CO 2 retrievals from IR sounding measurements and its influence on temperature retrievals By

1. 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?

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

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

4. -0.34 +0.59 +0.28 -0.33 +1.36 -0.38 -1.17 +0.27 -1.71 +0.77 -0.27 Flask Inversion Errors in Retrieved Flux (GtC/yr/region)

5. July Column CO2 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. Emission Spectroscopy Linearize around some a priori state xa: This provides a linear relation with kernels or weighting functions K:

9. 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

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 High noise Low 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. HIRS HIRS AIRS AIRS Singular values for TOVS/AIRS (4ppmv/correlated) i i li li ds ds H H li li ds ds H H 1 1 0.44011 1.4027 0.6630 0.16226 0.78465 0.1277 3.04587 10.8022 0.99150 0.90270 3.4394 1.6807 2 2 0.10856 0.3331 0.0999 0.01165 0.07590 0.0085 1.45140 4.7688 0.95788 0.67810 2.2847 0.8177 3 3 0.06558 0.1011 0.0101 0.00428 0.00734 0.0031 0.81144 1.0198 0.50980 0.39702 0.5143 0.3649 4 4 0.03169 0.0436 0.0019 0.00100 0.00137 0.0007 0.39950 0.7621 0.36742 0.13763 0.3304 0.1068 Total Total 0.7751 0.17939 0.86941 0.1401 2.89061 2.21119 6.6158 3.0410 Singular values for TOVS/AIRS (4ppmv/uncorrelated)

16. 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 Total 1.4072 2.30055 3.98153 11.1655 Singular values for TOVS/AIRS (10 ppmv)

17. Influence on Temperature?

18. CO2 and temperature Retrieved simultaneously Regionally varying CO2 specified Engelen, Denning and Stephens, GRL 2001

19. 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.

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 measurementsanalyzed 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)

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