Nearshore Bathymetric Mapping along a 7-mile Reach of Lake Sharpe Shoreline near Lower Brule, South Dakota, 2013

By

Ryan F. Thompson

99°35' 99°34'30" 99°34' 99°33'30"

44°04'

44°04'30"

EXPLANATION

Line of equal water depth—Shows water 

depth from water surface to lake bottom, in 

feet. Depth interval 1 foot, with supplemental interval of 3.5 feet. Lines of equal depth 

had vertical accuracy of 0.560 foot at the 

95-percent confidence level

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Base from U.S. Department of Agriculture, National Agriculture 

Imagery Program (NAIP), 2012

Universal Transverse Mercator projection, zone 14

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Lower Brule

Lake Sharpe

Figure 5. Lines of equal water depth in nearshore areas of Lake Sharpe adjacent to the community of Lower Brule, 2013.

DATA PROCESSING AND INTERPRETATION

Once the data collection effort was completed, data editing was necessary to remove erroneous data points and apply water-surface elevations. Bathymetric data can be affected by anything that happens to be in 

the water column below the depth transducer. HYPACK® software has a 

data editing module that allows the user to remove erroneous data points 

caused by submerged vegetation or timber, fish, bubbles (from waves or the 

motor), or rock/cobble on an otherwise smooth bottom. Submerged vegetation was present in many parts of the surveyed area, and sometimes in large 

patches. In some areas, part of the echosounder signal was able to penetrate 

through the vegetation so that some of the returns were actually from the 

lake bottom. In other areas, the vegetation was very thick, and the signal did 

not reach the bottom. In areas of thick vegetation, the edited data has gaps 

where the erroneous vegetation returns were removed.

The boat-based data from the echosounder is produced at a high frequency (as many as 20 pulses per second). This results in very closely 

spaced data points when the boat travels at the slow speeds typically used 

during the survey. Individual data points commonly were less than 0.2 foot 

apart along the transect. This high frequency of data collection would be 

useful when traveling at higher speeds or in areas with a steep and rapidly 

changing bottom terrain. However, the bottom within the study area was 

generally very smooth, and the shallow depths commonly encountered 

required a relatively slow travel speed. This resulted in a very dense dataset 

with many redundant data points. The HYPACK® software allows the user 

to select a subset of the data, based on a desired distance between points 

or when the depth change between adjacent points exceeds a user-defined 

threshold. This capability was used on the boat-based data collected on the 

regular transects to provide a dataset of a more manageable size. The maps 

of water depth and bottom elevation described in the next section were 

developed from the edited subset of the original data.

DEVELOPMENT OF MAPS

Although lakes such as Lake Sharpe might sometimes be assumed to 

have a flat water surface, data points collected at the water surface throughout the surveyed area and during each day of data collection indicated 

a decrease in water-surface elevation in the downstream direction. The 

change in water surface throughout the study area was approximately 

1 foot. Although dam releases for hydropower generation upstream at Oahe 

Dam and downstream at Big Bend Dam typically followed a diurnal cycle 

during data collection (Darin Larson, Civil Engineer, U.S. Army Corps of 

Engineers, written commun., 2014), the study area appears to be far enough 

away from the dams to allow at least some of the diurnal cycle changes to 

be attenuated. Because of the changing water surface throughout the study 

area, lines of equal water depth will not be parallel to elevation contours of 

the reservoir bottom. Therefore, separate maps for water depth and bottom 

elevation were developed for the nearshore areas of the study area.

WATER-DEPTH MAP

The boat-based data were exported into a spreadsheet and subsequently 

loaded into a geographical information system software, ArcGIS (Esri, 

2014). Within ArcGIS, each data point could be plotted on-screen and 

labeled with its corresponding water depth (distance from water surface to 

lake bottom). By interpolating water depth between points and from one 

transect to the next, lines of equal water depth were manually digitized 

for 2, 3, 3.5, 4, and 5 feet deep. A few transects had data points of depths 

greater than 5 feet, so segments of these lines of equal depth also were 

digitized where adequate data were available. Lines of equal depth for the 

nearshore area adjacent to Lower Brule (fig. 5) and for the study area 

(fig. 6) indicate that water depths stay shallow for quite a distance from 

shore. In the 288 transects that crossed a 2 foot depth line, this depth 

occurred an average of 88 feet from shore. Similarly, in the 317 transects 

that crossed a 3 foot depth line, this did not occur until an average of 

343 feet from shore.

BOTTOM-ELEVATION MAP

The contour map of the elevation of the lake bottom in nearshore 

areas of Lake Sharpe was developed in a manner similar to that used for 

the water-depth map, but with the wading-based data collected near shore 

included. For the bottom-elevation map, contours were manually digitized 

for elevations of 1,419; 1,418; 1,417; and 1,416 feet above the North American Vertical Datum of 1988. Some transects had data points at lower elevations, so segments of these elevation contours also were digitized where 

adequate data were available (fig. 7).

ACCURACY ASSESSMENT OF DATA AND MAPS

Each physical measurement has two components: the number representing the estimated value of the property being measured, and the degree of 

uncertainty associated with that measurement. The analyses of uncertainty 

associated with the data and the maps derived from the data are described in 

this section.

Horizontal accuracy of the boat- and wading-based data is dependent 

on the horizontal accuracy of the RTK GNSS equipment and the surveying 

methodology used in data collection. Holding the rover rod and base tripod plumb ensures that the GNSS antenna is directly above the point being 

measured. A birds-eye level mounted to the base tripod and each rover rod 

helps to minimize horizontal errors because of the GNSS antenna being out 

of plumb. Horizontal accuracy of the GNSS equipment being used in RTK 

mode is specified by the manufacturer as 0.3937 inch (10 millimeters) 

plus 1 part per million times the baseline length (Topcon Positioning Systems, 2007). The data points farthest away from the GNSS base station (that 

is, the data points at the southern end of the study area) are approximately 

24,813 feet away, for which the 1 part per million increase in horizontal 

error equates to 0.3 inch. The manufacturer’s estimated horizontal error 

associated with the RTK GNSS equipment over the study area ranges from 

0.4 to 0.7 inch (fig. 8). Horizontal errors of this magnitude are essentially 

inconsequential because changes in water depth and bottom elevation were 

found to be very gradual. No steep drop-offs were evident in the study area. 

Horizontal errors of the base coordinates are expected to be within 0.05 foot 

based on OPUS peak-to-peak root mean squared errors. The peak-to-peak 

root mean squared error is the difference between the three baseline solutions computed by OPUS (National Geodetic Survey, 2014b).

Proper equipment and surveying methods can help to minimize vertical 

errors associated with the GNSS equipment. Using a fixed-height tripod at 

the RTK GNSS base station and fixed-height rover poles largely eliminates 

errors associated with incorrectly measured antenna height. Vertical errors 

specified by the GNSS manufacturer used in RTK mode are 0.5906 inch 

(15 millimeters) plus one part per million times the baseline length (Topcon Positioning Systems, 2007). The data points farthest away from the 

GNSS base (that is, the data points at the southern end of the study area) are 

approximately 24,813 feet away, for which the 1 part per million increase in 

horizontal error equates to 0.3 inch. The manufacturer’s estimated vertical 

error associated with the RTK GNSS equipment over the study area ranges 

from 0.6 to 0.9 inch (fig. 9). This vertical error is small relative to the accuracy of the bathymetry data, as discussed in the following paragraphs.

Accuracy assessments of the data collected for this study were computed according to the National Standard for Spatial Data Accuracy 

(NSSDA; Federal Geographic Data Committee, 1998). This standard is 

mathematically robust and well-suited to large datasets. The data are compared to an independent dataset to compute the vertical root mean squared 

error (RMSEz) using equation 1: 

 RMSEz

 =

(Zdatai - Zchecki) n

i=1

n

∑ (1)

where

RMSEz is the vertical root mean square error, 

Zdataiis the vertical coordinate of the ith check point in the dataset, 

checki

is the vertical coordinate of the ith check point in the 

independent dataset,

i is an integer from 1 to n, and

n is the number of points being checked.

Assuming the errors are normally distributed, vertical accuracy at the 

95-percent confidence level (Az

) is then computed from the RMSEz value 

using equation 2:

 Az = 1.960 × RMSEz (2)

where

Az is the fundamental vertical accuracy calculated at the 

95-percent confidence level.

For this study, boat- and wading-based data from the regular transects 

were considered the primary dataset, whereas the boat- and wading-based 

data from the oblique transects were considered the independent dataset. 

The boat-based data from the regular transects were compared with the 

boat-based data from the oblique transects where lines intersected to evaluate the repeatability of the echosounder data at various depths over the 

study area. Using ArcGIS software (Esri, 2014), any boat-based data 

point from an oblique transect that was within a selection distance of a boatbased data point from a regular transect was identified and their elevations 

compared. Points within 0.33 feet of each other were assumed to be coincident (Wilson and Richards, 2006). This criterion was met by 119 point 

pairs, giving an RMSEz

 value of 0.228 feet and an Az value of 0.448 feet 

(table 2). 

Z

Differences in bottom elevations from boat-based and wading-based data 

sources were compared between the two datasets. For this comparison, the 

boat-based data from regular transects were again used as the primary dataset, and the wading-based data from regular transects were considered the 

independent dataset. Using ArcGIS software (Esri, 2014), any boat-based 

data point on a regular transect that was within a selection distance of a 

wading-based data point on a regular transect was selected for comparison. 

Because spacing between wading-based data points typically was larger 

than spacing between boat-based data points, far fewer points were available using the same selection distance of 0.33 feet used for the comparison 

between boat-based data on regular and oblique transects. Accordingly, the 

selection distance was increased in an effort to identify enough point pairs 

for a comparison. A 2-foot selection distance was initially tried, but less than 

100 points met this distance criterion. Using a 3-foot selection distance, 

347 pairs of data points were available for comparison. The mean bottomelevation difference between paired data points from these datasets was 

0.013 foot, with a median difference of 0.02 foot. Although the maximum 

(0.40 foot) and minimum (-0.56 foot) differences between paired elevations 

were large, it must be remembered that the points compared could be as 

much as 3 feet apart. The RMSEz

 value for the pairs of data points was 

0.140 foot, and the Az

 value was 0.247 foot (table 2). The better accuracy of 

these data than those used in the comparison between boat-based data from 

regular and oblique transects may be because the point pairs were concentrated in shallower areas near shore, where the bottom tended to be more 

smooth and uniform. The shallower depth would help minimize elevation 

differences between the datasets even though the point pairs were potentially 

much farther apart.

Table 2. Summary of accuracy assessments for bathymetric survey in nearshore 

areas of Lake Sharpe, 2013.

Primary datset Independent 

dataset

Selection 

distance 

(feet)

Number of 

data point 

pairs

Vertical 

root mean 

squared error 

(RMSEz) (feet)

Fundamental 

vertical accuracy at 95-percent 

confidence 

level (AZ

 )(feet)

Regular transects, 

boat-collected

Oblique transects, boatcollected0.33 119 0.0228 0.448

Regular transects, 

boat-collected

Regular transects, wadingcollected.3 347 0.140 0.247

Lines of equal 

water depth

Oblique transects, boatcollected.0.33 1,333 0.286 0.560

Bottom-elevation 

contours

Oblique transects, boat-collected0.33 1,095 0.261 0.511

Additional analyses were completed to assess the accuracy of the maps 

of water depth and bottom elevation derived from the boat- and wading-based water-depth and bottom-elevation data for the regular transects. 

Comparisons were made between each set of lines or contours for the 

water-depth map or bottom-elevation map, respectively, and the boat- and 

wading-based data from oblique transects. These comparisons incorporate 

inaccuracies that may be introduced from the effects of data processing and 

interpretation. For these comparisons, the lines or contours derived from 

boat- and wading-based data on the regular transects provided the primary 

dataset, and the boat-based data from the oblique transects provided the independent dataset. Using a 0.33-foot selection distance, 1,333 point pairs 

were identified for comparison between the lines of equal water depth 

and the boat-based data on the oblique transects. The RMSEz

 value was 

0.286 foot and the Az

 value was 0.560 foot (table 2). Using a 0.33-foot selection distance, 1,095 point pairs were identified for comparison between the 

bottom-elevation contours and the boat-based data on oblique transects. The 

RMSEz value was 0.261 foot, and the Az value was 0.511 foot. Thus, both the 

water-depth map (fig. 5) and the bottom-elevation map (fig. 6) are able to 

support a 1-foot interval using NSSDA vertical accuracy standards, which 

require RMSEz and Az of 0.30 foot and 0.60 foot or better, respectively (Federal Geographic Data Committee, 1998).

ACKNOWLEDGMENTS

The author would like to acknowledge the Lower Brule Sioux Tribe for 

their cooperation on this study and previous investigations in the Lower 

Brule, South Dakota area. The work and local knowledge contributed by 

their staff has ensured that science needs are met in the areas where it is critically needed.

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99°35' 99°34'

44°08'

44°07'

44°06'

44°05'

44°04'

0 0.25 0.5 MILE

0 0.25 0.5 KILOMETER

Lower Brule

Lake Sharpe

Lake Sharpe

Lake Sharpe

Base from U.S. Department of Agriculture, National Agriculture 

Imagery Program (NAIP), 2012

Universal Transverse Mercator projection, zone 14

Area shown on figure 5

EXPLANATION

Line of equal water depth—Shows 

water depth from water surface to 

lake bottom, in feet. Depth interval 

1 foot, with supplemental interval of 

3.5 feet. Lines of equal depth had 

vertical accuracy of 0.560 foot at 

the 95-percent confidence level

U.S. Geological Survey 

reference point used for base 

station—Punch point in top of 

rebar driven into ground along 

the edge of concrete pad. 

Elevation of reference point is 

1,428.86 feet above North 

American Vertical Datum of 

1988

2 4 7

3

3.5

5

6

Figure 6. Lines of equal water depth in nearshore areas of Lake Sharpe in the study area, 2013.

REFERENCES CITED

Esri, 2014, ArcGIS: accessed January 22, 2014, at http://www.esri.

com/software/arcgis.

Federal Geographic Data Committee, 1998, Geospatial Positioning 

Accuracy Standards, part 3—National Standard for Spatial Data 

Accuracy: Federal Geographic Data Committee and U.S. Geological Survey, accessed January 30, 2014, at http://www.fgdc.gov/

standards/projects/FGDC-standards-projects/accuracy/part3/

index_html. 

HYPACK, Inc., 2013, HYPACK® Hydrographic Survey Software 

user manual: Middletown, Connecticut, HYPACK, Inc., 1,784 p., 

accessed April 17, 2014, at ftp://ftp.hypack.com/Documents/Manuals/English/HYPACK%20Manual/2013%20Release/2013%20

HYPACK%20User%20Manual.pdf.

National Geodetic Survey, 2014a, OPUS—Online Positioning User 

Service: accessed February 5, 2014, at http://www.ngs.noaa.gov/

OPUS/about.jsp#about.

National Geodetic Survey, 2014b, OPUS—Online Positioning User 

Service: accessed July 7, 2014 at http://www.ngs.noaa.gov/OPUS/

about.jsp#FAQ.

Neitzert, K.M., Honeywell, G.L., and Thompson, R.F., 2012, Monitoring bank erosion on the Missouri River on the Lower Brule 

Reservation, 2011‒2012 [abs]: 2012 Eastern South Dakota Water 

Conference Program and Abstracts, October 30, 2012, Brookings, 

S. Dak., p. 18., accessed April 17, 2014, at http://www.sdstate.edu/

abe/wri/activities/ESDWC/upload/esdwc-program-2.pdf.

1,4191,418

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1,417

1,419

1,414

1,415

1,416 1,417

1,418

1,419

1,416

1,413

1,415

1,414

1,413

1,415

1,414

1413

1,415

1416

1,412

1,413

1,414

1,415

1,416

1,415

1,418

1,417

1,415

1,415

1,415

1,415

1,416

1,417

1,418

1,419

1,414

1,414

1,414

1,413

1,414

1,415

1,416

1,419

1,418

1,417

1,414

1,414

1,414

1,414

1,414

1,413

1,413

1,413

1,417

1,413

1,414

1,413

1,417

1,413

1,412

1,412

1,412

1,413

1,412

1,414

1,414

1,414

1,413

99°35' 99°34'

44°08'

44°07'

44°06'

44°05'

44°40'

0 0.25 0.5 MILE

0 0.25 0.5 KILOMETER

Lower Brule

Lake Sharpe

Lake Sharpe

Lake Sharpe

Base from U.S. Department of Agriculture, National Agriculture 

Imagery Program (NAIP), 2012

Universal Transverse Mercator projection, zone 14

Elevation contour—Shows elevation 

of the lake bottom. Contour interval 1 

foot. Datum is North American 

Vertical Datum of 1988. Contours had 

a vertical accuracy of 0.511 foot at 

the 95-percent confidence level

U.S. Geological Survey reference 

point used for base station—Punch 

point in top of rebar driven into 

ground along the edge of concrete 

pad. Elevation of reference point is 

1,428.86 feet above North American 

Vertical Datum of 1988 1,412

1,413

1,414

1,415

1,416

1,417

1,418

1,419

EXPLANATION

Figure 7. Elevation contours of the lake bottom in nearshore areas of Lake Sharpe in the study area, 2013.

Rydlund, P.H., Jr., and Densmore, B.K., 2012, Methods of practice 

and guidelines for using survey-grade global navigation satellite 

systems (GNSS) to establish vertical datum in the United States 

Geological Survey: U.S. Geological Survey Techniques and 

Methods, book 11, chap. D1, 102 p. with appendixes, accessed 

April 17, 2014, at http://pubs.usgs.gov/tm/11d1/.

Topcon Positioning Systems, 2007, HiPer Ga/Gb operator’s manual: 

Topcon Positioning Systems, Incorporated, variously paginated.

Wilson, G.L, and Richards, J.M., 2006, Procedural documentation 

and accuracy assessment of bathymetric maps and area/capacity tables for small reservoirs: U.S. Geological Survey Scientific 

Investigations Report 2006‒5208, 24 p. plus oversize figures, 

accessed April 17, 2014, at http://pubs.usgs.gov/sir/2006/5208/.

99°36' 99°35' 99°34' 99°33'

44°08'

44°07'

44°06'

44°05'

44°04'

Lake Sharpe

0.6

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0.5

Lower Brule

0.4

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EXPLANATION

Horizontal error, in inches

U.S. Geological Survey reference 

point used for base station—Punch 

point in top of rebar driven into 

ground along the edge of concrete 

pad. Elevation of reference point is 

1,428.86 feet above North American 

Vertical Datum of 1988

0 0.5 1.0 MILE

0 0.5 1.0 KILOMETER

Base from U.S. Department of Agriculture, National Agriculture 

Imagery Program (NAIP), 2012

Universal Transverse Mercator projection, zone 14

0.4

0.5

0.6

0.7

Figure 8. Estimated horizontal error for Real-Time Kinematic Global Navigation Satellite system equipment.

99°36' 99°35' 99°34' 99°33'

44°08'

44°07'

44°06'

44°05'

44°04'

Lake Sharpe

Lower Brule

0.6

0.8

0.7

0.9

0 0.5 1.0 MILE

0 0.5 1.0 KILOMETER

Base from U.S. Department of Agriculture, National Agriculture 

Imagery Program (NAIP), 2012

Universal Transverse Mercator projection, zone 14

EXPLANATION

Vertical error, in inches

U.S. Geological Survey reference 

point used for base station—Punch 

point in top of rebar driven into 

ground along the edge of concrete 

pad. Elevation of reference point is 

1,428.86 feet above North American 

Vertical Datum of 1988

0.6

0.7

0.8

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Figure 9. Estimated vertical error for Real-Time Kinematic Global Navigation Satellite System equipment.

U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Map 3307

Sheet 2 of 2

Prepared in cooperation with the

Lower Brule Sioux Tribe

Any use of trade, product, or firm names in this publication is for descriptive purposes only and does not 

imply endorsement by the U.S. Government.

This map was printed on an electronic plotter directly from digital files. Dimensional calibration may vary 

between electronic plotters and between X and Y directions on the same plotter, and paper may change 

size due to atmospheric conditions; therefore, scale and proportions may not be true on plots of this map.

For more information on the USGS—the Federal source for science about the Earth, its natural and living 

resources, natural hazards, and the environment—visit http://www.usgs.gov or call 1–888–ASK–USGS 

This report is available at http://dx.doi.org/10.3133/sim3307.

Suggested Citation: 

Thompson, R.F., 2014, Nearshore bathymetric mapping of a 7-mile reach of Lake Sharpe shoreline near 

Lower Brule, South Dakota, 2013: U.S. Geological Survey Scientific Investigations Map 3307, 2 sheets,

http://dx.doi.org/10.3133/sim3307. ISSN 2329-132X (online)