Principal Component Analysis of
MGS-TES Data and
Comparison with Modeling
Guo, Xin
October 7th 2004
Advisor: Yung, Yuk L.
Outline
 Mars, Mars Global Surveyor (MGS),
Thermal Emission Spectrometer (TES)
 Principal Component Analysis (PCA)
 Results of PCA on TES data
 Results of PCA on synthetic data
 Results of PCA on GCM output
 Conclusions and future work
Mars Facts
 A Martian year is 668 sols
(Martian days), 687 Earth
days
 A Martian day (sol) is 24
hours 37 minutes 22 sec
 Atmospheric gaseous
components: CO2 (95%), CO
(700ppm), H2O (100ppm), N2,
O2,O3, NO, H2, Noble Gases
 Major Aerosol Components:
Dust, Water Ice
 Atmosphere shows annual
variation and diurnal variation
Pater, I.d. and L. Jack J, Planetary Sciences. 2001,
Cambridge: Cambridge University Press.
MGS & TES
http://mars.jpl.nasa.gov/mgs/images/mgs-mons.jpg
MGS (Mars Global Surveyor)



Orbit covers almost the whole
surface of Mars
One orbiting period of MGS at
normal mapping phase is 118
minutes
At normal mapping phase, a global
mapping takes 7 sols = 3.78º Ls =
172.62 hours
http://tes.asu.edu/images/newtesimage.jpg
TES (Thermal Emission
Spectrometer)





Spatial resolution 3 km
Spectral range 200 cm-1 to 1700 cm-1
Spectral resolution 10 wavenumbers
(cm-1) or 5 wavenumbers (cm-1)
SNR around 400 at 1000 cm-1
Sample rate around 800 per second
Principal Component Analysis (PCA)
[Terminology: Meteorologists call it Empirical Orthogonal Function (EOF)
Analysis, Factor Analysis … I am trying to be a statistician here]
 Linearly transforms an original set of variables to a
substantially smaller set of uncorrelated variables
that represents most of the information in the
original set of variables
 Capture the variation of data
 1st principal component (PC1) captures the largest
variation
 2nd principal component (PC2) captures the largest
variation orthogonal to that captured by the 1st
principal component
Previous work of Huang et al.
 PC1 is associated with surface or near
surface brightness temperature
 PC2 is associated with atmospheric
variability
 Signal from surface emission (surface
or near surface temperature) is
dominant
Manipulation of Data
I obs ( )   ( ) B[Tsurf , ]e

0


I obs ( )   ( ) B[Ts , ]e
When
 1
 0 ( )
0

0




B[T ( ), ]e d
 S ( )
(nadir view), and  0  1 (thus
e  0  1   0 ( 1)
).
R '( )  I obs ( )   ( ) B[Tsurf , ]  S1 ( )   0 ( ) B[Tsurf , ]
Ignore the strong CO2 absorption band between 510 cm-1 and 810 cm-1
Apply PCA to the residual spectra.
R( )  I obs ( )   ( ) B[Tsurf , ]
PCA on TES data: MY25 Ls 30º-45º
(a) PC1 59.0% of total variance
Radiance (mW cm -1 sr-1)
20N
0
0
-1
20S
-2
0
180
400
270
800
1000
0.2
0.4
(c) SP1, Yr 2 Ls 30-45
180
Latitude
0
20S
180W
40N
0.4
18090W
270
0
0
-1
0
-2
1200
1400 cm
400
0.6
0.8
(b) water ice opacity zonal average
40N
20N
0
270
270W90
180W
180
270
(b) PC2 32.4% of total variance
0
-1
90
600
180
270
0
Ls
1400 cm
800
1000
1200
1
1.2
(d) SP2,Yr 2 Ls 30-45
20N
0
20S
180W0
90W
90
180 0
270 270W
0
180W
Ls
-2
-10.02
0
1
2
-2 0.1 -1
0 0.121
2
3
4
5
0.04
0.063
0.08
0.14
0.16
(e) dust opacity, TES retrieval, year 2 Ls 30-50(c)
 regional aerosol opacity average
(f) water ice opacity, TES retrieval, year 2 L s 30-50
40N
20N
0.3
Latitude
Latitude
90
600
40N
Latitude
0
Radiance (mW cm -1 sr-1)
(a) dust opacity zonal average
1
1
40N
0.2
0
0.1
20S
180W
0
90 0.04
90W
0.06
180
0.08 270
0.1
0
270W
0.12 0 0.14
0.16
90 0.18
0
20S
180W
180W
180
dust
water ice
20N
270
00.04
90W
0.06
90
0
0.08 1800.1
270W
0.12
270
0.14
180W
00.16
Ls
-1
PCA on TES data: MY25 Ls 90º-105º
(a) PC1 75.6% of total variance
Radiance (mW cm -1 sr-1)
Radiance (mW cm -1 sr-1)
(a) dust opacity zonal average
1
1
40N
0
20N
-1
0
-2
-3
20S
-4
0
180
400
0
600
90
800
1000
0.2
0.4
(c) SP1, Yr 2 Ls 90-105
40N
180
270
0
0
-0.5
0
-1
1200
1400 cm
400
0.6
0.8
(b) water ice opacity zonal average
40N
0
18090W
0
-1
20N
20S
180W
0.5
270
Latitude
Latitude
270
270W90
180W
180
270
(b) PC2 19.4% of total variance
90
600
180
270
0
Ls
1400 cm-1
800
1000
1200
1
1.2
(d) SP2,Yr 2 Ls 90-105
20N
0
20S
180W0
90W
90
180 0
270 270W
0
180W
Ls
-1
0
1
2
3 0.06 4
-2 0.1 -1
00.12
1
2
3
0.02
0.04
0.08
0.14
0.164

(e) water ice opacity, TES retrieval, year 2 L s 100(c)
-120
(f) dust opacity, TES retrieval, year 2 Ls 100-120
regional aerosol opacity average
40N
40N
0.4
dust
20N
20N
0.3
water ice
Latitude
Latitude
0
0.2
0
0.1
20S
180W
0
0.05
90
90W
180
0.1
0
0.15
270
270W
0.2
0
0.25
90
20S
180W
180W
0.3
180
0
270
0
90W
0.05
90
0
180
0.1
270W
270
0.15
0
180W
Ls
PCA on TES data: MY25 Ls 330º-345º
(a) dust opacity zonal average
1
Radiance (mW cm -1 sr-1)
0
20N
-1
0
-2
-3
20S
-4
0
180
400
90
180
40N
0.4
-1
0
-2
600 0.2
800
10000.4
1200
1400
0.6cm
0.8 400


(c) SP1, Yr 2 Ls 330 -345
(b) water ice opacity zonal average
40N
Latitude
0
0 -2
270
18090W
270
0
0
270W90
180W
180
270
(b) PC2 2.5% of total variance
0
-1
20N
20S
180W
Latitude
0
90
180
270
0
Ls
1400 cm
600
1000 1.2 1200
1 800
(d) SP2,Yr 2 Ls 330-345
20N
0
20S
180W0
90W
90
180 0
270 270W
0
180W
Ls
-10.02
0
0.04 1
0.06
2
0.08
-3 0.1 -2
0.12
-1
0
0.141
2 0.16

(e) dust opacity, TES retrieval, year 3 Ls 330-350
(f) water ice opacity, TES retrieval, year 3 L s 330-350
(c) regional aerosol opacity average
40N
20N
0.3
Latitude
Latitude
40N
270
Radiance (mW cm -1 sr-1)
(a) PC1 94.4% of total variance
40N
1
0.2
0
0.1
20S
180W
0
90 0.1
90W
180
0.15
0
0.2270 0.25
270W
0.3
0
0.35 90 0.4
0
20S
180W
180W
180
dust
water ice
20N
270
0
90W
0.01 90
0
270W
0.02 180 0.03 270 0.04
180W
00.05
Ls
-1
Discussion of Results
 Variability of
atmospheric dust and
water ice
 Incompleteness of the
removal of surface
emission
Smith, M.D., J.L. Bandfield, and P.R.
Christensen, Separation of atmospheric
and surface spectral features in Mars
Global Surveyor Thermal Emission
Spectrometer (TES) spectra. Journal of
Geophysical Research, 2000. 105(E4): p.
9589-9607.
Smith, M.D., Interannual variability
in TES atmospheric observations of
Mars during 1999-2003. Icarus,
2004. 167: p. 148-165.a
PCA on Synthetic Data
(b)PC2
PC213.6%
1.8% of
(b)
oftotal
total variance
variance
Radiance (mW cm -1 sr-1)
Radiance (mW cm -1 sr-1)
97.3% of total variance
(a) PC1 85.6%
0
0.5
0.2
0
 Feed the Radiation Model with temperature profile,
pressure profile, atmospheric dust mixing ratio profile,
atmospheric water ice mixing ratio profile (12 levels)
0
-0.5
-0.5
-1
400
600
800
1000
1200
-1
cm-1
1400 cm
0.2
0
-0.2
0
-0.2
0.2
400
600
(c)
(c) PC1
PC1 pattern
pattern
800
1000
1200
1400
cm-1
(d) PC2 pattern
 Generate IR radiation spectra with different
abundance of dust and water ice
2
3
3
2
1
2
1
0
0
1
0
-1
-1
 Get rid of the surface emission and CO2 absorption
band
-2
-1
0
10
20
30
40
-2
0
10
dustice
opacity
(e)(e)
water
opacity
20
30
40
30
30
40
40
(f)dust
ice opacity
(f)
opacity
0.4
0.7
0.25
0.16
0.35
0.6
0.3
0.5
0.25
0.2
0.14
0.4
0.2
0.05
0.08
 Apply PCA on data
0.15
0.12
0.1
0.1
0
0
10
10
20
20
30
30
40
40
0
0.06
0
0
10
10
20
20
PCA on GFDL Mars GCM Based Data
(b) PC2 7.6% of total variance
Radiance (mW cm -1 sr-1)
Radiance (mW cm -1 sr-1)
(a) PC1 89.7% of total variance
0
2
 Geophysical Fluid Dynamic Laboratory (GFDL)
Mars General Circulation Model (GCM)
 Spatial resolution:
6 degrees longitude, 5 degrees latitude, 20
vertical levels
 Output fields:
eight 3D fields, eleven 2D fields
 Output interval:
2 sols, 2 Martian hours
-2
-4
-6
-8
400
600
800
1000
1200
-1
1400 cm
1
0
-1
-2
-3
400
600
40N
20N
20N
0
20S
180W
90W
-1.5
270W
-1
-0.5
0
(e) water ice opacity
0.5
1
1.5
40N
20N
20N
0
90W
0.5
0
1
1.5
270W
2
180W
2.5
90W
-2
40N
20S
180W
1200
1400
cm-1
0
20S
180W
180W
Latitude
Latitude
-2
0
1000
(d) PC2 pattern
40N
Latitude
Latitude
(c) PC1 pattern
800
0
270W
-1
0
(f) dust opacity
180W
1
0
20S
180W
90W
0.4
0.6
0
0.8
270W
1
1.2
180W
1.4
1.6
Comparison between GCM and TES
[Smith 2004]
Conclusion and Future Work
 Atmospheric aerosol variability is well captured
using this method. It is independent of the retrieval.
 Better removal of surface emission would lead to
better results.
 A better radiation model (such as MODTRAN)
would improve the understanding of the roles of
various species.
 PCA is a good way to test the GCM and help to
improve it. Eventually, we would like to predict the
weather on Mars.
Acknowledgements
Xianglei Huang, Yuk Yung, Michael Smith, Run-Lie Shia, Xun
Jiang, Dave Camp for useful guidance and discussions
Oded Aharonson for the access of Martian surface emissivity
data
Mark Richardson, Shabari Basu, Michael Mischna, Jiafang Xiao
for the access of GCM outputs
The End
Thank you for listening
References









Pater, I.d. and L. Jack J, Planetary Sciences. 2001, Cambridge: Cambridge University
Press.
Albee, A.L., et al., Overview of the Mars Global Surveyor mission. Journal of Geophysical
Research, 2001. 106(E10): p. 23291-23316.
Christensen, P.R., et al., Mars Global Surveyor Thermal Emission Spectrometer
experiment: Investigation description and surface science results. Journal of Geophysical
Research, 2001. 106(E10): p. 23823-23871.
Weisberg, S., Applied Linear Regression. Second Edition ed. Wiley Series in Probability
and Mathematical Statistics, ed. V. Barnett, et al. 1985, New York: John Wiley & Sons.
Jolliffe, I.T., Principal Component Analysis. Springer Series in Statistics, ed. D. Brillinger,
et al. 1986, New York: Springer-Verlag.
Huang, X., J. Liu, and Y.L. Yung, Analysis of Thermal Emission Spectrometer data using
spectral EOF and tri-spectral methods. ICARUS, 2003. 165: p. 301-314.
Smith, M.D., J.L. Bandfield, and P.R. Christensen, Separation of atmospheric and
surface spectral features in Mars Global Surveyor Thermal Emission Spectrometer (TES)
spectra. Journal of Geophysical Research, 2000. 105(E4): p. 9589-9607.
Richardson, M.I. and R.J. Wilson, Inverstigation of the nature and stablility of the Martian
seasonal water cycle with a general circulation model. Journal of Geophysical Research,
2002. 107(E5).
Smith, M.D., Interannual variability in TES atmospheric observations of Mars during
1999-2003. Icarus, 2004. 167: p. 148-165.
Solar Longitude (Ls)
 A Martian year is
defined 360 degree of
Solar Longitude (Ls) or
Heliocentric Longitude
 Ls = 0, northern
hemisphere vernal
equinox
 1 Ls ~ 45.67 hours
Manipulation of Data
I obs ( )   ( ) B[Tsurf , ]e

0


 0 ( )
0
0


B[T ( ), ]e d
where  ( ) is the surface emissivity at frequency
surface temperature,


, Tsurf
is the
is the normal column-integrated (aerosol)
opacity,  is the cosine of the emission angle.
B[T , ] is the
Planck function, T ( ) is the temperature profile
Denote
S ( )  I obs ( )   ( ) B[Tsurf , ]

When   1 (nadir view), and  0  1 (thus e 0  1   0 ( 1) ).
Ignore the strong CO2 absorption band between 510 cm-1 and 810 cm-1
“Blue Mars”
(Michael Carrol, space artist)
Simplified Geologic Map
Christensen, 2002
Epithermal Neutrons
(Boynton et al, Science, 2002)