1. Modeling of spectral fine-structure in GOME spectra Rutger van Deelen Otto Hasekamp Jochen Landgraf KNMI November 29, 2006

2. 2 Measured GOME spectra solar irradiance spectrum Earth radiance spectrum

3. 3 The GOME reflectivity spectrum

4. 4 1. absorption bands spectral fine-structure

5. 5 The GOME reflectivity spectrum 1. absorption bands 2. Ring effect 3. Doppler shift spectral fine-structure <1nm

6. 6 Rotational Raman scattering Cabannes 96 % elastic Raman 4 % inelastic AIR (N 2, O 2 ) Raman

7. 7 The Ring effect

8. 8

9. 9 Complication with reference solar spectra KuruczChance & Spurr

10. 10 The origin of the shift v = 6.9 km s -1 v = 0 solar measurement earthshine measurement Earth Sun 0.01 nm

11. 11 The shift between the solar and the earthshine spectrum pixnr pix Earth pix sun shift sun-Earth 693 389.9478 389.9585 0.0107 nm 694 390.0575 390.0682 0.0107 nm : : : : 740 395.0995 395.1112 0.0117 nm : : : : 784 399.9164 390.9290 0.0126 nm 785 400.0258 400.0384 0.0126 nm

12. 12 The interpolation error

13. 13 An improved method Common method Interpolate GOME solar spectrum onto Earth grid Take ratio Fit interpolation error correction and Ring effect correction (using reference solar spectrum)

14. 14 An improved method Common method Interpolate GOME solar spectrum onto Earth grid Take ratio Fit interpolation error correction and Ring effect correction (using reference solar spectrum) Improved method Retrieve solar spectrum on fine grid from the GOME solar spectrum Use as input for modeling of Earth radiance spectra (for sampling on Earth wavelength grid and for Ring effect) Reconstructed solar spectrum on fine grid

15. 15 The forward model: GOME solar spectrum 1 pixel Slit-averaging and sampling

16. 16 The forward model: GOME solar spectrum 1 pixel All-in-one: Instrument response function Slit-averaging and sampling

17. 17 The forward model: GOME earth spectrum 1 pixel Atmospheric radiative transfer, slit-averaging and sampling solar earthshine

18. 18 The forward model: GOME earth spectrum 1 pixel All-in-one: system response function Atmospheric radiative transfer, slit-averaging and sampling solar earthshine

19. 19 The forward model: 1 pixel

20. 20 The forward model M << N

21. 21 Retrieval of a solar spectrum on a fine grid from the GOME solar measurement The inverse of underdetermined problem: solution of minimum length (Menke, 1989) Forward model:

22. 22 The retrieved solar spectrum is a smooth version of the true solar spectrum x ml null- space part

23. 23 Data set: two orbits 807021658103031 fit albedo clear sky land

24. 24 Mean residual 121 clear sky above land 25

25. The undersampling problem of GOME Specifications of GOME: slit-fwhm=0.17 nm pixelwidth=0.12 nm 1.4 pixels/fwhm GOME pixel-width is too course: Reconstruction of incident solar spectrum on fine grid contains undersampling errors

26. 26 Determining the undersampling error A Model GOME solar spectrum Retrieve solar spectrum on fine grid Input for GOME earthshine spectrum B Use true solar spectrum for GOME earthshine spectrum

27. 27 Determining the undersampling error A Model GOME solar spectrum Retrieve solar spectrum on fine grid Input for GOME earthshine spectrum B Use true solar spectrum for GOME earthshine spectrum

28. 28 Retrieval of a solar spectrum from the combination of a GOME earthshine and the GOME solar measurement The inverse for underdetermined problem: solution of minimum length (Menke, 1989) Forward model:

29. 29 The inversion retrieval from combination of GOME earthshine and solar measurement x ml null- space part

30. 30 The inversion (before) retrieval from GOME solar measurement x ml null- space part

31. 31 Data set: two orbits 807021658103031 Fit albedo

32. 32 Mean residual 120 24 clear sky above land

33. 33 Mean residual (before) 121 25 clear sky above land

34. 34 Conclusion A higher degree of accuracy can be reached with our method No interpolation error No reference solar spectrum required Ring effect taken into account in a consistent way Two approaches: retrieve solar spectrum on fine grid from GOME solar spectrum: undersampling error retrieve from combination of GOME Earth and solar spectrum: ~ GOME noise 0.1%

35. Thank you for your attention www.sron.nl/~rutgervd

36. 36 Residual over ocean

37. 37 chkurnewkur GOME grid 1 cm -1 grid GOME Simulated solar spectrum with two different solar spectra chkurnewkur difference with GOME

38. 38 Simulated Earth radiance spectrum for two different solar spectra

39. 39 Interpolation error versus undersampling error

40. 40 The retrieved solar spectrum is a smooth version of the true solar spectrum A = GK G = K T (KK T ) -1 x true = A x true + (I-A) x true x ml null-space part