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 soundingmeasurements (contrast HIRS/AIRS)?

What effect does the assumption of fixed CO2 have on temperature retrievals?

The Global Carbon CycleThe Global Carbon Cycle

Atmosphere

750 + 3/yr

Ocean

38,000

Plants and Soils

2000

Fossil Fuel

~90

~120

~120

6

~90

Flask Sampling Networks•GlobalView 2000•Weekly samples•Very accurate measurements (~ 0.2 ppm)*•Surface CO2

Flask InversionFlask Inversion

Errors in Retrieved Flux (GtC/yr/region)

+0.28

+0.27

-0.34

+0.59

-0.33+1.36

-1.71 +0.77-0.27

-1.17-0.38

July Column CO2 with Gaussian Noise

Column Errors and Flux Errors

Mean Absolute Inversion Error Per Region

0

0.1

0.2

0.3

0.4

0.5

0 1 2 3 4

instrument error (ppm)

(GtC

/yr)

Column Means

Flasks @ 1 ppm

• Even a poor column measurement everywhere adds information relative to sparse flasks

(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

)())(()(

0

xFdzz

ezTBI

zxk

)()( aa

a xxx

FxFI

0

)()()()( dzzxzKxKxxx

FxFI a

aa

Linearize around some a priori state xa:

This provides a linear relation with kernels or weighting functions K:

Emission Spectroscopy

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

1/ 2 1/ 2y aK S KS

Information Content?

11/ 2/ 2

1 1( ) exp ( ) ( )

2(2 )T

a a ana

P x x x S x xS

1 1 1Tx y aS K S K S

11 1 1 1( )T Ty a y a ax K S K S K S y S x

Using Gaussian statistics

Information Theory

SH ( ( )) ( ( | ))

1 1ln ln

2 2a x

S P x S P x y

S S

1nd tr( )x aS S

Information content of a measurement: the change in entropy going from the prior state to the retrieved state.

Degrees of freedom for signal of a measurement: number of elements in the state vector that can be observed given the measurement noise.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

X

P(X)

0

0.05

0.1

0.15

0.2

0.25

0.3

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

X

P(X)

1sd tr( )T

x yS K S K

Simple Example

y x

2

S

2

2 0.235

dfs

4

0.2

0.94

H 2.0

5

4

a

x

y

2a

2

x

S

y

2 = 0.235

dfs = 0.

=

06

H

0.25

=

= 0 4

4

4

.0

Low noise High noise

Same retrievalerror but verydifferent inform-ation content

Information content vs. degrees of freedom

0

1

2

3

4

5

6

Acc

urac

y

1 2 3 4 5 6 7

Variable

0

1

2

3

4

5

6

Acc

urac

y

1 2 3 4 5 6 7

Variable

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.

Maximizing the degrees of freedom will maximize the number of elements in the state vector that are actually observed.

HIRS information content

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.60

10

20

30

40

Hei

ght (

km)

Singular Values :

1.4027

0.3331

0.1011

0.0436

y = 0.5 %

a

AIRS information content

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.60

10

20

30

40

Hei

ght (

km)

Singular Values :

10.8022

4.7688

1.0198

0.7621

y = 0.5 %

a

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

  HIRS AIRS

i i ds H i 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

Total   0.17939 0.1401   2.21119 3.0410

  HIRS AIRS

i i ds H i 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

Total   0.7751 0.86941   2.89061 6.6158

Singular values for TOVS/AIRS (4ppmv/correlated)

Singular values for TOVS/AIRS (4ppmv/uncorrelated)

  HIRS AIRS

i i ds H i 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

Total   1.4072 2.30055   3.98153 11.1655

Singular values for TOVS/AIRS (10 ppmv)

Influence on Temperature?

CO2 and temperatureRetrieved simultaneously

Regionally varying

CO2 specified

Engelen, Denning and Stephens, GRL2001

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:

21min N

1. Setting Requirements: Inverse Modeling1. Setting Requirements: Inverse Modeling

Air Parcel Air Parcel

Air Parcel

Sources Sinks

transport transport

SinksSourcesAdvectiont

C

(model) (solve for)

concentration transport sources and sinks(observe)

Sample Sample