ice sheet change detection by satellite image differencing
TRANSCRIPT
Remote Sensing of Environment 114 (2010) 1353–1362
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Remote Sensing of Environment
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Ice sheet change detection by satellite image differencing
Robert A. Bindschadler a,⁎, Ted A. Scambos b, Hyeungu Choi c, Terry M. Haran b
a Hydrospheric and Biospheric Sciences Laboratory, NASA Goddard Space Flight Center, Code 614, Greenbelt, MD 20771, United Statesb National Snow and Ice Data Center, Cooperative Institute for Research in Environmental Sciences, 1540 30th Street, University of Colorado, Boulder, Boulder, CO 80309-0449, United Statesc SAIC, 4600 Powder Mill Road, Suite 400, Beltsville, Maryland 20705-2675, United States
⁎ Corresponding author. Tel.: +1 301 614 5707.E-mail address: [email protected] (R.
0034-4257/$ – see front matter © 2010 Elsevier Inc. Aldoi:10.1016/j.rse.2010.01.014
a b s t r a c t
a r t i c l e i n f oArticle history:Received 6 November 2009Received in revised form 19 January 2010Accepted 22 January 2010
Keywords:Image differencingIce sheet altimetryLandsatALIMODISSub-glacial lakes
Differencing of digital satellite image pairs highlights subtle changes in near-identical scenes of Earthsurfaces. Using the mathematical relationships relevant to photoclinometry, we examine the effectiveness ofthis method for the study of localized ice sheet surface topography changes using numerical experiments.We then test these results by differencing images of several regions in West Antarctica, including somewhere changes have previously been identified in altimeter profiles. The technique works well withcoregistered images having low noise, high radiometric sensitivity, and near-identical solar illuminationgeometry. Clouds and frosts detract from resolving surface features. The ETM+ sensor on Landsat-7, ALIsensor on EO-1, and MODIS sensor on the Aqua and Terra satellite platforms all have potential for detectinglocalized topographic changes such as shifting dunes, surface inflation and deflation features associated withsub-glacial lake fill-drain events, or grounding line changes. Availability and frequency of MODIS imagesfavor this sensor for wide application, and using it, we demonstrate both qualitative identification of changesin topography and quantitative mapping of slope and elevation changes.
A. Bindschadler).
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1. Introduction
Recent ice sheet observations have forced a radical revision of thenotion that ice sheets change only slowly. Increased ice flow activityat and near the margins (e.g., Howat et al., 2007; Rignot, 2008),changes in grounding line location (Rignot, 1998) and localizedsurface inflation and deflation (Fricker et al., 2007; Gray et al., 2005;Wingham et al., 2006) have sparked new interest inmethods to detectchanges of ice sheets on annual to sub-annual time scales.
Differencing optical images has been applied in several fields,perhaps most extensively in medical imaging (e.g., Pluim et al., 2003),astronomy (Alard & Lupton, 1998), and detection of land use changes(Singh, 1989) but to our knowledge has never been applied to icesheets. Here we demonstrate that quantitative differencing of visible-and near-infrared (VNIR) band digital satellite images of ice sheets iscapable of detecting and mapping surface slope changes in ice sheetsthat are associated with a variety of glaciologically significant events.The motivating application for this study was the detection of surfaceelevation changes from interferometric SAR observations believed tobe associated with the movement of sub-glacial water (Gray et al.,2005). The initial discoveries of these local features indicated a rapidchange in surface topography (interpreted as sub-glacial lake filling ordraining), with the change being a persistent, nearly circular shape
having a diameter of 5 to 10 km and vertical changes of up to 5 m.Similar features, though not circular in outline, were later identified insatellite laser altimetry profiles (Fricker et al., 2007). In conjunctionwith elevation change data, image differencing was considered as ameans of providing confirmation of the sign and scale of inflation anddeflation events, and a spatial context of the region of change forprofile-based elevation change measurements (Fricker et al., 2007).Acquiring repeat satellite images of the same ice sheet region andsubtracting them is conceptually simple and a heretofore underap-preciated method to detect subtle slope changes in ice sheets.
We investigate this method in terms of the general theory and theanticipated radiometric sensitivity for particular satellite sensors. Weconfirm the theory with some control experiments and illustratemeaningful change detection with examples of grounding linemigration and an inferred Antarctic sub-glacial lake undergoing adrainage event. We also discuss other possible cryospheric applica-tions of this approach, and discuss how image differencing cancomplement other data of more limited spatial or temporal extent.
2. Background
Visible and near-infrared band satellite sensors have had broadapplication in ice sheet studies since the first spaceborne digitalimagers in the 1970s. Single images have been used tomap prominentfeatures, such as coastlines, glaciers, moraines and nunataks, andmore subtle features, such as grounding lines, flowstripes (or“streaklines”) and crevasse fields (Fahnestock & others, 2000;
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Scambos & Bindschadler, 1991; Williams et al., 1995). Over much ofthe vast ice sheets there is only smooth snow-covered terrain whereimage brightness variations are caused by subtle surface slopevariations of a uniform high-albedo surface.
Changes in surface features are usually extracted by coregistrationof image pairs and comparative mapping of common features (e.g.,Lucchitta & Ferguson, 1986; Williams et al., 1995) or automatedtracking of moving features to measure ice flow (e.g., Scambos et al.,1992). Over ice sheet areas lacking fixed ground control, thesetechniques depend on optical similarities between images to achievea precise coregistration—a prerequisite to detecting differencesbetween images. Noise, both random and systematic, contributessignificantly to the differences between very similar images. Thus, anessential aspect of this method is the radiometric accuracy andprecision of the sensor, as well as its spatial resolution. These varygreatly among active orbiting optical sensor systems. The imagedifferencing technique discussed here is equally dependent on theseimage characteristics, but it differs from mapping or tracking featuredisplacements in that it extracts its information from the difference ofimage content at fixed spatial locations.
Any satellite sensor is limited by transmission bandwidth. Inoptical sensors, this usually means trade-offs have been madebetween swath width, spatial resolution and radiometric resolution.A general guideline is that lower resolution sensors can either image awider swath of the earth and/or do so with a greater radiometricresolution. As will be shown, for detection of local surface topographicchanges, radiometric resolution and spatial resolution are related.
3. Theory
Surface snow on cold ice sheets has a nearly constant albedo,typically 0.85 to 0.9 (Stroeve et al., 1997; Warren & Brandt, 2008).Deviations from this case are discussed later but, in general, variationsin sensor-measured radiance from such a target are dominated byvariations in the illumination geometry; most importantly, the surfaceslope in the direction of the illumination. The fundamental relation-ship is:
DN = CIR cos 90B−ϑ−α� �
+ S ð1Þ
where DN is the digital number, or image brightness, of a pixel in theimage; C is the scaler that converts the radiance detected by thesensor to a DN; I is the direct irradiance incident on the imagedsurface; R is the surface reflectivity; θ is the elevation angle of theilluminator (the sun in our cases) above the horizon; α is the surfaceslope (positive if tilted toward the illumination source); and S is anadditional radiance source term caused by atmospheric scatteringupward toward the sensor (Bindschadler & Vornberger, 1994). Eq. (1)also contains the implicit assumption that the reflecting surface isperfectly diffusive. This is only an approximation for snow, and thenon-diffusive effects become significant when sun elevations arebelow 30° (Bindschadler et al., 2008; Warren & Brandt, 2008). Eq. (1)forms the basis for the extraction of elevation fields from imagery,called photoclinometry (Bindschadler & Vornberger, 1994; Scambos &Fahnestock, 1998).
Our focus here is on revealing temporal changes by differencingtwo optical images. The difference image is created through thesubtraction of two images. The expression that describes thedifference image is:
ΔDN = CIR sin ϑ2 + α2ð Þ− sin ϑ1 + α1ð Þ½ � + S2−S1 ð2Þ
We do not consider the case where the illumination azimuths ofthe two images are substantially different and we further assume thatthe incoming irradiance, I, and surface reflectance, R, remain constant.
The difference of the scattering terms, S1 and S2 represent a constantoffset (ΔS), or bias, in the difference image.
Given these constraints, the case of θ1=θ2 represents an imagepair with identical illumination geometry. This reduces Eq. (2) to
ΔDN = CIR sinϑ cosα2− cosα1ð Þ + cosϑ sinα2− sinα1ð Þ½ � + ΔS ð3Þ
If the surface slopes are small, then to first order, Eq. (3) simplifies to
ΔDN = CIR α2−α1ð Þ cosϑ½ � + ΔS ð4Þ
This relationship illustrates that lower sun elevations amplify anydifferences in surface slope. Identical illumination geometry at lowsun angle is the ideal case for using image differencing to detectsurface slope changes.
It also is instructive to examine Eq. (2) for the case when α1=α2.This corresponds to the regions within the images that do not changeslope. Again assuming that the surface slopes are small, to first orderin α, Eq. (2) reduces to:
ΔDN = CIR sinϑ2− sinϑ1ð Þ + α cosϑ2− cosϑ1ð Þ½ � + ΔS ð5Þ
The first term in the square bracket expression represents aconstant offset that is independent of surface slope. Its effect is similarto the bias ΔS caused by scattering differences. The second term in thesquare bracket expression contains the surface slope and represents aresidual signature of the surface topography across the differenceimage. The magnitude of this residual topographic signal is related tothe difference in solar elevation angle. In the ideal case of exactlyrepeated illumination geometry, this variation disappears, but thisideal is rarely achieved.
4. Sensors
Imaging and resolution characteristics vary greatly among avail-able satellite sensors. In this section, we consider spectral bands fromthree different instruments with distinct fields-of-view, spatialresolutions, and radiometric resolutions (Table 1). These threeinstrument characteristics all impact data acquisition rates andtherefore are interdependent to some degree. Very high spatialresolution sensors have either a more limited field-of-view or lessradiometric resolution, while wide-swath sensors have either lessspatial or radiometric resolution, or both.
Radiometric resolution, radiometric precision and pixel dimen-sions are also important sensor properties for detecting significantsurface slope changes with image differencing. The entries in Table 1illustrate that for the candidate sensors considered here, theradiometric resolution, radiometric noise and signal-to-noise ratios(SNR) vary within roughly an order of magnitude.
The sensor with the poorest radiometric noise performance is thepanchromatic band of Landsat-7 Enhanced Thematic Mapper Plus(ETM+) sensor. Earlier Landsat Thematic Mapper (TM) sensors havesimilar spectral band performance to the ETM+ spectral bandperformance. Because the ideal background of a difference image isa random distribution of noise, radiometric noise is a very importantmeasure of the capability of any sensor for image differencingapplications. The panchromatic band of the Advanced Land Imager(ALI) onboard the Earth-Observer-1 (EO-1) satellite is a factor of threeworse than the spectrally narrower Band 4p. Bands 2 (near-infraredwavelength) of theMODerate-resolution Imaging Spectroradiometers(MODIS) onboard both the Terra and Aqua satellites have the lowestnoise values in Table 1. However, MODIS's Band 2 sensitivity to snowgrain size (Scambos et al., 2007) leads us to favor Band 1, a spectralrange where snow grain size has much less effect on reflectance. Laterwe examine two techniques to reduce noise: spatial averaging, whichis best for the higher resolution sensors of ETM+ and ALI; and image
Table 1Comparison of important characteristics of the examined sensors. Spatial resolution, spectral range, radiometric range and radiometric resolution are from sensor specifications; forMODIS, signal-to-noise ratio (SNR) is from Xiong et al. (2007) and is used with exo-atmosphere irradiance and reflectance to calculate radiometric noise; for Landsat and EO-1,radiometric noise is from Markham, pers. comm. and from Mendenhall et al. (2001), respectively, and used with Exo-atmosphere irradiance and reflectance to calculate SNR; exo-atmosphere irradiance is from Neckel and Labs (1984); mean snow reflectance is from Painter and Dozier (2004); andminimum detectable slope change is from Eq. (7) using a solarelevation angle of 25°.
Sensor SpatialResolution(m)
SpectralRange(nm)
RadiometricRange(DN)
RadiometricResolution(W/m2/μm/str/DN)
Signal-to-NoiseRatio(bright target)
Radiometric Noise(W/m2/μm/str)
Exo-atmosphereIrradiance(W/m2/μm)
Mean SnowReflectance
MinimumDetectableSlope Change(milliradians)
MODIS (Band 1) 250 620–670 4096 0.21 (Terra) 177 (Terra) 1.40a
(DN=6.6a)1614 0.95 6.37a
0.22 (Aqua) 186 (Aqua) 1.31a
(DN=6.0a)5.96a
MODIS (Band 2) 250 841–876 4096 0.080 (Terra) 466 (Terra) 0.29a
(DN=3.6a)986 0.85 2.41a
0.076 (Aqua) 493 (Aqua) 0.27a
(DN=3.6a)2.25a
Landsat-7 ETM+
(Band 4-High Gain)30 760–900 256 0.64 225 (279 for
Low Gain)0.65 (DN=1.0) 1085 0.85 4.92
Landsat-7 ETM+
(Pan band-Low Gain)15 520–900 256 0.98 87 2.50
(DN=2.5)1520 0.90 12.75
EO-1 ALI (Band 4p) 30 850–890 4096 0.063 1015 0.13(DN=2.1)
975 0.85 1.09
EO-1 ALI (Pan Band) 10 480–690 4096 0.154 821 0.33(DN=2.1)
1792 0.95 1.35
a The MODIS values of radiometric noise and minimum detectable slope change may be too large by a factor of 3 or more as discussed in the text.
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series averaging, a better approach for the continuously operatingMODIS.
As a check on the sensor noise values listed in Table 1, weproduced images predominantly comprised of noise by shifting animage one pixel in both the line and sample directions and thensubtracting the second image from the original. This techniquesucceeds in quantifying noise if the majority of the coherent, i.e.non-random, information in the image is at wavelengths much longerthan one pixel. To further limit the effect of real topography, imagesubsets were used as areas small enough to avoid significanttopography, but large enough to obtain a meaningful statisticalmeasure. In all cases, the mean of the difference image was zero, ornearly zero—a further validation of the statistical significance of thetest. For an ETM+ Band 4 sub-image, the standard deviation was0.72 W/m2/μm/str.; for ALI Band 4p the standard deviation was0.13 W/m2/μm/str.—both of these values are very close to the entriesin Table 1. ForMODIS Band 2, the standard deviationwas 0.098 W/m2/μm/str., a factor of 3 lower than the noise value calculated from theSNR value from Xiong et al. (2007), however, other tests presentedlater in this paper suggest a better sensitivity. It is possible the Xionget al. (2007) values are not applicable for a target as bright as snow.
The sensitivity of a sensor to a change in the surface slope can bederived by differentiating Eq. (1):
∂DN=∂α = CIR cos ϑ + αð Þ ð6Þ
Dividing by C expresses the slope sensitivity in radiance units, L,and rearranging terms expresses the sensitivity of a sensor to changesin slope.
∂α =∂L
IRcos ϑ + αð Þ ð7Þ
By setting ∂L equal to a sensor's radiometric noise level, Eq. (7) canbe used to calculate the minimum slope change detectable by thatsensor. Values of I (from Neckel & Labs, 1984) and R (from Painter &Dozier, 2004) are included in Table 1 along with the calculated valueof the minimum detectable slope change from Eq. (7), assumingθ=25° and α is small. It is important to note that this is an absoluteminimum value, making pixels whose surface slope changed thisamount equal in magnitude to sensor noise. Distinguishing these
pixels from sensor noise requires either some discernible spatialpattern and/or a higher signal-to-noise ratio.
5. Examples and numerical models of image differencing overice sheets
5.1. Null tests using real sensor data
Our first set of examples is intended to test the theory and sensorspecifications presented above with a goal of demonstrating a nulldifference image, or one that expresses diminished residual topogra-phy, in real images of ice sheet surfaces. We apply these tests toLandsat, EO-1 ALI and MODIS data. Sensitivity of slope detection byother sensors can be estimated by applying the above equations to theappropriate sensor specifications.
Surface change detection in a difference image requires accuratecoregistration of the initial image pair. Image location data may notsuffice for this application unless a precise orthorectification isperformed using re-projection software that incorporates accurateregional elevation data. However, if the imaging geometry is nearlyidentical, this step may be unnecessary, and in the cases exploredbelow, we use image pairs with nearly identical illumination andviewing geometry. A method to coregister imagery based on longwavelength surface features is discussed in Scambos et al. (1992).Additional coregistration problems can arise if two different sensorsare used and there are sensor-specific internal distortions. For ourexamples, each image pair was coregistered by one of a variety ofmethods and residual mis-registration is not believed to affect theresults of the difference image, unless specifically discussed.
Differencing coregistered images whose pixel values have beenconverted to radiance values proved to be ineffective. The differenceimages should have resulted in a narrow distribution of low radiancedifference with a zero mean, however, this was rarely the case and islikely caused by the non-diffusive reflectance of snow at sunelevations below 30° (Bindschadler et al., 2008; Warren & Brandt,2008). Amore successful approachwas tomatch theDN histograms ofthe two images prior to differencing. Histogram matching, anoperation offered with most image processing software packages,typically matches the maximum and minimum values of one image'shistogram to another image's histogram and then applies a lineartransformation to all values between. In cases where the minimum
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(maximum) values were extremely large (small) and well separatedfrom the main histogram, we replaced the minimum and maximumvalues with the 4σ values. This approach works well for ice sheetimages because the histograms typically are nearly ideal Gaussiandistributions, resulting in an excellent histogram match. A disadvan-tage of this approach is that it can complicate the conversion of thedifference image values to radiance and, therefore, to a precisequantitative measure of any detected change in surface slope.
Our first example, differencing two full Landsat TM images(nominally 185 km×185 km), encompasses a West Antarctic icestream and adjacent ridge (Fig. 1). Here two Landsat-5 images, onecollected on17 January 1987 (Sun elevation/azimuth: 19.7°/97.7°) andthe second on 24 February 1992 (Sun elevation/azimuth: 8.0°/100.1°),both acquired over path 14, row 118 of the Landsat World ReferenceSystem-2 (WRS-2) system, are differenced after histogram matching(the ±4σ points were matched). These images were selected becausethe sun elevations and azimuthswere closest among the collection on-hand. More similar illumination conditions can be achieved if the twoimages are acquired on consecutive orbital periods, i.e., 16 days forMODIS, EO-1, or Landsat-4, 5 or 7. The difference image eliminatesmost topographic features, except crevasses (which shift due to iceflow over the five years). The contrast of the difference image has beenamplified to show its content. The noise level is∼2DN, consistent withTable 1 values. The gradual, larger scale tonal variations express slightdifferences in surface reflectance (at the 2–5 DN level) between thetwo images.
In Fig. 2, we illustrate a difference image set (originals plusdifference) covering a sub-scene of a similar crevassed ice streamregion as in Fig. 1 but collected by the ALI sensor (Band 4p) on 20February 2001 and 18 October 2001. Sun elevations/azimuths were9.8°/96.4° and 9.9°/90.1°, respectively. This is much closer match insolar elevation than the Landsat example of Fig. 1. Note again that ice
Fig. 1. (a) ETM+ image of a 185 km×185 km portion of MacAyeal Ice Stream, WestAntarctica, collected on 17 January 1987 (WRS-2 Path/Row: 14/118). Left side is asmooth-surfaced, slow-moving ice ridge and right side is a fast-moving ice stream withan undulated surface, flowing from image top to bottom and containing numerouscrevasses and visible crevasse fields. (b) Difference image formed by subtracting asimilar image collected 24 February 1992 (not shown) from image (a). Differenceimage has been contrast stretched more than the original image to show residual imagecontent.
stream topography at large scales (several kilometers) is suppressedin the difference image, while moving objects like the surface crevassefield remain and are more easily seen because the background of lightand dark shading caused by the large-scale topography is removed.The crevasses are included in the difference image as bright–darkcouplets separated by their motion during the time between the twoscene acquisitions. Note also the presence of thin cloud shadows inthe October image as two sub-horizontal stripes below the imagecenter; these also appear in the difference image because the otheroriginal image is cloud-free.
A MODIS example of image differencing is given in Fig. 3. Theoriginal images are of a portion of the Whillans Ice Stream, from 20November and 6 December 2000. The short 16-day time separation,representing the repeat cycle of the Terra satellite platform orbit,provides near-identical illumination azimuths and only a slight solarelevation change between the two images. The small time separation,as well as the relatively large 250-meter pixel size, minimizes theappearance of moving crevasses in the difference image, but somedetection of the crevasses is apparent in the regions of large contraston the pixel scale. The subset region in Fig. 3 shows that most, but notall, of the fixed topographic variation, i.e., the broader light and darkregions, has been removed by differencing.
5.2. Tests using synthetic images of a localized transient elevation feature
In this sectionwe explore the likelihood of detection, and the likelyappearance, of an elevation change in difference images by applyingthe image brightness equivalent of a known elevation change to anactual image. Guided by the scale of topographic change associatedwith sub-glacial lake activity initially identified by Gray et al. (2005),the elevation change corresponds to a circular depression describedby
h = −H 1−2rR
� �2+
rR
� �4� �
ð8Þ
where h is the vertical change in elevation (in meters) and r is theradial position from the depression's center (in kilometers). Thedepression has a maximum depth of H at r=0, decaying to zero at aradial distance r=R. The maximum slope of the feature described byEq. (8) is 1.54 H/R. If the maximum slope is detectable by a sensor,then we assume the associated depression also would be detectable.Fig. 4 illustrates how this maximum slope varies with depressions ofvarious depths and radii.
Using Eq. (7) and Table 1, we calculate and include in Fig. 4 theminimum detectable slope changes for MODIS Band 2, Landsat ETM+
Band 4, and ALI Band 4p (each is the most sensitive detection band foreach sensor) at a sun elevation of 25°. A lower value of detectableslope indicates a more slope-sensitive sensor: ALI has the greatestsensitivity, MODIS Band 2 is slightly less capable, while Landsat ETM+
performs poorest.The noise thresholds of minimum detectable slope change shown
in Fig. 4 should not be interpreted as the absolute limit of sensorimage detection capability. Fig. 4 indicates the slope changedetectable at a single grid point (pixel) given the sensor noise level.Detection may also be achieved by some combination of a largersignal, decreased noise, or spatial coherence. The signal-to-noise ratiocan be improved by either spatial averaging or stacking multipleimages. Both are considered in this paper. A further improvement indetectionmay be realized by using shaped filters, if the spatial patternof the expected signal is known.
Sensor-specific DN patterns were calculated from Eq. (8) usingthe Table 1 characteristics for depressions 1, 5 and 10 m deep and10 km in diameter (5 km radius). Fig. 4 shows that these threecases are distributed between the detection thresholds of MODIS,ALI and ETM+. The simulated depressions were added to an actual
Fig. 2. EO-1 ALI images of a 12 km×12 km portion of Bindschadler Ice Stream,West Antarctica collected in (a) 20 February 2001 and (b) 18 October 2001. Ice flow is from upper rightto lower left at a rate of a few hundred meters per year. Crevasses are formed as the ice stream moves over two diffuse surface undulations. Panel (c) is the difference image formedby subtracting the two original images illustrating the removal of broader-scale surface topography and the retention of moving surface crevasses.
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image and then subtracted from a second image to create adifference image. In all cases, the sun elevation applied to generatethe depression was equal to the value of the image into which itwas introduced and the mean brightness of the depression set wasequal to the mean brightness of the image. In the initial tests, thesecond image was generated by shifting the original image(without the simulated depressions) one pixel in both the rowand column direction. This approach resulted in an accuraterepresentation of the pixel-scale noise background in the differ-ence image, as discussed earlier.
In the ETM+ example (Fig. 5), the trio of depressions is difficult tosee in the original, undifferenced image (upper left image). Aftersubtraction of the shifted image, the 10-meter and 5-meterdepressions are apparent, but the 1-meter depression remainsdifficult to discern. The surrounding content of the difference imageconsists mostly of fine-scale crevasses and flowstripes whosebrightnesses vary at the one-pixel spatial scale. A DN profile across
Fig. 3. MODIS image difference example. (a) sub-image (15×20 km) from 20November 2000 image of upper Whillans Ice Stream, West Antarctica showing surfacetopography; (b) difference image subtracting shown image from image collected in 6December 2000.
the depressions of the difference image (Fig. 5, upper right plot)shows the depression's topographic signal relative to image noise.To examine whether spatial averaging would enable a cleareridentification of the depressions, the difference image was averagedwith kernels of 5×5 and 15×15 pixels. These image averages areshown in Fig. 5 (lower left and lower center images), with the samecontrast stretch as applied to the initial difference image. Qualita-tively, although the background became smoother, there was littleimprovement in detection capability, however the profile of pixelvalues across the depression trio shows a clearer discernment of thespatial pattern as compared to the same pixel profile with no spatialaveraging.
Fig. 6 shows the same experiment carried out for ALI and MODISimage data using the same radiance grey-scale as Fig. 5. The lowernoise of ALI and MODIS relative to ETM+ is apparent in both thedifference images and the DN profiles. Detection of the one-meterdeep depression is still difficult in either case, however, the 5-meter deep depression is slightly clearer in ALI and MODIS thanETM+. Also apparent is the lower spatial resolution of the MODISimage; the depressions were placed in a smoother portion of theMODIS image to avoid difference image artifacts created by ourone-pixel method of creating a second original image. In terms ofthe ability to visually detect the depressions, MODIS is similar toALI, as suggested by the similar noise values in Table 1. Comparingthe noise of the DN profiles for ALI and MODIS indicates that MODIShas the lower noise, in fact considerably lower. This is consistent
Fig. 4. Maximum feature slope versus feature radius for circular depressions of variousdepths described by Eq. (8). Feature depth (in meters) is indicated by the numbers nextto the curves. Horizontal lines correspond to minimum detectable slope change forMODIS-Terra Band 2 (solid line), ALI Band 4p (long-dashed line), and ETM+ Band 4(short-dashed line) from Table 1 and Eq. (7).
Fig. 5. Four Landsat ETM+ images showing results of image difference test with synthetic depressions added to a scene. (a) Original image with circular depressions of 1, 5 and10 meter depth and 10-km diameter added; (b) difference image formed as described in text; (c) profile of pixel values (in DN) across the line indicated in image (b); (d) 5×5 pixelaverage of difference image; (e), 15×15 pixel average of difference image and (f) profile of pixel values across the line indicated in image (e). All images use the same grey-scalerepresentation of radiance. Sun elevation in the initial image is 9.9°.
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with our noise values calculated by creating a second image with aslight shift of a single image (discussed earlier where ALI andMODIS Band 2 noise values were 0.13 and 0.098 W/m2/μm/str.,
Fig. 6. (a) Original EO-1 ALI image with simulated circular depressions of 1, 5 and 10 meter d(c) profile of DN values across the center of difference image (b). (d) Original MODIS imadescribed in text; and (f) profile of DN values across the center of difference image (e).
respectively), but is not consistent with Table 1 values. We suspectthat the SNR value of Xiong et al. (2007) used in deriving theMODIS radiometric noise value included in Table 1 may be
epth and 10-km diameter added; (b) difference image formed as described in the text;ge with simulated depressions identical to image (a); (e) difference image formed as
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inappropriate for snow surfaces. Further support of this position isgiven in the following section.
6. Observations of real surface changes
6.1. Uncalibrated difference images
Several areas of actual surface slope change in the RossEmbayment region of West Antarctica were recently identified byanalysis of repeat laser altimetry (Fricker et al., 2007 and personalcommunication). These regions were interpreted to be a result of sub-glacial water movement similar to the Gray et al. (2005) regions, andareas of grounding line retreat. To investigate the potential of imagedifferencing to detect real surface slope changes, we used a series ofMODIS images to generate several image differencing pairs over theperiod November 2000 to November 2005.
To improve radiometric sensitivity and reduce noise, severalMODIS images from each year were selected and “stacked” to forman annual-average image for each year by averaging the griddedvalues at each grid cell of the geo-located image grids. The selectionof MODIS images for the annual-average scenes was limited to onesatellite platform (Terra, Band 1) and a narrow temporal windoweach day (80 min) for a short period (2 to 4 weeks) of the sunlit
Fig. 7. (a) Sample of a MODIS single-season multi-image-averaged sub-image (here for 200periods formed by differencing single-season multi-image average sub-images. Region is ndrainage of Subglacial Lake Englehardt illustrated by the difference images are discussed in tjust downflow of the grounding line is also labelled.
season. These constraints kept the solar azimuths within a rangeof ±20°, and solar elevations to a range of a few degrees. By limitingthe search area to 100 km on a side and springtime (when cloudcover and surface frost patches are minimal), it was possible to find1 to 5 images for each year of the MODIS record for the lowerWhillans Ice Stream region.
Histogram matching was applied to the series of annual-average images, yielding a series of scenes with matching contrastand brightness variations over mostly unchanged surface featuresand slopes. The single-year images were then differenced toproduce a series of year-to-year difference images that are thenprocessed further to have matching brightness histograms. Fea-tures in the difference images include frost patch and surfacealbedo variations, thin clouds or haze, and crevasses, as well as thesought-after changes in ice sheet surface slope. Surface slopechanges show up as spatially continuous bright or dark regionsagainst the relatively featureless background of regions with noslope change.
Fig. 7 illustrates examples taken from a longer image series thatincludes single-season, multi-image averaged sub-images from2002 to 2005 and the corresponding season-to-season differenceimages (additional scenes are shown in supplemental onlinematerial for Fricker et al., 2007). The sub-images in Fig. 7 are
2 where 3 images formed the average). (b–d) Difference images for the indicated timeear the northern downstream edge of Whillans Ice Stream, Antarctica. Changes in thehe text. The grounding line is delineated by a white dashed line. A dense set of crevasses
Fig. 8. (a) MODIS single-season averaged image for 2006 of a region over MacAyeal Ice Stream, West Antarctica that shows surface lowering due to inferred sub-glacial watermovement. Bold line indicates location of ICESat Track 1337. (b) Difference image formed by subtracting a similar 2003 averaged image from the single-season averaged image for2006. Vectors indicate mean solar directions for the two averaged images. (c) Altimeter-derived slope values (ICESat Track 1337) for 29 October 2006 versus 2006 image DN valuesshowing linear fit given in Eq. (9a). (d) Profiles along the ICESat track: open circles, DN of the difference image (b); open diamonds, derived from DN using mean values of DN-slopecoefficients from Eqs. (9a) and (9b); and open squares, derived by differencing ICESat elevations from 20 October 2003 and 29 October 2006.
1360 R.A. Bindschadler et al. / Remote Sensing of Environment 114 (2010) 1353–1362
roughly centered on the location of an inferred sub-glacial lake at thenorthern boundary of Whillans Ice Stream, West Antarctica called‘Subglacial Lake Englehardt’. All image data were acquired betweenlate November and early December of a given year. Three scenes in2002 were averaged to form the sub-image shown in Fig. 7(a). Theother three sub-images (Fig. 7(b–d)) illustrate the ability ofdifference images to show both vertical elevation changes andgrounding line retreat over a multi-year period, as well as crevassemovement and cloud changes from year to year. A region ofelevation and slope change near the center of the scenes has beeninterpreted as a sub-glacial lake drainage event (Fricker et al., 2007).The 2004–2003 difference image captures most of the lake drainagethat is expressed as a change in slope around the perimeter of theaffected area. On the right side of this area, the slope steepens awayfrom the sun causing a darkening of the surface, whereas on the leftside of the area, the slope tilts more toward the sun causing abrighter surface. The 2005–2004 difference image shows a contin-uation of the change, but with a lower amplitude than in the 2004–2003 difference image. The crevassed area in the lower rightcontinues to appear in each difference image because theirmovement prevents the differencing from cancelling their high-contrast signature. In a similar manner, the grounding line alsocontinues to appear in the difference images. This indicates that it,too, is moving—a characteristic that suggests dynamic changes in theWhillans Ice Stream. In the lower portion of Fig. 7(c and d), a cloud in
the 2004 annual-average image leads to a bright feature in the 2004–2003 difference image and a dark area in the 2005–2004 differenceimage.
6.2. Calibrating images and difference images using other sensors
Precise surface elevations measured by satellite laser altimetrycan provide an independent check on the DN sensitivity values ofsatellite images derived earlier in this paper. This is turn can be usedto quantify surface slope change from difference image DN values.Fig. 8(a) shows a 3-image average MODIS image (Band 1 collected inDecember 2006: 10:05 UTC and 11:40 UTC, 07 December; 10:45UTC, 08 December), and a difference image (Fig. 8(b)) generatedfrom this image and a similar one acquired 3 years earlier (also a 3-image average, but from December 2003: 11:25 UTC, 09 December;12:05 UTC, 10 December; 12:05 UTC 26 December), of a region in thelower trunk of MacAyeal Ice Stream. Individual images wereprocessed, removing striping from the MODIS sensor (Haran et al,2002), and resampled to a georegistered grid without changing thescale of the DN range from the Level 1b MODIS Band 1 data. Dailyacquisition times of all images were limited to +/−70 min of 11:00UTC to constrain solar azimuth and solar elevation variations. ThisUTC time rangewas selected to provide a solar azimuth that is nearlyparallel to an ICESat laser altimetry track (orbit track 1337) that wasacquired during campaigns within one month of the mean image
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acquisition date of both image sets (laser campaigns 2a and 3g; seeShutz et al., 2005). Acquisitions of Track 1337 occurred on 20October 2003 and 29 October 2006, i.e. about 50 days before themean acquisition dates of the image groups.
We compared slopes derived from the ICESat laser altimeterdata to the DN values of the image transited by the altimeter (Fig. 8(c)). In both cases, 2003 and 2006, crevasses and frosts contributedconsiderable scatter in the plot (affecting the altimetry and imagedata, respectively). For the two images, the following linearrelationships were determined:
2006: DN = 1590α + 402:5 ð9aÞ2003: DN = 1640α + 445:5 ð9bÞ
where α is the ICESat-determined surface slope. These linear fitsrepresent an approximation to Eq. (1) over a narrow range of surfaceslopes and the difference in values for the two years represents boththe difference in surface conditions as well as the uncertainty of thelinear fit. Using a value of 1615 DN per radian—the mean of Eqs. (9a)and (9b)—the radiometric noise of 6.6 DN for Terra Band 1 (seeTable 1), reduced by a 3-image factor of 1.7, converts to a MinimumDetectable Slope sensitivity of 2.4 mrad, roughly 2.5 times moresensitive than suggested from the noise values given by Xiong et al.(2007). Aqua Band 1 is probably similar, and a similar improvement islikely to be the case for Band 2, based on the low noise we observe inour Fig. 6 comparison with ALI.
The difference image in Fig. 8(b) shows a series of troughs withaxes running from upper left to lower right centered in the sub-sceneand crossed at a near orthogonal angle by the ICESat track. This troughis interpreted as the surface expression of the boundary of anothersub-glacial lake based on the ICESat-measured elevation change andthe qualitative interpretation of the difference image (Fricker et al.,2007, supplemental online material, and Fricker & Scambos, 2009).These ICESat-derived elevation changes can be compared to elevationchanges derived from the image difference image by applying themean values of the two empirical linear fits (Eqs. (9a) and (9b)) toconvert the difference image DN for pixels along the ICESat profiletrack to elevation change values (relative to a zero mean) (Fig. 8(d).This conversion represents an approximation to Eq. (5), derivedearlier, when the two illumination directions are nearly parallel, sothe sinθ2–sinθ1 term can be neglected. The agreement is particularlygood over the central portion of the profile and represents the firsttime optical image data have been used to measure elevation change.This demonstrates an exciting new capability to extend linearlyconstrained elevation change measurements to map elevation fieldsin greater detail. The profile portions where agreement between theimage difference-derived elevation differences and those from ICESatis less good illustrate the possible pitfalls in blind application of thisnew technique without careful examination of both image andaltimetry data. It is expected that, in general, there will need to bealtimetric data in temporal and spatial proximity to the image data toassist in determining accurately the values of the coefficients inEqs. (9a) and (9b).
7. Additional applications of image differencing
Although we have focused on the use of image differencing todetect surface slope changes that may be associated with sub-glacial water movement, surface slope changes can be caused by amuch wider range of phenomena that make their detection of widerinterest. Surface slope is a primary factor in determining the drivingstress that drives ice sheet flow and changes in surface slope canvary temporally much faster and by proportionally much largeramounts than ice thickness and temperature, the other primaryfactors determining driving stress. Driving stress and ice flow arelinked through complex non-linear relationships and departures
from a flow field in equilibrium with local climate (when ice massgain and loss terms are in balance) will change the surface shapeand alter ice flow. Image differencing is most effective when thesurface slope changes are localized but local changes in basalconditions can affect a large region of the ice sheet (Sergienko et al.,2007).
Our examples have tended to avoid clouds, but cloud detectionmay well prove to be another very useful application of imagedifferencing. Automatic detection in satellite imagery of bright whiteclouds over equally bright and white snow and ice sheets hasremained a challenge. Occasionally, new techniques are developed,but they tend to be computationally intensive, e.g., Choi andBindschadler (2003), limiting their operational attractiveness. Gen-eration of a set of cloud-free reference images that can be differencedwith new images whose cloud content is unknown, could provide thebest solution to this long-standing problem.
Other uses of a set of reference images include using it to monitorlocal surface phenomena such as seasonal meltwater lake formationand evolution, areal change of blue ice areas, migration of megadunestructures, and albedo monitoring for changes in surface snow grainsize or the detection of soot or dust plumes.
8. Summary and future plans
Recent awareness that ice sheets are capable of change in localareas on short time scales and that these changes are relevant to icesheet's various roles in the climate system provide multipleopportunities to employ image differencing in glaciological researchapplications. We provide the theoretical foundation for assessing theefficacy of specific sensors to a wide variety of possible applications.Radiometric noise and resolution are primary considerations as arethe ability to accurately coregister images and obtain images withillumination conditions as similar as possible.
The large number of MODIS images allowed us to successfullydemonstrate the use of image differencing in concert with othersensors to map the areal extent of ice sheet regions affected bywhat has been inferred as the movement of sub-glacial water. Thisexample also illustrated the ability to decrease noise by tempo-rally averaging multiple images with similar illumination char-acteristics and demonstrated the capability of extending altimetermeasurements of elevation change to the larger field. The higherspatial resolution sensors of ETM+ and ALI provided no directexamples of surface slope changes, but simulated depressionsillustrated how results might appear. Spatial averaging did notappear to be effective in reducing noise to increase depressiondetection.
Ice sheets are changing in our warming world. As sensorcapabilities and the means to acquire and automatically analyzelarger numbers of images improve, it is likely that the potentialapplications involving image differencing will be developed further.This includes the automatic detection of clouds, monitoring thegrounding lines of ice sheets and the areal extent and possiblediscovery of new blue ice areas, changing albedo of the ice sheet andthe evolution in space and time of surface meltwater lakes.Comprehensive collections of both MODIS and Landsat ETM+ imagesfor both the Antarctic and Greenland ice sheets already exist and arefreely available (Bindschadler et al., 2008; Scambos et al., 2007).These serve as a valuable reference set from which to difference otherimages.
Acknowledgements
This work was supported by NASA grant NNG06GA60G. Inparticular, we thank both Patricia Vornberger and Jennifer Bohlanderfor performing some of the image processing and helpful commentsreceived from two anonymous reviewers.
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