Springer 2006
Marine Geophysical Researches (2006) 27: 19–34 DOI 10.1007/s11001-005-2095-4
An evaluation of publicly available global bathymetry grids* K. M. Marks* and W. H. F. Smith NOAA Laboratory for Satellite Altimetry, Silver Spring, MD, 20910, USA; *Author for correspondence (Tel: +1-301-713-2860, ext. 124; Fax: +1-301-713-3136; E-mail:
[email protected]) Received 30 August 2004, accepted 11 August 2005
Key words: bathymetric grids, bathymetry, Coral Sea, DBDB2, ETOPO2, GEBCO, GINA, satellite bathymetry, Woodlark Basin
Abstract We evaluate the strengths and weaknesses of six publicly available global bathymetry grids: DBDB2 (Digital Bathymetric Data Base; an ongoing project of the Naval Research Laboratory), ETOPO2 (Earth Topography; National Geophysical Data Center, 2001, ETOPO2 Global 2’ Elevations [CD-ROM]. Boulder, Colorado, USA: U.S. Department of Commerce, National Oceanic and Atmospheric Administration), GEBCO (General Bathymetric Charts of the Oceans; British Oceanographic Data Centre, 2003, Centenary Edition of the GEBCO Digital Atlas [CD-ROM] Published on behalf of the Intergovernmental Oceanographic Commission and the International Hydrographic Organization Liverpool, UK), GINA (Geographic Information Network of Alaska; Lindquist et al., 2004), Smith and Sandwell (1997), and S2004 (Smith, unpublished). The Smith and Sandwell grid, derived from satellite altimetry and ship data combined, provides high resolution mapping of the seafloor, even in remote regions. DBDB2, ETOPO2, GINA, and S2004 merge additional datasets with the Smith and Sandwell grid; but moving from a pixel to grid registration attenuates short wavelengths (250 m (green area). This area has ship track control in the Smith and Sandwell grid, but there is no ship track control in the GEBCO grid. We find that, in general, the large-scale features of the two grids are similar, but they may be significantly different where one grid has control data the other lacks. At shorter spatial scales the two grids also appear very different. In the Smith and Sandwell grid (Figure 3), short-wavelength (20–160 km) tectonic details of the seafloor in the Woodlark Basin are resolved (e.g., north–south trending lineations along about 154.1 E, 155.1 E, and 156.4 E are fracture zones, and small circular bathymetric highs, e.g., at 155.5 E, 10.25 S and 155.75 E, 9.75 S, are seamounts). The pervasive ‘‘bumpy’’ background fabric, while due in part to noise in the altimeter data, may also be related to small-scale morphology of the ocean floor (Goff et al., 2004). Even though the GEBCO grid spacing is 1-min, it has a generally smooth appearance (Figure 4), and neither the bumpy fabric nor the above tectonic details are evident. The GEBCO grid is derived primarily from digitized 500 m contours drawn at 1:10 million scale. At this scale, contours can only be drawn about 3 mm apart. Thus the map scale alone limits the horizontal resolution to about 30 km, and the slope of the ocean floor to about 1 degree. The map scale also limits the vertical resolution – for example, abyssal hills will not be detected because their maximum relief is only 300 m (Goff, 1991). The contours appear as terraces in the GEBCO grid and are particularly
visible around the Louisiade Plateau (see Figure 4). These terraces cause spikes in the histogram of GEBCO depths to appear at contour values (Figure 10a). In contrast, the distribution of depths in the Smith and Sandwell grid (Figure 10b), displays a smooth distribution of
Figure 9. Low-pass (wavelengths >160 km) filtered bathymetry from (a) GEBCO and (b) Smith and Sandwell. The RMS of the difference between the two low-pass fields is 119 m, and the mean difference is 34 m. The red box in (a) and (b) is enlarged in (c). (c) Smith and Sandwell ship control points (black dots) cover the region where differences are >250 m (green area), but GEBCO ship tracks (red lines) do not, indicating this seafloor high is not detected in the GEBCO grid.
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Figure 10. Histograms of (a) GEBCO depths and (b) Smith and Sandwell depths, at a bin width of 50 m. The GEBCO depths (a) spike at the 500 m contour values. The spike at 4500 m in the Smith and Sandwell grid reflects flat sediments in the southwestern portion of the study area, while the spike at 0 m reflects the use of a high-resolution land-sea boundary.
depths except for spikes at 4500 and 0 m. A region of flat sediments in the Coral Sea (southwest portion of the study area, see Figure 3) accounts for the large number of 4500 m depths. The spike at 0 m occurs because Smith and Sandwell constrained the land–sea boundary in their grid with the high-resolution World Vector Shoreline (Wessel and Smith, 1996).
Registration, Sampling, Interpolation and Smoothing We turn now to compare Smith and Sandwell to the other grids in our study, which have incorporated it (DBDB2, ETOPO2, GINA, S2004). Smith and Sandwell’s original product is given on a Mercator-projected and pixel-registered coordinate system, but all the other grids have interpolated it onto meshes having equidistant sampling in longitude and latitude (not Mercator-projected). One immediate consequence of this interpolation is that the encoding of the location of control soundings was lost. In this section and the next we examine some additional consequences. The particular coordinate system used by Smith and Sandwell (1997) facilitated their work. Their calculations required a conformal map projection. Among conformal projections, the Mercator was a good choice because its increasing magnification of area at increasing latitude counteracts the increasing spatial density of the satellite ground tracks, effectively spreading the data out more nearly uniformly. Having chosen to compute the solution in Mercator map coordinates, it then made sense to use a pixel registration so that imaging software could plot maps directly without further interpolation.
However, care must be exercised when interpolating between grid meshes, lest fine-scale information be lost. Figure 11a demonstrates what happens when the 2-arc-min pixel-registered mesh of Smith and Sandwell is resampled onto a 2-arcmin grid-registered mesh such as used in DBDB2 and ETOPO2. In this interpolation, the original data are sampled on meridians at odd-numbered minutes of longitude, and the derived data are sampled on meridians at even-numbered minutes of longitude. The Nyquist wavelength of the original mesh is a waveform with amplitudes of 1 and )1 at odd arc-minutes. If this waveform is sampled at even arc minutes the waveform vanishes. More generally, at wavelengths longer than the Nyquist wavelength, amplitudes will also be attenuated, though they will not go entirely to zero. The amplitude loss in going from the Smith and Sandwell grid to the DBDB2 or ETOPO2 grid is cos(2p/k), where k ‡ 4 is the wavelength in arcminutes. This transfer function, as a function of wavelength, is shown in Figure 11b. The DBDB2 and ETOPO2 grids should be smoother than the original Smith and Sandwell grid, at least in areas where they have resampled it without incorporating any new information. The ETOPO2 grid in the Woodlark Basin (Figure 5) looks very similar to the Smith and Sandwell grid (Figure 3), because ETOPO2 is based on the Smith and Sandwell grid at these latitudes. Closer inspection, however, reveals a slightly smoother appearance to the ETOPO2 grid – for example, note how the fracture zones and seamounts are not as crisp. This smoothing results from NGDC’s interpolation of the pixel-registered Smith and Sandwell grid onto a grid-registered ETOPO2 grid. Like ETOPO2, DBDB2 (V2.2 and
29 V3.0, Figure 6a and b) was interpolated from Smith and Sandwell bathymetry onto a grid-node registration, so it demonstrates the same smoothing as a result.
Figure 11. (a) The Nyquist wavelength of the 2-arc-min, pixel-registered Smith and Sandwell grid has local maxima and minima at odd meridians (black circles) and zero crossings at even meridians (open squares), where DBDB2 and ETOPO2 are sampled. (b) The transfer function for moving between odd (pixel) and even (grid) 2-arc-min registrations. At a wavelength of 20 arc-min (36 km at 11.5 N), the amplitude is reduced by half. (c) The spectral density of the grids based partly on satellite altimetry is similar at long wavelengths but significantly different at wavelengths shorter than 20 km. (d) The spectrum of amplitude ratios for the other grids with respect to Smith and Sandwell, compared to the theoretical pixel-to-grid transfer function (TF).
Spectral Analyses Figure 11c plots the spectral density of each of the grids incorporating altimetry. The attenuation caused by moving from a pixel to a grid registration is exhibited as a reduction of power at wavelengths shorter than about 20 km for ETOPO2 and DBDB2, as compared to Smith and Sandwell. Although we plot only the spectrum for DBDB V2.2, V3.0 has a similar loss in power. The spectral density of the S2004 grid is slightly lower at shorter wavelengths than for Smith and Sandwell. This is because, in shallow water, the smoother GEBCO data were added to the S2004 solution. Even though the GINA grid is sampled on a pixel-registered grid that includes the original Smith and Sandwell points, it still exhibits a reduction in power at shorter wavelengths (Figure 11c). Discussions with one of the authors (Engle, pers. com., 2005) about the details of how the GINA grid was constructed did not reveal any reason for the cause of the attenuation. There was no filtering when the 2 min Sandwell and Smith grid was resampled onto a 30 arc-second grid. This leaves us to speculate the attenuation may be due to the bilinear or bicubic interpolation used in the resampling. We note that both the Smith and Sandwell and S2004 power spectra appear to flatten out at wavelengths shorter than about 15 km (Figure 11c). This flattening may be the signature of white noise in the altimeter data. The power spectra for the other grids do not flatten out, but instead maintain the spectral slope to shorter wavelengths. For the ETOPO2 and DBDB2 spectra, this can be a result of noise (along with short wavelength signal) being smoothed out due to moving to a grid registration. This is not necessarily a bad thing, if noise suppression is preferred over seafloor fabric resolution. In Figure 11d we divide the amplitude spectra of the different grids by the Smith and Sandwell amplitude spectrum, and compare that ratio to the transfer function for moving between a pixel and a grid registration. In this way we can visualize the amplitude loss at different wavelengths due to changing the grid registration. The transfer function models the ratio of ETOPO2/Smith and Sandwell well at wavelengths >10 km, demonstrating how the loss of amplitudes in the ETOPO2
30 grid is mostly a result of changing the grid registration. The DBDB2/Smith and Sandwell amplitudes are higher than those of the transfer function at shorter (
