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

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

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 Why a tropospheric correction for InSAR?

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

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

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

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

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

School of Earth and Environment 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 )

School of Earth and Environment 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 )

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

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

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

School of Earth and Environment Power-law example 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 )

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

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!

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!

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 e -5

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 e -5 rad/m α rad 9.97 Power-law est (Δ ɸ tropo ) 4.7e 4 2.4e 5 1/m α

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

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

School of Earth and Environment rad 10.7 Interferograms (original) El Hierro

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

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

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

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

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

School of Earth and Environment MERIS Mexico rad 9.97

School of Earth and Environment MERIS Clouds Mexico rad 9.97

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

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

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

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

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

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

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

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

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