Atmospheric Phase Screen (APS) estimation and modeling for radar interferometry Ramon Hanssen¹, Alessandro Ferretti², Marco Bianchi², Rossen Grebenitcharsky¹, Frank Kleijer¹, Ayman Elawar¹ ¹ Delft University of Technology, The Netherlands ²Tele-Rilevamento Europa, Milano, Italy 1 Fringe Workshop, 28 Nov 2 Dec 2005, Frascati, Italy
Goal Identification and validation of Atmospheric Phase Screen Present new covariance function for atmospheric signal in InSAR February 14, 2006 2
Problem description Permanent scatterers interferometry (PSI) is successfully used to measure 1. Topographic height differences 2. Relative displacements Interferometric phase contributions: TOPO + DEFO + ATMO + ORBIT + PHASE AMBIGUITIES + NOISE Necessitates identification and separation of phase contributions February 14, 2006 3
Interferometric phase decomposition Noise Topography Atmosphere Displacement Incorrect identification of phase components leads to over- /underestimation of displacement signal February 14, 2006 4
Atmospheric signal What is atmospheric signal? Turbulent mixing Vertical stratification How do we estimate it? Temporal smoothness condition TOPO DEFO ATMO NOISE Baseline dependent Y N N N/Y Temporally correlated Y Y (?) N N Spatially correlated Y Y (?) Y N Spatial correlation can be in identical: mixing signal contributions is possible! February 14, 2006 5
Basic assumptions First assumption (temporal): Signal components that are slowly varying in time are related to deformation, not atmosphere Signal components that are quickly varying in time are atmosphere, not deformation Where to draw the line? Second assumption (spatial): Signal components that are smoothly varying in space might be atmosphere Signal components that are quickly varying in space can t be atmosphere Where to draw the line? How do we check these assumptions? February 14, 2006 6
Checking the assumptions Two options: By checking the stochastic behavior of the estimated APS, and comparing this to theoretical models By evaluating the observed APS with atmosphereonly interferograms (tandems over flat area) February 14, 2006 7
Atmospheric variability 8 100x100 km atmospheric interferograms, for varying weather conditions Very different weather situations, but similar in a stochastic sense February 14, 2006 8
Corresponding Power spectral density Shifted to match Regime 1 (rel. rough) Regime 2 (rel. smooth) 100 km 10 km 1 km 100 m 100 km 10 km 1 km 100 m February 14, 2006 9
Scaling effects The radar observes effectively integrated values of 3D and 2D turbulence 2D turbulence ~100 km Planetary boundary layer 3D turbulence <5 km February 14, 2006 10
Corresponding Power spectral density Shifted to match Regime 1 (rel. rough) Regime 2 (rel. smooth) 100 km 10 km 1 km 100 m 100 km 10 km 1 km 100 m Up to a constant offset, the spectral representations (scaling) of the atmospheric signal is identical One order of magnitude variation possible! February 14, 2006 11 Need for tailor-made, tunable covariance function / variogram, to account for weather conditions
A Matérn class covariance function for atmospheric signal Spectral 2 P( ω) = Φ ω + α Spatial = P α f r β 1 e r C( r) = πφ + r e α β 1 f Γ( β )sin π 2 α = 2πα, ω = 2πf ω representation (PSD) 2 β / 2 ω f f 2 + α 2 β / 2 f representation (CVF) Function characterized by 3 parameters αω r mm 2 10 6 10 4 10 2 10 0 10-2 10-4 10-6 10-8 Matérn class includes the Gaussian and exponential covariance functions as special cases Fit between empirical signal and PSD of analytical Matérn covariance function regim e 8/3 regim e 5/3 Analytical PSD 10-2 10-1 10 0 10 1 10 2 10 3 cycle/km February 14, 2006 12
Power Spectral Density mm 2 Effects of Matérn parameters on PSD and CVF Changing 10 5 10 0 10-5 10-10 Φ 10-2 10-1 10 0 10 1 10 2 10 3 0 cycle/km A B C D E F G H Changing β Changing alpha 7 x 104 Covariance function mm 2 6 5 4 3 2 1 0 A B C D E F G H -1 0 5 10 15 20 25 30 35 40 45 50 kilometers February 14, 2006 13
Atmospheric tandem interferograms sampled at PS locations, followed by interpolation using 3 covariance functions Model validation O R IG IN A L D A T A 600 [m m ] New model - predicted signal 600 New model - differences w.r.t. data 600 10 590 595 10 590 0 570 585-5 5 560 580 0 575 230-10 235-5 565 2 580 0 570-2 240 245 250 255 260 265 270 560-4 230 275 Gauss model - predicted signal 600 570 590 5 580 10 240 245 250 255 260 265 270 275 Gauss model - differences w.r.t. data 600 590 235 590 2 580 0 570-2 5 560-1 0 580 0 570 555 230 235 240 New model Gauss model Treuhaft, Lanyi model 245 250 255 260 min max -9.93 7.72 265 270 275 mean 0.07-5 560 std 1.31 230 600-10 235 240 245 250 255 260 265 270 275-13.50 12.73 0.06 1.54 February 14, 2006 8.16 0.06 1.35 600 10 5 580 235 240 245 250 255 260 265 270 275 Phenomenological model - differences w.r.t. data 590 2 580 0 570-2 0 570-9.91-4 230 Phenomenological model - predicted signal 590 560-5 560 230-10 235 240 245 250 255 260 265 270 275 560 230-4 235 240 245 250 255 260 265 WEATHER TYPE A: UNITS [mm] 14 270 275
Stochastic comparison PS-APS and Tandem APS (55 acquisitions) Scaling behavior comparable Order of magnitude difference, due to Nugget effect, (phase noise interpreted as APS)? APS filter too smooth for small distances? Trends still in PS-APS? February 14, 2006 15
Validating PS-APS with atmosphere-only tandems PS analysis of 55 images, APS is estimated 10 acquisitions were part of a tandem-pair Computing atmosphere in tandem pair Comparison of PS-APS with tandem-aps ifg Assumptions: Trends are largely eliminated Some features of the PS acquisition are prominent in tandem interferograms February 14, 2006 16
Color range: 6 cm Color range: 2 cm February 14, 2006 17
Color range: 6 cm Color range: 2 cm February 14, 2006 18
Color range: 3.5 cm Color range: 2 cm February 14, 2006 19
Color range: 7 cm Color range: 2 cm February 14, 2006 20
Color range: 1 cm Color range: 2 cm February 14, 2006 21
Color range: 4 cm Color range: 2 cm February 14, 2006 22
Color range: 1.5 cm Color range: 2 cm February 14, 2006 23
Color range: 1.2 cm Color range: 2 cm February 14, 2006 24
Color range: 2 cm Color range: 2 cm February 14, 2006 25
Color range: 3 cm Color range: 2 cm February 14, 2006 26
Conclusions New (Matérn class) covariance function for atmospheric signal proposed Validation of PS results possible using 1. Systematic checking tandem APS 2. Stochastic validation Fine-tuning of APS estimation still possible Variance component estimation algorithms need to be developed to estimate atmospheric power February 14, 2006 27