Towards an Error Budget for Single- and Multi-Beam Data
Transcript of Towards an Error Budget for Single- and Multi-Beam Data
Towards an Error Budget for Single- and Multi-Beam Data
K. M. Marks and W. H. F. Smith
NOAA Laboratory for Satellite Altimetry, Silver Spring, Maryland, USA
Mapping the ocean basins requires a combination of single- and
multi-beam depth measurements to obtain the most complete
coverage. In order to give each data source proper weight, one
should have a model for the expected uncertainty in each
measurement. We are developing an error budget for single- and
multi-beam data by comparing their values in areas where survey
tracks overlap.
We present here preliminary results from some overlapping
survey lines near the Caroline Islands of Micronesia, in the western
Pacific Ocean. Ships proceeding between Guam and New Guinea
frequently take the same course in this area, as there are only a few
north-south passages between the atolls, as shown at right.
Before doing this analysis, we expected that single beam data would
be much less accurate than multibeam data, and that single beam
would measure the shallowest point within the ensonified cone. Both
assumptions seem to be wrong. We find that multibeam
measurements are repeatable to within about 0.25% of depth,
though errors are systematic and apparently due to roll bias. Single
beam data seem at least as accurate as multibeam.
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Example Single-Beam Cone on MR02-K01
Multibeam data ● A single-beam system samples a patch of seafloor within its ensonified cone
(half-angle 15°). The size of the patch depends on the depths within the cone.
In the example at left, the diameter of the patch is ~2.8 km.
● At each digitized single-beam sampling point along track MW9204, we found
all the multibeam data within the ensonified cone, assuming the cone axis was
vertical. From the multibeam data in each such single-beam patch area we
calculated:
Shallowest depth
Deepest depth
Mean depth
Standard Deviation
● We also calculated the slope of the least-squares plane best-fitting the
multibeam depths in the cone, and also the residuals about the plane.
● We anticipated that the reported single-beam depth would be the
shallowest depth in its ensonified cone.
● However, we find that single-beam depths are systematically deeper
than the shallowest multibeam depth found in the cone.
● While this could be due to 1) incomplete multibeam coverage in
cone or 2) location errors of sounding points, it is also possible that the
single-beam system does a rather good job of averaging the depths
within the patch it samples.
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MW9204 Depth, m
Shallowest Multibeam Depth vs Single-beam depth
Study Area Overlapping surveys
● Multibeam (JAMSTEC)
MR00-K08 (2000)
MR02-K01 (2002)
MR01-K01 (2001)
MR02-K06 (2002)
MR99-K06 (1999)
R/V Mirai
Seabeam 2112.004
150° swath width
● Single-Beam (NGDC)
MW9204 (1992)
MW9205 (1992)
R/V Moana Wave
3.5 KHz
30° beam width144˚
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Predicted Topography V9.1
MW9204
MW9205
Swath Paths
We thank JAMSTEC and NGDC for making these data freely available.
● Red and green dots locate the profiles shown to the left.
● The image shown is the difference between MR00-K08 and MR02-
K01 bathymetry grids, each made at 0.1 arc-minute.
● There is a systematic difference, an east-west tilt, which might be
due to a roll bias error in one or both swaths.
● The largest differences are around 10 m. If we assume each swath
system is equally in error, the error is ~ 0.1% of depth (here, ~5 m).
● Red dots are MR00-K08 ping points, red lines are from
swath data gridded at 0.1�(roughly 200 m) spacing.
● Green dots are from MR02-K01 ping points, green lines
are from swath data gridded at 0.1� spacing.
● Black star is single-beam sounding from MW9204
● 0.1�grids from swath bathymetry accurately honor ping
data points here.
● The center portions of the overlapping profiles have
similar depths.
● Differences in depths between MR00-K08 and MR02-K01
increase towards the outer beams of the profiles.
Overlapping Ping Profiles
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Longitude, deg.
Depth Difference Grid
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● MR00-K08 multibeam depths are about
the same as single-beam depths at
corresponding locations.
● MR02-K01 multibeam depths (directly
beneath MW9204 location) are
systematically ~10 m deeper than the
corresponding single-beam depth.
● Assuming navigation of all three is good,
MW9204 samples the east side of the
MR00-K08 swath and near the center of the
MR02-K01 swath. Do these results
suggest there is no roll bias in MR00-K08?
Histograms of the differences show the same offsets, and a surprise in
the spreads of the distributions.
● There is a -10 m median offset of MR02-K01 multibeam minus
MW9204 single beam depths (green area), despite the fact that MW9204
runs nearly down the middle of the MR02-K01 swath.
● The median offset of MR00-K08 multibeam minus MW9204 single
beam is only -4 m (red lines), despite the fact that MW9204 runs along
the eastern edge of the MR00-K08 swath.
● The histogram of differences between multibeam depths from MR02-
K01 and MR00-K08 (black lines) appears wider than the red and green
histograms of differences between multibeam and single-beam depths.
This suggests single-beam measurements may be at least as accurate
as multibeam measurements.
Histogram of Multibeam and Single-beam Depth Differences
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Distance along MW9204, km
Multibeam minus Single-beam Depths along MW9204
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● Depth differences MR02-K06 minus MR99-K06
multibeam swath grids.
● These also show an east-west tilt of the
differences, again possibly due to roll bias error.
● Single-beam tracks V3404 (1977) and
70042204 (1970) traverse this area. ● MR02-K06 multibeam depths (purple lines) match single-beam depths (black dots). MR99-K06 multibeam depths (blue lines)
are tilted with respect to the single beam depths. Note that both multibeam swaths are from the R/V Mirai�s Seabeam 2112 system
operating in ~4450 m of water, yet the system seems to have operated in two different modes on these two cruises, as the swath
widths are different.
● It appears multibeam swath MR99-K06 contains a roll bias error, which shows up as a tilt in the difference grid (left), and also as
a tilt in the profiles above.
Note this implies we can use old single beam to find errors in new multibeam data!
Data along V3403
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Distance along V3403, km
Data along 70042204
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Distance along 70042204, km
Depth Difference Grid