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