1. CO 2 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 CO 2 have on temperature retrievals?

2. The Global Carbon Cycle Atmosphere 750 + 3/yr Ocean 38,000 Plants and Soils 2000 Fossil Fuel ~90 ~120 6 ~90

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

4. Flask 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

5. July Column CO 2 with Gaussian Noise

6. Column Errors and Flux Errors Even a poor column measurement everywhere adds information relative to sparse flasks (assumes perfect transport)

7. 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

8. Linearize around some a priori state x a : This provides a linear relation with kernels or weighting functions K: Emission Spectroscopy

9. 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 K T 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 Information Content?

10. Using Gaussian statistics

11. Information Theory 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.

12. Simple Example Low noise High noise Same retrieval error but very different inform- ation content

13. Information content vs. degrees of freedom 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.

14. 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

15. HIRSAIRS i i dsds H i dsds H 10.440110.162260.12773.045870.902701.6807 20.108560.011650.00851.451400.678100.8177 30.065580.004280.00310.811440.397020.3649 40.031690.001000.00070.399500.137630.1068 Total 0.179390.1401 2.211193.0410 HIRSAIRS i i dsds H i dsds H 11.40270.66300.7846510.80220.991503.4394 20.33310.09990.075904.76880.957882.2847 30.10110.01010.007341.01980.509800.5143 40.04360.00190.001370.76210.367420.3304 Total 0.77510.86941 2.890616.6158 Singular values for TOVS/AIRS (4ppmv/correlated) Singular values for TOVS/AIRS (4ppmv/uncorrelated)

16. HIRSAIRS i i dsds H i dsds H 13.50680.92481.8665527.00530.998634.7562 20.83270.40950.3799911.92190.993013.5806 30.25230.06010.044672.54950.866671.4534 40.10900.01170.008521.90540.784031.1056 Total 1.40722.30055 3.9815311.1655 Singular values for TOVS/AIRS (10 ppmv)

17. Influence on Temperature?

18. CO 2 and temperature Retrieved simultaneously Regionally varying CO 2 specified Engelen, Denning and Stephens, GRL 2001

19. Conclusions We have shown that the retrieval of CO 2 column concentrations from high spectral resolution infrared sounders looks promising. These retrievals have high enough accuracy to be useful for CO 2 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 CO 2 concentrations, the HIRS radiances have a clearer signal.

20. 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)

21. 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 CO 2 (ongoing) The assumption of fixed CO 2 introduces undesirable errors in the retrieval of temperature (approaching 0.8K locally in some regions)

22. 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:

23. 1. Setting Requirements: Inverse Modeling Air Parcel Sources Sinks transport (model) (solve for) concentration transport sources and sinks (observe) Sample