CO2 retrievals from IR sounding measurements and
its influence on temperature retrievals
By
Graeme L Stephens and Richard Engelen
Pose two questions:
What information is contained in IR sounding
measurements (contrast HIRS/AIRS)?
What effect does the assumption of fixed CO2 have on
temperature retrievals?
The Global Carbon Cycle
Atmosphere
~90
750 + 3/yr
~120
~120
~90
6
Ocean
Plants and Soils
Fossil Fuel
38,000
2000
Flask Sampling Networks
•GlobalView 2000
•Weekly samples
•Very accurate measurements (~ 0.2 ppm)*
•Surface CO2
Flask Inversion
Errors in Retrieved Flux
(GtC/yr/region)
-0.34
+1.36
+0.28
+0.59
-0.38
+0.27 -1.17
-1.71
+0.77
-0.27
-0.33
July Column CO2 with Gaussian
Noise
Column Errors and Flux Errors
Mean Absolute Inversion Error Per Region
• Even a poor column
measurement everywhere adds
information relative to sparse
flasks
0.5
0.4
(GtC/yr)
0.3
0.2
ColumnMeans
0.1
Flasks@1 ppm
0
0
1
2
3
4
instrument error (ppm)
(assumes perfect transport)
Candidate global CO2 measurement approaches
+ emission spectroscopy (AIRS, CRiS, TESS, ATOVS)
capability ‘today’
+ absorption spectroscopy (Siamarchy, OCO?,’carbosat’)
capability of ~2004/5
aircraft demonstration ~2003
+ laser absorption spectroscopy (pulsed, cw..)
capability ~2010+
aircraft demonstration ~2003
Emission Spectroscopy

I   B (T ( z ))
0
e
 k x ( z )
z
dz  F ( x )
Linearize around some a priori state xa:
F
I  F ( xa ) 
( x  xa )
xa
This provides a linear relation with kernels
or weighting functions K:

F
I  F ( xa ) 
( x  xa )  Kx   K ( z )x( z )dz
xa
0
Information Content?
Twomey’s Method:
• How much information is contained in the
observations?
• How many independent pieces of information can we
retrieve from those observations?
• Expressed as eigenvectors/eigenvalues of C=K KT
Rodgers’ Method:
• How much information can we obtain from the
observations given our prior knowledge?
• How many pieces of independent information can we
obtain from the observations given our prior
knowledge?
•Information in the Shannon form and
K  S 1/y 2 KSa1/ 2
Using Gaussian statistics
P( x) 
1
(2 )n / 2
 1

T 1
exp  ( x  xa ) Sa ( x  xa ) 
1/ 2
 2

Sa
Sx1  K T S y1K  Sa1
x  K S K  S
T
1
y

1 1
a
( K T S y1 y  Sa1 xa )
Information Theory
HS  S ( P( x))  S ( P( x | y))
1
1
 ln Sa  ln S x
2
2
0.14
0.3
0.12
0.25
0.2
0.08
P(X)
P(X)
0.1
Information content of
a measurement: the
change in entropy going
from the prior state to
the retrieved state.
0.06
0.15
0.1
0.04
0.05
0.02
0
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
X
X
1
y
ds  tr(Sx K S K )
T
d n  tr( S x S a1 )
Degrees of freedom for
signal of a measurement:
number of elements in
the state vector that
can be observed given
the measurement noise.
Simple Example
y  x 
 4
 = 0.25
  0.25
 =4
2
a
2
a
2
y
2
y
High noise
Low noise
  0.235
2
x
dfs  0.94
H S  2.04
Same retrieval
error but very
different information content
 x2 = 0.235
dfs = 0.06
HS = 0.044
Information content vs. degrees of
freedom
5
4
Accuracy
The same value of information
content can be used to measure
one variable to very high
accuracy or to measure several
variables at lower accuracy.
6
3
2
1
0
1
2
3
4
5
6
7
Variable
6
5
Accuracy
Maximizing the degrees of
freedom will maximize the
number of elements in the
state vector that are actually
observed.
4
3
2
1
0
1
2
3
4
Variable
5
6
7
HIRS information content
40
Singular Values :
sy = 0.5 %
1.4027
0.3331
30
sa = 4 ppmv
4.7688
0.1011
1.0198
0.0436
0.7621
10
sy = 0.5 %
10.8022
sa = 4 ppmv
20
0
-0.6
Singular Values :
Height (km)
Height (km)
30
AIRS information content
40
20
10
-0.4
-0.2
0.0
0.2
0.4
0.6 0
-0.6
-0.4
-0.2
0.0
0.2
0.4
First 4 singular vectors with their corresponding singular
values for HIRS (left panel) and AIRS (right panel).
Measurement error was set to 0.5 % and a priori error
was set to 4 ppmv
0.6
Singular values for TOVS/AIRS (4ppmv/correlated)
HIRS
AIRS
i
li
ds
H
li
ds
H
1
1.4027
0.6630
0.78465
10.8022
0.99150
3.4394
2
0.3331
0.0999
0.07590
4.7688
0.95788
2.2847
3
0.1011
0.0101
0.00734
1.0198
0.50980
0.5143
4
0.0436
0.0019
0.00137
0.7621
0.36742
0.3304
0.7751
0.86941
2.89061
6.6158
Total
Singular values for TOVS/AIRS (4ppmv/uncorrelated)
HIRS
AIRS
i
li
ds
H
li
ds
H
1
0.44011
0.16226
0.1277
3.04587
0.90270
1.6807
2
0.10856
0.01165
0.0085
1.45140
0.67810
0.8177
3
0.06558
0.00428
0.0031
0.81144
0.39702
0.3649
4
0.03169
0.00100
0.0007
0.39950
0.13763
0.1068
0.17939
0.1401
2.21119
3.0410
Total
Singular values for TOVS/AIRS (10 ppmv)
HIRS
AIRS
i
li
ds
H
li
ds
H
1
3.5068
0.9248
1.86655
27.0053
0.99863
4.7562
2
0.8327
0.4095
0.37999
11.9219
0.99301
3.5806
3
0.2523
0.0601
0.04467
2.5495
0.86667
1.4534
4
0.1090
0.0117
0.00852
1.9054
0.78403
1.1056
1.4072
2.30055
3.98153
11.1655
Total
Influence on Temperature?
CO2 and temperature
Retrieved
simultaneously
Regionally varying
CO2 specified
Engelen, Denning
and Stephens, GRL
2001
Conclusions
• We have shown that the retrieval of CO2 column
concentrations from high spectral resolution infrared
sounders looks promising. These retrievals have high
enough accuracy to be useful for CO2 inversion studies.
• Both the HIRS singular vector and the first two AIRS
singular vectors represent a broad vertical pattern
without any vertical resolution. Only the third AIRS
singular vector adds some vertical resolution, but is
hardly significant.
•If we increase our a priori uncertainty to 10 ppmv, which
is close to the seasonal amplitude of atmospheric CO2
concentrations, the HIRS radiances have a clearer signal.
• For 10 ppmv, AIRS now has 4 significant singular
vectors, which allows the retrieval of almost 3
quantities. This can be interpreted as the retrieval of
a total column with some added vertical structure (e.g.,
2 vertical layers)
• Use of known structure functions that define the
correlation between layers, the information extracted
from IR measurements can be significantly improved.
This certainly helps in HIRS type retrievals where
information approaches the 4 ppmv level (10 ppmv
otherwise)
•When the kinds of IR measurements analyzed here
are combined with other measurement types (eg
absorption spectroscopy), then it may be possible
to extract further information about the vertical
structure of CO2 (ongoing)
• The assumption of fixed CO2 introduces
undesirable errors in the retrieval of temperature
(approaching 0.8K locally in some regions)
Result after estimating the last 2 terms (see
Twomey, pp 193-194):
Provided the system is properly scaled,
the independence of N measurements in
the presence of a relative error of
measurement |ε| is assured if the
eigenvalues (λ) meet the following
treshold:
lmin  N 
1 2
1. Setting Requirements: Inverse Modeling
transport
Sinks
Sources
Air Parcel
Air Parcel
Sample
transport
Air Parcel
C
 Advection  Sources  Sinks
t
concentration
transport
(observe)
(model)
sources and sinks
(solve for)
Sample