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Abstract

Tables and Work flow Methodology used in the analysis of the Climate of Titan. (Loaded as Excel 97 because all previous versions of this file would not download)
 
 
 
 
 
 
 
  !"
"#$
$%&'!"!# &(!#!)&
*%
)&$+
)&$+$!
'#''# &$
'# &$$!
$'+$!
*"&,$%!&-& 
$!"'.- $/,0 &1,'#
$%&'!"!# &(!#!)&
'"
(!"#.$&/
2#&!#-!%)&
.3+3/
$!'# ""#)&.3+3/'#
'$!
'# &%2&

$!' &#'#
'$!%0
&#,1.$&/
4-$!"'- $'&
"''# ,5,0,$!
"',
$%&'!"!# &(!#!)&
'
&!#.$&
6/
Calculated Diabatic Model Air Temperature
of 82.3 Kelvin (-190.7O Celsius) (See Table
8)
&!#16.$&
/
Computed Titan Global Air Temperature of
94 Kelvin (-179 Celsius) (See Table 10)
$!'&!'7%
'8'!&#7&,
$!"# $!"'
!'#$!"'
9":' !"$'
"""$!"",$
$9 !"'#;"#
$7!<"!!"

$%&'!"!# &(!#!)&
('
&
''-'=,
*&&)! 
&"
!>'!:'+5
-'=
$'#
"'"=
$"&%-&'#
!"$!"'!"
.,,'#"'/#
&."'/
'?"',!"
'="'"
=."@,(,?%/
#A&=,
! !& $ 4
(  B,1
'#0 17C7 !
0 & ,1 (
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6,1 F
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0 &
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,
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,6
,B
,
,
,C
,
,
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! F
1,C1 ,CA 6,11
1, ,CA 1,6
6,C , C,B
6,B ,B ,6
6, , ,
1,C1 6,1 ,B
1,6 ,6 B,C
, C, 6,
, C6, 6,11
,1B ,B 1,B
,C 1, ,CB
, B, ,
,6 6, ,1
,B , ,
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A,C
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C,B ,
, ,B
1,6 ,
C,B ,C
C, ,B
C1,1 ,
C,C ,C
, ,
6, ,
6, ,B1
, ,C
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0 &
6,C ,
, 6, ,
, 6, ,
,1 6, ,6
,6 6, ,
,B 6,B ,
, 6, ,
, 6,B ,B
,C 6,B6 ,1
, 6,6 C,
, 6,6 C,C
, 6,61 C,B
, 6,1 C,1
,1 6,1B C,
,6 6,1 ,C
,B 6,C ,
, 6,6 ,1
, 6, ,
,C 6, ,C
, 6,1 ,B
, 1, ,1
,1 1, B,
,1 1, B,
,11 1,C B,B
,16 1,6 B,
 &%
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,1B 1, 6,
,1 1,C 6,
,1 1,C1 6,1
,1C 1, 6,
,1 1, 1,C
,1 1, 1,B
,6 1,C 1,
,6 1,B ,
,61 1, ,
,66 1,B ,1
,6B 1,B6 ,
,6 1,6 ,
,6 1,6 ,6
,6C 1,61 C,
,6 1,1 C,
,6 1,1B C,6
,B 1,1 C,
,B 1,C C,
,B1 1,6 C,6
,B6 1, CC,
,BB 1, CC,
,B 1,1 CC,1
,B , C,
,BC , C,
,B , C,1
,B ,C C,
, ,6 C,B
, , C,
,1 ,C CB,
,6 ,C1 CB,1
,B , C6,
, , C6,B
, , C6,
,C ,C C1,
, ,B C1,1
, , C,C
, ,B C,6
, ,B6 C,
,1 ,6 C,B
,6 ,6 ,
,B ,61 ,B
, ,1 ,
, ,1B ,B
,C ,1 C,
, ,C C,B
, ,6 ,
,C , ,6
,C , ,C
,C1 ,1 ,
,C6 , B,
,CB ,B 6,
,C , 6,6
,C ,C 1,
,CC ,6 ,
,C , ,1
,C ,C ,
, ,C1 ,C
, , ,
,1 , ,1
,6 , C,6
,B ,C ,B
, ,B ,
, , B,
,C ,B 6,
, ,B6 1,B
, ,6 ,1
, ,6 B,
, ,6 B,
,1 ,1 BC,
,6 ,1B B,B
,B ,1 B6,
, ,C B,B
, ,6 6,
,C , 6,
, , 6,
, ,1 16,
, , ,
C,B , ,
C,6C , ,
C,6 , ,
C,11 ,B ,C
C, , ,C
C, C, ,C
C, C,C ,C
,6 C,B ,
, C,1 ,
,C C, ,
,C ,C ,
,6 , ,
, ,6 ,
,B , ,
,B , ,B
,6B , ,B
,1 ,6 ,B
, , ,B
, B, ,6
,B B, ,6
,C B,1 ,6
, B, ,6
,1 6,C ,1
,CB 6,B ,1
,C 6,1 ,1
I!")&
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)=
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, 1, ,
,1 1, ,
,B 1,6 ,
,6C 1, ,
,6 , ,
,11 , ,
, ,1 ,
, , ,
, , ,
B,6 ,6 ,
B, , ,
B,C C,C ,
B,C C,B ,C
B,6 C, ,C
B, C, ,C
B,B C,B ,
B,B C, ,
B,66 CC, ,
B,1 CC,B ,
B, CC, ,
B, C, ,
B,B C,B ,B
6, C, ,B
6, C,C ,6
6,1 C,6 ,6
6,CB C, ,6
6,C CB, ,1
6, CB,1 ,1
6,1 C6, ,
6,B C6,B ,
6,6C C6, ,
6,6 C1, ,
6,11 C1,1 ,
6, C, ,C
6, C,B ,C
6, C, ,C
1,6 C, ,C
1, C, ,CC
1,C , ,CC
1,C , ,C
1,6 , ,C
1, ,1 ,C
1,B C,C ,C
1,B C, ,CB
1,66 , ,C6
1,1 , ,C6
1, , ,C1
1, , ,C1
1,B B,B ,C
, 6, ,C
, 6,1 ,C
,1 1, ,
,CB , ,
,C ,1 ,C
, , ,C
,1 , ,
,BB , ,
,6C ,6 ,B
,6 C, ,6
,11 ,C ,1
, , ,
,C B, ,
, 6, ,
,6 1, ,
, , ,C
,C , ,
,C B,B ,B
,6 B, ,6
, B, ,
,B BB, ,B
,B B6, ,BC
,66 B, ,B
,1 6, ,B1
, 6,B ,6
, 6, ,6B
,B 16, ,1
, , ,C
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0.75
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1.00
1.00
0.50
0.50
1.50 1.50
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Building the Dynamic-Atmosphere Energy-Transport Model
Diabatic Equipartition Ratio 50.0000% 50.0000%
Cycle Number
0 1
1
1 1
0.5 0.5
2
1 1.25
0.625 0.625
3
1 1.3125
0.65625 0.65625
4
1 1.328125
0.6640625 0.6640625
5
1 1.33203125
0.666015625 0.666015625
6
1 1.3330078125
0.6665039063 0.6665039063
7
1 1.3332519531
0.6666259766 0.6666259766
8
1 1.3333129883
0.6666564941 0.6666564941
9
1 1.3333282471
0.6666641235 0.6666641235
1 1.3333333333 Energy Surplus Thermal Cell
Lit Hemisphere Budget
0.6666666667 0.6666666667
Process Insolation
Hemisphere Energy Budget 1.3333
Total Global Energy Budget
2.0000
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Building the Dynamic-Atmosphere Energy-Transport Model
Diabatic Equipartition Ratio 50.0000% 50.0000%
Cycle Number
0 1 0 0 0
1 1 1 0.5 0.5
2 1 1.25 0.625 0.625
Space Incoming
Captured Radiation
(Units)
Heating the Lit
Hemisphere (Units)
Lit Hemisphere
Thermal Radiation
Loss to Space (50%
Lost)
Thermal Cell Export to
Dark Side (50%
Retained)
Infinite Series
Limit
Insolation plus
Thermal Recycled Air
Final Lit Side Thermal
Radiant Energy Lost
to Space
Atmospheric Energy
Transported to the Dark
Side
Space Incoming
Captured Radiation
(Units)
Heating the Lit
Hemisphere (Units)
Lit Hemisphere
Thermal Radiation
Loss to Space (50%
Lost)
Thermal Cell Export to
Dark Side (50%
Retained)
3 1 1.3125 0.65625 0.65625
4 1 1.328125 0.6640625 0.6640625
5 1 1.33203125 0.666015625 0.666015625
6 1 1.3330078125 0.6665039063 0.6665039063
7 1 1.3332519531 0.6666259766 0.6666259766
8 1 1.3333129883 0.6666564941 0.6666564941
9 1 1.3333282471 0.6666641235 0.6666641235
10 1 1.3333333333 0.6666666667 0.6666666667
Process Insolation
Hemisphere Energy Budget 1.3333
Total Global Energy Budget
2.0000
Insolation plus
Thermal Recycled Air
Final Lit Side Thermal
Radiant Energy Lost
to Space
Atmospheric Energy
Transported to the Dark
Side
Building the Dynamic-Atmosphere Energy-Transport Model
50.0000% 50.0000%
0
0.25 0.25 0.75
0.3125 0.3125 0.9375
0.328125 0.328125 0.984375
0.33203125 0.33203125 0.99609375
0.3330078125 0.3330078125 0.9990234375
0.3332519531 0.3332519531 0.9997558594
0.3333129883 0.3333129883 0.9999389648
0.3333282471 0.3333282471 0.9999847412
0.3333320618 0.3333320618 0.9999961853
Energy Deficit Thermal Cell
Dark Hemisphere Budget
0.3333333333 0.3333333333 1
0.6667
Units
2.0000
Building the Dynamic-Atmosphere Energy-Transport Model
50.0000% 50.0000%
0 0 0
0.25 0.25 0.75
0.3125 0.3125 0.9375
Dark Hemisphere
Thermal Radiation
Loss to Space (50% of
50% lost)
Surface Return Loop
from Dark to Lit
Hemisphere (50% of
50% Returned)
Radiant Energy
Exiting to Space
(Units)
Final Dark Side
Thermal Radiant
Energy Lost to Space
Atmospheric Energy
Returned to the Lit Side
Space Outgoing
Radiation Balance
Dark Hemisphere
Thermal Radiation
Loss to Space (50% of
50% lost)
Surface Return Loop
from Dark to Lit
Hemisphere (50% of
50% Returned)
Radiant Energy
Exiting to Space
(Units)
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,1
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,
,C
,
,
,
,1
,6
,B
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I!"$!".3/
$!(?").3/
)I!"$!".3#3/
'#'"#!)I!".3#3'/
?".4/
0.328125 0.328125 0.984375
0.33203125 0.33203125 0.99609375
0.3330078125 0.3330078125 0.9990234375
0.3332519531 0.3332519531 0.9997558594
0.3333129883 0.3333129883 0.9999389648
0.3333282471 0.3333282471 0.9999847412
0.3333320618 0.3333320618 0.9999961853
0.3333333333 0.3333333333 1
0.6667
Units
2.0000
Final Dark Side
Thermal Radiant
Energy Lost to Space
Atmospheric Energy
Returned to the Lit Side
Space Outgoing
Radiation Balance
"' , ,66 1.33
)&
0'

.4/
$!
.4/
$-
.4/
$
.4/
  1 6 B   C   
,
,1
,6
,B
,
,
,C
,
,
,
,1
,6
,B
0')!A !"A$"
"!("'.4/
II!".4/
I!"$!".3/
$!(?").3/
)I!"$!".3#3/
'#'"#!)I!".3#3'/
?".4/
 0.67 ,C 1.33
)"'  ,C 0.67
) 0.33 ,66 0.67
1.00 2.00 2.00
*'1+0-&%&)& *%+%>4)&',
)& "'  )"' )
G 
A1H6 AH6
GH6 G1H6
A1H6 AH6
-&0
0'
'#

$!

Global Energy
Budget
  1 6 B   C   
,
,1
,6
,B
,
,
,C
,
,
,
,1
,6
,B
0')!A !"A$"
"!("'.4/
II!".4/
I!"$!".3/
$!(?").3/
)I!"$!".3#3/
'#'"#!)I!".3#3'/
?".4/
*'1+0-&%&)& *%+%>4)&',
0
G
A
G
A
2
" 
1 'J%##!
6 $&!
B
 )"#!%!'#
C
 "#!'
 'J%#'##!
$&B+')!A !"A$"M!4"N,
"#&'#
+ "#"&%'
+A
#&7#%&"
#%!
+ "#&%'
+A
*%
',
H6'
4/3 unit
1H6'
1H6'
H6'
H6'
$&B+')!A !"A$"M!4"N,
Parameter Value Units
Diameter of Titan 5150 Km
Radius of Titan 2576 Km
Average Surface Atmospheric Pressure 146.7 Kpa
Average Surface Temperature 94 Kelvin
Average Surface Temperature -179 Celsius
83.2 Kelvin
Greenhouse Effect 10.8 Kelvin
Eclipse duration Minimal % time in eclipse
Surface gravity 1.352
Tropopause height 45.3 km
Tropospheric lapse rate 0.533 K/km
Average Solar insolation per solar orbit 14.82
Bond Albedo 0.265 A (Constant)
Average Surface Solar Insolation 5.45
Average Orbital Distance (Saturn) 1,427,000,000 Km
$&+$#$.>''/,
Expected Te
m/s2
W/m2
W/m2
Source
[10] Solar System Small Worlds Fact Sheet.
[11] Methane Sea of Titan
[11] Methane Sea of Titan
[11] Methane Sea of Titan
[11] Methane Sea of Titan
[8] The early faint sun paradox
[8] The early faint sun paradox
[12] Titan Occulations NASA JPL WebGeocalc
[10] Solar System Small Worlds Fact Sheet.
[13] Saturn Fact Sheet
[14] The Global Energy Balance of Titan
From Irradiance [13] and Albedo [14]
[13] Saturn Fact Sheet
[2] Mapping of Titan's tropopause and surface temperatures from
Voyager IRIS spectra.
[2] Mapping of Titan's tropopause and surface temperatures from
Voyager IRIS spectra.
'
!7),,71,!!*,
!71,#$
!71,#$
!71,#$
!71,#$
7(,(&7(,7C,$#'"?
7(,(&7(,7C,$#'"?
$9'5  @&-
!7),,71,!!*,
!7),,1'*
7,7,1,$-&0#$
*!.!71/ &.71/
!7),,71,'*,
('7,F!7,@,711,""#$<""'
'#!"'#!>",
('7,F!7,@,711,""#$<""'
'#!"'#!>",
Hypothetical Circulation Type
5.446 5.446 99.0
5.446 2.723 83.2
$&+$!"-&'#$!"'#  !">''!$,
Incoming Solar
Radiant Energy
(W/m2)
Lit Hemisphere
Outgoing Thermal
Radiant Energy
(W/m2)
Lit Hemisphere
Surface
Temperature
(Kelvin)
No Atmosphere, No Solar Day,
Vacuum Titan
No Circulation Static Atmosphere
Titan
0.000 0 49.5 N/A
2.723 83.2 83.2 2.723
$&+$!"-&'#$!"'#  !">''!$,
Dark Hemisphere
Outgoing Thermal
Radiant Energy
(W/m2)
Dark Hemisphere
Surface
Temperature
(Kelvin)
Global Average
Surface
Temperature
(Kelvin)
Hemisphere Average
Outgoing Thermal
Radiant Energy
(W/m2)
! ! F ('
5.45 ,CA , ACB
B,1 ,CA 127.15 AB
H!1
*%
A0
:'

A0
:'
Metric S-B Sigma Kelvin
2.723 5.67E-08 83.2
4.427 5.67E-08 94.0
Titan Thermal Energy Deficit 1.704
$&C+$$&'!"!2,
Thermal Radiation
(W/m2)
Titan Average Annual Solar Insolation
(Expected Te)
Target Global Average Annual Air
Temperature (Actual Ts)
>''+>'!
'+< !
Celsius
-189.8
-179.0
10.8
$&C+$$&'!"!2,
! !
*%A0:' 236.13 ,CA
A0:' 11, ,CA
H!1
F ('
1B, A,
251.25 A1,C
*'B+$):'#>''!:'$"# !"?'$!"'. !/%)&(!'# !"$!"'./,
, 1, 6, B, , , C, , , ,
,
,
1,
6,
B,
,
,
C,
,
,
,
#.?/O,C?
PO
)&-&$!"''>''!?'$!"'$?.F/
>''!?'$?.F/
)&-&$!"'.F/
*'B+$):'#>''!:'$"# !"?'$!"'. !/%)&(!'# !"$!"'./,
, 1, 6, B, , , C, , , ,
,
,
1,
6,
B,
,
,
C,
,
,
,
#.?/O,C?
PO
)&-&$!"''>''!?'$!"'$?.F/
>''!?'$?.F/
)&-&$!"'.F/
*'B+$):'#>''!:'$"# !"?'$!"'. !/%)&(!'# !"$!"'./,
, 1, 6, B, , , C, , , ,
,
,
1,
6,
B,
,
,
C,
,
,
,
#.?/O,C?
PO
)&-&$!"''>''!?'$!"'$?.F/
>''!?'$?.F/
)&-&$!"'.F/
, 1, 6, B, , , C, , , ,
,
,
1,
6,
B,
,
,
C,
,
,
,
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60.0 70.0 80.0 90.0 100.0 110.0 120.0 130.0 140.0 150.0 160.0 170.0 180.0
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Source Discipline Astronomy
Analytics Vacuum Planet Equation
Illumination Intensity Divisor 4
Power Intensity Distribution Mode Rapid Planetary Rotation
Surface Environment Uniform whole globe
Analytical Approach Descriptive Physical Equation
Initial Conditions Starts by assuming that there is no atmosphere
Physical Process Low frequency Radiant Flux recycling
Application Treats the atmosphere as an opaque system
Appropriate Use
Critical Distinction
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Measures the external low frequency radiant flux exhaust
temperature of a planet
Applies the concept of energy balance to the top of the
atmosphere
Meteorology
Dynamic-Atmosphere Energy-Transport
2
Atmospheric Mass Motion
Two distinct hemispheres
Explanatory Mathematical Model
Starts by assuming that the planet is tidally locked
Air Motion Thermal recycling
Treats the atmosphere as a compressible mobile fluid
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Studies the internal process of solar energy capture and
atmospheric distribution
Applies the concept of energy balance to the base of
the atmosphere
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Titan: a Satellite with an Atmosphere.
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The Astrophysical Journal, 100, p.378.
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