1. School of Earth and Environment Institute of Geophysics and Tectonics Robust corrections for topographically- correlated atmospheric noise in InSAR data from large deforming regions By David Bekaert Andy Hooper, Tim Wright and Richard Walters

2. School of Earth and Environment Why a tropospheric correction for InSAR? Tectonic Over 9 months 100 km cm -1013.5 To extract smaller deformation signals

3. School of Earth and Environment To extract smaller deformation signals Tropospheric delays can reach up to 15 cm With the tropospheric delay a superposition of -Short wavelength turbulent component -Topography correlated component -Long wavelength component Troposphere 1 interferogram (ti –tj) Tectonic Over 9 months 100 km cm -1013.5 Why a tropospheric correction for InSAR?

4. School of Earth and Environment Auxiliary information (e.g.): Limitations GPS Weather models Spectrometer data Station distribution Accuracy and resolution Cloud cover and temporal sampling Tropospheric corrections for an interferogram

5. School of Earth and Environment Auxiliary information (e.g.): Limitations GPS Weather models Spectrometer data Interferometric phase Linear estimation (non-deforming region or band filtering) Station distribution Accuracy and resolution Cloud cover and temporal sampling Assumes a laterally uniform troposphere isolines Tropospheric corrections for an interferogram

6. School of Earth and Environment A linear correction can work in small regions Interferogram Tropo GPS InSAR and GPS data property of IGN Linear est isolines A laterally uniform troposphere

7. School of Earth and Environment However Spatial variation of troposphere est: Spectrometer & Linear isolines + + - + A linear correction can work in small regions A spatially varying troposphere Topography

8. School of Earth and Environment Allowing for spatial variation Interferogram (Δ ɸ ) Why not estimate a linear function locally? -9.75 rad 9.97 A spatially varying troposphere

9. School of Earth and Environment -9.75 rad 9.97 A spatially varying troposphere Why not estimate a linear function locally? Does not work as: Const is also spatially-varying and cannot be estimated from original phase! Interferogram (Δ ɸ )

10. School of Earth and Environment -9.75 rad 9.97 We propose a power-law relationship that can be estimated locally A spatially varying troposphere Why not estimate a linear function locally? Does not work as: Const is also spatially-varying and cannot be estimated from original phase! Interferogram (Δ ɸ )

11. School of Earth and Environment With h 0 the lowest height at which the relative tropospheric delays ~0 7-14 km from balloon sounding Sounding data provided by the University of Wyoming Allowing for spatial variation

12. School of Earth and Environment Allowing for spatial variation With h 0 the lowest height at which the relative tropospheric delays ~0 7-14 km from balloon sounding With α a power-law describing the decay of the tropospheric delay 1.3-2 from balloon sounding data Allowing for spatial variation Sounding data provided by the University of Wyoming

13. School of Earth and Environment Power-law example -9.75 rad 9.97 Interferogram (Δ ɸ )

14. School of Earth and Environment Power-law example -9.75 rad 9.97 Band filtered: phase (Δ ɸ band ) & topography (h 0 -h) α band (Y. Lin et al., 2010, G 3 ) for a linear approach Interferogram (Δ ɸ )

15. School of Earth and Environment Power-law example Band filtered: phase (Δ ɸ band ) & topography (h 0 -h) α band (Y. Lin et al., 2010, G 3 ) for a linear approach

16. School of Earth and Environment Power-law example Band filtered: phase (Δ ɸ band ) & topography (h 0 -h) α band For each window: estimate K spatial (Y. Lin et al., 2010, G 3 ) for a linear approach Anti-correlated!

17. School of Earth and Environment Power-law example Band filtered: phase (Δ ɸ band ) & topography (h 0 -h) α band For each window: estimate K spatial (Y. Lin et al., 2010, G 3 ) for a linear approach Anti-correlated!

18. School of Earth and Environment Original phase (Δ ɸ ) Power-law example Band filtered: phase (Δ ɸ band ) & topography (h 0 -h) α band Tropo variability (K spatial ) rad/m α -1.1e -6 9.8e -5

19. School of Earth and Environment Original phase (Δ ɸ ) Power-law example Band filtered: phase (Δ ɸ band ) & topography (h-h 0 ) α band Tropo variability (K spatial ) Topography (h 0 -h) α -1.1e -6 9.8e -5 rad/m α -9.75 rad 9.97 Power-law est (Δ ɸ tropo ) 4.7e 4 2.4e 5 1/m α

20. School of Earth and Environment Allowing for spatial variation -9.75 rad 9.97 Original phase (Δ ɸ ) Power-law est (Δ ɸ tropo ) Spectrometer est (Δ ɸ tropo ) Power-law example

21. School of Earth and Environment Regions: El Hierro (Canary Island) -GPS -Weather model -Uniform correction -Non-uniform correction Guerrero (Mexico) -MERIS spectrometer -Weather model -Uniform correction -Non-uniform correction Case study regions

22. School of Earth and Environment -11.2 rad 10.7 Interferograms (original) El Hierro

23. School of Earth and Environment WRF (weather model) El Hierro -11.2 rad 10.7 Interferograms (original)

24. School of Earth and Environment WRF (weather model) El Hierro -11.2 rad 10.7 Interferograms (original)

25. School of Earth and Environment WRF (weather model) Linear (uniform) El Hierro -11.2 rad 10.7 Interferograms (original)

26. School of Earth and Environment WRF (weather model) Linear (uniform) Power-law (spatial var) El Hierro -11.2 rad 10.7 Interferograms (original)

27. School of Earth and Environment El Hierro quantification ERA-I run at 75 km resolution WRF run at 3 km resolution

28. School of Earth and Environment MERIS Mexico -9.75 rad 9.97

29. School of Earth and Environment MERIS Clouds Mexico -9.75 rad 9.97

30. School of Earth and Environment MERISERA-I MERISERA-I Mexico -9.75 rad 9.97 (Weather model)

31. School of Earth and Environment MERISERA-I MERISERA-I Misfit near coast Mexico -9.75 rad 9.97 (Weather model)

32. School of Earth and Environment MERISERA-I Linear MERISERA-I Linear Mexico -9.75 rad 9.97 (Weather model)

33. School of Earth and Environment MERISERA-I Linear MERISERA-I Linear Mexico -9.75 rad 9.97 (Weather model)

34. School of Earth and Environment MERISERA-I Linear Power-law MERISERA-I Linear Power-law Mexico -9.75 rad 9.97 (Weather model)

35. School of Earth and Environment MERISERA-I Linear Power-law MERISERA-I Linear Power-law Mexico -9.75 rad 9.97 (Weather model)

36. School of Earth and Environment MERISERA-I Linear Power-law Mexico techniques compared: profile AA’

37. School of Earth and Environment MERIS accuracy (Z. Li et al., 2006) Mexico quantification

38. School of Earth and Environment Fixing a reference at the ‘relative’ top of the troposphere allows us to deal with spatially-varying tropospheric delays. Band filtering can be used to separate tectonic and tropospheric components of the delay in a single interferogram A simple power-law relationship does a reasonable job of modelling the topographically-correlated part of the tropospheric delay. Results compare well with weather models, GPS and spectrometer correction methods. Unlike a linear correction, it is capable of capturing long-wavelength spatial variation of the troposphere. Summary/Conclusions Toolbox with presented techniques will be made available to the community