PSI Precision, accuracy and validation aspects Urs Wegmüller Charles Werner Gamma Remote Sensing AG, Gümligen, Switzerland, wegmuller@gamma-rs.ch
Contents Aim is to obtain a deeper understanding of what PSI can do, where it works as well as limitations and errors - PSI Rational, limitations of 2D continuous interferometry - PSI processing strategy - Nature of PS interferometric characteristics and identification of PS - Precision vs Accuracy - Systematic errors - Atmospheric effects Wet and Dry Delay, filtering - Phase unwrapping PSI temperal and spatial unwrapping - Reference point central role in processing, selection and phase filtering - Time series potential and limitations 2
SAR Radar Image Formation Z European Space Agency ERS-1 v Launch: July, 1991 --> 2000 X SAR Frequency: C-Band 5.3 GHz, 5.6 cm Bandwidth: 15.55 MHz Incidence angle: 23.5 degrees n Sla r0 Pixels: 4m range, 7.9m slant range an tr h θ ge 0 Orbit: 800 km, 35 day repeat im z A h ut Image swath: 100 km Y 2v l 2v cosθ fd = = λ λ Spacecraft travels along-track and is sidelooking recording echoes as a function of slant range Successive echoes are recorded coherently (phase) and processed as an ensemble 3-dimensional scene is projected into 2 dimensions (slant range, azimuth) Range sphere is surface of constant range Doppler cone: Surface of constant Doppler. Intersection with ground is a hyperbola 3
SAR Coherent Speckle Backscatter phase is determined by the coherent sum of contributions from all elemental scatterers in the resolution element. The phase recorded at the radar includes a propagation phase delay, a function of the slant range ρ and wavelength λ. 4π φ = ρ λ 4
SAR Interferometric Repeat Track Geometry B γ B ρ22 = ρ12 + B 2 2 Bρ1 cos γ α ρ B cos γ = B B θ ρ1 φ = ρ2 2πp ρ λ φm = φ mod 2π T Path and phase difference Angle Sensitivity: Interferometrically measured phase φ 4π 4π = B sin γ = B θ λ λ Slant Range The difference in the slant range vectors ρ is one component in offset between SLC images used to form the interferogram. Other components in the shift between SLCs include azimuth shift due to the exact lines processed 5
Differential Interferometric Phase φ=φtopo φdispl φ atmos φ noise 4π 4π 4π φ= B r displ r atmos φnoise λ λ λ The interferometric phase is linearly proportional to the path length but is wrapped (modulo 2PI). This gives radar interferometry very high sensitivity to deformation. The deformation signal has the same magnitude as the atmospheric phase Hence a strategy to obtain accurate estimates of the deformation phase include: 1. Accurate modeling of noise and signal 2. Numerous data acquisitions 3. Selection of wavelength, resolution, and geometry to maximize SNR 6
Interferometric Phase Noise Sources of Phase noise in the interferometric signal include: 1. Thermal noise from the environment and electronics ~ktb 2. Interferometric decorrelation due to movement of scatterers, baseline related decorrelation (spectral shift), track rotation 3. Atmospheric propagation delay (non-dispersive, essentially same for all frequencies) 4. Ionospheric propagation effects dispersive delay, Faraday rotation of the polarization 5. DEM errors (insufficient resolution) 6. Baseline error 7. Phase unwrapping errors 7
PSI Processing Approach 1. Find a set of points in the image that are phase stable for at least a period of time in the scene. If interferograms with large baselines are used for analysis, these points must be dominated by a single scatterer 2. Estimate corrections to the height and a nominal linear velocity to assist with unwrapping the phase. Subtracting phase contributions from topography, atmosphere, or any apriori knowledge of the deformation. 3. Phase unwrapping can occur in either space or time or both dimensions. To unwrap the phase, phase differences must be below PI between points or the multiple of 2PI cannot be estimated. 4. Once the phase has been unwrapped, partition the phase between velocity, atmosphere, topographic phase, and noise 8
Precision and accuracy Precision The precision relates to the separation of values that can be distinguished in a measurement Accuracy The accuracy of a measurements relates to how well the measurement corresponds to the truth 9
Precision in DINSAR and PSI context Precision of SAR phase measurement is a very small fraction of a phase cycle precision < 0.1mm Interferometric phase difference partial decorrelation of signal reduced coherence (0.9) higher phase noise reduced precision (e.g. 0.3 radian precision 1.3mm); this value can be improved by spatial averaging Considering the atmospheric path delay effects as an uncertainty of the measurement results in a phase standard deviations of the order of 1.5 radian precision 7mm A PSI result is based on many observations. So the estimation of an average deformation rate based on 50 observations over 5 years results in a precision < 1mm/year 10
Precision in DINSAR and PSI context (cont.) This precision of the linear rate estimation can be calculated with or without subtracting atmospheric phase screens typical precisions as small as 0.1mm/year if atmospheric phase screens are subtracted and precisions around 0.4mm/year if atmospheric phase screens are included in the statistical uncertainty estimation Precision of linear rates at outer boundary of a result and next to spatial gaps is lower. The precision of a specific observation in the time series is again different. There the conservative assumption is that it corresponds to the uncertainty of the single observation (precision of 7mm). Assuming that some of the atmosphere can be modeled results in lower values (e.g. 3mm). In any case it is significantly larger than just the coherence related signal noise unless we are sure that we can reliably model the atmospheric delay. Precision of specific observation is at beginning and end of series (and next to longer gaps in temporal coverage) is lower. 11
Accuracy in PSI context The accuracy of a measurements relates to how well the measurement corresponds to the truth. The precision of the measurement is one factor that relates to the accuracy (but often not the main one). Other relevant factors potentially affecting the accuracy of the deformation rate include: - phase unwrapping errors (see below) - overall tilts of the result (see below) - errors related to subtracted atmospheric phase screens (see below) 12
Estimation of accuracy of a PSI result Based on the data itself the precision can be estimated statistically. Based on the result the temporal and spatial consistence can be checked (e.g. to detect and discard outliers). During the TF project special processing was conducted to crosscompare results obtained by the different OSP and to compare the results against in-situ observations (see contributions / reports by Michele Crossetto). Validation with in-situ measurements can be done. In practice this is often not trivial due to non-identical locations and observation times. 13
Systematic errors (1) Large scale tilts There are causes to have large scale phase trends (e.g. phase ramps) across the image (related to SAR processing, slight errors in baseline model, ). A typical approach to scope with these is to assume that the terrain is not tilting at large scale. If that is a correct assumption then such tilts are correctly removed. Nevertheless, if the area shows a real large scale tilting (e.g. significant subsidence near the left border of the processed section) then the processing possibly removes this trend. This problem is most critical in the case of tectonic movements which are at scales larger than the size of the typical area processed. Be aware of this possibility; consider this in selection of area to be processed (ideally stable part around moving area) 14
Systematic errors (2) Underestimation of deformation rates Some people postulate a general underestimation of deformation rates in PSI results. There are clear limitations to the applicability of PSI in the case of fast deformations. Slower moving targets may be more easily identified as PS than moving targets, especially than non-uniformly moving targets. In the validation experiments we did not really identify such a general underestimation. 15
Atmospheric component (1) Scope and Approach Atmospheric path delay heterogeneity causes a phase component not related to the deformation. - Temporally and spatially variable - Altitude dependent - Fronts and waves between layers - Diurnal effects and sensitivity to surface heating This atmospheric phase is spatially quite smooth. A typical approach is to estimate the uniform movement, identify then for each pair the residual phase not modeled by the uniform motion model, to spatially filter this and to subtract it as atmospheric phase. This approach permits to significantly reduce the noise on the time series considered. A limitation of this approach is that non-uniform motion at intermediate and large spatial scale is may also be removed from the result. 16
Valais, Switzerland 20080923 20090925 Temperatures -3 to +15C Obtain limits on phase stability over 3 days High Coherence Altitude: 2500m
Short-Time Diff. Interferograms, Valais 20080924 55 interferograms, t =15 min/interferogram, starting time: 11:45 Delay close to the antenna affects entire range line 1 rad=1.39 mm @ 17.2 GHz 18
Reconstructed Time Series, Valais 20080924 55 interferograms, covering13.5 hrs Starting time: 11:45 1cycle = 8.72mm @17.2 GHz 19
Atmospheric component (2) Height dependent atmospheric component The atmospheric path delay has a term relating to the dry atmosphere and a part relating to the water vapor. Depending on the topographic height of the terrain there is more or less atmosphere and water vapor above a site height dependent atmospheric component Simple linear model can be used to approximate height dependent atmospheric component modeling and compensation Possible errors: - height dependent atmospheric component may be interpreted as deformation -deformation that correlates with terrain height may be reduced by correction of height dependent atmospheric component 20
Phase unwrapping (1) Phase unwrapping is the most challenging step in SAR interferometry as well as in PSI Limits applicability Possible source for errors An unwrapping (ambiguity) error results in an offset of 2.8 cm (at Cband). Spatial or temporal steps in the deformation values (not rates) of 2.8 cm may be cause by an unwrapping error. For spatially and temporally smooth motion patterns and low deformation values between observations there is a high spatiotemporal consistency of the result high reliability of result, robustness of processing 21
Phase unwrapping (2) Higher probability for unwrapping errors in case of: - Faster deformation / higher deformation gradients - Coarse spatial coverage (areas with few points) - Non-uniform motion - Coarse temporal sampling (e.g. gap between 2001 and 2003) - Noisy data Characteristics of unwrapping error: - Single point, single date - Single point dates after a specific date - Entire section (=several to many points, e.g. patch or isolated region with points) 22
Reference point PSI result is relative to a spatial reference point Reference point can be changed - to transform average deformation rate result subtract reference point rate from all other values - subtract reference point values from all other point s time series 23
Time series potential and limitations PSI time series potential? What is included in a PSI time series? - terms included : linear model phase + noise + non-linear model What is not included in a PSI time series? - terms excluded : - subtracted topographic phase - atmospheric phase - orbital phase - residual linear or quadratic phase trends ( see also tilts) PSI time series provides some quality information (on reliability of average rate estimate / detection of potential unwrapping errors) -PSI time series provides some information on non-uniform motion 24
Non-uniform motion potential and limitations Potential of PSI with respect to non-uniform movements - Very localized, low amplitude ( good potential with PSI) - Intermediate to large scale, low amplitude (separation from atmospheric phase is critical as overlapping spatial scale) - Intermediate to large scale, high amplitude (PSI processing very challenging, standard processing may fail gap in result) - Sensors with good spatial resolution and good temporal coverage improve potential of PSI for non-uniform motion monitoring 25