The accuracy of digital elevation models of the Antarctic continent
Jonathan Bamber *, Jose Luis Gomez-Dans
Centre for Polar Observations and Modelling, School of Geographical Sciences, University of Bristol, UK Received 9 December 2004; received in revised form 9 June 2005; accepted 9 June 2005
Available online 9 August 2005 Editor: E. Boyle
Abstract
The accuracy of two widely used digital elevation models of Antarctica was assessed using data from the Geoscience Laser Altimeter System onboard ICESat. The digital elevation models were derived from satellite radar altimeter and terrestrial data sets. The first, termed JLB97, was produced predominantly from ERS-1 data while the second, termed, RAMPv2 included other sources of data in areas of high relief and poor coverage by ERS-1. The accuracy of the models was examined as a function of surface slope and original data source. Large errors, in excess of 100 m, were ubiquitous in both models in areas where terrestrially-derived elevation data had been used but were more extensive in RAMPv2. Elsewhere, the systematic error (bias) was found to be a monotonic function of slope for JLB97, with a more complex, less predictable bias for RAMPv2. The magnitude of the global, slope-dependent, bias ranged from less than a metre to slightly over 10 m but with much larger regional deviations. The random error ranged from about 1 m to over 100 m depending on the DEM and slope. The random error was consistently over a factor two larger for RAMPv2 compared to JLB97.
D2005 Elsevier B.V. All rights reserved.
Keywords:Antarctica; digital elevation model; satellite altimetry; ICESat
1. Introduction
Ice sheet surface topography is an important data set for a wide range of applications from field plan-ning to numerical modelling studies. It can, for exam-ple, be used to validate the ability of a model to reproduce the present-day geometry of the ice sheet.
It can also be used as an input boundary condition for modelling. Another application that has become in-creasingly important in recent years is in interferomet-ric synthetic aperture radar (InSAR) processing, which has been used to derive mass balance estimates from ice flux divergence calculations[1,2]. Here, two SAR images are acquired at different times and slight-ly different locations in space and combined to pro-duce an interference pattern (or interferogram), which is a combination of phase differences due to the motion of the ice surface and its topography [3]. Accurate information on the latter, in the form of a
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* Corresponding author. Tel.: +44 117 9288102; fax: +44 117 928 7878.
digital elevation model (DEM), can be used to remove the (unwanted) topographic signal [3]. Errors in the DEM, however, introduce errors in the estimated motion field and, hence the resultant mass balance. Also required for this type of mass balance study is an estimate of the catchment area or drainage basin for a particular glacier. Again, this information comes from a DEM of the ice sheet [4]. For these and other applications, it is important not only to have accurate topographic information, but also to have knowledge of the errors in the topography. In this paper, we use spatially extensive, decimetre accuracy spot measure-ments from a satellite laser altimeter (the Geoscience Laser Altimeter System, GLAS, onboard ICESat) to assess the accuracy, both globally and regionally, for the two most ubiquitous and up to date DEMs of Antarctica.
2. Data sets
Until the launch of the first European Remote Sensing Satellite, ERS-1, in 1991, the topography of the Antarctic ice sheet was poorly known, with errors of hundreds of metres and a paucity of measurements
[5]. ERS-1 carried onboard a radar altimeter that provided range estimates at 335 m spacing in the along-track direction. In April 1994, the satellite was placed in its geodetic phase comprising a single 336-day cycle, which provided across-track spacing at 608
S of about 4 km. The radar altimeter (RA) data from this geodetic phase were used to derive a DEM with 5 km postings for all areas where there was adequate coverage. South of the latitudinal limit of the satellite (81.58 S), and in areas of steep relief, terrestrially-derived data sets were used[6]. This DEM has been used in a range of modelling and remote sensing studies and was made available through the National Snow and Ice Data Center (www.nsidc.org) and will be referred to as the JLB97 DEM henceforward. As part of a project to produce a SAR mosaic for the whole of the Antarctic continent, known as the RADARSAT Antarctic Mapping Project, RAMP[7], a second DEM was produced using the same ERS-1 RA data but with a different set of processing algorithms
[8]. In addition to using ERS-1 RA data for areas with a slope below 0.88, the RAMPv2 DEM includes data from a number of other sources, such as GPS,
air-borne radar, and large scale cartography [9]. These sources were selected to provide a better spatial sam-pling, and have been used instead of the ERS-1 RA data where available. In areas with slopes up to 1.08, where no alternative data were available, ERS-1 RA data were used. In areas with higher relief than this, data from the Antarctica Digital Database (ADD)[10]
were added. This will henceforward be referred to as the RAMPv2 DEM. Although, both DEMs utilise the same RA data, different processing methodologies were used to extract elevation estimates [11–15], which has led to substantial differences between the two DEMs, even in areas where only RA data are present.
To examine the accuracy of the two DEMs de-scribed above, we employed data from the GLAS sensor, launched onboard ICESat in January 2003
[16]. The satellite was initially placed in an 8-day repeat cycle before being moved to a 91-day repeat in October 2003. Originally, it was planned to place ICESat in a 186-day repeat cycle, which would have provided dense coverage of both the Greenland and Antarctic ice sheets up to 868 latitude. Due to a degenerative failure of the three laser sub-systems, the mission operation plan was changed and, in gen-eral, GLAS has been switched on for a nominal 33 days of each 91-day cycle. This has provided an across-track spacing of around 45 km at 608latitude and an along-track spacing of 170 m. The ice sheet elevation product (called GLA12) distributed by the National Snow and Ice Data Center, Boulder, Color-ado was used in this study[16]. We used release 181 of GLA12 covering two time periods: the laser 1 8-day repeat period from 20-02-2003 to 19-03-2003 and 55 days of laser 2a from 25-09-03 to 19-11-03. Before undertaking the comparison a number of processing and filtering steps were necessary. First, the GLAS data were referenced with respect to the WGS84 ellipsoid. The data were then filtered to re-move samples that might have been contaminated by cloud cover or other atmospheric interference. Data quality flags in the GLA12 product were used to remove data with gross errors, which test for attitude
1We use release 18 as more data were available than for release 21, which is probably the final release for laser 2a. Our statistics were nearly identical for both releases for the same orbital time periods.
control, minimum reflectivity and single peak wave-forms. Geophysical filters were then applied. The RAMPv2 and JLB97 DEMs were bilinearly interpo-lated to estimate the elevation of each DEM at every GLAS sample location. If the difference between both DEMs and the GLAS sample was larger than 400 m, the GLAS sample was discarded. A number of clearly erroneous points were still visible in the resulting data, so a second, statistical criterion was applied. A 3r
filter was performed on the GLAS data. This was done by calculating the mean and standard deviation,
r, of GLAS samples over a 5-km grid, and discarding points that were more than three standard deviations away from the mean. Finally, some of the parameters in the GLA12 product can be used as an indicator of abnormal data. It was noted that the GLAS-derived surface roughness parameter was a good indicator of abnormal points over flat surfaces such as ice shelves. The filtering criteria used for this parameter were:
if (slopeN0.88) use sample
if (slopeb0.28) and (number of GLAS points in
grid cellN3): edit if roughnessN3.0 m
if (slopeb0.28) and (number of GLAS points in
grid cellb= 3): edit if roughnessN8.0 m
if (0.2bslopeb0.88) edit if roughness N8.0 m.
3. Methods
To assess the internal accuracy (i.e. ignoring any potential geographically-correlated biases) we exam-ined cross-over differences between ascending and descending tracks of GLAS data. In order to find the difference in heights at the crossover points, the track values were interpolated using a first order polynomial. The results are slope dependent, degrad-ing with increasdegrad-ing slope, but it was found that the mean difference was close to zero with a standard deviation of less than 0.5 m for slopes of 18. The results broadly agree with those reported by the GLAS engineering team and, based on this analysis, we assume that errors in the GLAS data are negligible compared with the DEMs. Differences between GLAS data and the DEMs studied here will, therefore, be assumed, henceforward, to be due to either the influence of sub-grid scale topography on the bilinear interpolation used or errors in the DEMs. There is,
however, also an approximate 10-yr time interval between the acquisition of the GLAS and RA data, which could result in differences in elevation due to a height change over the time interval. We note, how-ever, that elevation changes, derived from two 5-yr periods of ERS RA data suggests that, except for one region of West Antarctica, the differences, at a region-al scregion-ale, are on the order of a few centimetres per year
[17,18]. We conclude, therefore, that the time interval will increase the random error of the differences by about 20–50 cm, depending on location as the eleva-tion changes are not uniform with slope[18]. This is a
-10 0 10 5 30 55 80 Difference [m] GLAS-RAMPv2 GLAS-JLB97 5 20 35 50 65 80 95 5 30 55 80 FWHM [m] GLAS-RAMPv2 GLAS-JLB97 0 10 20 30 40 50 60 70 0 0.2 0.4 0.6 0.8 1 5 30 55 80 Std Dev [m] %Area %Area %Area Slope [deg] GLAS-RAMPv2 GLAS-JLB97 a) b) c)
Fig. 1. Statistics of the comparison of GLAS data with the JLB97 and RAMPv2 digital elevation models of Antarctica as a function of surface slope for the region covered by ERS-1 radar altimeter data (north of 81.58). (a) Mean difference (GLAS-DEM). (b) Full width half maximum for the histograms of differences. (c) Standard deviation of the histograms of differences. The solid line in the plots shows the cumulative percentage ice sheet area with slope.
small effect compared to the calculated random errors presented later. Even in the areas of greatest elevation change, the mean difference is likely to be no more than about 1.5 m.
The elevation of the DEM at the precise location of a GLAS footprint on the ground was obtained using bilinear interpolation. This implicitly assumes a planar surface. Where this is not the case (i.e. where the second derivative of elevation is non-zero) this will increase the random error of the differences, particu-larly in the higher slope, greater relief regions of the ice sheet. The differences were examined both in terms of their spatial pattern and as a function of surface slope, which was calculated from the RAMPv2 DEM over a 10-km distance for both DEMs.
4. Results
Fig. 1 shows the mean difference (or as defined above, the systematic error or bias), full width half maximum (FWHM), and standard deviation, r, of GLAS-JLB97 and GLAS-RAMPv2, plotted as a
func-tion of surface slope (at 0.028intervals) for the region covered by ERS RA data (everywhere north of 81.58
S). The errors south of this latitude are not included in the statistics presented inFig. 1 and Table 1as they are not representative of the rest of the ice sheet. FWHM was plotted, in addition tor, as the histograms of differences do not have a Gaussian distribution (Fig. 2). As a consequenceris not necessarily an appropri-ate metric for the random error. We believe the reason for the non-Gaussian distribution of errors may be due to the fact that the RA ranges to the top of small-scale (sub-kilometre) undulations, while GLAS can bseeQ
down into the troughs and other small-scale features such as rifts and crevasses. This would explain the negative tail in the distributions (i.e. points where GLAS is below the DEM) and is also the explanation for the systematic trend in the bias for JLB97 (Fig. 1a), as discussed later. It is interesting to note that there is a marked increase in FWHM for RAMPv2 at slopes above about 0.68. At slopes greater than this value, much of the data used in RAMPv2 came from sources other than RA data. These sources appear to provide lower accuracy overall, as shown later.
Table 1
Statistics of the elevation differences for the two digital elevation models as a function of the regional surface slope Slope (deg) JLB97 RAMPv2 N Mean difference (m) FWHM (m) Std Dev (m) Mean difference (m) FWHM (m) Std Dev (m) 0.0–0.05 0.49 1.5 2.86 1.46 4.2 4.23 1434162 0.05–0.1 0.83 2.3 3.58 1.94 4.3 7.28 2426442 0.1–0.15 1.56 3.7 4.46 1.6 6.6 10.83 1887812 0.15–0.2 2.77 5 6.09 1.54 9.4 15.4 1103051 0.2–0.25 4.16 7.2 8.18 1.15 13.6 20.88 677814 0.25–0.3 5.49 8.8 10.15 0.42 18 25.31 458705 0.3–0.35 6.69 11 12.53 0.05 22.2 29.55 339196 0.35–0.4 7.97 11.5 14.67 0.81 25.6 35.55 260270 0.4–0.45 8.55 12.8 16.09 1.84 26.5 40.05 208907 0.45–0.5 9.07 12.2 18.77 2.48 29.9 45.42 165112 0.5–0.55 9.29 13.3 20.53 4.89 31.8 50.62 131466 0.55–0.6 9.74 13.1 22.42 6.99 39 54.57 115556 0.6–0.65 10.86 14.4 25.04 8.49 37.6 58.28 98733 0.65–0.7 9.41 15.2 26.6 8.37 41.5 60.92 84432 0.7–0.75 8.59 13.2 29.77 5.8 51.8 62.31 73270 0.75–0.8 9.17 15.9 33.2 4.91 10.1 63.64 63492 0.8–0.85 10.89 16.2 34.76 2.92 52 65.27 57512 0.85–0.9 10.95 17.7 37.64 5.06 52 66.11 50602 0.9–0.95 9.68 14.4 38.7 4.24 66.2 65.49 43387 0.95–1.0 10.3 15.2 42.7 5.53 57.5 67.12 35658
Note that the statistics were calculated for a 0.058slope interval for the table but a 0.028interval forFig. 1so the values are not identical, in particular for FWHM.
A small number of both positive and negative out-liers are apparent inFig. 2. These are probably due to a combination of erroneous GLAS data that have not been removed during filtering, errors in the DEMs and geophysically related artefacts due to sub-grid scale features such as crevasses and rifts, which are detected by the relatively small GLAS footprint (60 m) compared with the RA footprint, which is typically around 2–3 km over undulating terrain. The mean bias between GLAS and, in particular, RAMPv2 is also evident inFig. 2. The full statistics of the compar-ison are tabulated inTable 1using a slope interval of
0.058, whereN is the number of samples for a given slope interval. It is evident that at the lowest slopes (less than 0.28, which accounts for over half the ice sheet area), the biases are below about 2 m and the FWHMs are less than 5 and 9.4 m, respectively (seeTable 1). A contribution to the FWHM is due to real topographic variation within a 5-km DEM grid cell, which is not an error but a function of the spatial resolution of the DEM. There is a monotonic increase in the bias (as well as random error) between GLAS and JLB97 with increasing slope. This is expected, and was also noted for a similar study in Greenland [19]. There is, by contrast, no obvious trend in the bias for RAMPv2. The solid line in Fig. 1 indicates the cu-mulative percentage area covered as a function of slope. About 60% of the ice sheet has a slope less than 0.28, covering all of the ice shelves and high elevation ice sheet interior.Fig. 1is a summary of the global trends as a function of surface slope. It does not indicate the spatial pattern of the errors, however, which show marked regional trends (Fig. 3a and b). The most obvious feature is the area of large errors south of the latitudinal limit of the RA data (81.58S). Here, only sparse, low accuracy, terrestrially-derived, data were available and the errors are therefore large and similar in both DEMs. The central, plateau region of East Antarctica is a low slope area where the FWHM in JLB97 is on the order of 1–2 m with a bias of around 50 cm. Toward the margins, where surface slopes
Fig. 3. Plots of the spatial pattern of GLAS minus (a) JLB97 and (b) RAMPv2, scaled betweenF20 m. The green square indicates the colour of a zero elevation difference.
4 × 104 3 × 104 2 × 104 1 × 104 0 Count -40 -20 0 20 40 Elevation difference (m)
Fig. 2. Histograms of the difference (GLAS-DEM) for the surface slope interval 0.1–0.158. The black line is for GLAS-JLB97 and the grey line is for GLAS-RAMPv2.
increase, the differences are larger and, in general, negative (i.e. DEM higher than the GLAS data). In the case of RAMPv2 the bias over the plateau is slightly higher (at around 2–3 m) and positive (see alsoFig. 1a andTable 1). In addition, there are both positive and negative biases near the margin and the larger errors (blues and reds) cover a greater proportion of the coastal area compared with JLB97. The non-monoton-ic characteristnon-monoton-ic of the bias in RAMPv2 is reflected by much higher random errors for larger slopes, exceeding 100 m for slopes greater than 0.758, for example. The scale inFig. 3isF20 m to illustrate the spatial pattern of errors in the DEMs over most of the ice sheet. Some of the differences are, however, considerably larger than 20 m and the plot is, therefore,bsaturatedQ
in places.Fig. 4shows the errors on a scale ofF100 m to illustrate the distribution of these larger errors. Not surprisingly, they are ubiquitous throughout the region south of 81.58but are also apparent along the Transan-tarctic Mountains and parts of the AnTransan-tarctic Peninsula. It is evident, also, that RAMPv2 contains a greater area of these larger errors compared to JLB97 and it is notable that many of these regions are areas where cartographic sources were used to supplement the RA data[9]. Detailed examination of the DEMs shows that these areas in RAMPv2 possess information at higher spatial resolution compared to JLB97 but, seemingly, at the cost of a poorer vertical accuracy. Most of the marginal areas of the ice sheet appear to have errors on the order of 100 m in RAMPv2 (Fig. 4b) with both positive and negative differences.
5. Discussion
The random errors (both FWHM and r) show a fairly linear trend with slope as was found in Green-land[13,19] but the values for Antarctica are higher. This is most probably due to the 5-km resolution of the DEMs used here (for Greenland a 1-km DEM was available) combined with the effect of using bilinear interpolation over this length scale. In addition, the time difference between the radar and laser measure-ments, as discussed earlier, will increase the random errors marginally. The result for the bias as a function of surface slope (Fig. 1a) for JLB97 is not unexpected and is similar in behaviour and magnitude to that observed for RA data analysed using similar methods, and an airborne laser data set, over Greenland[13,19]. It has been hypothesised previously that this effect is due to the use of the relocation method for slope correction, which relocates RA measurements to the nearest point on the surface. This results in a clustering of observations towards the peaks of undulations and away from the troughs [12]. As a consequence, the sampling of the surface by the RA is biased towards higher points. This may appear to be a disadvantage of the relocation method, but it reflects the true sampling behaviour of the RA, which does not uniformly sample all parts of the surface. In addition, the bias this introduces can be easily characterised and is a well-behaved function of slope unlike other methods for slope correction, which have an unpredictable and noisy error distribution [12,19]. As the amplitude of
the peaks and troughs increases, we expect the bias in the relocation method to increase. The amplitude of undulations is, in part, a function of ice thickness, which, in turn is a function of surface slope[20]. To examine this relationship quantitatively, we estimated the amplitude of undulations within a 5-km grid cell by identifying all GLAS data that were located within the cell, fitting a plane to them, and calculating the stan-dard deviation of the residuals. The stanstan-dard deviation was taken as a proxy for the amplitude of undulations.
Fig. 5 is a plot of the amplitude of undulations versus slope, calculated in this way. There is a mono-tonic increase in the undulation amplitude proxy with slope. The JLB97 bias, estimated from Fig. 1a, is also shown for comparison. The two agree remark-ably well up to a slope of about 0.68at which point the bias appears to level off while the undulation am-plitude continues to increase. The divergence in behav-iour above 0.68 may be due to increased errors in estimating slopes over a 10-km scale in areas of high relief and to the inclusion of non-glaciated terrain at higher slopes. When the slopes were estimated over a
shorter distance2, for example, the trend in the JLB97 DEM bias was found to have less variability at higher slopes.
6. Conclusions
We have used data from the GLAS instrument on-board the ICESat satellite to assess the accuracy of the two, currently, most up to date, and commonly used, DEMs of the Antarctic ice sheet. The accuracy of both DEMs, south of the coverage of ERS-1 RA data, was relatively poor, with errors in excess of 100 m. Over the central, low-slope plateau area of East Antarctica, the JLB97 DEM had a bias between 0.5 and 1.6 m and random error of between 1.5 and 4 m. The RAMPv2 DEM had a regionally varying bias of between 1.4 and
-5 0 5 10 15 20 25 30 35 40 0 0.2 0.4 0.6 0.8 1
Mean Height Difference [m]
Slope [deg]
GLAS variation DEM difference 10km
Fig. 5. Plot of a measure of the amplitude of surface roughness within a 5-km grid cell as a function of regional surface slope (in 0.028bins) compared with the bias estimate for GLAS-JLB97 shown inFig. 1a (solid line). The error bars indicate the standard deviation of the amplitude estimates for all grid cells that lie in each 0.028slope bin used.
2
To do this, we used a new but, at the time of writing, unpub-lished, 1-km resolution DEM that is a combination of GLAS and ERS data, which draws on the analysis presented here to correct for biases between GLAS and ERS data.
3 m and a slightly higher random error. Biases and random errors increased with local slope with a mono-tonic trend for JLB97 and a complex, unpredictable trend for RAMPv2. The former consistently had over a factor two lower random error compared with the latter. This, we believe, was due to the method employed for slope correcting the RA data used in the RAMPv2 DEM, which introduces significant errors for surfaces with a non-zero second derivative[12](i.e. for surfaces with curvature). By fitting a function, such as a second order polynomial, to the bias observed for JLB97 it is possi-ble to reduce the bias to around a metre for all slopes up to 18, as was done for a DEM of Greenland[13]. We conclude that the RA processing chain used to generate JLB97 produces lower noise and, with addition of the correction described, a lower bias than the method used to process the RA data used in RAMPv2 [15]. The former have been, as a consequence, combined with GLAS data, to produce a new DEM of Antarctica that is both more accurate, particularly near the margins and south of 81.58, and higher resolution. A true spatial resolution of close to 1 km is achievable (dependent largely on latitude), due to the smaller footprint size of GLAS (60 m) compared to the ERS-1 RA, which produces elevation estimates that are typically corre-lated over distances of about 4 km over ice sheet terrain.
Acknowledgements
This work was funded by UK NERC contract for the Centre for Polar Observations and Modelling. We would like to thank NSIDC for providing the GLAS data and advise on processing and Robert Thomas for providing comments on a draft version of the paper.
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