topographic correction for alos palsar interferometry · topographic correction for alos palsar...

3020 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 48, NO. 7, JULY 2010

Topographic Correction for ALOSPALSAR Interferometry

Sergey Samsonov

Abstract—L-band synthetic aperture radar (SAR) interferome-try is very successful for mapping ground deformation in denselyvegetated regions. However, due to its larger wavelength, thecapacity to detect slow deformation over a short period of time islimited. Stacking and small baseline subset (SBAS) techniques areroutinely used to produce time series of deformation and averagedeformation rates by reducing the contribution of topographic andatmospheric noise. For large sets of images that are presently avail-able from C-band European Remote Sensing Satellites (ERS-1/2)and Environmental Satellite (ENVISAT), the standard stackingand SBAS algorithms are accurate. However, the same algorithmsare often inaccurate when used for processing of interferogramsfrom L-band Advanced Land Observing Satellite Phased Arraytype L-band SAR (ALOS PALSAR). This happens because only alimited number of interferograms is acquired and also because oflarge spatial baselines often correlated with the time of acquisition.In this paper two techniques are suggested that can be used forremoving the residual topographic component from stacking andSBAS results, thereby increasing their accuracy.

Index Terms—Advanced Land Observing Satellite (ALOS)Phased-Array-type L-band synthetic aperture radar (SAR)(PALSAR), interferometry, SAR interferometry (InSAR), smallbaseline subset (SBAS) topographic correction, stacking.

I. INTRODUCTION

D IFFERENTIAL synthetic aperture radar (SAR) inter-ferometry (DInSAR) is a powerful tool for measuring

ground deformation on a large spatial scale with high resolutionand high accuracy [14], [15]. Presently, DInSAR is routinelyused for mapping seismic and volcanic deformation [11], [12]as well as deformation caused by various anthropogenic sourcessuch as mining and extraction of groundwater, oil, and gas[7], [8]. There are a few factors limiting the accuracy ofinterferometry, such as temporal and spatial decorrelation, andatmospheric and topographic noise. The decorrelation effectis perhaps the largest limitation, which has been partiallyovercome by developing a permanent scatterer (PS) technique[4], [6]. By using the PS approach, it is possible to calculatelinear deformation rates and even to reconstruct nonlinear timeseries of each PS [5]. This technique works best when a densenetwork of PSs is found, which is not often the case for many

Manuscript received May 12, 2009; revised July 21, 2009, November 11,2009, and January 15, 2010. Date of publication April 8, 2010; date ofcurrent version June 23, 2010. This work was supported by the Foundationfor Research, Science and Technology, New Zealand.

The author is with GNS Science, Lower Hutt 5010, New Zealand, and alsowith Department of Earth Sciences, the University of Western Ontario, London,ON N6A5B7, Canada (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TGRS.2010.2043739

regions. In areas of moderate to good coherence, it is possible toapply stacking technique [18] that produces mean deformationrates, and also small baseline subset (SBAS) technique [1] thatproduces nonlinear time series as well as linear (average) de-formation rates. The SBAS technique works only on pixels thatare coherent above a chosen threshold on all interferograms.

When a large set of SAR images for a single region isavailable, it is almost always possible to pick the best co-herent interferometric pairs that have small spatial baseline,thereby reducing sensitivity to residual topography. This is of-ten the case for the C-band European Remote Sensing Satellites(ERS-1/2) and the Environmental Satellite (ENVISAT), whichhave been operational for many years and have produced largeamounts of data since the early 1990s. Unfortunately, in someregions such as those covered by dense vegetation or snow,C-band interferometry is unsuccessful. The only option thenis to use L-band data from the only presently operationalsensor, Phased-Array-type L-band SAR (PALSAR), onboardthe Advanced Land Observing Satellite (ALOS) [16].

In our previous work [17], we showed that ALOS PALSARinterferometry produces excellent results in the New Zealandenvironment where the standard C-band approach is mostlyunsuccessful. Interferograms are collected over a time span oftwo–three years with spatial baselines of up to 2–3 km. Dueto the relatively small number of images available and becauseof good coherence, it is often impossible and unnecessary toapply PS techniques. On the other hand, stacking and SBAStechniques are very successful for calculating the time seriesof deformation and for producing linear (average) deformationrates. Both these techniques remove random noise, thereforeincreasing the sensitivity of the measurements. However, in[17], it was shown that the residual topographic noise cannotbe considered random in case of ALOS PALSAR, and it isbelieved to be the single largest source of error limiting theinterpretation of results (Fig. 1). In this paper, sensitivity ofthe stacking and SBAS results to the residual topography isexplained, and methodology for removing this signal by cal-culating a topographic correction is suggested.

II. METHODOLOGY

A. Stacking

A stack of K interferograms is calculated for each pixel bythe following equation:

Vobs =∑

φkobs∑tk

(1)

0196-2892/$26.00 © 2010 IEEE

SAMSONOV: TOPOGRAPHIC CORRECTION FOR ALOS PALSAR INTERFEROMETRY 3021

Fig. 1. Differential interferogram (path 325, HH) January 13–February 28,2007, Bperp = 826 m. Full color cycle (purple to pink) corresponds to about12 cm of line-of-sight displacements. Topographic component was removedwith 90-m SRTM DEM. Residual topographic noise is clearly observed.

where Vobs is the average deformation rate measured inradians/year and φk

obs is the observed phase of the kth interfer-ogram (measured in radians) calculated over a time period tk

(measured in years). It is generally assumed that φkobs consists

of deformation φkdef , topographic φk

topo, and atmospheric φkatm

components, i.e.,

φkobs = φk

def + φktopo + φk

atm. (2)

Here, it is assumed that the atmospheric component alsoincludes all other small errors that are uncorrelated in time(orbital, thermal noise, and so on). By substituting (2) into (1)one gets

Vobs =∑

φkdef +

∑φk

topo +∑

φkatm∑

tk. (3)

Since the atmospheric component is uncorrelated in time, it isassumed that the quantity

∑φk

atm/∑

tk is small and thereforecan be omitted, and φk

topo can be expressed as dependent on theperpendicular baseline length

Vobs =∑

φkdef∑tk

+∑

φktopo∑tk

=∑

φkdef∑tk

− H

R sin(θ)

∑Bk

⊥∑tk

(4)

where R is the line-of-sight distance, θ is the look angle, H isthe residual topographic height, and Bk

perp is the perpendicularbaseline of the kth interferogram.

Fig. 2. Temporal variation of perpendicular baseline relative to first acquisi-tion for descending path 628 and ascending path 325. Nonrandom dependenceis clearly observed. A similar pattern is observed for many ascending anddescending paths of the ALOS satellite over New Zealand.

TABLE IALOS PALSAR DIFFERENTIAL INTERFEROGRAMS FROM DESCENDING

PATH 628 FRAME 4400 (HH POLARIZATION). LAST LINE SHOWS

CUMULATIVE PERPENDICULAR BASELINE B⊥ AND TIMESPAN t

From this equation, it is clear that the total topographic con-tribution depends on

∑Bk

perp and is negligible only when thisterm is close to zero. However, for most ALOS PALSAR tracks,this value is presently large and therefore cannot be omitted.At the same time, it is desirable to remove the topographiccomponent in order to improve the accuracy of the calculatedstack.

In [13], it was proposed to remove this term by calculating atopographic correction based on dependence of the topographicphase φk

topo on perpendicular baseline Bkperp. This would be

a method of choice if variation of Bkperp is random in time.

However, in Fig. 2, it is clearly observed that the ALOSPALSAR perpendicular baselines are correlated with the timeof acquisition. For example, for a subsets of eight images frompath 325 and four images from path 628 acquired betweenFebruary 2007 and June 2008, all possible interferograms haveperpendicular baselines of the same sign, and therefore, the


Fig. 3. Area of 360 × 360 pixels (approximately 10 × 10 km) of central TVZ in New Zealand from descending path 628. Two distinctive regions of subsidenceare (top left) Tauhara and (center) Wairakei geothermal fields. Residual topographic noise is clearly observed on (a) original stack and removed from (b) correctedstack. (c) Residual topographic correction calculated with proposed technique. (a) Original stack. (b) Corrected stack. (c) Topographic correction.

absolute value of∑

Bkperp is large. In this case of correlated

baselines, it is clear that the topographic component φktopo of the

observed signal φkobs cannot be separated from the deformation

component φkdef , and therefore, standard approach cannot be

applied.In order to estimate and remove the topographic component

in the case when perpendicular baselines correlate with the timeof acquisition, it is proposed to apply the following techniqueconsisting of four steps.

Step 1) Calculate initial stack using (1).Step 2) For each pixel of each differential interferogram k,

calculate the deviation of observed phase from thespatial average calculated in a neighborhood win-dow φk

topo = φkobs − φ̄k

obs. The residual term φktopo

contains mostly topographic contribution becausethe deformation contribution and spatially correlatedatmospheric noise averaged over some spatial win-dow are removed.

Step 3) Apply linear regression between the calculated termφk

topo and Bkperp in order to calculate residual topo-

graphic ratio H/R sin(θ).Step 4) Calculate the corrected stack applying topographic

correction according to the following equation:

∑φk

def∑tk

=

∑(φk

obs − HR sin(θ)B

kperp

)∑

tk. (5)

The size of the neighborhood window in Step 2) dependson the spatial characteristics of the topographic errors. In orderfor the technique to produce correct results, the spatial windowneeds to be larger than the correlated features of the topographicnoise but smaller than the spatial extent of deformation signal.

B. SBAS

In case of correlated baselines, the methodology proposedearlier can be successfully applied for removing residual topo-graphic noise in the SBAS processing. For example, in [10],

Fig. 4. Dependence of residual interferometric phase on perpendicular base-line for points of various magnitude of residual topographic errors. Values ofresidual topography and corresponding residual velocity are calculated.

a similar methodology of isolating uncorrelated noise fromcorrelated signal was applied in PS processing. However, ifonly a partial correlation is observed, it is possible to solvefor velocities and residual topographic error simultaneouslyutilizing standard SBAS approach.

In matrix form, the standard SBAS method is formulated inthe following form:

AV = Φobs (6)

where matrix A has dimensions of K lines by N − 1 columns(N is the number of SAR images) and created in the followingway. If a kth interferogram spans the time represented by thecolumn n, then the ak

n term is equal to the time interval betweenthe consequent images, otherwise, it is zero. Vector V consistsof n − 1 velocities that are to be calculated, and vector Φobs

consists of k observed phases φkobs.

Since φkobs consists of both deformation φk

def and topographicφk

topo components, (6) can be modified in order to solve for both


Fig. 5. Area of 360 × 360 pixels (approximately 10 × 10 km) of central TVZ in New Zealand from descending path 628. (a)–(f) Cumulative displacementscalculated between July 15, 2007, and the date shown with modified SBAS technique proposed in this paper. Two distinctive regions of subsidence are (top left)Tauhara and (center) Wairakei geothermal fields. Linear deformation rates were calculated with (g) standard SBAS and with (h) modified SBAS proposed inthis paper. (i) Estimated residual topographic correction. (a) March 1, 2008. (b) June 1, 2008. (c) April 16, 2008. (d) August 17, 2008. (e) September 1, 2008.(f) January 17, 2009. (g) Linear deformation rates. (h) Corrected linear deformation rates. (i) Topographic correction.

velocities and topographic errors simultaneously by addingto matrix A the column with perpendicular baselines and anunknown term at the end of the vector V that represent residualtopographic ratio.

For example, let us assume that there are three SAR imagesacquired at times t1, t2, and t3, and three interferograms werecreated, spanning time intervals t2 − t1, t3 − t2, and t3 − t1

with perpendicular baselines b21, b32, and b31. In this case, theSBAS formulation looks like this

⎛⎝

t2 − t1 0 b21

0 t3 − t2 b32

t2 − t1 t3 − t2 b31

⎞⎠

⎛⎝

vt1

vt2H

sin(θ)

⎞⎠ =

⎛⎝

φt1,t2

φt2,t3

φt1,t3

⎞⎠ . (7)


The solution of this problem can be found by applyingsingular value decomposition (SVD) to matrix A and by solvingthe inverse problem V = A−1Φobs, where A−1 is the pseudoin-verse of matrix A calculated with SVD.

III. RESULTS

Both techniques described above were used for processingof ALOS PALSAR acquired over Taupo Volcanic Zone (TVZ)in New Zealand. The TVZ is an active tectonic area withdimensions of approximately 50 (NW–SE) by 350 (SW–NE)km located in the central North Island of New Zealand andcurrently experiencing active continental extension related tothe subduction of the Pacific plate beneath the Australian plate.In the past, a few studies have been performed in the TVZusing C-band InSAR. In [8], it was shown that conventionaldifferential interferometry produces limited results because ofsignificant decorrelation caused by dense vegetation. Even PSanalysis was not particularly successful because of the lack of adense network of PSs [9]. Since late 2006, the ALOS PALSARsensor has been acquiring data in the L-band. However, becauseof the large size of the area, only a few SAR images are avail-able for each path, and at the same time, most interferogramshave very large perpendicular baselines that partially correlatewith the time of acquisition (Fig. 2).

Nine ALOS PALSAR images from descending path 628frame 4400 (Fine Mode Single Polarisation and Fine BeamDouble Polarisation, HH polarization) acquired betweenJuly 15, 2007 and January 17, 2009 were used in this study.The data were acquired in raw format, and SAR and DInSARprocessing was performed with GAMMA software [19]. Dur-ing the interferometric processing, all images were coregisteredto a single image acquired on July 15, 2007, and 19 interfero-grams with perpendicular baseline of less than 2500 m werecalculated (Table I). The Shuttle Radar Topography Mission(SRTM) 90-m resolution digital elevation model (DEM) wasused to remove the topographic phase, and interferograms wereunwrapped using the Minimum Cost Flow algorithm [2].

In general, all interferograms were coherent above the cho-sen threshold of 0.35 almost everywhere within the regionof interest. Because of the large L-band wavelength and theshort time span of the interferograms, the unwrapping processwas fast, and no errors were observed. A small subregionof 360 × 360 pixels (approximately 10 × 10 km) coveringWairakei and Tauhara geothermal fields was extracted fromeach interferogram for stacking.

The stacking algorithm described in the previous sectionwith a spatial window of 32 × 32 pixels was applied inorder to calculate the average deformation rates corrected fortopographic noise. The sensitivity to topography is apparent forthis particular stack because of

∑Bk

⊥ being large, about 6 km.The results of stacking are shown on Fig. 3(a) and (b) beforeand after applying the topographic correction. The residualtopographic noise is clearly visible on the first image andsignificantly reduced on the second. The values of topographicnoise were converted to errors in elevation, and these results areshown in Fig. 3(c). Most errors range from about −3 to +3 mwhich are slightly better than the 7-m reported accuracy of the

Fig. 6. Cumulative displacements calculated with standard and modifiedSBAS for (center of subsidence) Tauhara, (largest subsidence) Wairakei, and[red spot in (i)] area of largest topographic error. Values were averaged in a10 × 10 pixel window.

SRTM DEM [3], but a few larger errors (up to 25 m) were alsoobserved. The dependence of residual interferometric phase onperpendicular baseline for a few points with various magnitudeof residual topography is shown in Fig. 4. In this figure, absolutevalues of residual topography and the corresponding residualvelocity vary from about 13 m (1.3 cm/year) to about 0.5 m(0.01 cm/year). Large values of residual topography are rare;however, values of residual velocity can be significant if aset of interferograms with a large value of

∑Bk

⊥ is usedinstead.

In order to demonstrate the second technique, the proposedSBAS processing was performed that simultaneously solved fordeformation rates and residual topographic error. Examples ofthe time series are shown in Fig. 5(a)–(f), and linear defor-mation rates calculated from SBAS time series are shown inFig. 5(h), and the calculated residual topographic error is shownin Fig. 5(i). For comparison purposes, linear deformation ratescalculated without applying correction are shown in Fig. 5(g).A few areas with significant topographic errors are clearlyidentified.

For the two regions of fastest subsidence at Tauhara andWairakei as well as for the area of the largest topographicerror [red spot in Fig. 5(g)], uncorrected and corrected timeseries with the proposed technique (Fig. 6) were produced. Theresidual topographic noise is apparent in the uncorrected seriesand mostly removed from the corrected series. The temporalpattern of the residual topographic noise is correlated with thetemporal pattern of the perpendicular baselines (Fig 2).

In order to show the limitations of the first correction tech-nique, the calculated linear deformation rates are presentedhere for the ascending path 325 that covers not only theTauhara–Wairakei area (in the bottom-left corner) but also amuch larger area of the TVZ, including the Ohaaki geothermalfield (in the center). The linear deformation rates were cal-culated with SBAS technique without topographic correctionFig. 7(a), with the first topographic correction Fig. 7(b), andthe second topographic correction Fig. 7(c). In this case, thespatial extent of the topographic noise for some areas is larger


Fig. 7. Larger area of approximately 36 × 36 km of central TVZ in New Zealand from ascending path 325. Linear deformation rates calculated with (a) standardSBAS and (c) modified SBAS, and (d) estimated topographic correction. In (b), the first topographic correction is applied. Subsidence at [center (c)] Ohaakigeothermal field and at [bottom-left corner (c)] Tauhara–Wairakei geothermal system is clearly observed. (a) Linear deformation rates. (b) Corrected (1) Lineardeformation rates. (c) Corrected (2) Linear deformation rates. (d) Topographic correction.

than (or comparable with) the spatial extent of the deformationsignal. Therefore, if the spatial window for the first topographiccorrection is chosen to be smaller than the correlated features of

the topographic noise, the correction is incomplete. However, ifthe spatial window for the first topographic correction is chosento be larger than the correlated features of the topographic


TABLE IISTANDARD DEVIATION OF LINEAR DEFORMATION

RATES PRESENTED IN FIG. 7

noise, the correction would not be able to distinguish betweentopographic and deformation components. An error analysiswas performed that estimated the standard deviation from themean value (Table II) of the results shown in Fig. 7. Thestandard deviation of results without applying any type ofcorrection was about 1.91 cm/year. This value decreased to1.46 cm/year when the first type of correction was applied(using 32 × 32 pixel window) and to 1.18 cm/year when thesecond type of correction was applied (simultaneous inversionfor deformation rates and topographic errors).

The nature of the residual topographic noise is not absolutelyclear at this time and needs to be studied further. It is believedthat at least, partially, the residual topographic noise is causedby either changes in land cover since the time of acquisitionof C-band SRTM data that was used for DEM generation or bythe different wave propagation and interaction of C- and L-bandSAR with vegetation and soil.

IV. CONCLUSION

Two useful methods were presented in this paper for re-moving the residual topographic noise from stack and SBASprocessing of differential interferograms when the baselinelengths within the set of interferograms are large and vari-able. This approach is particularly applicable to L-band ALOSPALSAR data because of good coherence in vegetated regions,smaller number of images presently available, lower sensitivityto slow deformation, and the observed temporal variation ofspatial baselines. Because of good coherence and large wave-length (about 0.23 m), unwrapping is successful in most cases,which significantly simplifies further processing. Due to thelarge L-band wavelength, the sensitivity to small deformation(slow deformation over a short period of time) is limited,and interpretation of single interferograms is complicated bythe presence of atmospheric and topographic noise. Therefore,stacking and SBAS processing are the methods of choicein most interferometric studies based on ALOS PALSARdata.

It was demonstrated here that because of the particular tem-poral pattern of perpendicular baselines, the standard stackingapproach is not accurate, and topographic correction needs tobe applied. If only a small set of interferogram is availableand perpendicular baselines are perfectly correlated with thetime of acquisition, such as for a subset of eight images frompath 325 and four images from path 628, acquired betweenFebruary 2007 and June 2008, the standard topographic-correction technique cannot be applied [13] because it is notpossible to separate the deformation and topographic compo-nents of the observed signal. The technique proposed herewill produce better results because it separates the spatiallycorrelated deformation and atmospheric components from the

uncorrelated residual topographic component and uses the latterto calculate the topographic correction. However, this approachcan be applied only if the spatial extent of correlated noiseis smaller than the spatial extent of deformation signal. Exactparameters may depend on the magnitude of deformation andneed to be carefully evaluated.

The same topographic-correction technique can be appliedin SBAS processing if the correlation between perpendicularbaselines and the time of acquisition is perfect. In case ofpartial correlation, it is recommended to apply the modifiedSBAS technique proposed here that simultaneously solves fordeformation rates and the residual topographic error. Examplesof both techniques were presented here and showed valuableimprovement to the final results.

ACKNOWLEDGMENT

The author would like to thank J. Beavan and N. Fournierfor their valuable recommendations regarding the manuscript.The ALOS PALSAR data in this paper was used with the per-mission of the Japan Aerospace Exploration Agency (JAXA),Ministry of Economy Trade and Industry (METI), and the Com-monwealth of Australia (Geoscience Australia) (“the Com-monwealth”). JAXA, METI, and the Commonwealth have notevaluated the data as altered and incorporated within this paperand therefore give no warranty regarding its accuracy, com-pleteness, currency, or suitability for any particular purpose.The images were plotted with GMT software.

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Sergey Samsonov received the Ph.D. degree in geo-physics and environmental science from the Uni-versity of Western Ontario, London, ON, Canada,in 2007.

He is currently a Remote Sensing Scientist withGNS Science, Lower Hutt, New Zealand, and anAdjunct Professor with the Department of Earth Sci-ences, University of Western Ontario. His researchinterests are synthetic aperture radar (SAR), InSARand Pol-InSAR, signal processing, geodesy, andseismology.

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