
." '....-.,%..'•'.'.-
r
SEgURITY CLASSIFICATION OF THIS PAGE
UNCLASSIFIED
.- , ,
.-
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.-- --
.
TABLE OF CONTENTS
Section
Pagc
1.0
INTRODUCTION
2.0
THE MODTRAN CODE,
...............
5
3.0
MOLECULAR BAND MODEL PARAMETERS ...........
..............
3.1
Line Center Parameters
..........
................
3.2 Line Tail Parameters ...............
.................
3.3 Parameter Data File ............
..................
..
7
7
9
10
4.0
BAND MODEL TRANSMITTANCE FORMULATION ......
............
4.1
Line Center Transmittance ........
...............
4.1.1 Curtis-Godson Approximation ..... ..........
4.1.2 Uniformly Mixed Gases ....... .............
4.2 Line Wing Absorption ...........
.................
.. 12
.. 12
13
.. 15
.. 16
5.0
INTEGRATION INTO LOWTRAN 6 ..........
5.1 MODTRAN Subroutines ............
5.1.1 Subroutine BMDATA ..........
5.1.2 Subroutine CONDEN ........
5.1.3 SubrouLine BMOD ..............
5.1.4 Subroutine CALC ..........
5.1.5 Subroutine EWIDTH. .........
5.1.6 Subroutine ERFU ..........
5.1.7 Subroutine CPFI2 .........
5.2 Modifications to LOWTRAN 6 .........
.. 17
.. 17
.. 17
.. 18
19
.. 21
.. 21
.. 22
.. 22
22
6.0
VALIDATION ..................
.........................
6.1 Band Model Parameters ..........
.................
6.2 Comparison with FASCOi12 ..............
................
7.0
CONCLUSIONS AND FUTURE WORK ...........
8.0
REFERKNCES.....
APPENDIX:
. . . . . . . . . .
. . . . . . . ...
AN OVERVIEW .............
. ..........
.
.................
..................
................
................
.................
.................
................
.................
................
..............
.. 24
.. 24
25
................
28
.........................
... 29
Derivation of the Band Model Parameters
.....
... 31
Accesion For
DT!C
T,-,9
~~
I
. . ..
,'
-
~'A-f
.. ...
El
.........
.
,
.......
LIST OF ILLUSTRATIONS
F i gure
1
2
4
5
6
A--I
Page
Lorentz Line Shape at Optical Depths of 0.2, 2.0, and 20.
In the Band Model Transmittance Formulation, Absorption
Due to Lines Whose Centers are Within a Bin (Between the
Dashed Lines) is Modeled Separately from that Due to Line
Tail Absorption (Outside the Dashed Lines) .......
..........
3
Transmittance Curves for a 150 from Zenith Slant Path
from 5 to 10 lkm Through the US Sta-ndard Atmosphere.
The
1
Solid Curve was Obtained from MOOTRAN by Passing a 5 cmFWHM Triangular Slit
Over the 1 cm- 1 Calculations.
The
Dotted Curve is the Regular LOWTRAN 6 Result also Obtained
from MODTRAN (20 cm- 1 Resolution with DV Set to 5 cm-1.
Comparison of Continuous and Discretized Triangular Slit
Functions.
FASCOD2 Uses the Weighting from the
Continuous Function, but MODTRAN Uses the Discretized
Approximation ..................
........................
..
23
Comparison of Band Model LOWTRAN 5 (Dotted Curve) and
Band Model LOWTRAN 6 (Solid Curve) Molecular Absorption
Coefficients for Water Vapor at 300 K ........
............
..
25
Comparison of i FASCOD2 and a MODTRAN Calculation.
N2 0
and CO2 are the primary absorbers ..........
..............
..
26
Comparison of a FASCOD2 and a MODTRAN Calculation is
Microwave .....................
..........................
..
27
Comparison of FASCOD2 and MODTRAN Calculations.
The
MODTRAN Curve was Generated with the Old Band Model
Parameters, Eqs. (A 4) & (A--)
, and no N 2 0 Continuum
Function .....................
..........................
iv
the
35
1.0 INTRODUCTION
This interim technical report describes work done in
-
1986
11
May
1987)
increase the spectral
of
a
resolution of LOWTRAN 6(")
transfer model and attendant computer
effects.
*
Specifically,
(Contract
program
subroutines
No.
(12 May
F19628-86--C-0079)
to
by developing a radiative
for molecular absorption
the goals for this effort are to:
develop algorithms providing at least 3 cm. 1
-
year one
resolution (FWHM
full width tit half maximum),
as a
0 to
*
model molecular absorption of atmospheric molecules
function of temperature and. broadening density from
17,900 cm- 1 ,
0
treat the following atmospheric molecules:
methane,
nitrous
ozone,
carbon
dioxide,
monoxide, molecular nitrogen and oxygen, and
•
integrate the new algorithms and subroutines into LOWTRAN 6.
The upper limit of the spectral
range,
17,900 cm- 1 , is
water
oxide,
vapor,
carbon
determined
by
the
HITRAN line atlas for atmospheric molecules.(2)
1.
2.
F. X. Kneizys, E. P. Shettle, W. 0. Gallery, J. H. Chetwynd, Jr., L.
W. Abreu, J. E. A. Selby, S. A. Clough and R. W. Fenn, "Atmospheric
Computer Code LOWTRAN 6," AFGL-TR--83--0187,
Transmittance/Radiance:
Air Force Geophysics Laboratory, Hanscom AFB, MA 01731, (August 1983).
ADAI137786
R. A. McClatchey, W. S. Benedict, S. A. Clough, 1). F. Burch, R. F.
Calfee, K. Fox, L. S. Rothman, and J. S. Garing, "AFCRL Atmospheric
Absorption line Parameters Compilations," AFCRL--TR--73-0096, Air Force
Geophysics Laboratory, Hanscom AFB, MA 01731 (January 1973); L. S.
Rothman, App]. Opt., 20, 791 (1981).
AD762904
fraction
A substantial
model
3 5
techniques.(
into
partitioned
the
present
bins
for
In
)
cm-1
1
this work has
completed.
been
Moolecular
bandI
the atmosphere has been modeled using standard
through
transmittance
of
the
approach,
each
Within
molecule.
each
region
spectral
is
bin,
contributions from lines whose centers are within the bin and from nearby
lines centered outside of that bin are modeled
separately
with
their
temperature and pressure dependences;
see Figure 1.
The absorption
lines within
by
integrating
Voigt
line
accurate
the
is
shape(5).
for
variations
bin
the
The
calculations
and
isotropic one.
integrated
with FASCOD2(
8
definition for the standard
new definition
5.
6.
7.
8.
9.
is
LOWTRAN
in
line density
approximation,
pressure,
The
) resulted
)
and
due to
over
the
which
is
concentration
used to replace multilayered
transmittance
6.
a
band
algorithms
Comparisons
reexamination
model
to
"exact"
of and
parameter,
have
l/d;
a new
this
by taking the finite bin
A complete band model tape has been generated for the
listed above.
resolution LOWTRAN 6,
4.
9
7
'
lowers the line center absorption
widths into account.
3.
into
'
6
temperature,
found in the earth's atmosphere,
coded
molecules
numerically
Curtis--Godson(
moderate
paths by an equivalent
been
calculated
own
A preliminary
version of MODTRAN,
this moderate
has been delivered to AFGL for evaluation.
D. Anding, "Band Model Methods for Computing Atmospheric Slant-Path
Molecular Absorption," Rpt. No. 7142-12-T, Willow Run Laboratories,
Environmental Research Institute of Michigan, Ann Arbor, MI (1967).
A. J.
LaRocca and R. E. Turner,
"Atmospheric Transmittance
and
Radiance: Methods of Calculation, Rpt. No. 107600--10--T, Environmental
Research Institute of Michigan, Ann Arbor, MI (June 1975).
W. L. Wolfe and G. J.
Zissis,
"The Infrared Handbook:
Revised
Edition,"
The Infrared
Information
and
Analysis
(IRIA)
Center,
Environmental Research Institute of Michigan, Ann Arbor, MI (19851,
A. R. Curtis, Q. J. R. Meteor. Soc, 78, 165 (1952).
W. L. Godson, J. Meteor., 12. 123 (1955).
S. A. Clough, "Preliminary User Instructions for FASCOD2," Letter,
AFGL/OPI, Hanscom AFB, MA 01731 (1 October 1985).
H. J. P. Smith, D. J. Dube, M. E. Gardner, S. A. Clough, F. X. Kneizys
and L.
S.
Rothman,
"FASCODE
- Fast Atmospheric Signature
Code
\Spectral Transmittance and Radiance),"
AFGL-TR-78--G1B1,
Air
Geophysics Laboratory, lHanscom AFB, MA 01731 (1978).
ADA!57506
-2
-
Force
-
Ii
I
"+a- Sw
I
I
0
Cf)
C-0
-3
2
-t
-U
(cm- 1 )
WQvenumber
Figure 1.
An
analyzed
6
the MODTRAN
two sections,
transmittance
LOWTRAN
Spectral
Absorptivity
for
Lorentz
Line
Shapes.
Curves Generated for Products of Line Strength and
Absorber Amounts Equal to 0.1,
1.0 and 10.0 cm-1
The Halfwidth has been fixed at 0.1 cm'-1.
In
the
Band Model Transmittance Formulation, Absorption Dlue
to Lines Whose Centers Are Within a Bin (Between the
Dashed Iiines) is Modeled Separately from That Due to
Line Tail Absorption (Outside the Dashed Lines).
overview of
.•ubsequent
are
for
3
formulation
presented
the purpose
code
is
presented
calculnt ion of the
are
in
descrihed.
Section
5.
of validnt on.
-3-l
in
Section
band model
Section
Conclusions
6,
In
the
wnd
the
and addit.ionls
to
parameters
Modifications
In
2.
MODTRAN
and
future
output
plans
is
are
The following indexing convention is
Symbol
i
m
n
a
ft
The species
symbol a. will
water or ozone,
(1ING).
used throughout the report:
Indexed Quantity
spectral bin
mclecule
temperature
species
atmospheric layer
refer to either an individual
such as
or a mixture of molecules such as the uniformly mixed gases
The atmospheric layers I are characterized
pressure,
species
by a fixed temperature,
Constants used include:(5)
and molecular constituency.
c = speed of light
(2.997924580x10 1 0 cm sec 1)
k = Boltzmann constant (1. 3 8 066 2 xlO-16 erg K-1)
h = Planck constant
(6.626176xi0- 2 7 erg-sec)
N = Avogadro constant
(6.022045xI0 2 3 mole- 1 )
Ts = Standard temperature used in the HITRAN line atlas (296 K)
To = Standard temperature used in LOWTRAN (273.15 K)
4-
2.0 THE MODTRAN CODE
MODTRAN is
moderate
the name given to the LOWTRAN
resolution
have been written
radiative
in
interfacing
additional
elements
LOWTRAN 6;
rather
5
-
with
do
they
resolution.
transport
portable
that their
spectral
AN OVERVIEW
-
not
ANSII
6
Interfere
represent
an
with
The
FORTRAN
minimizes
the
additional
The only modification
10 KM AT 15
code affixed
algorithm.
standard
LOWTHAN
6
new
with
a new
subroutines
and constructed
coding
changes.
regular
capability
These
operation
for
ci
to the input data sequence
_ US Std Rtm
-
-
C:
C-
w
.-
5 cm' 1 MOOTRRN
20.OWII)WN
.
Wovenumber
Figure 2.
(cm -1)
Transmittance Curves for a 150 from Zenith Slant Path
from 5 to 10 km Through the US Standard Atmosphere.
The
Solid Curve was Obtained from MODTRAN by Passing a 5
cm- 1 FWHM Triangular Slit Over the 1 cm- 1 Calculation,
The Dotted Curve is the Regular IOWTRAN 6 Result also
Obtained from MODTRAN (20 cm- 1 Resolution with DV Set to
5 cm- 1 ).
5
-
of
higher
1-4--
so
is
L
~~
r-11
~
10(lti it j 1041,
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who
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e
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t vnlpvi';a
S/d)'
abiove
are
(S d
2-
300
300 K)
betweein
K,
the
.(A
is
extrecme
I lic i Iid ivi (I la
to calunilate
tuscd
200
mo lecul ar'
'The
Iused.
t's aiI-(- cill c~il I ut ed I r'oi
1) i alcti
I
275 K,
temperatures
Z1nd
.
250 K.
it I i near. i uit er'po 1,11 ifll
at.
200
i vely
tuspect
,
225 K,
andI
vilii
300
F C)r'
(S/d)Ian
OtiS
absorpt ion
1 ilie st r
K.
band
modelI
Iitls.
(2)
Sjn(l
j
lievuSj
('1'11
t hie
is
1ille oft Moiecuilet
(-.ln
he scaled3
int egitit (!(1
M ill il
lii
from
the
I i i(,
st reiipl-.
'Fihe I Iit(
.
lin e
III TRAN
It ut
temlierat ure T,
sI leigth it t ani
s trenogthIila.
(if'
j
thei
It
arbi 1 i'iiy I empei'at he
i ts
st andir d
temuperat ur'e
Q(,Q v(' Ii)'
('I'n
Q'kQrv*Ir,
e-xi(
whiere Q,,
and( Q,
t
I"(
i(-v
enp
ey*T)exp(-!
Si P (1T
.1'eherl'y
To
-
Si nee(d lo'eU11Si'
widtlhI
of t he
- 2 71.
thti'
m)L
is vilslS
ii Ylundi' Iid
1t.
lo. ixpoiiiiit
wh
oi ( h x
st ri'vligt
11 wt. iglited
)
I'
','j(T,,)
3
.
partit1ion fuin-tions,
1114
and
lower t raolsit ion sta~te.
0w
L~ireiitz i. iLi
15 K . I
S;til'v
PO
.iid
width
piutramet en
=~ 10 13. 25 nuhuir's)
ti'ipiriat
is' del iielf-
A singfle vali-
thi'jwndiwiti'iiii
il'ý
(f,),)
of
wL'loriruit
nn ieo'
except ('2
*:an
hI
,Ii
me.
.
P
C
Wlive1-
Ta Ts4
j
re thev rot at i onal and v lu'itit
A ee(il Iision lirolcid-iid
at
E
X,,, hls hlnen "(.I
T Iw
Cy
aVul ;i1g( liv(.-
to 1/2
IaIII lI T1 leIt1
(to
;1I
Ihr
)i itrMt E.l
It(li t aill flilt ed
l'Vureilt z
cCit (711i l ut ud(I
I ill(- widt his
byol
a
I i nv
(Y .) j cr s
Cyo
(T /To0 )xM
I~Y~(I,
Cy(
5)
s)~jIQ
tlfl j~(')s(ý;]
7-
i,iw
ke
ite
aibs(3tpt olou couff icieuit s
I /(li )D ( rn)
p~ironete
ar'e
ed Wle-il liserl by
jo
II (lpol' ill
I
,itIi cul ated
ht
Iii]
I hev
(it-Its itI y
at. the 5 r
Ioitld iiiodt.l
eie
sour 0111ii Iews.
baind
modelI
i
eiprtile
I tille (It.[Is i tY
Th(,.
(11I!1
Ii ied by
N
~
(I~
uef illit ioit
fhisi
diffet-
/d
s
fori
the
the Ii ille st ref'li" O
I.
3.2
Iii te
bSfiiic)t.",
usuwil def iii it ionl
the
fromt
N
WhichI
is
i[ivo)lv lg
skli
i
ill
d(letiVt(l,
over the
thf
lie
teildtx,
squiiir&'
root
of
.41011
LineTail Parameters
1 joe
'Ihle
cut ::d
locýatucd
asr
li al
iolV
colnsist
Iloirilmtnicts
of
a
hilt
1-f 'Jeri
couff ic ent
bauid
but
mode-lI
2.
) t Sd
(1
wit~hiti
t
coilt r jhot iolis
25
Ii tii
I tite
tall
mlit
shape. over tt iisi
1 1,~
I [ie's
f romtI
The
cm
piwircimt er3cis(R
detIe rmi tied by int egraut iig the Lo tent.
C.
1 i Itie
of
ir
lit e l'Vit
(7)
'k Ifi( i)~
AV
ki-251/
del t.i
where t li
Bitict mul
the
Iiitie ce titer cootilr i
cut
V Ihutj(ioii5
tieg'ijjf
t ioi) .For
ht-yoti(l '15 ciw -'
iulec0t1010011tinn
1),
C.
SerIves, to exc:]
Roburt oi x
dt-1
tlii,
k- i
mnolecules olhor
frtont a
liltie
terit
from
I.halt
cenIter- hive bweln
1120 anld C02 1 tail
assitiiie'l
to the. ttoi-r'n.jltctare aitd withinl theo
I
.S.
CMI
Ilrit
Spie ra I Re so lut iit-iiilbu
AResearch
,
I n'a.c
,
It ill
ii
wid
R.
s
(l~t~l%
iloul(f.
to
25 cm''
"ajm
Add it jolt
Opt ioni to IOWTIIAN !),"
MA (October- 1'J80).1cial
11 C.~~
1) Rlwr
~ ~ ~sol
S.
11 iti
c.1t
iii, P.
Ilto lnes
J.
W11uitiulet
5 UMg~
ii
iitud Modec I Opt i oitt to IOWITAN !i,
ApiJ) I. 01t
Model
er ici
stin
Othe
it
limit ;I
if
5
it
ARI IMP 2,12
1
ilit
.
2.318 3z
Carn
fiW;l
faic t r
C0 2 .
1For
wxwunhIt
the
of
thet
from
hcv
CI 4*Cvitatnh(j~-1
( u)
Hiere ,C
/F0
I
Iu
the
illifhl
l1it e1;i 1 lo
cont. I- hintt ion
3.3
Parameter
11!
li-callrs
Iil'imt't
iii
lul
eivoi 1
bt ore'1
for'
thre
liirniei
fill(
cord
thIto
I ilbelI
(It
ilit )f'
tt
he
;1
cente(r
ialso
5tIeiii
(ati
ditt a
reduccf2(
cont r jibut i oi
cant i nutum
wr'itteeli i
it
t
runt r i huit v
t oi
A.
I'I-SOii ilI
whont.
C-:IItiiihi
tirel
(:0111 ei;
t I he ic
i It
binairy
formal
Each ent ry
pilraruni
by
an
thIi s
s i ne
C1
2)
1'h
the'
bitrid
eiti
.r'set
forI
which
art:c
01-
set
Se
I,,
it- eri./i-i-
is
)iitIi
Oh .
o
the
als
I "'m
e it(
1 ji Ii n
tI peneill
alilows
dat; aT-
.ZerIOed(
.
for
cm1
Wi'ont
Tit!rerefort-,
ored.
tl wrfifti
ca18i ly cii ciii
lii) I Iiiiti I thl I
toinirrirri vl.i
i
milst
marie~v
to itI
corrusepnnids
I ; it(,- to it IT ivteir I it erva I
no
pararneit
ra -inieiii
iocs
-.-.
lASCOIWs iblok
fiCr'om
('1 hiii,
(lit t i
(it
nirolecuri ii
Ii
.
in
i
I v:i cont. -iju t.o inpli
,ti
(lit
ii)
t
iiills,
Irlid itIi I
V
1 ine
f rom
irmoonti
lt-
I S.
.
k.0
liaite
lii
.
vaiii
the( valtic of
duiiring the cal culat ion.
mii Iecu
ii. Ii '.~
(6
Data File
ilit
ol'm~it 11111 witui cli
I.
to
to p~ressure
is an~ cXUI~l'~Id
qipiIci'r ;wcvs55
Cii
bteyond 25 cm
linez
I ii id
jti
a I ready
hov prlipor~t ionll
to
to
C(V1
inv
cm 1
25
i it(-cI udeld
is
take~n
F
y--
2'
oh120adC
-;o1Its'
added
been
lu
TS
t iet( frequielicy
is
(for
cm "
cm 1
25
beyond
has
FASCOD2f"O
uicnt i ihutin Ofl5Cromi
lil
25
withli
6
The( usua I LOWTRAN
.
conritib Ut ionis
tailI
tIt(-
cont r'iution
tlt!
continuum
thle
lot'
of
coni'si3ts
vil(-
raoae
ass ilmed
equii I to I has hec(It
i ) AV
CMI t i ouurrr
1 r
eI
f I (k
,
i
.
rom the
iijii
A /2
V'
atvoIl
i lit a'v~I- II
vV
"
A
".
'.
~etwueeo
iumber" m
.s.
1 and 8 desigmnat:-s
..
thiet
.
mno irecle
Except
i
1
2
K20
002
3
03
4
Ili
6
entries
Cttjfkieents
t1PII(t'ltlt
in
NO
(20
COI
f iVt'
the
paramete.r
1imagits
a(tm
entrcies are
mutltillied by 10
toe1-
tilth
I
T'hlu
li',"es
(-Ic)o,
11d
(.
for NZ
2
.
.-
We"
)
set
02
thlet
are
by
t he
atlsorptitonl
five
1,0iclitz
referente
lice
hltf
widtl,
I.i tie sjnici og pa t'met ers
toinlpiete the
res
molectular
STP
and stored as an ilntvc-p2.
1'Aet t'rCllCV tempeur-"t
'
at
the
N2
L
calctilet.d
followed
8
7
L
The. next
.
set by Ihlie II'TRAN tape (2)
follow tlie conventionit
mo I ecu I e
.
.
I ille
larfimt.er
cenitert'
se
vs1
E.1ch pýaT'amelt
molecules.
ceitt 'r
• set
These
foir
line tail
lltriute c`
+ setpst.
second
entry
pa-ametet
sets
is
the
line tails
informatiton
parameter sets usk. the
Agatinl,
thti.
molecule
denot c. I ine
contains
first
entrty is
designation
t!t: i I
m.
toltrihihut ion. ,
same
on onei.
the ir
"
as tlie. lint!
format
the binl number
To
or two
recogn zc,
i
atnd
tilth
that
thesev
]1s
aeI-t'
i
(S/i lln
The
molecule
]u
offset by 8
Tile
m
9
mo I ecu Ie
1120
con0t iimui,,
moletuulra
unkl, red
11
12
13
14
15
16
C02
0
N2 0
CO
cif
02
N_,
parameters,
i,:sigelttttit
ill pl
10
tre (if
ChI,
are
anutd euolilillpn
the hIalf width
stored
In
place
of
the
parameters for a second molecul.
caru hle
.l
mid (l/d)n pInral~meters.
.1
' -i"
4.0 BAND MODEL TRANSMITTANCE FOR~MULATION
4.1
Line
Center Transmittance
The haind
opt ion to 1.OW'1RAN
CeR
I or
opjt ion
fiII itv 11untTTi.
-i
Tl.
is
(fit
the
'li-S
il
it
equivilenit Width lot
(it'll
ib
spectrlill
trainsmilt aiice,
basied
finter'il
on
at
CiltIC11:11C
<lid?
-AV
piath ilvvle
thle
more- ree-(og,,ii
I
Fur
t hec
di st rHurt ion
t ll!
ear It
s
In(S /d)
ahlc exponential
form given
by
)
<11>
<WS1>
<i/d>
spec loes
a t [Do',[Iiere
powerl
and
foun
rel I
tt
yeVk
Iy
the ave ragt! 111irumer
lilvw
13 .
of
at
'Jo it
hii
I int.
shcl1w:
ifeei
-implififes to at
larige
I ow
(1)
t einjiveriit tLlE'
of
I i leiii
t rihism it Utnet! ap'rox imat ion
'I i-ire ai-o many iipprTox imiiationb oivaitilab l
W idthI
interval,
line- qpacinig.
lilthe
t rasmi ttillice
Ninal 'if 111t;1t lilte
jut'v
ill ia spedi'al
All f ixed],
melI cu Iit
a
iir
il
andl
e.xp(
11104(lecl]itl
.
<lid-' iS the' jlatilvrae
For' large
5
is; 1ivenl by
anid <[I,> is the path averilged effet- lye number of' I ines in th I(
<11>
t li
mo~t:it
stati st ; !o
anld
.
li-
cWt
tregt
line
lhlxws tfo
u;ed
in
ceniters,
luIinte
(110
tor
deve lopedl
hitzz beent used to cruirttv a itiodet ate resoluit i n
5"'~
LOWIllAN
trarim
ittdlne
where
formu 1 t ion("-101)
mode 1 t.riinsmni ttaricu
i nt
('ico.ulit er
at
is
h iti
is
#'(t
i 11
usuirI Ily
p re 1''rred.
for- calvieaat i rij, the ie(q1ivoltIrt
onles
are( voll il
fun
dIi f lo-el lIt
F. X. Klre-iZYs, 1:1. P. siet t It', W. 01. Galle
Iry
.-I. It. cltetwyiid.
r, It.L.
W. Abi--i,
.J . F . A . Se Ilby,
H. W. l".i-nn,
andl R.
A.
Mcd hiOt crt'y.
5 ,"1
Comput or
Code~ LOWl IýAN
Triii~sTT itIt ilrTU v/Paid i once(:(
"At mosplivr' ii u
lF
ItR 30) 00h7, Air, la nce Geophys ic-, Larhornaliw y , lb uscorn Alit.
MA
(01731 (Ut-liruary 19B)i0).
AI)AMtt,215
12
.
rej~ines .
oweve r
opt icii
Rdhet-
oi
)oppIe r
coIlI is ioti bro i~derinrg.
no s inrglIe approx i milt ioaizi
path liIengthis encoun l.ere~i
than
incorp()rati ril,
thre exitct express ion for
iline Slape;
<WSO
is
1
sI l'o gI~ 1i iut'
ort
for 1he rangei
(it p resitir'cs and
ittmosplIttr i cIrrrlri
di ffereift
approxinrat.ion's'
the cqriivul Ir!t. W-*,(tl
olC
we
tc
at iomrs
cii
directly
eva 1 irate.
I ira' with at Va i 't
oi(f a single
givell by
j
V
1
adequate
in
Ii ine
weak
ed> (
( Sit/di
(/a
-V1rr2/iT F(XYV(<YU/d>)dX
0
CD
Y
F (X'Y)
V
=
4112
is
I ht
vo it~
P
Whe~re
F (X Y)
pa t h
ave raged
resp~ctI i ye. I
4.1.1
Dopp1)1e r
'ie
Th
(141))
0 c/(1>/('Yd/d>
Iitie
anid
facto r of
(41
func t oll
shape
co' i Ii s i oil
11/2 ini Eq
.
,ind
broadened
(14 c)
<ld/id>
I ine
Bi(
c'
shil[iC
cor1responrds
>
'
ar
pa rame t v rss
to tire huit1f w idthi
Cturt is Godsuit Approximation
11;thi
civu rages
aprpjoX imat init. ((.7
14)
wit h a homogeneous
one
14.
exp T'qd
2) (IT2
2 , (0(T)
ir
al ['e
1,11'i
is
ca I cul I iatve
lpprl_1x iR
wIiit 11
t it,,, rupi acts
by us intg ave'rage
valu es
for
ite
alln
Curvt is
ririrrrrtigerw1ous
the varci urs
uodsonl
pathi
ihanrd modle
C. Ii. ILudwi1g. W. WMitImrs.
J.
F..
Rteurdor
arnd J.
A.
1, Thomrnson,
lianildiook 0 f I r1f Frared Rild i alt io01 f ruOm Combus t i onr Gasez;, "NASA
Re~portL
parameters.
lilt '
The Curtis Godson approximation
t (illlpeIit ur'e
certainly
f our
the
case
ait irt ra -y
for
pt Its
depleth
Ioptlicl
species
or
is
u i-mosspher i c
f ill
;I sum
gra'dieni
wit
over
ii n
is
not
paths
tic
is
whtiere
the
uof
from
200
tho
for pllhs where
st eep1).
laliticularly
range
con. ribut ions
very I,.)d
This
is
lempcrature
vari at ions
to
The
300
K.
individual
totnl
I ay•,s and
iSo/d/
is
(1 t
I
Ltwhere
the
byt
(bu ),
lioi
1i1i1in
ltie
is
t
Iciu ;lli nI
-ilcue.fici
c l
f
A.
absorber
ililt
Note,
mbodel
opt ica I
tu
14
amounint
piollf';111am
frequency
t.his and t he stibseqmuet
depth
ter
nid
f'romn
Ht
1v
the
species
"
I
eni
-;lknl
rt'
indices
kS/d)J
Ut e
are
is
ittV(d
die
implicitly
equatl ionss
is
used
a.s
thet(
weightt i ng
funnt ion
in
p
llell
Iiverages
h
<lid>
i.
ieni.enwtal
index,
total
Tih
(il
(
layer
assumend for
t ihe
i Soildld)
SdI(A)
~i
1
0Y 1.d>
<"Tdld>
()
1
1;
(!/d)
!(','
(S/d)
tSl/dtCy
tid)tI
(S/d)m
(17)
WOut
(ul)
(18)
I
'liu'SC
boiild iiui(l p;lil;ali(cter,
ij, I h,
al•tip, I Dol
Cy (1)
eV
I
w
lilt
We're defill.d
(rc.
in
ti lpe'reviotus
s 'cl iou., and1(
('Td) l
i.
(•,.1) i.c ('r)
-..- . -j2 (1ni,2)N kT/ tM
(it.))
C
With M equll Ito
1liet
Tit
•lecul I
-
nmlass
( g/miolte)
.ii~d a
lIhv slpe
ies
in(-udex.
4
t1nii
formlIy Mixed Gases,
4. 1 .2
'Emis far
*
we. havye
Witlli th-1k
molecules
N2 )
C02
&±tnitsplueIric mixinig ratios,X
11101
t he spe!c-i(s ain 1,0W'IUAN are.
lit actuality, LOWTRAN b assumes
Simply mole~cules_ n.
(lMG)
imp!lici tly as stimed thain
cuiciv
C0 2
xm
3. 3X10
,
co,
anld
c!I.
N2 0
CO
accordilug
to
ind~ividua~lly accor-dinlg to thle erjuat
0
1.ixIOt -C
7.5x10-8
2.$x10'7
4
calculated
M INGANe
comb itind
C'11 4
pa r'imi'
t' rs
I li
(12
()
IBalid modelW
Fo r
a untiformly mixedga
for thle 11olurm Eu ril y mixed gases,
I"2'
*
ind i vi dual
jotas
ptz came I r s
aiid model
2.095x10
anid
03,
were(
the subsect ionl 3.1.
from
we-re. comb I ted accord i tg
to their ratios3
(S/d)
1
UM6
I d) 1UMG
7
X11!
Sd) 1
(S/d),1 1IU
0
(20)
1
Im
2 /m
2
(S/tlLI~m2
ldn
W2)
Ini
I
1
A.15 . McC
R. I it L divy ,
AFT2 0 97
AFB,
MA
10731
1G
2n'1G
(S/ti)
R.
i
W.
Xjp
MI
~~~~I,'-iiii
o ce
12Nk/
CtIi 11
(S/d)3
'
'ý(-
.
RPS
~~~(24Ags.92.A737
(22
S!Ib
tUC I
.
Ii
F
0 -
OIz,
k-)t
ai
H11 I(23)O
iti'the( sui-scr iplnm
ii
ci
er'it 1
hse ilh~p
r~d
Ulii furn'ily MiXed
42
gaISeS
or i 9i
0
onily thicll
ct e
lrklilsonaic I e
ialhsorpt
w i th; n
fraictilon
in t he
Vitly
is
it
tjoco(iflt-5
from iviidrhy
of'
poor
lithe
locial
Thel'1ayeru
f l.w
iii
terms
the
ih
is
d
ut ilons
ablsorpt ion
thell
This approx imatio
iu
t bcand;
is
dominated
i Ili, 1tide~d
in
because
the
also
of
ta il
ori
ceniti-l
Focr
by the accu~mkia~ted
1,11v
by
ef fed
t
ee
tailis of
of,
adjo iin i nl
linet
all
tl25e.
tlt(! lct al cont inuum
slill~crcuipt
acid fuit-
int ervals
spectral
'sl rCoil ll IinI es
t ransun i t ta;ince
lines
nonexistent
i ri 11th
inl
ut io011
(co~iuc '
IXcuu~
is,
the(
line zitrength dist-ribution,
tlie( I nterIval
the
l
however,
fromI Iwt-k
tiiy
es
widcth.
and
vi c~i
.tes
ie
This I yp i ccal y Occurs
ill
I
l-a
iSwher
ieiols
e
a bill
ih
the- local
past the hand heca'i),
Ita r
%isage of
t ice
f l t
reirion (if
of
h
t~ll:e
iitteIv
11i als or il'ilatiutIg outs5idie
aibsorpjt icoil
[Cu]
r
1 (h jut]
uccc 1 i Ile ,; wit jci(
lilest--ronlgec
where
Iitit
i
1ilbe, s
ING6
have suppressed
ictraI
i ni-s doem inat e the cont-rl
( i e..
iW
n
g i voit
itHptox ititit i oilIII
w ings of it bondi
~uiltimns,
i(
expressed
cit icvi-
c() i t o i 1i lic
-,
rd
,ae
stronjly alisorhincg
Wit hiii a giveni
w ing
we
Agaiin,
the concpctat, ion of thit. equnivaleýnt
hinc iidcod Iil
si
spucies.
0
iperse r i lit
tIt(
he
Line Witiq AbsorpjA on-Icou
wit i ch
it
oim (:n f f i c. i vi t.arnd
It (),
for the stanidard teMper~atkUre
added to ( S/d)
zero lias
mibý;crip
sum);
(sk ippi ng
mu lectil,-s
ilndexoes
R oil C labvhe
opdtical
ll othi
depthl
thle prues-s~urk anid t.umpI'Ilt
16A
iiIur
5.0 INTEGRATION INTO LOWTRAN 6
I Itt 'i'at
aiccompli shed
he tv1
tilt-
io(il
w ithi
m iniuim~
ret',iil.
I.li
teit
mburotitim eIMDtATA
B
~d ~iliI.'lS
tili
waivetimtiirn
t-hunr
ill
chainges
5. 1 A
tIoIL
isS
T'RANS
wnvit-nimbtl
ic
axt fluS)hc
hiock
qioieitti
i ige it
callsci
, i
each
F'or
iajl i zo I
m
and(
t es- the,
calrkl
timht
to
hand modelI
of
es.
toi- hin
l ayers
intiierfaice
houpl
A s
.
c
i Iidept-Iitvielt.
mao
ttio'
lice ii
t eatlIistiittIucce
MODTHAN
stibroitt itines
are
descr ibed
inI
sec t.
Ithis
lit
olt.
tot a
.
conitalin less than 750) lnt-is- of code.
Sibr out ille lIftAItf
call1ed tnce cit,-.t en Iculat i oit by -itibout i ne ITANS
Stihr'uu it ilIML)A'I'A
I
is
This subroutilne reads thlt
to -uitborit item
for Subscquimtvl.
Aft er
by
progra1,;m
thle
thtý'
jutex'va I
w jiti
ploceeds
waveinimliec
ýslops
IinttervalI
readjalsts
hin;cks,
couitajiitg"F VI.
t ilt-
is
is
only
in
BDM)'IA
,
totatl y
(utilhide
cite kN
and/onr
of
mcs sage.
pactki a Iy
fill-
the
iniitial1
qutn tiitIe s
inde-peitdeiit
it fallis withlin the
(tilts i (l
lower Waivcnui
cot cutlrtionl.
the(,
m;-kes
.
htMOD)
wit h ano erroe
the~ upper.1
the
if
tape lvad'ru.
ates W~iveititrider
t'ile. header
to --e(
t he p cogaina
w~iveioumbfc
anidcicalv
use' by Suhroo t.iii:
request ed
range,
binary band modti4
UCNII)N,
read Iiig
1
I
1
are mode ruict
BMOfl
loop over
lie
these zieven siuheoutttiiie:
autd
lie
(
has
6I
codr.'1111e
or'ifyi nait
subriout ine
nicCU 5fatty
L (W'ITAN
into
MOLOTRAN Subroutineg
Thei
1tit(
6
watvelitiiitlr
caills to siihiout
MTolIecularii
c~i iI
thu
tilie MUDI)RAN
f ir'st
tilt
calclCOI i.Ps
Ini
to
LOWMRAN
I.lie
reads
ardit i onri;11y
5.1
subrout i ies
LiItWIL{AN f; andr
two~ subroutintes
to
MOD'lTHAN
Th' lie. vt
unti
ii
t
ut it i a IWiivellittliret
17
the
wavei mmlw
rangev
the
blaid
Ilt1w
t
file.
mode i
f
Hioweverci
of
t he
tii
If
parameter
the
owe-d
raneiit~
requiestted
ei'
thle
trrmle to thtilt-fet' ; Vil Iltes
i-tad
Ireachest"
bt itt eniit'it
thle
sk ips
w;)vei111mhcc[
ovvt
bloul%
If
option
the
1RPT
4
=
is
used,
the
next
calculation
atmospheric and path parameters but a new wavenumber
the call
to BMDATA only
rewinds
The common block /CARD5/
When
using
Incremental
calculated
by
MODTRAN
so it
subroutine
Finally,
for
layer are
latur
use
atrmosphere
BMOV.
(P/P1),
and
each
when
the
the
array
layer.
path
the
same
this case,
initial
several
in
reads.
the
FT.
Cemperature
the
WPATH
completely
subroutine
wavenumber
are
contains
However,
in
the
pressure
indices
for
the
is
within
BMUATA
independent
BMDATA and stored
These
WPATtl
lies
must be specified In
calculated
by
for
PATH
atmospheric layer,
each
option,
amounts
subroutine
BMOD.
and performs
in
the
wa.s added to pass the value of IRPT to BMDATA.
the
absorber
the file
range.
has
not
one
for use by
quantities
appropriate
for
arrays
normalized
to
one
interpolation
of
the
band model parameters.
5 1.2
Subroutine CCGNDEN
Subroutine CONDEN makes binary file
tape.
.....u
reads
The tape contains information on each
pr.........r.
+..
reqas ft.-,d
h,
CONDEN also condenses the molecular
Data is
therefore,
th
of the band model
molecule separately.
TA.OWTRAN
6
structure,
is
convenient
to
To
form
subroutine
information
only stored for molecules contributing to a spectral
It
pLrameter
use
recurrence
formulas
to
interval;
sum
over
molecules fox, defining the. UMG band model parameters:
(S/d)n(m'l)
(i/d) 11 n1'
(Sldln(m)
)
÷Xm+1 (S/d)n,m+1
I (S/d) 1 1 m( l)
Y,
5m
2
(S/d)nim'1
12 /
2
/
(27)
(S/d)n(m)
(l/d)nm~i
-
12 /
b
(1/d)n(m)
}
(28)
13-
i
(y f
c
o
('0S/
I;
1
m On I
lh
whiere
jilit s
SIljI'vsII
NaiI.te
it -tset -(Iu
'Ve
v' I
re(spi.et ive.'ly
.
at'
rtecurvi'ic.te
(if
th11
diriivvd fropi EqN.
I aiols it I-(
U.MG
(20))
i v.
011
ii)
mode'l
banid
I
(
i,
aid
Oni
aiter
t hrutighi(4
Sutirokt i lie IMOD)
I..
S iiokitt ilie
biand intdi-e
11MOl
eaIch
Ithe
il
depthi
'I.
I i ries
to leoI
call(s)
inl
a
loopi
r'ad i~it iotlt
dtelilfds
Ites
.1 t~tbsiqtlieii
I
MODI c~i leo:
Th
Ipe
lls.
is
I (-m
s.ILored
inl
!-Ied
rad
(.1W
Is
I rnifsfli it t ance~t
vlie
oi
at.t
t
I olt i.
cuiit, ilint ions
erva I
joll
ioreq
i't'ea, I i I-
I
ci i
due.
ided
the it. 11lfrttl;I
Iit-'
tar
cil I I
I atI estlt1,
I ot
olltck
madel
cat.l'i
tar
Iiii.
mado
col 1s v'rc
colittIitilum
t ijiismlut taioce
ure
sitiltist i oll
!oijiii1m
h
Ol t
layers.
inspdit'r I
ilt TRANS
eons ists
th.e,14TKI.%NS
lie!
for calcuololt
l oot
i itre'iniiti.IthI
ante
ot
is
t le
ccitt r uit
bil
Iiis
tn
hi'
o'
1 f'Inn
Ii'eht
over'
iii
clikmtit)'
philI usuoilly of
I iye!-
loop11
is
I tyler
mijlp thtt'
Whenl
Cuort i s hudsonl appetix Ima t i on for thlit
Ilit keepl i hig w it11
plir
callI
O
oil~'
, Ith tirstI
for each
loopl tvt'r- at
i S cil -It Ietll
t'rpqui
ott
out qoiolit it ir's
made 1)y TRANS to ItMODl
11hI'M1
T1h1
hent, zerois
rutis'm it t. U1it!S
i-Ad iiit i ull
.
izat ion
initial
thle
ill
slirc tif's
6
LIITRAN
arraty(')
iat!d,
I ayi'r
,
tis j o
mol
of
(IIliiO btelL
itMOl) retui-lII. ilte
T'I.
ailt:t
I.'Mlddeti
Ani
or-i gina ti ng outs idt! thle
ct'eilcaultit ion.
T[he
. tralB wtlice
iim
11lieZiotran-TSM it t
tJOC
and (ransmittimoce
IR~S.
jAolt
t hie stihs.eqiieitI cai11I
01h.
1(1115.
Iratismi
Sct
var i ahitIv1n ;11(
to1 1ai Is of
to
in
I
iwx~t
thle
cokni Ill,
c~i I (:t llit
thet(
troin s;ulroulit ilorHANS
aityer- tO calclt
CONIIEN
co Icilat t..
dti'scr'iht'd
evei'v w;ltvIt'tiuriihr'
N:
h I
h
demliit vt
the ol d and new Vailue
arviil
li
iSd (S/(l) 1)
MIR'~
(m 'I)
H/d)
feor
piass
oil
ill
.
tr.tismil
it
Wilkeii
layers,
I liiii
alice
is
in'
11
is
'
itiilliosphici''iI
tit'aoist'
mfi t ! mic
fun
LI-
tI i''
c-it
i
-3t t i st I calI I'nit miod'. I aI I so
t ri'isnt i t t~niwc
min1inun i z i jg cli.ijigi's
'hate
only
II.i'nnI itt
lIMOD
Io
tof.
calI oi I' i
til.
I hir l;is icuLOWiRAN Gi
r~imisni ittac.
tily
onti
,iii
~iat
u
ill IMOD
vi
~iid
i 'ls
conrisi si s of
vursiu.
(t'
~iyer
I
uiiP.-
or all
kie
oi t:i
Iayers
l
of 1rn
ILOWTHAN
S1EFI
t hoske
iltirlt
Thli
t\(-v
1 'ilt il
ofI
us I
:1
riq,
I ilue
'v' ie!t
I
hio1pp ci'
Iuoino'iieuuit-s
pii lli.
5I teUCvirii
ili'
'-Ivol
is,
11sed
Siltt'ix
.1re1
to
'Pt
amaigt
w i dlhi
alsot
ccdi uiuiitut
Ct(1l11ll01l0ls'i
TX? for
t Ilve
is
(S2)
are
thle
ised
and I
e
x
10
x
10
I
(m
1
1h
I
ouIiuuuihit
anu
lgatl~
t hie
1 i ien
troli
jons
titii
it I one.
l-
(( 111
'utlil
l1
I
Od
20'
I im
for
t hue
from
Wit hiin
Lii
i
)Wi'
i i1
shapes
bie
veqivii vi ri
li ated.
liitis
lile
jit'
'XtvrlijI~
hiive- i sinuitut;
colia r iluit ionls
I opel Ii~IV
P)
muist-quenliuse- by -,ittrout iine TRANS.
ill- 'w
is also cai i
ils
'I'ltesvt'
su11111u
''i
1.or'iit Y. iit Ift wi (it1
( S"')
oS(f
he
o
The OqIiivijlent
Iort'iiII
c thei
denusit y
of
Iy
arid
ti;It
cal
Sines'th-s
hisliI
Iitrousm
(('tlli)
I. (IctI
IlS bse141
i [tt!rva I
0bhpl Iv
uonitr uhl
coTtrltIut joltS
jita'o
s of II[ he liull
Irom the
modt.Il
cvleuill;ltulI
liet
riimiuluer-
llated
iii1 all
iao
i 11ie
c
ithemolecl'uir
;ohi
l(o
i-te
C-oIVo
are,
N1,it i s I i ra I
uomb in
The vte ctij
inter'vail
(Jvi'
c H! amiin l'a
t rillsiulit taunres
to
arv
With t het uniti
I
ill
.iluprox jnoutl i (1
alf
Ill add itionn
cml
iA)WITAN
.25
shiape' Io
jli
is
MiiI)TRAN
S lg ', i k!a
Cciit cr
loop
lOY"IrS ilnd
ill TRANS
(oliVe.-is IOU1actors'
l
ini MOOlTRAN
hi~eo
Pýrowt 1i
[TIII- Cuirt i5 C(hil~tii
(Si j
in
e
SITP'
.t
ivletIr 1t w idth1 olf a1
t III(.
ar iaible accord inu;I y.
r.0
t1
It 1
;iunld
loopl
E/tli1
0 *(.I
wiIth
loui'
1 OWTRAN 6
11S
IINI(~~ I
cku11
the
ownl
I(PATIII ) caiicu lat 'd
use~d
11201
wiut'.
adjusts its
Thuss
loop ilill Over a i
is
whe-tliur
lThv alsmoihci. dt-isi ty
to
G kiiit.s
dt-etiiiiues
at ions.
BAMOO to be~ consist ciii
in
(imag~Jts
CitI icuI
whvin 'I ANS
ucnd 1.heni
deiis it j es
p~iitram't cr's.
mmolt
onev pass
just
Sulrout ince ItMOl
Thw abslus'iii
111
ItorIit
C(I iait ion
inl TRANS
and
St _WVII
cot-ch
I
halt
spit-utruil
tou
aoid
ill
tilhl.
t
'W
5 . I1 4 Solirouut i it
is
CAt .t
CAIX
en III
bi~y
biubrtiut inc
13M01
par'ame ters fokarbi t ra ry t emperat ures
l inearlIy
are
inuterpol1atIed
atmospher i
t ed
t almIl
out side
is
emperat-ure
tvi
paramieters,
the
t empehit ure
overF
enitry
of
the
of a
aver-age
sinogle
numer icallty
at
the
i iittgrated over- the
center- is
liint
um
less
than
re
the
lowest
Suibsect.ion 3.1
int erval.
full
XMIN./¶,
Whien
VW I flhl compaire-, tit( relatlive valures of t he D~opplecr
and1 spe its
The Vo igt
euvalent' width,
err'ior
region
out
combinat ions
MOT
1
nnp
id
for
region
16.
the
half
is
criiirulnt eu
niinlir- of
inttegrantion
hanlfI
wi
to thrmee half widths
t radeofft
beyond threei
btieIwen
hialf
nmimr ic
widths
is
ini
tis.
Frm-r
of5ci the
I Wet
real1
w i dths.
t he
rig'
part
of
for
and
found
ve~cco
is
vni:1i
ion
linear
a
o)f
various
halif
cenqt er
to
1,lthe
The
using
I ine
thle
Cuvtvir
I cuI itt i
ai study
iinter'vu s
from
a if
subiroutinICPFI'2.
in six steps was
Iarucnty
non
ra
biy
.
dept i
Otheivrw ise
rent z
the
isSCalCUltetd
erval
line
1line shape
usetd.
ill
tised
funct ion
shape
widths
of
itre
the
lteio
iiomerivai
fintegraion
iinijt
the numtwr
the
integraLting out
reasonabltl1e
three
in
alppro~ximat ion
linp
iid
un
funtii~on"
to
the
approx imat i ons
Muveral Inuinvrici n
conqilv
fur
proiper formula
tie
and j
w idthI
opticlnI
the
is
law
Beteers
hiighest
to
Mo gt
the
of
vq i va I emt
the
,
iIf tie
or
add it ion
in
int erval1
As discussed in
ce!nt er transmit tance.
is
I
t he
line fur
pa rame ters(
range
temperaut
enlcleoIatIe thte
EW I Will Is cal led by subrout inle IIMO11 to
modelI
hanid
ehchlIaye r.
for
eithter-
fur
thi-
tabul1at ed band modelI
The
.
de t erlinile
to
width
INAL.F)
represent
t i me.
ca lcul ated
usinog
:1
'The
no
Furt ioins,
"Hanldb~ook nf Mathemleii Wil
M . Abrnumow it z and I . A. St Cgu,'i
Auiil i d
NtIS
Tables,"
Mathlimait i l
and
Graphs,
Furmut ah,
withI
I 96i) .
55 (lWeMOiibe
Mathtemmit ius Serlies
21
5. 1.6
Sll)rolti tiou IFliU
L"i-,
mSite(i by Lw ir1m1
al 1 iprnx imit- lon wit ic(h
anid
the. first.
Wlticn
ch wit-,
order flernitii e poly~nomtial
inclititomid
J
/ CARD I/
hats
heeri made
ifC .JDM01
OnltIy
mid
mod ifet
je
o
ditet tin'ned
".I'tIIlItIT
thle
aI
tiltii.
Ihtlouk
'11i1.
ham:d
I h;;
at
' ildul
S len
Mi
niode I
a div idt.
error
An
shiape
i-s
furict ionl
onl
a
2 'thi
approx imart.ion
ob(rder
V)
dependence
e!rroc
based
t
fuictintoll,
frequtency
uomplex
8'
I'Lnctionii
was
suifficientlIy itccuralIe.(10)
not
to
miniimijze niod ificationis
frequiency
of
0
essilie
t11
at it luits
for' iiis'
ýlit ioil
doutiI
rigi
oh
t oit
ilt I
R. M. Good,
J.
Ilium I ie(--
hu
it
si I)!', I
layer. d imri:;i
mtbrout
ines.
i on
of
sca-t t tkr i rill
the
modelI
hanoi
Rad jilt Iriti
T~ronsfer,
21I
22
.
,
i IMOl)
MA IN has
when
coltlimit
GEur0a 01
been
ALAMI
dens iiy
tiImbv
is
iii
sl tpvitt
modeltILtraism i Itiance
I.OWIRAN
6
ions" and) storiage of too manty puitit
'Atinspher ic.
MAI1N
thli
resulIt
liit
inl
has bleln aldded
Also(,
molectiltir
iltaye
,
IRatvi.
not
it,
'Ant IFrf jct-Wn~
Met hod
l'rT01,I i I i t N'IMI
lun
lou:
'The Voirtlott
Ijiinit.Spe
does
As
LOWTRAN 6.
ated.
Ini
openued.
Thk-
.
i
bty the: MOD~'IT'AN
ipp I iriit
is
error-
cm-
fji(:111 iotis.
li(ti
fille
pacitmetver
Zero
Itli
change-s i n iti
erqullIs 1 are any
I.
to
the! Nw iteli .BMOI)
;ectioln,
this
by
st riaIi-'ti forward
t~lt
o1111
1 11.
its
Th
'rim1
used. ( 16)
l inte
Horn]i cek,"6
.
aipproximatiion.
the hieji :1in iitg ol
ini
readl
17.
the( Vo ig'
approximate
A 1ew vou1l~tins have rqijit i ed niiii no
is
2. 5 x 10 5is
LWIDH
by
A polyno
om ial
Moc.lj~ications to LOWTRAN 6
An att1.empt
to
to
hilt thle results were
jinves t iated,
5 2
used
developed
I unict ion.
Ft V
than
is
part
the. j 11t cgra t i Otti ;1
subirou t ine, .Wh~i
it
calculate the complex
to
The real
der' vat ivu is
per torni i t
t ie
is accurate to better
de-i Ivittlye.
f ivzst
midi~ it-,
citima h
0(;
cal led by EWIFITI?
is
('lF'l2
t
woiuIld
(tatia
rttpi iire
poi litES
LIXo.(
oil
Uiver1sitIy Press
t196').
f or
"vtil I tui.t ion
(if
tI lie
CoimtI tox
ion ;Irid it-, lIeniv~it iv.S.
31)')
(197k0
proble m was
Th is
path.
slibrutotill1 es'
and
enp a
Sog ir
ie
nSG(
When
sets
freuImiitty stief)
"*
byis
ses ClI)TA.
which
.J IN10i)
size
C21Y1A
i;
to
layl r
Cutrt is Goidsonl
mod if icat ions
to..
to INT(l)V)
5.1 .1
Subisectiontti
.
to
and
5.1 .3,
t his s ubrouut ite,
is
at I clIi
FWHM
F ilgore 3
.
peoe
requIl i red
hitlt
callIs
reel anguilar sl it
tw
lie
it s hia~sit
P)FHAN
to
Withi FWIIM set
b~in results.
MOhDlRAN
sli
ftitict ion,
t
Steps) lot-
subrout ints
funict ion
as ziliuwi
DISCRETIZED
SLIT
SLIT
TRIANGULAR
riiuuIa
P i sure I.i ed
the Weip1
fllI ig from theui11 hIu1t MO DIRAN Usevs the 1)i s reý iz v
Cu lit inuous and
Cow par i son of
Uses
VASCOI))2
S I it 1`111l1 't i uris .
L
3
werk:
when DV
inl F igurt
CONTINUOUS
TRIANGULAR
n
C o itIi nIrolkoos Funt
Al pI
rox Imat i oi ii.
f or
I cm
Note that the- di screLi zed triangular
to I cm
MODYWAN
to ow-,' THANS
set. t-iual
fuiitrc tiol
slit
ly deerade the 1 cm'
the
the
were
t -imingkililt
~iwtounaticil
by
sol il
;aver~liged
tes tia'ism it tances ca leoL1i tted ill 5 CMW1
01him 1120, 11MG' and 0-), an
pe.Sotlici
it diSGcret ir('ed
pr imary
thie
uste(I
onl1y
is
;rId C31V1'A and callIs
,
for
Oturppo1
C MplIOY,
set
,
cill cu l ilt i oil o)f
Sti gol i f i call t
"*
d iscussed
a s ing I e
i
code have bee~n atdded
rema iris timi ti-t'rd,
*i
]it
t he
requ it res
1 ties ()f
2Q(!
def i iii
1y
1jyeir approx imat ion
single
Till
THANS.
Lvo idtied
is
3.
6.0 VALIDATION
Val1i dait ion of
F-comp
I t- ed.
t
f-
1.t
li iiid
m
lloweve-r
only
ranisiuit I iiiC
Formulhnat ion
hIIe (;ode
be. toy
C(Sg)
Iti~ii
0- 3
will
1(131-
1
cill
t
fle.w
ri'so ut i on
paraet
modf-I
1,131(1
lo~f.ii per forimed
ioos
nct
of
par.Inwet 01 5
thols
(1h
3dat
tape3
iniý
test
beell
11.1
of'
M0)I)THAN's
All1 v 1itIidt ion ol'
1I1nr
it
-:inuv~
the
-is
FAS.CI1)? whichii
MOl)TRAN
is
r Pva1i~li~tU(
algai tinst
thle
us cani lot- dIegradied
'qua
the
losinig
to ', cm
I
cm
Isquare
slit
71we
liniai
i-it
at templintg
(
:
m ith'1
~iIII(I
;Ii;Ir~nwi
Ill.
btIind nmoeit
band
pranet
modu]
r
(JI
I~
~iii
c riii-
l3
i1 .t
oiml
(1 )
g
21
-
iil
(.)
(Niut v
rci p.c t i'.jr I
1.
awn"
sl it
S/d ) 1
j
ii
i;(ttam
iiIri(
in:
j
hil1~1t
i
of
to l'AS(,0[)2- Cie3iAItz
i)v~ii1 oCi.
(
1.01W'RtAN
(S n,d
hini
ori'31l
onuont
ai
limitmi
Silo
i
(Tililjr
Ilrtliflie
Band Modu'1Parameters
Tlie
(111()
a
hats
)j m.
o
l ly
miodlel
-.
N
(I
j
fCi)
l
O
r-1lt(I.
to the' I
cm
t h.1t
Iho.
ta
lim-
andl .
I1
k 11
iA
ihsfoipt, i o(il
H2 0 Vopor oi- 300K
L
I.
-
07
zr
1
c'
V.
I
1.
0
220.4
26
!
18
8
.K.
6.
C
Cmarsnwt
IlFigure4
a lo
alttud,
-it-cira regiont
coe f f
ACD
5.
ComTarisondo
BAuCd2 Modellsitic
LOWTRAN 5rl (Dotted'"andl
piaud Mhodel-1
tilt!A US So llidaCrve ) Mo
Itipiueu il
2160
2260t cm
'I ent
to11
n! w tere Vuapor
wit h a0 I
igui t1olshn
K ogadt o
i
ais
nt
overl
app
ei iva Ie
ing
)
fote ar MOT
InF g ic
Na nd over
,t.hespcta
lappion
gfor i. ts
srutue2f5h
fore
r
tilt
".,
spC tr)I
1-0 KMATI15'-
US Std Atm
(I)
oip
]/
(iNý)((I~
r u
WI.LvcrIum
Fiue
(i
Cma io
5.
221()I
rn,
it;
;Ill
a
rpio
il c / m ilrilNlIJý
('Xu
(m-1
twoi~
Ir-"1
callh
f
i
oh
iIlio
-v111 andiCO
moo
1hsorp tion perftorim
aPosuts~~
Im ier 0r1
2211)ared to I:A
SjiniI
Iysi
i
ai
il
iSOD
n
MODTAN
-a t
Cl Io 0 cmi
t
Wremry
Ahorenu
pmhletr
Il-cgi onIs
Itv-
iumo
except)'i Fi on
I'I
il
thid
p
1
rusciullbcit(cK
S"i~r
N?0
ILltil.
M
D2adaMDRNC
rmryAsres
h
aIdC2ae
cr
e
ai
r ibimp
rune ol y
pmh uscath
~io
ore C.)
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11
1iei
o
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t
thau
led
citturo
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is
uiW
om N il0
N
,M.TA
~diSct~ai
good
ie
i
dll
I
I hc
i but
iij
iml
i26ta
ar
aip.
evident
A series
MOI)TRAN
cal cuIit ion.
of
1 ines at 7,
Further
11,
13,
anwl 15 cm 1 are Mi-iss.ing
invest itt.tt ion
:cc.;ssary
is
to
det erliii
in tilw
I,
the
origin of these discrepancies.
I.1 IKM P9TH at 0 tKM ALT
~~~~~~
..........
....
",........
I&
US Std Attm
i
DI
A.
"
1Nt
tlUMlMfN
I cmI
[0tS)2
no corli inuurme_
0
cJ
C)
Wavenumber
Figure 6.
Comparison of a FASCOD)
(cm-1)
and a MODTRAN Calculation
In
the Micr:Iowave.
40
-
27,
,7
"...r
1.0 CONCLUSIONS AND FUTURE WORK
A
~duvelI
*
radiaitive
ped tor- LOWTAN 6.
coiled and
I
jut egralccl
model
Th is
intoa
ed to a s NOIY'IAN,
i-ferr
~
transfer
appl icable
upper
mode ratt ti pect~ral
LOWTIiAN
and al
to
6
Ttes ti
.
altitudes
reso I tli
g hats
IrCligiifii Inay
- yei-si
model ihas beeni
art
begun ort
l~s
ha
lids- been
thle
niew
codle
Iceit tie live red to
a the
ir~A
Fe rcv Git-ophysies Laboraiitory.
Ili
vaii
thle
~-t
toillowling
most
idat ion and opti miza tfit
17,900 cm I
high
MOI)WAN
,
altitulde
P.corrected
more. vfi icicot
.
our,
oif thle code.
mnd FASCOII2ý
to
effort
val1i dot ion
Mi-thlods
is
ou lot Ions will
campletedr
whit i-d
may
will
conceit trate
(ill
For 1thle f reclue icy range from 0
bef
Sign if icait d iscrepanc ies
pat its.
At tert
.
of
be,
comparted
will
be
the MOiPIltAN
fruitful
far
f or- 1low
ident if ied
code
wil
1
opt imizring
to
arid
and
boi made
the
code
t ic I uldt
* dcif i [Iii lip,
cut
coef-f icu i eiit s,
a
itti-it
s
tlmiit
iieiiii
oire
det er-in i niziigl
off
va 1 11C.5
i i
i,
ofns
i,ri
I ras;I
absar-pi
fat
t ittce
of
eaclt
aht
bit
ri'''p
sni vc- ies
NS(!1ii r zIt e I y
*
deve 1 (11)i rig a mot-e ef fi icient roo t i tie
Ili- Voiii
lIiiit shape! and/az'
faor i nt egrail i ng
* allow inig far- thle sped rtial resolutit tl. of' tilt!
modle
pa ront- t etr to hIe deg ratted i nt e rnally.
To I tic ext '-itt
t Intie
jIr-n it
c ticti
t
tIhese
ariitroiiciits
wi
iratid
1 bIeIt i Itvs*
v I
t rI
- I
j1
8.0 REFERENCES
1.
I,.
F. X. Knvizys, E. 1. Shettle, W. 0. Gullery. J. IH. Chetwy'id, Jr.
W. Abreo, .1. 1. A. Selby. S. A. Clough and R. W. Fenn, "Atmospheric
TR 83 0187.
CompunItcr Code LOWTRAN 6 ," AFG(.
Trutism iltit nc/Rad i a
(August
Hlanscom AFI3, MA 01731.
Lahoratory,
;eophysics
Air For'ce
A11A137786
198)..
2.
R. A. McClatchey, W. S. Beltudict, S. A. Clough, D.. F. lhutch, 1. F.
('alfee. K. Fox. L. S. Rothman, and .1. S. Gu1aring, "AFCRI, Almtnsplher''i c
Air Fo'vc(
Absorrpt ion li ne Par'ameters Compilations," AFCRI, TR 73 0096.,
MA 01731 (January 1973); L. S.
Geophysics Laboratory, Hanscom AFB.
AI)762904
RI t tii n, Appl]. Opt , 20, 791 (1981).
3.
1). Andiug-;, "Banid Model Methods for Compnting Atmosphvric Slanit .Path
No. 7142-12-T, Willow Run Laboratories,
Molecular Absorption," Rpt.
Research Institute of Michigan, Ann Arbor, M• (1967).
Unvironmenilja
4.
Transmit tance and
"Atmospheric
Turner,
F.
LaRocca and R.
A. J.
Rildiincv: Methods of Ctlculation, Rpt. No. 107600-10-T, Envi'ronimental
Research Institute of Michigan, Ann Arbor, MI (June 1975).
5.
W.
6.
A. R.
7.
W, L.,Godson,
8.
"Preliminary User Instructions for
A. Clough,
S.
AFGI,/OPI , limiscom AFI,. MA 01731 (1 October 1985).
9.
Handbook:
Infrared
"The
J.
ZisIb,,
and t].
L,. Wo ite
(IRIA)
and Analysis
Itnformation
Infrared
Edition. " The
s
f M! ct iiga n, Anni A1-1 i- , Mk
Re1.s-e;trchI iI st itA ute
I.inv i I-noi n it
H.
J.
Curtis,
P.
Q.
R.
Meteor.
.J, Meteor.,
Smith,
Kne izys and 1.-
J.
U.
J.
S . Rhohlmi,
12,
Oube.
78,
Soc,
123
M.
Rev ised
Center.
(.1%
1
165 (1952).
(1955).
F..
'"AASCOUDZ
Gardner,
S.
Ltter,
FASCOD2,"
A.
F.
Clough,
X.
;-ast Atmosphe, ric Si gnatuore Cod.
Air Force
AVGL TR 78 OO-R!
(Spectral Truansmittance kind Radiaace}),"
Ai)A057506
Geophysics Inxboratory, ltanscom AFBI, MA 01731 (1978).
10,
"Add t ion of a 5
S. Bernstein, end R. Haimvs,
C. Robertsoin. L.
m I Spectral Retisolution Band %odel Option tro 1,OvWIAN 5," ARI RR 2.)32
Ac rodyni- Ve e.;arch. Inct., 1itllerlca, MA (October 1900).
11 .
3.
D). C. R~obertson, L,. S. Iternstuin, R, Ilaimes,
to I.OWTRAN 5,"
Vega,
'5 cm-I Band Model Opt im
(1981).
12.
I).
S.
A.
Cl ough.
p)QrsVIUjl CoImnuI icatinnj.
29-
and 1.,
Wkinderlich,
__t.0ppl
.
20,
3218
-
13.
F. X. Kiteizys. E. P. Sheltle, W. 0. Gallery, J. H. Chetwynid, Jr., L.
McClatchey.
A.
and R.
W. Fenn,
R.
A. Selby,
E.
J.
W. Abreu,
5,"
LOWTRAN
Code
Computer
Transmittz,nce/Radiance:
"Atmospheric
MA
APB,
Hanscom
AFGL-TR-80 0067, Air Force Geophysics L•boratory,
ADA088215
01731 (Felbruary 1980).
14.
C.
15.
S.
It. A. McClatchey, H. W. Fenn. J. V. A. Selby, F. F. Volz, and ..
,
ed.
3rd
Atmospherp, "
the
of
Properties
"Opt i-al
Garing,
Hunscom
Air Force Cambridge Research Laborat ories,
A"CRI, 72 -0497.
AD753075
AFIB, MA 01731 (24 August 1972).
16.
A.
J. F. Reardon and J.
W. Malkmus.
Ludwig,
Gases,"
Combustion
from
Radiation
Infrared
"iHandbook of
SI, 3080 (1980).
B.
Thcmson,
L.
NASA Report
Functions
,'
1. A. St-gun , "Handbook of Mat hemat Ic ,
M. Abranowitzrind
Applied
NBS
Tables,"
Mathematical
and
Graphs,
Formulas,
with
1965).
(December
55
Series
M;tthlminiiic.
"Atmospheric Radiation,"
Oxford University Press
(1964).
17.
R. M. Goody,
18.
"An EIfficient Method for Evalunt ion of the Complex
.1. Blumlicek,
Derivatives."
The Voigt Function and its
Probability Function:
(1978).
309
.1. Quantt. Spoecol. Rud. Transfe'r, 21..
-
-
-
- -
- -
--
-
- -
- -
-
30 -
- - ----
APPENDIX:
In
MQIA*RAN,
molecular
tile
within a spectral
bin,
tu, is
av/2
(
1
DERIVATION OF THE BAND MODEL PARAMETERS
elins
fron,
T,
origi
11ti
lug
determined from an exprvss ion of the for-i
dv )n
e-Sulv)
.i 2=
traisnmittuice,
(A 1)
,
0
why're i'W
6.' )
ai line shape furctiton, *
is
1 is
the alis?)t'
are function.s of the absorptiout coefficient
itmotint,
illd
line
dit-sity
anrd
(S/d)
S at!d 11
(1/:tl
.
(A 2)
A
moth'I1 )arimet vs
-
h1til
(S/d)
(l/d)
S
I
n (1/d) Av.
I
(A-)
-A
(A 1)results
from Eqs. (11)
and (14a).
A staudarid method for determining buid model
E'q.
by
Gootdy (A 1)
transmittance
warik
and
The
weýak
expressior
strong
line
resultirig equations
expressions
for
1
-(S/d)
lin.e
at runlg
ire determined.
limits
are
llis a ppi ro'ttcth
i11)plI ed
and
to
of
thie
solved
for
Iwo
tt'itl1
"band..
}itlenu lode
..
limits
of
a
two
l11iId out
parameter
These results are equated to
Ladethbur' -Re icht.
the
.
partame ters wits
unknown
parameters.
t ritsllm it tiulic.
,d.f the
ClauntioIL,
ard
When
fto u-mull s,
both
the,
thie
Goody
!'AiveC
fotrm"
5i
S-
(A 4)
I
-'-
!
A I .
-
M.
Goody,
"Atmospheric
RadIitat ion,
()Oxturd
l1ii
IV 'S ity
(196C4).
-31
--
P
P
-'
"Lt
p"
l'ress
".
N
V-
4ISi-. )2
P4=
N is
]Jline
i
line
(A 5)
i-I
the number
(the
S
2-
'I v
tlere,
N
/ 2
of
line,
spacing
and
formula
Si is
tihe
assumezi
all
integratted
N lines
line
have
strength
the
sallue
of
half
width).
It
is
imnportnlt
expression
tramismittaucee
throul
'h
bi n.
to noti e that
ii set ofi
in
lines whose
centers
fall
function,
absorption due to those lines
- not
on
(A-i)
just
models
withiii
the
i% inappropri'ate
the
a givein
other
hand,
for the
transmittance
finite
mode•is
•pectralr
the
total
their contribut ion withitt a finite
bin.
lnstend of
equating the weak kind strong ]ine! limit (if
Ludenhurg Re iche fxinction,
(A I)
Eq.
MODTRAN.
The Ladenhiirg-Reiche
spectrual
Goody's approach
to
P;tss'
we equate the weak and
expression(A 2)
centerms ir,' randomly distributed
for
the
Av/2
Shitll).
fulmil
to the
line
limit
of Eq.
due
to
lines
whose
interval,
Au/2
Snl
v)
dii
n
{ -j
(V
0
all
(A 1)
2¢
,
here,
transmission
in a given spectral
2• r
TV-
strong
Eq.
expi-Siult(u)] dv
((A 6i)
0
N line•s
ion
are
assumed to hlve
iS irbitzaryfl'-fi;'..d !:b
--
b(al-)]
th
/ji
.
the same half
w i.ith,
but
the
line
i
di',
(A- 7)
0
I'hen,
A 2.
in
the weak I ine
G. N. P•ass,
Am., 48. 690
limit,
"Mode].s
(!95B).
:q.
for
(A
6)
heromesn
Siec trail
32
-
lhuind
Absolrpt ion,
3.
O1,
.
Soc.
1 ,,
o
u2
(B1 n S)
22
(
(I •
~J2
(B2 --- '•--) "
)
''c.a)=
1
t
1ZNB
Ok 2
i)
t)s
(
f irst orde''
i on
C'jutil
~
sEi2
2
1s2
+
,'
•
'(
3
(i)(A8
i -I
i -
i -I
Tit
2
2
ZN
y
11u2
(A2
N
N
22
2
I12
ill u I'CeeS tab Ii~lk~1
:-(Iq. (A 4)
p.
N
n S
2.. i
Cs
=
a
bounded
il(ctra.sinsg
non
th,
of
iit-jgrr.l
of
limit
the strong line
To detrnminke
positivye
(A
Eq.
fulictiotl
oil
as.ume
1(v)
Consider
a
we
6)
O,D)
.
(A
9)
to
bit
1 l,
geIItt x'n
form'.
AVI2..
edv
(A
10)
(A
11"
0
It
follows
t hut
re(quiras
inequdlity
ex pot ui
th.t
by the
limit
C
<
.Sul)(t/V/2)
u<
<
0
T'his
that.
as u
is
-4
rnlir u
thait
I intear
in
I
off
fdils
u . The c x ponnt
1
eXpontentiUlly
til
logarithm of
of the negative
dcay•
I
witt)
o
fltct oi',
larg(!
c,
u
vivc 1
is
.ye
divided by it
(A
lI(1)/uI
11(
and
12)
Z6
AI'p'lyinlt;
Idhl
n
, one obtains
U._
'S
C
(A
S <t)(v)>
13)
3e
33
-
',
Ie
LL
I.
wnere
Av/2
av/2
<1(V)>
-
J
U
li.,
bNv) e-Sub(-
d
r
0
0
Note that
this limit
Taking the
r.quilt
is
independent
logaritthm
(A 14)
dv.
•-Sub()
of
the value of S as long as S > 0.
of both sides
ing the asymptotic limits,
cC' Eq.
(A6),
dividing
by
u,
and
one r)tins
N
SiZ-I
n S <b(u)>
<b(v)> is
(.ine
N
Si <b(v)>.
(A 15)
il
the weak line
Iine
independ-nt,
limit,
To determine
is
also thlt
n and S.
the surprising
TIh,
is
that
Eq.
(A 9)
strong line limit!
we return to the weak line
consider the equation obtained from the
in u.
result
coefficient
limit,
Eq.
(A 8),
of the quadratic
This e(qIut ion gives
N
n c
2
2
Si 2
and
terms
(A 16)
result in g expressions for the banmd Inodel
parameters are
N
(S/d)
Si
(A 4)
i--
N
(lid)
--
N
(
Si
)2
Ii •1i
("/d()
has
obtained,
F,'l.
the
simine
because
form
/
si2
(A 17)
:1
as
thhe weaker
before,
but
a
smallier
I ini'-s are weighted
(A 5)
34
-
1less
valuet
in
Eq.
for
(A 17)
(I/d)
thaln
is
in
Figures
I.
and A-1
5
a
compare
non-overlappitng
1 cm-'1
MODTRAN calculation with the new and old band model
overlappinrg
rectangular
formulation
are
much
The results
FASCOI)2 calculation.
slit
and
investigation
Further
improved.
slit
to a 1 cm 1
rectangular
parameters
with
the new
validation
are
planned.
5'- I1
KM RT 15 0 -- US Std Rtm
C'
I i "I
E|
_
U)
1o Fft3COD?
old U/du€nd noN20 COW€I IULnJu
P17-
F160
1
,_a]s(I
..
Figure A-1.
2210
190 o2f
2Imar
21
_S~Wavenumber
i]
d_.1
a2n
IPR3 ?Aqo
?o.
,)cuti
(cm-i)
S..oc,
Calculations.
and MODTRAN
Comparison of FASCOD2
The MOD)TRAN Curve was Generated( w#ith the Old Band
and no N20
(A-5)
(A-4)
Model "or.=.-,tertý, Eqs.
Continuum
Fun•ctilon.
RIEF.ERENCES
Goody,
"Atmeosph,;r-ic
A 1.
R(. M.
A-2.
"Models
Plass,
0. N.
(i9,58).
48,
690
Am.,
for
Raidiation,"
Spectr'al
-35
-
IPrrs%,
Oxford Unive:rsity
Band
Absorpt ion, "
Jl
Opt.-
1964.
Soc'