Bathymetric Data Collection

Bathymetric data (water depths and positions; fig. 2) were collected using high-resolution multibeam mapping systems (MBMSs). The data were collected concurrently by four boats surveying different sections of Table Rock Lake. The various components of the MBMSs used for this study are described in more detail in reports on the Missouri and Mississippi Rivers in Missouri (not shown; Huizinga, 2010, 2022; Huizinga and others, 2010) and Sugar Creek water supply lake near Moberly, Missouri (not shown; Richards and others, 2019). The survey methods used to obtain the data for Table Rock Lake were similar to these studies, as were the methods used to ensure data quality.

An MBMS is an integration of several individual components—the MBES, an inertial navigation system (INS), and a data-collection and data-processing computer. The MBES systems used were the NORBIT iWBMSh, the NORBIT iWBMSc, and the R2Sonic 2024, all operated at a frequency of 400 kilohertz (NORBIT, 2020; R2Sonic LLC, 2014). The iWMBSh and R2Sonic 2024 are similar in performance and operation to the MBES systems used in previous studies in Missouri (Huizinga, 2010, 2022; Huizinga and others, 2010, 2022; Richards and others, 2019). The iWBMSc also is similar to systems used in previous studies but has a less accurate INS.

The NORBIT MBES systems have a curved receiver array that enables bathymetric data to be collected throughout a swath range of 210 degrees. Optimum data generally are collected in a swath of less than 160 degrees (80 degrees on each side of nadir, or straight down below the MBES); nevertheless, the swath can be electronically rotated to either left or right of nadir, enabling data to be captured along sloping banks up to a depth just below the water surface. The R2Sonic system has a flat receiver array and is limited to a swath range of 160 degrees (80 degrees on each side of nadir) but can be physically tilted to enable data to be collected along sloping banks. The INS—Applanix OceanMaster for the iWBMSh and R2Sonic (Applanix Corporation, 2017) and NovAtel MarineSPAN with OEM–STIM300 for the iWBMSc (NovAtel, 2021)—provides position in three-dimensional space and measures the heave, pitch, roll, and heading of the vessel (and, thereby, the MBES) to accurately position the data received by the MBES. Survey data were collected using HYPACK/HYSWEEP software (HYPACK, Inc., 2020).

Real-time navigation during the survey used a real-time kinematic differential global positioning system solution. The navigation information from the iWBMSh and R2Sonic systems was postprocessed using the POSPac Mobile Mapping Suite software (Applanix Corporation, 2021). The iWBMSc navigation information was postprocessed with the Waypoint Inertial Explorer software (NovAtel, 2019). POSPac Mobile Mapping Suite and Waypoint Inertial Explorer provide tools to identify and compensate for sensor and environmental errors. These programs compute an optimally blended navigation solution from the global navigation satellite systems (GNSSs) and inertial-measurement unit raw data from the INS. The location solution was further enhanced by collecting static GNSS data with a GNSS base receiver set up over a temporary reference mark near Table Rock Lake, the coordinates for which were determined using techniques detailed in Rydlund and Densmore (2012), corresponding to a Level I survey. The blended navigation solution (called a smoothed best estimate of trajectory, or SBET, file) generated by postprocessing the daily navigation data was applied to the corresponding daily survey data.

Most of the bathymetric survey data within Table Rock Lake were collected with the swath range limited to 140 degrees (70 degrees on each side of nadir); however, along the banks and in the shallow areas at the upstream ends of the lake arms, the swath range was widened to 160 degrees to cover a wider swath of the bottom. The receiver array also was electronically or physically tilted to port or starboard as needed to enhance acquisition of bathymetric data in the shallow areas near the shoreline, in coves, and in the upper reaches of the lake arms. The electronically tilted swath from the NORBIT systems was generally about 160 degrees wide, extending from about 10 degrees above horizontal on the landward side of the survey vessel to about 60 degrees past nadir below the vessel.

The bathymetric data generally were collected along longitudinal transect lines in the main lake area, following the dominant valley orientation. The transects were spaced to create about 10- to 25-percent overlap of the survey swaths to ensure complete coverage of the lake bottom and minimize sonic shadows. Data along the shoreline were collected by navigating the boat parallel to the shore while overlapping the data collected in the main body of the lake. Cove data were collected by navigating into a cove along the approximate centerline of the cove as far as practical (generally the point at which forward progress was blocked by vegetation or water depth decreased to less than about 10 ft [or 3.0 meters]), pivoting the boat 180 degrees, and egressing the cove along the ingress line.

The speed of sound in water needs to be known to accurately determine the depths acquired by an MBES. In a lake, the speed of sound in the water commonly varies in space and time. To mitigate variations in sound speed near the water surface, sound velocity data are collected at the MBES head continuously throughout the survey; however, the speed of sound also can vary over the water column because of water temperature variations with depth. Therefore, sound velocity profiles were measured with a sound velocity probe at various locations throughout each survey day and were applied during postprocessing in the HYPACK/HYSWEEP software.

Preparation for the bathymetric survey, data collection during the survey, and postprocessing were done in HYPACK/HYSWEEP software (HYPACK, Inc., 2020). During postprocessing, the data were georeferenced using the navigation and position solution data in the SBET file and visualized in HYPACK/HYSWEEP as a triangulated irregular network (TIN) surface or a point cloud. The acquired depth data were processed further to apply sound velocity profiles, to apply patch test corrections, and to remove data spikes and other spurious points, often caused by fish and submerged woody debris. The georeferenced point data were then filtered and reduced to a 6.56-ft (2-meter) data resolution and exported to a comma-delimited text file.

Bathymetric Surface and Contour Map Creation

About 38,000,000 data points, spaced 6.56-ft horizontally, were exported from the raw data collected during the 2020 survey (Rivers and others, 2022). For the survey, the vertical datum was the North American Vertical Datum of 1988 using the geoid model GEOID18, and the horizontal datum was the North American Datum of 1983. Geographic information system (GIS) software was used to filter the 6.56-ft spaced bathymetric data points so that the points would be spaced about 19.7 ft (6 meters) apart. The data reduction retained about 4,370,000 surveyed data points from the 2020 MBES survey.

Data outside the MBES survey extent (fig. 2) and between about 915 and 940 ft in elevation (hereinafter referred to as “upland data”) were obtained from the USGS National Elevation Dataset (U.S. Geological Survey, 2017). The upland data were sourced from USGS 1/3 arc-second DEM data and, where present, lidar data collected in 2010 and 2017 were combined and resampled to a 19.7-ft (6-meter) spacing. About 1,710,000 upland data points were used.

In addition to the MBES and upland data, additional data in bathymetric surface analyses were developed using the linear enforcement techniques described in Wilson and Richards (2006). About 208,000 points were created based on surrounding MBES, DEM, and lidar data values to anchor the bathymetric surface in areas of sparse data along some shoreline areas and in the upper ends of coves where the water was too shallow for the MBES equipment.

The MBES, DEM, lidar, and linearly enforced point datasets (a total of about 6,290,000 points) were used to produce a three-dimensional TIN surface (also referred to as a “bathymetric surface”) of the lake-bottom elevations. A surface area and capacity table at specified lake water-surface elevations was produced from the three-dimensional TIN surface (table 1). The surface was contoured at a 20-ft interval using GIS software, and the contours were cartographically smoothed and edited to create a bathymetric contour map (fig. 2) using the techniques of Wilson and Richards (2006).

Patch Tests

Patch tests are a series of dynamic calibration tests that are used to check for subtle variations in the orientation and timing of the MBES with respect to the INS and real-world coordinates. The patch tests are used to determine timing offsets caused by latency between the MBES and the INS and angular offsets to roll, pitch, and yaw caused by the alignment of the transducer head (Huizinga and others, 2010). These offsets have been observed to be essentially constant for a given survey, barring an event that causes the mount to change such as striking a floating or submerged object (see Huizinga, 2022). The offsets determined in the patch test are applied when processing the data collected during a survey. Patch tests were completed for each MBMS at various times during the Table Rock Lake survey, and angular offsets were determined to be constant for a given system throughout the survey and entered in the data-collection software as appropriate. This study did not have any measured timing offsets for any system, which is consistent with latency test results for survey boats and for similar equipment configurations used in other surveys (Huizinga, 2010, 2022; Huizinga and others, 2010, 2022).

Beam-Angle Checks

A beam-angle check is used to determine the accuracy of the depth readings obtained by the outer beams (greater than 25 degrees from nadir) of the MBES (U.S. Army Corps of Engineers, 2013). The accuracy of the outer beams may change with time because of inaccurate sound velocities, physical configuration changes, and water depth. A beam-angle check was done for each MBMS during the survey; the R2Sonic system check was done on October 13, 2020; the Missouri iWBMSh system check was done on October 21, 2020; the Oklahoma iWBMSh system check was done on November 10, 2020; and the iWBMSc system check was done on November 11, 2020. Each test included a sound velocity cast to document and quantify any stratification in the water column near the reference surface. The results of the R2Sonic beam-angle check were within the recommended performance standards used by the U.S. Army Corps of Engineers for hydrographic surveys for all the representative angles less than 70 degrees (U.S. Army Corps of Engineers, 2013); therefore, the central 140 degrees of the echosounder swath for that system could be used with confidence. The results of the Missouri iWBMSh beam-angle check were determined to be outside the recommended performance standards used by the U.S. Army Corps of Engineers for hydrographic surveys for all the representative angles because the depth of the beam-angle check area was substantially deeper than the recommended depth of 100 ft in the standards. However, a beam-angle check for the Missouri iWBMSh system had been done on June 23, 2020, at Mozingo Lake near Maryville, Mo. (not shown; Huizinga and others, 2022), with depths of less than 100 ft, and the results of that beam-angle check were within the recommended performance standards for all the representative angles less than 70 degrees, permitting the use of the central 140 degrees of the echosounder swath with confidence. The results of the Oklahoma iWBMSh system and the iWBMSc system checks were determined to be within the recommended performance standards for all the representative angles less than 55 degrees, permitting the use of the central 110 degrees of the echosounder swath with confidence for these systems. Points acquired outside of the central 100–110 degrees of the echosounder swath (regardless of the system) generally had overlap with adjacent swaths, which increases the quality of the survey in the overlapped areas because of duplication.

Uncertainty Estimation

Similar to the previous studies of bathymetry in Missouri (Huizinga, 2010, 2022; Richards and others, 2019), uncertainty in the multibeam survey was estimated for each 6.56-ft survey-grid cell in the surveyed area using the Combined Uncertainty and Bathymetry Estimator (CUBE) method (Calder and Mayer, 2003) as implemented in the MBMax processing package of the HYPACK/HYSWEEP software (HYPACK, Inc. 2020). The CUBE uncertainty is a measure of the variability of the individual points in the cell used to determine the CUBE-derived elevation for the cell. The CUBE uncertainty data were output and combined with the three-dimensional bathymetric data and are included with metadata in the USGS data release associated with this study (Rivers and others, 2022).

Most of the uncertainty values (more than 95 percent) were less than 0.60 ft, which is within the specifications for a “special order” survey, the most stringent survey standard of the International Hydrographic Organization (International Hydrographic Organization, 2020). The median uncertainty value of the data was about 0.10 ft, and the mean value was about 0.29 ft. The largest uncertainty in this survey was about 65.6 ft; however, uncertainty values of this magnitude typically are near high-relief features—near vertical surfaces such as bridge abutments or submerged cliffs that may exist on some parts of Table Rock Lake (figs. 2 and 3). The uncertainty values were larger near moderate-relief features (steep banks and submerged channels and ridges; figs. 2 and 3). The uncertainty values also were larger in the outermost beam extents of the MBES swath in the overlap with an adjacent swath, particularly when the swath was tilted for the survey lines along the banks or widened in the upper extent of the lake (fig. 3).

The less accurate INS of the NORBIT iWBMSc system also resulted in larger uncertainties. The iWBMSc was used in shallower survey areas because the INS is less sensitive to movement, resulting in larger error and uncertainty in deeper water. Therefore, larger uncertainties are apparent in areas with greater depth where the iWBMSc system was used on the upper end of the Long Creek arm south of the Arkansas State line (figs. 1 and 3), the upper end of the Kings River arm (figs. 1 and 3), and a part of the upper White River near the Roaring River and on the Roaring River arm (figs. 1 and 3).

The James River arm (fig. 1) was surveyed with the Oklahoma NORBIT iWBMSh system, which is exactly like the Missouri NORBIT iWBMSh system used on the White River in the main body of the lake; however, the gridded CUBE uncertainties for the James River arm were about two orders of magnitude (100 times) larger than the uncertainties on the White River near the James River arm. The MBES instrument settings, data-collection methods, and data-processing methods were the same as for the main body of the lake, so the substantially larger uncertainties were deemed erroneous. The computed uncertainties for the James River arm were divided by 100 to bring them into better agreement with the neighboring White River data (fig. 3). The points with adjusted uncertainties are flagged with “100” (original uncertainty value divided by 100) whereas the points with unadjusted uncertainties are flagged with “1” (uncertainty divided by 1, or unchanged) in the bathymetric data in the USGS data release associated with this study (Rivers and others, 2022). Some residual larger uncertainties are nonetheless evident in the James River arm (fig. 3). The mean and median uncertainty values reported earlier in this section use the adjusted uncertainties on the James River arm.