Propagation delays in InSAR

1. Propagation delays in InSAR GE 167 - California Institute of Technology, 2013

2. Propagation delays in InSAR TerraSAR-X CosmoSkyMed Envisat ERS-1/2 RadarSat Sentinels Kollias et al, 2007, BAMS

3. An example... - One month temporal baseline (no deformation) - Topography <=> Atmospheric delay

4. An example...

5. An example...

6. An example...

7. Differential delay First pass Second Pass

8. First pass Second Pass Differential delay

9. A bit of theory Air Refractivity: Refraction index : Total Pressure : Temperature : Cloud Water Content : Electron Density : Frequency : Constants

10. A bit of theory Air Refractivity: : Total Pressure : Temperature : Cloud Water Content : Electron Density Real-life range : Frequency - Small perturbation - Very hard to estimate : Constants Hanssen, 2001

11. A bit of theory Air Refractivity: : Total Pressure : Temperature : Cloud Water Content : Electron Density Real-life range : Frequency - Small perturbation - Very hard to estimate : Constants Hanssen, 2001

12. A bit of theory Air Refractivity: : Total Pressure : Temperature - Dispersive effect - Long wavelength perturbations (~100 km) - Effect is small in C-band (too short wavelength) - Significant in L-band : Cloud Water Content : Electron Density : Frequency : Constants

13. Ionospheric perturbation Shen et al., 2009, Nat. Geosci.

14. Ionospheric perturbation “clean” Interferogram Azimuth offsets Phase gradient - Estimate the azimuth offset - Compute the phase gradient - Extract the proportionality factor - Correct the interferogram Problem: Only works where there is no deformation along azimuth Ionospheric phase screen Interferogram Raucoules & de Michele, 2010. IEEE GRSL

15. A bit of theory Air Refractivity: : Total Pressure : Temperature Ionosphere (not today) : Cloud Water Content : Electron Density Troposphere (today) : Frequency : Constants

16. A bit of theory Air Refractivity: and Nadir Delay: : Dry Air Pressure : Total Pressure : Temperature : Specific Constant for dray air and vapor : Cloud Water Content : Gravitation : Electron Density : Partial pressure in Water Vapor : Frequency : Constants

17. A bit of theory Delay along the Line-Of-Sight wrt. reference altitude: : Dry Air Pressure : Total Pressure : Temperature : Specific Constant for dray air and vapor : Cloud Water Content : Gravitation : Electron Density : Partial pressure in Water Vapor : Frequency : Constants

18. A bit of theory Delay along the Line-Of-Sight wrt. reference altitude: If I had a pressure profile...

19. A bit of theory Delay along the Line-Of-Sight wrt. reference altitude: ... and a temperature profile...

20. A bit of theory Delay along the Line-Of-Sight wrt. reference altitude: ... and a Water Vapor Partial Pressure profile...

21. A bit of theory Delay along the Line-Of-Sight wrt. reference altitude: ... I could compute the total delay:

22. A bit of theory Delay along the Line-Of-Sight wrt. reference altitude: ? ... I could compute the total delay: But usually, I don’t have all those things (actually, never...).

23. Do we really need to correct for that delay? Can’t we just filter it, or whatever?

24. Do we really need to correct for that delay? Can’t we just filter it, or whatever? Yes, you can...

25. Do we really need to correct for that delay? Can’t we just filter it, or whatever? Yes, you can... ... but you should not.

26. Single interferograms Mw 7.7 Depth ~ 100 km

27. Time filtering, then...? Stacking:

28. Time filtering, then...? Stacking: If we have independent interferograms, with random noise (in time)

29. Time filtering, then...? Stacking: If we have independent interferograms, with random noise (in time) Doin et al, 2009, J. App. Geophy.

30. Time filtering, then...? Stacking: If we have independent interferograms, with random noise (in time) Now that we can do better, still no!!!

31. How to correct then? Turbulent Delay Stratified Tropospheric Delay + ==> Stacking or Time Series - Random in Space and Time - Numerous Acquisitions to average or smooth the signal

32. 2 Separating the delay Turbulent Delay Stratified Tropospheric Delay + ==> Stacking or Time Series

33. Separating the delay Turbulent Delay Stratified Tropospheric Delay + ==> Stacking or Time Series Semivariogram: Covariance:

34. Separating the delay Turbulent Delay Stratified Tropospheric Delay + ==> Stacking or Time Series

35. Empirical Correction Estimating a phase/elevation relationship

36. Empirical Methods Estimating a phase/elevation relationship Joint inversion model/orbit/troposphere Cavalie et al, 2008; Jolivet et al., 2012

37. Empirical Methods Estimating a phase/elevation relationship Joint inversion model/orbit/troposphere Cavalie et al, 2008; Jolivet et al., 2012

38. Empirical Methods Estimating a phase/elevation relationship Multi-scale approach Lin et al, 2010

39. Empirical Methods - Deformation/Topography correlation

40. Prediction Methods - Most methods focus on constructing vertical profiles of delay Available Data: GPS zenith delays Local Atmospheric data Multi-spectral imagery systems Global Re-analysis Available Methods: Interpolation (2D / 3D / Ray tracing) Meso-scale modeling

41. Prediction Methods Local Atmospheric Data - Data from a meteorological station - Radio sounding profile Delacourt et al. 1998, GRL

42. Prediction Methods GPS zenith delays Onn & Zebker, 2006, JGR

43. Prediction Methods GPS zenith delays Onn & Zebker, 2006, JGR

44. Prediction Methods Multispectral Images • Multi-spectral imagery system onboard Envisat: • - Passive system (captures the electro-magnetic field reflected by the ground surface) • - 15 Bands • - Combination of band 14 and 15 gives the Integrated Precipitable Water Vapor • - Integrated Wet delay and and : Specific Constant for dray air and vapor : Ratio of molecular masses of water vapor and dry air : Constants Puyssegur et al, 2007, JGR; Li et al, 2012, GJI

45. Prediction Methods Multispectral Images Good: Does not only correct for stratified features Predicts turbulence Bad: Does not work for night-time acquisitions Does not work if dense cloud cover Li et al, 2012, GJI

46. Interferogram MM5 Modeling Prediction Methods Meso-Scale Modeling Goal: Reproduce the turbulences using fine modeling Puyssegur et al, 2007, JGR

47. Prediction Methods Available Data: GPS zenith delays Local Atmospheric data Multi-spectral imagery systems Global Re-analysis These data are not always available This is fine over SoCal, but Tibet is another story ERA-Interim Dee et al, 2011 - ECMWF atmospheric model - Global ~75 km grid - 1989-... - 4 solutions a day at 0 am, 6 am, 12 pm and 6 pm - Altitude, temperature and water vapor partial pressure at 37 pressure levels (surface to 50 km alt.)

48. Computing Delay Maps from GAM 1 - Computing delay functions

49. Computing Delay Maps from GAM 1 - Computing delay functions 2 - Spatial bilinear interpolation and spline interpolation for altitude

50. Computing Delay Maps from GAM One month temporal baseline == no deformation expected