Prepared in cooperation with Northern Arizona University

Monitoring Fine-Sediment Volume in the Colorado River 

Ecosystem, Arizona—Construction and Analysis of Digital 

Elevation Models 

Open-File Report 2014–1052

U.S. Department of the Interior

U.S. Geological Survey
COVER 

Digital elevation model (DEM) of a part of the Colorado River in Grand Canyon (river miles 44.3 to 44.7) in Grand Canyon National Park, Arizona. DEM is 

constructed from aerial lidar, ground topographic and multibeam bathymetry data collected in December 2004 and has a grid resolution of 1 meter.
Monitoring Fine-Sediment Volume in the Colorado River 

Ecosystem, Arizona—Construction and Analysis of Digital 

Elevation Models

By Matt Kaplinski, Joseph E. Hazel, Jr., Paul E. Grams, and Philip A. Davis 

Prepared in cooperation with Northern Arizona University

Open-File Report 2014–1052

U.S. Department of the Interior 

U.S. Geological Survey 
ii

U.S. Department of the Interior

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia 2014

For product and ordering information:

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Suggested citation:

Kaplinski, M., Hazel, J.E., Jr., Grams, P.E., Davis, P.A., 2014, Monitoring fine-sediment volume in the Colorado River 

ecosystem, Arizona—Construction and analysis of digital elevation models: U.S. Geological Survey Open-File Report 

2014–1052, 29 p., http://dx.doi.org/10.3133/ofr20141052.

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

endorsement by the U.S. Government. 

Although this report is in the public domain, permission must be secured from the individual 

copyright owners to reproduce any copyrighted material contained within this report.

ISSN 2331-1258 (online)
iii

Contents

Abstract ......................................................................................................................................................................... 1

Introduction.................................................................................................................................................................... 1

Study Area, Place Names, and Units............................................................................................................................. 2

Study Reaches .............................................................................................................................................................. 3

Data Collection and Processing..................................................................................................................................... 5

Geodetic Control Network.......................................................................................................................................... 6

Ground-Based Topographic Surveys......................................................................................................................... 6

Bathymetric Surveys .................................................................................................................................................. 7

Airborne Lidar and Photogrammetric Surveys ........................................................................................................... 7

Data Collection....................................................................................................................................................... 7

Land-Cover Maps for Lidar Postprocessing ........................................................................................................... 9

Postprocessing Airborne Topographic Data..........................................................................................................11

DEM Construction.........................................................................................................................................................12

DEM Uncertainty ..........................................................................................................................................................17

Bathymetry................................................................................................................................................................18

Bed-Texture Classification.....................................................................................................................................18

Multibeam Uncertainty...........................................................................................................................................18

Singlebeam Uncertainty ........................................................................................................................................21

Lidar and Photogrammetry Uncertainty.....................................................................................................................22

Uncertainty Surfaces.................................................................................................................................................23

Summary ......................................................................................................................................................................25

Acknowledgments ........................................................................................................................................................26

References Cited..........................................................................................................................................................26

Figures

Figure 1. Map showing location of study reaches along the Colorado River corridor within Glen, Marble, and

Grand Canyons, Arizona. .............................................................................................................................................. 3

Figure 2. Discharge hydrograph from U.S. Geological Survey gaging station Colorado River near Lees Ferry

(Blue, station 09380000), Arizona, during the period of study ....................................................................................... 5

Figure 3. Map of a part of reach 5 showing the different landform surfaces in along the Colorado River corridor

in Grand Canyon, Arizona ........................................................................................................................................... 10

Figure 4. Map of a part of reach 5 in Grand Canyon, Arizona, showing final digital elevation model (DEM) from 

December 2004 with May 2002 orthophotography ...................................................................................................... 13

Figure 5. Maps of a part of reach 3 in Grand Canyon, Arizona, showing (A) the raw data points and (B) 

polygon boundaries used to exclude or prioritize the input datasets, clip triangulated irregular network (TIN) model 

and digital elevation models (DEMs), and generate uncertainty surfaces ................................................................... 15

Figure 6. Maps of a part of reach 4 in Grand Canyon, Arizona, showing stages in the bed-texture classification 

process using the December 2004 survey data........................................................................................................... 19

Figure 7. Map of a part of reach 6 in Grand Canyon, Arizona, showing examples of rough and smooth fiducial 

areas on a shaded-relief image derived from the May 2002 digital elevation model (DEM) superposed on the May 

2002 orthophotography................................................................................................................................................ 20

Figure 8. Maps of a part of reach 5 in Grand Canyon, Arizona, showing the stages involved in assigning

uncertainty values using the November 2004 survey data .......................................................................................... 24
iv

Tables

Table 1. Characteristics of the study reaches along the Colorado River corridor within Glen, Marble, and Grand 

Canyons, Arizona. ......................................................................................................................................................... 4

Table 2. Data types collected in study reaches along the Colorado River corridor within Glen, Marble, and Grand 

Canyons, Arizona, during each monitoring period. ........................................................................................................ 4

Table 3. Dates of data collection in the Colorado River corridor within Glen, Marble, and Grand Canyons, 

Arizona. ..................................................................................................................................................................... 6

Table 4. Lidar and photogrammetry sensor characteristics used in this study along the Colorado River corridor 

within Glen, Marble, and Grand Canyons, Arizona........................................................................................................ 8

Table 5. Digital elevation model (DEM) summary statistics used in this study along the Colorado River corridor 

within Glen, Marble, and Grand Canyons, Arizona...................................................................................................... 14

Table 6. Summary statistics of multibeam bathymetry uncertainty used in this study along the Colorado River 

corridor within Glen, Marble, and Grand Canyons, Arizona......................................................................................... 21

Table 7. Summary statistics of singlebeam bathymetry cross line check uncertainty used in this study along the 

Colorado River corridor within Glen, Marble, and Grand Canyons, Arizona. ............................................................... 21

Table 8. Summary statistics of singlebeam interpolation uncertainty used in this study along the Colorado River 

corridor within Glen, Marble, and Grand Canyons, Arizona......................................................................................... 22

Table 9. Summary statistics of lidar and Photogrammetry uncertainty used in this study along the Colorado River

corridor within Glen, Marble, and Grand Canyons, Arizona......................................................................................... 22

Table 10. Uncertainty estimates assigned to each data source category in final digital elevation models (DEMs)

for the Colorado River corridor within Glen, Marble, and Grand Canyons, Arizona..................................................... 25

Appendix

[Available online only at http://pubs.usgs.gov/of/2014/1052/]

Appendix 1. Maps of Study Reach DEMs
v

Conversion Factors

Inch/Pound to SI

Multiply By To obtain

Length

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

square foot (ft2) 0.09290 square meter (m2)

Volume

cubic foot (ft3) 0.02832 cubic meter (m3) 

Flow rate

cubic foot per second (ft3/s) 0.02832 cubic meter per second (m3/s)

SI to Inch/Pound 

Multiply By To obtain

Length

meter (m) 3.281 foot (ft) 

kilometer (km) 0.6214 mile (mi)

Area

square meter (m2) 10.76 square foot (ft2) 

Volume

cubic meter (m3) 35.31 cubic foot (ft3)

Flow rate

cubic meter per second (m3/s) 35.31 cubic foot per second (ft3/s)

Temperature in degrees Celsius (°C) may be converted to degrees Fahrenheit (°F) as follows:

°F=(1.8×°C)+32

Temperature in degrees Fahrenheit (°F) may be converted to degrees Celsius (°C) as follows:

°C=(°F-32)/1.8

Vertical coordinate information is referenced to the insert datum name (and abbreviation) here, for instance, “North American

Vertical Datum of 1988 (NAVD 88)”

Horizontal coordinate information is referenced to the insert datum name (and abbreviation) here, for instance, “North American 

Datum of 1983 (NAD 83)”

Altitude, as used in this report, refers to distance above the vertical datum.
Monitoring Fine-Sediment Volume in the Colorado River 

Ecosystem, Arizona—Construction and Analysis of Digital 

Elevation Models

By Matt Kaplinski,1 Joseph E. Hazel, Jr.,1 Paul E. Grams,2 and Philip A. Davis2

Abstract 

Digital elevation models (DEMs) of eleven 2–5 kilometer reaches of the Colorado River 

ecosystem (CRE) in Grand Canyon were constructed from repeat bathymetric and topographic surveys 

collected between August 2000 and December 2004. The DEMs will be used by researchers to study the 

effects of Glen Canyon Dam (GCD) operations on the sediment resources of the CRE in Grand Canyon 

by quantifying morphological changes and sediment transfer within and among the study reaches.

Airborne surveys collected light detection and ranging (lidar) and photogrammetric data, 

whereas ground topographic and bathymetric data were collected simultaneously on river trips. Surveys 

were conducted in August 2000, September 2000, May 2002, May 2004, November 2004, and 

December 2004. The aerial lidar and photogrammetric data were merged with the ground topographic 

and bathymetric data to create DEMs of the study areas with a grid resolution of 1 meter. For each 

survey period, the vertical component of uncertainty (specifically, reproducibility or precision) was

estimated for each data type (lidar/photogrammetry, ground surveys, bathymetry) and for two different 

types of bed-surface texture (smooth and rough).

The resulting DEMs from this study are a valuable contribution to ongoing efforts in assessing

the effects of GCD operations on the CRE. The DEMs can be used to map the spatial characteristics of 

geomorphic change within the study reaches and to estimate sediment budgets for different time periods 

by calculating the difference in sediment volume between surveys. In addition, the DEMs provide 

essential boundary conditions for numerical models of sediment transport and deposition, as well as help

define the spatial distribution of habitat for fisheries investigations.

Introduction 

The existence and operation of Glen Canyon Dam (GCD) has altered the morphology and 

ecology of the Colorado River in Grand Canyon (Webb and others, 1999; Gloss and others, 2005). For 

example, both the distribution and volume of fine-grained sediment deposits have been extensively 

altered as a result of changes in the flow regime and the upstream impoundment of sediment. Pre-dam 

seasonal variability in the river’s flow rate, which included spring snowmelt floods, has been replaced 

with a diurnally fluctuating flow regime that varies in response to demands for hydroelectric power. In 

the post-dam era, the Paria and Little Colorado Rivers are the primary sources of fine-grained sediment 

to the river downstream of GCD. These tributaries supply only 15 to 20 percent of the pre-dam sediment 

load (Topping and others, 2000). Studies have shown that the number and size of sandbars have 

substantially decreased in response to the change in flow and decrease in sediment supply (Schmidt and 

 1

Northern Arizona University, School of Earth Sciences and Environmental Sustainability. 2

U.S. Geological Survey, Grand Canyon Monitoring and Research Center.
2

Graf, 1990; Webb and others, 1999; Wright and others, 2005). Sandbars along the Colorado River in 

Grand Canyon are an important component of the ecosystem because they provide camp sites for river 

runners and hikers, crucial substrates for riparian vegetation that serve as wildlife habitats, protect predam deposits that contain culturally important archeological sites, and are an integral component of the 

natural landscape (Webb and others, 1999). An important goal of ongoing geomorphic research in Grand 

Canyon is to monitor sandbars and the status of fine-grained sediment storage to inform resource 

managers about the effectiveness of management efforts to maintain a positive sediment balance in the 

system and thereby rebuild degraded sandbars (U.S. Department of the Interior, 1995). 

The U.S. Geological Survey (USGS) Grand Canyon Monitoring and Research Center (GCMRC) 

has developed a comprehensive monitoring and research program to study the effects of GCD operations 

on the sediment resources of the Colorado River ecosystem (CRE) in Grand Canyon. This program is 

based on a sediment budget paradigm and consists of three integrated components: 

Monitoring suspended sediment transport (Topping and others, 2010). 

Measuring topographic change in sediment deposits by repeat total-station and bathymetric surveys

(Hazel and others, 2010). 

Modeling sediment transport and sandbar morphodynamics (Wright and others, 2010; Logan and others, 

2010). 

This report presents methods and data collected in support of the topographic change component of this 

monitoring program. 

Technological advances made over the past decade have made it possible to rapidly acquire 

highly accurate topographic and bathymetric data over large areas. Geomorphologists now routinely use 

these technologies to investigate fluvial processes and monitor geomorphic change (Brasington and 

others, 2003; Lane and others, 2003; Wheaton and others, 2010). Digital elevation models (DEMs) 

derived from such periodic surveys accurately record landform surface variations, which are used to 

quantify and monitor morphological changes and sediment transfer across a variety of spatial scales. In 

this study, repeat topographic and bathymetric surveys of 11 reaches, ranging in length from 2–6.5 

kilometer (km), of the Colorado River in Grand Canyon were conducted. The hybrid topographic 

surveys combined light detection and ranging (lidar) and photogrammetric topographic data from

airborne surveys with ground-based and boat-based topographic and bathymetric data collected during 

waterborne survey trips. All of these surveys were combined to construct DEMs of the river reaches. 

This report outlines the procedures used to collect and process the hybrid topographic data, to construct 

the DEMs, and to estimate the spatially distributed uncertainty associated with the DEMs. 

Study Area, Place Names, and Units

The study area is the Colorado River corridor within Glen, Marble, and Grand Canyons in 

northern Arizona (fig. 1). Locations discussed in this report are referenced by the GCMRC river mile 

(RM) system, which is distance in miles along the channel centerline downstream from Lees Ferry, 

Arizona (U.S. Geological Survey, 2006). Lees Ferry (RM 0) is located 15.5 miles downstream from 

GCD and 1 mile upstream from the mouth of the Paria River and the northeastern boundary of Grand 

Canyon National Park (fig. 1). Glen Canyon extends from GCD to Lees Ferry. Marble Canyon begins at 

the mouth of the Paria River and extends downstream to the Little Colorado River confluence. Although 

Marble Canyon is within Grand Canyon National Park, this report refers to Grand Canyon as the reach 

of the Colorado River that extends from the Little Colorado River confluence downstream to Diamond 

Creek (RM 226). 
3

Figure 1. Map showing location of study reaches along the Colorado River corridor within Glen, Marble, and 

Grand Canyons, Arizona. 

To integrate topographic datasets from different sources into a composite DEM, all topographic 

and bathymetric data were processed in the State Plane Coordinate System, Central Arizona, zone map 

projection in meters using the NAD83 (2011) vertical datum. Elevations are reported as ellipsoid heights

(EH) because the national geoid model does not incorporate sufficient gravity measurements in the 

Grand Canyon region to account for the large variation in crustal mass along the river corridor (Saleh 

and others, 2003). 

In this report, we define the term DEM as a “bare earth” elevation model that represents the 

ground surface that is free of vegetation, the surfaces of standing bodies of water, and other 

“nonground” objects (for example, power cables, buildings, and other structures), whereas, a digital 

surface model (DSM) refers to an elevation model that includes the tops of vegetation, standing bodies 

of water, and any other objects. 

Study Reaches

Eleven river reaches were selected for study within the CRE in Glen, Marble, and Grand 

Canyons, Arizona (fig. 1). The reaches are numbered increasing downstream from GCD (table 1). Some 
4

of the reaches were surveyed multiple times, whereas some reaches were surveyed less frequently (table 

2). Four reaches (reaches 2, 4, 5, and 7) were initially surveyed in August and September 2000 (Schmidt 

and others, 2007). In 2002, all 11 reaches were surveyed, whereas only reaches 2 through 8 were 

surveyed in May 2004, and reaches 2 through 7 were surveyed in November and December 2004. This 

report focuses on reaches 2 through 7, as these are the only reaches that include repeat surveys. Reaches 

2 through 7 have a total length of 22.2 km, which is 21 percent of the total channel length between RM 0 

and RM 66.4. The individual reaches range in length from 1.3 to 6.4 km and have an average length of 

3.5 km. Reaches 2 through 6 are located in Marble Canyon; reach 7 is in Grand Canyon, 3 km 

downstream from the Little Colorado River confluence. 

Table 1. Characteristics of the study reaches along the Colorado River corridor within Glen, Marble, and Grand 

Canyons, Arizona. 

Long-term monitoring reach River mile1 Average channel 

width2, in meters Channel slope3

Number Local name Starting Ending

1 Lees Ferry -2.4 0 123 0.0001

2 Paria 1.1 2.7 113 0.0002

3 Roaring Twenties 21.9 23.7 56 0.0016

4 Redwall Gorge 29.4 32.1 64 0.0009

5 Point Hansborough 42.5 45.5 82 0.0009

6 Granaries 54.5 56.3 90 0.0003

7 Tapeats Gorge 63.4 66.4 95 0.0012

8 Cremation 86.6 88.1 64 0.0020

9 Aisles 119.3 123.3 65 0.0010

10 Granite Park 207.7 209.2 72 0.0013

11 Diamond Creek 224.8 225.6 66 0.0002

1

Based on the river mile centerline (U.S. Geological Survey, 2006) downstream from Lees Ferry (river mile 0), in Grand 

Canyon National Park except, the Lees Ferry reach, which is in Glen Canyon National Recreation Area.

2

At 227 cubic meters per second (m3/s), average based on cross section data from Magirl and others (2005).

3

Based on measured water-surface elevations at a steady discharge of 227 m3/s. 

Table 2. Data types collected in study reaches along the Colorado River corridor within Glen, Marble, and Grand 

Canyons, Arizona, during each monitoring period. 

Long-term monitoring reach Monitoring year and data types1 collected

Number Local name Aug. 2000 Sept. 2000 May 2002 May 2004 Nov. 2004 Dec. 2004

1 Lees Ferry A, C, D, E

2 Paria A, B, D A, B, D A, C, D, E A, D A, B, D A, B, D

3 Roaring Twenties A, C, D, E A, D A, B, D A, B, D

4 Redwall Gorge A, B, D A, B, D A, C, D, E A, D A, B, D A, B, D

5 Point Hansborough A, B, D A, B, D A, C, D, E A, D A, B, D A, B, D

6 Granaries A, C, D, E A, D A, B, D A, B, D

7 Tapeats Gorge A, B, D A, B, D A, C, D, E A, D A, B, D A, B, D

8 Cremation A, C, D, E A, D

9 Aisles A, C, D, E

10 Granite Park A, C, D, E

11 Diamond Creek A, C, D, E

1

Data types: A, total station surveys; B, lidar; C, photogrammetry; D, bathymetric surveys; E, multispectral digital imagery. 
5

Data Collection and Processing

In Marble and Grand Canyons, sediment storage is concentrated in eddies and the adjacent 

channel (Hazel and others, 2006; Grams and others, 2013). One of the objectives of this mapping effort 

is to determine the distribution of these storage locations, which requires mapping as much of each study 

reach as possible. To accomplish this goal, a combination of remotely sensed and ground-based data 

were collected in August 2000, September 2000, May–June 2002, May–June 2004, November 2004, and 

December 2004 (fig. 2, table 3). Channel bathymetry was mapped by multibeam and singlebeam sonar

and subaerial topography was mapped by airborne lidar, aerial photogrammetry, and ground-based totalstation (table 2). Lidar and photogrammetric data were collected during aerial overflights that typically 

spanned a 4–6 day period. Ground-based topographic and bathymetric data were collected on research 

river trips lasting 14 to 20 days. To prevent error due to topographic change over the data collection 

period, the airborne and ground data collections were coordinated to minimize the time difference 

between collection of the datasets for a given time period. 

Figure 2. Discharge hydrograph from U.S. Geological Survey gaging station Colorado River near Lees Ferry 

(Blue, station 09380000), Arizona, during the period of study. Dates of airborne and ground-based survey trips 

are show by red dots. Note the daily and seasonal fluctuations in flow volume, the Low Steady Summer Flow 

(LSSF) experiment in 2000 that included a powerplant capacity-flow (~878 cubic meters per second, m3/s) 

event, and the High-Flow Experiment event (1,161 m3/s) in November 2004.
6

Table 3. Dates of data collection in the Colorado River corridor within Glen, Marble, and Grand Canyons, Arizona. [Date format is Month/Day; n.a., not applicable]

Data collection

method

August

2000

September 

2000

May

2002

May

2004

November

2004

December

2004

Lidar 8/29–8/31 9/15–9/18 n.a. n.a. 11/19–11/21 12/07–12/09

Photogrammetry n.a. n.a. 5/24–6/05 n.a. n.a. n.a.

Total station 8/19–8/27 9/03–9/17 4/28–5/16 5/29–6/9 11/12–11/20 12/1–12/10

Multibeam 

bathymetry

8/19–8/27 9/03–9/17 4/28–5/16 5/29–6/9 11/12–11/20 12/1–12/10

Singlebeam 

bathymetry

8/19–8/27 9/03–9/17 n.a. n.a. n.a. n.a.

The following sections briefly summarize the individual components of the ground-based data 

collections, including the control network, total-station method, and bathymetric method, because they 

have been previously described in detail (Hazel and others, 2008; Kaplinski and others, 2009). The 

airborne data collections and processing methods are discussed in greater detail because they have not 

been previously described elsewhere. 

Geodetic Control Network

All airborne and ground-based surveys are referenced to a geodetic control network developed 

by the GCMRC (Hazel and others, 2008). The control network consists of 16 primary control 

benchmarks that were established along the canyon rim and connected to the National Spatial Reference 

System (Doyle, 1994), with secondary and tertiary points located along the river corridor. Secondary 

control points along the river corridor were established by simultaneous Global Positioning System 

(GPS) occupations with the established rim-control points using the procedures described by Zilkoski 

and others (1997). Tertiary control points were referenced to the secondary point network using 

conventional survey techniques. The secondary and tertiary control points are stable survey marks 

monumented with a chiseled or scribed X, P-K masonry nail, or carriage bolt. The accuracy of the 

primary rim control network is constrained to 0.02 meters (m) vertical and 0.02 m horizontal, whereas

secondary and tertiary points have a positional error less than 0.03 m and a vertical error between 0.01 

and 0.10 m, at 95-percent confidence level (Hazel and others, 2008). 

Ground-Based Topographic Surveys

Ground-based collection of topographic data was undertaken using total-station survey methods. 

The narrow canyon setting and associated environmental conditions preclude the use of kinematic-GPS 

techniques for rapid acquisition of field-survey data (Hazel and others, 2008). As a result, conventional 

total-station surveying provided the means for collecting high-accuracy topographic data and for 

accurate positional referencing of the bathymetric data. The following data were collected or established 

using conventional total-station (TS) surveying techniques and are hereafter referred to as TS points: (1) 

topographic data, (2) check points for ground-truthing lidar data, (3) temporary benchmarks for 

bathymetric navigation shore stations or for additional total-station locations, and (4) locations of 

subaerial and subaqueous sample sites (for example, scour chains, digital microscopes, and video 

cameras). Benchmark and backsite coordinates were verified at all total station positions by comparing 

field measurements with benchmark coordinates in the GCMRC control network. Vertical and 

horizontal accuracies of the surveyed checkpoints (at the 95-percent confidence level) within the study 

areas were less than or equal to 0.05 m (Hazel and others, 2008). The TS points were edited, processed 

and checked for errors (such as rod height and coding mistakes), then exported to ASCII files containing 

the coordinate values in meters (northing, easting, EH) and surface-descriptor code for each point. 
7

Bathymetric Surveys

Bathymetric data covered the largest part of the study reaches and comprise approximately 74 

percent of the total DEM area. The bathymetric data collection system used a robotic total station, or 

shore station, to provide line-of-sight navigation data (Kaplinski and others, 2009). Shore stations are 

established on benchmarks referenced to the geodetic control network, and the data collected from each 

shore station location is treated as an individual survey. Each study reach required from 4 to 8 individual 

surveys to complete the mapping. The August and September 2000 data collections included both 

singlebeam and multibeam sonar, whereas subsequent data collections only used multibeam sonar 

(Kaplinski and others, 2009). Three individual surveys were collected using the singlebeam system in 

August 2000, whereas five individual surveys were collected in September 2000. Singlebeam data were 

collected by following a 10-m grid pattern along planned lines. The singlebeam soundings were 

manually edited to remove erroneous soundings and then filtered to output one point per meter along the 

vessel trackline, which results in a point density of approximately 0.2 points/square meter (points/m2). 

Soundings were filtered to optimize the generation of the triangulated irregular network (TIN) surface 

model of the topographic surface. All other parts of the study reaches were mapped using the multibeam 

system. This system collects approximately 1 to 5 million soundings per survey. Multibeam soundings 

were filtered by calculating the median elevation of soundings within 0.25-m and 1.0-m grid cells. The 

data filtered to 1-m resolution were used to construct the bathymetry part of the DEMs, and the data 

filtered to 0.25 m were used for bed-texture analysis. The 1-m grid resolution was selected by using a 

grid-size estimator (see section on DEM Construction) to determine the appropriate cell size for the 

hybrid datasets. This resolution is both computationally efficient and resolves the scale of features 

necessary for volume calculations. The number of soundings per square-meter grid cell varies from 1 to 

3,000, with an average of approximately 200 soundings per cell. All bathymetric data were collected and 

processed using Hypack and Hysweep software, and the filtered data were exported as ASCII files

containing the coordinates and EH for each point. 

Airborne Lidar and Photogrammetric Surveys

Data Collection

The above-water topography was mapped with airborne lidar and stereo panchromatic imagery, 

supplemented with ground-based total station surveys (Davis, 2004). Topographic data were extracted 

photogrammetrically from imagery collected in 2002. All other overflights collected lidar data using a 

variety of sensors (table 4). Unfortunately, the lidar collection system malfunctioned during the May

2004 mission, and the data are, therefore, excluded from this study. All of the successful aerial-survey

data were collected using fixed-wing aircraft flying at 100-knots at altitudes above 1,250 m; different 

laser pulse rates of the various lidar sensors produced a range of point densities (0.37 to 5.18 points/m2 ) 

in the final lidar point datasets (table 4).
8

Table 4. Lidar and photogrammetry sensor characteristics used in this study along the Colorado River corridor 

within Glen, Marble, and Grand Canyons, Arizona. [mm, millimeters; cm, centimeters; m, meters; m2

, square meters; km, kilometers; kHz, kilohertz; mrad, milliradians; AGL, 

above ground level; k, thousand; n.a., not applicable; GPS, Global Positioning System; CCD, charge-coupled device]

Characteristics

RAMS1 RAMS ISTAR2 DATIS III3 RAMS

lidar lidar (HRSC-AX4) lidar lidar

Collection dates Aug., 2000 Sept., 2000 May, 2002 Nov., 2004 Dec., 2004

Flight AGL (m) 1,250 1,250 6,096 1,828 1,250

Base stations per study area 1 1 1 2 2

Average baseline distance (km) 30 30 20 20 20

GPS recording interval (seconds) 1 1 1 1 1

Minimum GPS satellites used 5 5 6 6 6

Pulse rate (kHz) 15 15 n.a. 36.5 35

Scan rate (Hz) 13.4 13.4 n.a. 28 24.2

Swath width (m) 230 230 2,640 840 305

Beam divergence (mrad) 0.33 0.33 n.a. 0.25 0.33

Scan half angle (degrees) 5 5 15 13 7

Laser footprint (m) 0.4 0.4 n.a. 0.46 0.4

Along-track spacing (m) 1.4 1.5 0.22 2.2 2.3

Across-track spacing (m) 1.7 1.6 0.22 1 0.7

Line point density (points/m2) 0.37 0.44 21 0.5 0.57

Flight-line replications 21 21 6 4 4

Final point density (points/m2) 0.37 0.44 1 3.52 5.18

Returns 2 2 n.a. 2 2

Intensity recorded No No n.a. Yes Yes

Average noise level (cm)5 7.5 7.8 3.7 9.7 7.7

Recording media (CCD elements) 4k×4k 4k×4k 12k×12k None None

Focal length (mm) 90 90 151 n.a. n.a.

Image resolution (cm) 18 18 22 n.a. n.a.

Image bit-type 8 8 8 n.a. n.a.

1

RAMS, Remote Airborne Mapping System, Enerquest, Colorado.

2

ISTAR, Imagerie Stereo Appliquee au Relief, France. 

3

DATIS III, Digital Airborne Topographic Imaging System, 3-Di Technology, Maryland.

4

HRSC-AX, High Resolution Stereo Camera, aerial, version X. 

5

Determined using method of Crombaghs and others (2002).

Strict requirements were placed on all of the airborne data collections to optimize the accuracy 

and precision of their collected data. These specifications required that (1) at least five to six GPS 

satellites be within view (greater than15o above the horizon) and recorded during all airborne collections 

to provide position dilution of precision (PDOP) values less than 2.5, (2) at least two GPS base stations 

be operating within 30 km of any airborne collection and that all base-station data be used in the data 

processing, (3) lidar data collections use a maximum scan half-angle of 15o (to limit beam eccentricity), 

(4) the lidar ground spot diameter be less than 0.5 m (to reduce uncertainties as to the location and 

surface material that produced the measured laser return), and (5) lidar flightlines be collected four times 

and, because vertical offsets were observed among repetitive flight lines, each processed lidar flightline 

be delivered as a separate point file. The sensor characteristics and collection parameters for each of the 

airborne surveys are summarized in table 4. 

During each airborne survey, primary control points along the canyon rim were occupied with 

GPS receivers. These receivers recorded the dual frequency (L1/L2) carrier phase and pseudo-range 

measurements from each GPS satellite in view. During the 2000 airborne surveys, only one base station 

per study area was occupied, but all subsequent collections had at least two base stations that operated

within a 30-km radius of each study site. All aircraft used for the data collections were equipped with a 
9

similar GPS unit, as well as an Inertia Measurement Unit (IMU) to record the aircraft motion and 

heading. The canyon-rim base stations and the aircraft GPS/IMU systems used a one-second recording 

epoch. Before data collection, the aircraft passed over operating base stations to assure that on-the-fly 

integers were correctly fixed during the postprocessing phase. During postprocessing, the base-station 

GPS data were processed in static mode to verify their published positions and to detect problems. The 

airborne GPS/IMU data were then processed with the base-station data in both forward and reverse 

chronologic directions to obtain trajectory positions. The lidar data were processed to determine the 

northing, easting, and EH coordinates of each laser return and to remove obvious anomalies in each 

flightline.

The May 2002 photogrammetric data were derived from digital panchromatic stereo imagery 

using softcopy photogrammetry. The imaging sensor was a high-resolution, push-broom camera system 

(the HRSC-AX). The sensor simultaneously collected three ground lines of data using three separate 

optics—one lens looked forward (+20.5o), one looked nadir, and the other lens looked backward 

(−20.5o) along the flight path. Multiple (five or six) overlapping flight lines provided a minimum of five

stereo looks for each ground element. Each of the three panchromatic sensors had a 12,000-element 

charged-coupled device (CCD) that provided 0.22 m ground resolution at the flight altitude of 6,096 m 

using a 151-mm lens. Automatic triangulation was performed on the raw panchromatic image data using 

the on-board IMU and GPS data, the canyon-rim GPS base-station data, and the ground control panels 

that were placed throughout the study areas before airborne data collection. A DSM was produced from 

these data with a 1-m cell size.

Land-Cover Maps for Lidar Postprocessing

Preliminary examination of the lidar and photogrammetry datasets indicated that additional 

postprocessing was required to improve accuracy and consistency among the datasets. The issues that 

were observed in the lidar data included: (1) anomalous Ellipsoid Height (EH) values (data spikes) along 

the shoreline, (2) elevation differences (ΔEH) between flight-line and ground checkpoint EH values, and 

(3) vertical error increasing with slope, which suggested planimetric error. The two issues related to the 

photogrammetry data were vertical offset and horizontal tilt (from river right to river left) in delivered 

DSM surfaces. A series of processing procedures were applied to the lidar and for each study area and 

for each data collection period. The land-cover units were defined based on surface types that affect the 

accuracy of elevations determined by lidar. The land-cover units consisted of bare, smooth ground; bare, 

rough ground; standing water; damp ground; sparsely vegetated surfaces; and densely vegetated surfaces 

(fig. 3). These surfaces were initially identified and mapped using the color-infrared (CIR) 

photogrammetry data to resolve these issues. However, lidar mapping is more complex than 

photogrammetric mapping because the accuracy of lidar varies depending on land-cover characteristics

(for example, smooth bare ground, rough bare ground, damp ground, vegetation cover) and local slope 

(for example, Bowen and Waltermire, 2002; Raber and others, 2002; Hodgson and others, 2003; Peng 

and Shih, 2006). To treat such surfaces separately in the lidar postprocessing stage, land-cover maps 

were produced from imagery that was collected in May 2002 and orthorectified to a 0.25-m positional 

accuracy. This imagery has a 0.44-m spatial resolution, which is 2.5 times higher resolution than the 1-m 

resolution of the final DEMs. 
10

Figure 3. Map of a part of reach 5 showing the different landform surfaces in along the Colorado River corridor in

Grand Canyon, Arizona. A, May 2002 color-infrared image showing examples of a variety of landform features.

B, May 2002 land-cover classification map for same area shown in A. 
11

All of the lidar sensors that were used in this study also collected either digital imagery or laserreturn intensity. With sufficient spot density (4–5 points/m2

) laser-return intensity data (in raster-image

form) look quite similar to digital panchromatic imagery at 0.50-m resolution and can be used to 

determine changes in surface cover between consecutive surveys. All of the raster-image and intensityimage data collected during our lidar surveys were registered to the May 2002 image base. The initial 

May 2002 land-cover map for each study site was then modified for the different lidar collection periods 

using the images from each collection period. 

Three additional datasets were derived for each study site to facilitate error checking and 

quantification of uncertainty. Those datasets are (1) a local slope map, because vertical error increases 

with increasing slope; (2) a river-stage map that includes the 2,746 cubic meters per second (m3/s) stage 

elevation, above which there has been essentially no change throughout the collection periods and 

provides fiducial areas for calibration; and (3) a map of the orthogonal distance from the river’s 

centerline, which was used to examine potential topographic asymmetry. Each point within each lidar

point file (consisting of northing, easting, EH, return, and intensity) was then classified according to

corresponding land-cover unit, and local slope. 

Postprocessing Airborne Topographic Data

The first procedure applied to the lidar data was the detection and removal of shoreline data 

spikes, which are randomly occurring, anomalously high lidar EH values within 1–2 m of the water’s 

edge. The data spikes were most likely produced by sun glint, which produces an anomalous energy 

pulse to the lidar sensor when the lidar sensor is looking in the direction of the solar azimuthal angle and 

the Sun’s incidence angle on the water surface equals the airborne laser receiver’s look angle. To detect 

and remove these spikes, a modified Crombaghs and others (2002) method was used to determine local,

inherent noise levels in each lidar dataset; shoreline point values that exceeded their surrounding point 

values by at least two levels of local noise were deemed anomalous and were removed from the point 

file.

Lidar scan lines can be vertically and planimetrically shifted from true ground positions due to 

(1) inherent error in the GPS and IMU systems, (2) misalignment of the integrated GPS-IMU system on 

the aircraft, or (3) error in processing the GPS-IMU data. Vertical offsets and planimetric errors were 

minimized in the datasets using a second procedure, which applied an iterative procedure that uses a

data-driven approach (Filin, 2003), whereby point or DSM data are transformed (via translation, 

rotation, or polynomial corrections) so that the difference between a particular data collection and a 

reference surface is minimized (for example, Postolov and others, 1999; Crombaghs and others, 2000; 

Maas, 2000; Kager and Kraus, 2001; Maas, 2002). 

The first step in the second procedure provided initial estimates of vertical error by comparing 

flight-line data to (1) ground-truth checkpoints or TS points, (2) other flight-line data acquired the same 

day (intracollection comparison), and (3) other flight-line data acquired in different years 

(intercollection comparison). The latter comparisons were restricted to areas not inundated in the 

intervening period (above the 1,275 m3

/s flow stage). All three types of comparisons used only bare, 

relatively flat (slope less than or equal to 11°) areas. A least squares (LSQ) analysis of the all pairs of 

flight-line ΔEH values was then applied to determine the initial vertical offsets for each lidar flight line. 

The points in each lidar flight line were adjusted using these initial estimates of vertical offset.

In the second step, each lidar flight line was examined to detect and correct planimetric error

using the approach of Maas (2002), which compares each flight-line scan with a reference DSM.

Planimetric corrections (northing and easting adjustments) were determined for every point within a 

flight line by performing a LSQ analysis iteratively on various northing and easting DSM cell shifts to 

derive the northing-easting shifts that most closely produced target-surface and reference-surface

coincidence. The reference (or fiducial) surface for each study site was selected by producing shaded-
12

relief images of all lidar flight lines using the solar-elevation and solar-azimuthal angles that existed 

when the well-controlled, CIR imagery was acquired in May 2002. The shaded-relief, flight-line image 

that by visual inspection most closely matched the orthorectified CIR imagery above the 1,275 m3/s flow 

stage was selected as the fiducial surface for that study area. In most cases, the December 2004 flight 

lines were selected as the fiducial surface. Fortunately, both sides of the river corridor have numerous, 

abrupt bedrock scarps that made planimetric shift determinations easy and accurate. After all scanline 

points within each lidar flight line were analyzed the resulting point shift values were applied to the 

original lidar point datasets. In the final step, the true vertical offset for each planimetrically adjusted 

lidar flight line was determined and applied to produce corrected EH values for each flight line. The 

flight-line vertical offsets ranged from −0.18 to 0.45 m, but the majority were less than +/-0.01 m. 

The 2002 photogrammetric DSM had a vertical offset of 0.35 m within all study sites; the DSM 

EH values were adjusted downward by this offset. Comparison of the photogrammetric DSM with each 

study site’s reference DEM indicated that the photogrammetric DSM also had cross-channel tilt, which 

varied within the longer reaches. The magnitude and direction of surface tilt within each study site was 

determined by comparing centerline transects of the reference DSM and photogrammetric DSM every 

meter (or DSM cell) along the river’s centerline, above the 1,275 m3

/s flow stage. The photogrammetric 

DSMs were then adjusted using the ΔEH between the transects. The corrected DSMs were exported in 

ASCII format, so that the data could be further processed in the same manner as the other point datasets. 

DEM Construction

A link to digital products for this study that are posted on the USGS Grand Canyon Monitoring 

and Research Center (GCMRC) Web site, including DEMs and associated uncertainty surfaces, is 

available at http://pubs.usgs.gov/of/2014/1052/. 

The combined hybrid data point files (northing, easting, EH) were used to construct DEMs of the 

channel bed and banks for each reach and each monitoring period (fig. 4; table 5; appendix 1, available 

online only at http://pubs.usgs.gov/of/2014/1052/). The DEMs were constructed in ESRI’s ArcGIS 3D 

analyst extension. The general approach was to create a TIN model from the hybrid datasets, then 

interpolate a 1-m raster DEM from the TIN model using a natural neighbors interpolation method. 

Creating the TIN models, therefore, is a crucial stage in the process and required several processing 

steps to ensure the model best represented the ground surface at the time of the surveys. 
13

Figure 4. Map of a part of reach 5 in Grand Canyon, Arizona, showing final digital elevation model (DEM) from 

December 2004 with May 2002 orthophotography. DEM extent was clipped to remove vegetated areas, areas 

above the 2,746 cubic meters per second (m3/s) flow line, and areas with no input data.
14

Table 5. Digital elevation model (DEM) summary statistics used in this study along the Colorado River corridor 

within Glen, Marble, and Grand Canyons, Arizona. [m, meters; m2

, square meters; std. dev., standard deviation]

Survey date Reach Area (m2) Min (m) Max (m) Mean (m) Std. dev. (m)

August 2000 2 293351 907.95 928.47 918.38 3.02

September 2000 2 347747 907.34 928.44 918.52 2.97

May 2002 2 345763 906.98 927.90 918.55 2.84

May 2004 2 319268 907.06 925.09 918.09 2.33

November 2004 2 338667 910.20 928.46 919.35 2.30

December 2004 2 347227 907.06 928.47 918.78 2.84

May 2002 3 245215 860.56 889.77 876.95 5.66

May 2004 3 170310 860.44 882.66 873.93 3.75

November 2004 3 254226 860.58 890.10 876.96 5.54

December 2004 3 255570 859.48 890.11 877.02 5.63

August 2000 4 292930 832.05 866.50 850.73 5.57

September 2000 4 299560 831.45 866.32 850.65 5.70

May 2002 4 308403 832.00 866.50 850.69 5.42

May 2004 4 276881 832.10 858.93 849.49 4.59

November 2004 4 317940 832.55 866.00 850.87 5.27

December 2004 4 313751 830.17 866.62 850.72 5.68

August 2000 5 445079 817.77 847.27 835.65 4.62

September 2000 5 457655 816.41 847.26 835.67 4.72

May 2002 5 532917 819.09 847.04 835.09 4.67

May 2004 5 440230 817.61 841.61 833.92 4.02

November 2004 5 544847 818.12 847.12 835.22 4.63

December 2004 5 535372 816.25 847.16 835.04 4.83

May 2002 6 349453 806.05 826.94 817.33 3.62

May 2004 6 289920 804.67 821.60 816.19 2.88

November 2004 6 332992 805.23 826.95 817.29 3.69

December 2004 6 328477 801.59 827.00 817.01 3.89

August 2000 7 373727 777.05 806.57 793.75 5.06

September 2000 7 422879 776.13 806.57 793.55 4.99

May 2002 7 548697 776.45 806.57 793.81 4.56

May 2004 7 483500 775.66 801.43 792.85 3.73

November 2004 7 391826 776.88 806.57 794.64 4.85

December 2004 7 428893 777.33 806.57 794.33 4.88

To make sure that the TIN model represented the ground, or bare-earth surface, it was necessary 

to remove spurious and (or) contradictory points from the input datasets and to prioritize the datasets to

choose which dataset to use in areas of overlap (fig. 5). Lidar and photogrammetry points were 

processed to eliminate points associated with vegetated areas and standing water, as well as points that 

were lower than the 227-m3

/s stage elevation and higher than the 2,746-m3/s stage elevation. All lidar

and photogrammetry data collections were flown at a constant 227-m3

/s flow, so points lower than this 

elevation were removed using the 227-m3/s stage elevation lines derived from the land-cover 

classifications. 
15

Figure 5. Maps of a part of reach 3 in Grand Canyon, Arizona, showing (A) the raw data points and (B) polygon 

boundaries used to exclude or prioritize the input datasets, clip triangulated irregular network (TIN) model and 

digital elevation models (DEMs), and generate uncertainty surfaces.
16

The largest post-dam flow release occurred in 1983 and was approximately 2,746 m3/s . 

Therefore, we chose this level as the upper elevation limit to the lidar and photogrammetry datasets and 

points above this level were removed. The 2,746-m3/s stage elevation was derived using a combination 

of (1) a one-dimensional flow model (Wiele and Griffin, 1997), (2) measured stage elevation at longterm sand-bar monitoring sites (Hazel and others, 2010), and (3) GIS surface extrapolation routines 

(Magirl and others, 2005). Lidar and photogrammetry points located adjacent to the 2,746-m3/s stage 

elevation and having slopes greater than 45° (extreme slopes) were also removed. Bathymetric input 

files were processed to remove data points above 227 m3/s to exclude any data collected at higher flows.

For areas above the 227-m3/s stage elevation, lidar and photogrammetry data were prioritized over TS 

points. For areas below the 227 m3/s, bathymetric data were prioritized over TS points. TS points were 

only used in areas that occurred between the extent of the lidar and photogrammetry data and 

bathymetric data (fig. 5).

The absence of data for some parts of each study reach and the removal of bad data points 

discussed above resulted in gaps in the data coverage. Some of these gaps were left as voids and 

excluded from the final DEM, whereas some voids were interpolated across (fig. 5). We created several 

sets of polygons and associated rule sets to determine which areas to include in the DEM and which 

areas to exclude. The gaps typically occurred in areas where bathymetric measurements could not be 

made (such as rapids and riffles and shallow areas along the shoreline where depths were less than about 

1.5 m), areas of dense vegetation and standing water, and areas where datasets do not overlap. In gaps 

within the lidar and photogrammetric data, the land-cover classification polygons were used to prevent 

TIN model generation within data voids. 

Below the 227-m3

/s stage elevation, gaps typically occur in rapids and riffles and along the 

shoreline between the sonar data and the terrestrial data. Rapids and riffles were excluded from the 

DEM, whereas shoreline areas were typically interpolated across the DEM. Along steeply sloping 

shorelines, gaps between the bathymetric and terrestrial datasets were relatively narrow (approximately 

2–4 m). However, along the shallow, low-angle sandbars, these distances were sometimes quite large 

(greater than 10 m). In many of these gaps around sandbars, TS points were collected below the water 

surface to depths of approximately 1–1.5 m and were used in TIN model construction. Gaps without TS 

point data were interpolated across only if the difference in elevation between the two datasets was less 

than 2 m. Following interpolation, TIN models were visually inspected for errors, which were manually 

corrected by editing the TIN. These errors typically involved erroneous lidar points near vegetation that 

were not clipped by the land-cover boundary and anomalous (erroneous) bathymetry points that were 

not deleted in the editing process. 

An important aspect of DEM construction is selecting the proper grid resolution for the input 

datasets. The ideal grid resolution contains the same number of grid cells as data points (McCullagh, 

1988). The grid-size estimator of Hu (2003) was used to determine if the combined datasets have the 

necessary point density to be reliably interpolated to a 1-m cell size. Hu (2003) proposed that DEM grid 

sizes can be estimated using the equation: 

 

This equation was applied to the edited and filtered hybrid point datasets for all 32 surveys. The results 

show a mean cell size of 0.97 m with a standard deviation of 0.16 m and indicate that a 1-m grid cell 

size is appropriate for our datasets.

A 1-m resolution DEM was derived for each survey (fig. 4; appendix 1). All DEMs for a 

particular reach were derived in the exact same orthogonal space. That is, they share the same cell 

resolution, cell centers, and bounding northing and easting coordinates. The end result is a set of 

coincident DEMs, which ensures that no resampling errors are introduced during change detection 

between surveys.
17

DEM Uncertainty 

Accounting for uncertainty is a crucial component of monitoring studies that compare sequential

DEMs to detect spatial patterns and volumes of morphological change (Brasington and others, 2003; 

Lane and others, 2003; Wheaton and others, 2010). In this context, our definition of uncertainty is 

limited to errors in the vertical component associated with comparison among the DEMs described in 

this study. Horizontal (positional) errors are considered negligible from the survey methods used here at 

the scale of 1-m resolution grid cells. Even in consideration of the vertical component of uncertainty, 

some components of error are not relevant. For example, because the same control points were used for 

each repeat survey, the uncertainty in the absolute position of the control points is not included in our 

uncertainty estimate. This places the focus solely on the uncertainty that is involved in creating a DEM 

independently for each of the survey methods used in the study. For each survey, the vertical component 

of uncertainty for each data type (lidar/photogrammetry, ground surveys, bathymetry) was estimated. 

This results in nine categories of spatially variable uncertainty estimates that depend on the specific 

survey method and date of survey. The uncertainty estimates were tabulated in raster format, coincident 

with the corresponding DEM that contains uncertainty values for each survey date. Interpolation 

uncertainty was not estimated for areas of no data input (interpolated areas), with the exception of areas 

covered by singlebeam bathymetric surveys.

Each interpolated area was assigned uncertainty according to the adjacent data collection 

method. Thus, for areas above the 227-m3/s stage elevation, interpolated areas are assigned the 

appropriate lidar or photogrammetry uncertainty estimate. For areas below the 227-m3

/s stage elevation, 

interpolated areas are assigned the multibeam-sonar uncertainty estimate. The resulting uncertainty 

surfaces inherit spatial variability from the final survey method polygons (fig. 5) and have spatially 

uniform uncertainty estimates therein.

Several methods were used to estimate the vertical uncertainty associated with the datasets used 

to construct the DEMs, the details of which are discussed in later sections. Bathymetric uncertainty was 

estimated separately for multibeam and singlebeam datasets. Multibeam data were evaluated using a 

procedure that compares the elevations of the 1-m DEMs within areas of stable topography that have not 

changed over the course of this study. Such areas are referred to as fiducial surfaces, in the terminology 

of Brock and others (2001). For the singlebeam data, vertical uncertainty was estimated by combining a 

cross-line analysis of the precision within the surveys with the uncertainty associated with the 

interpolation of the singlebeam data to a 1-m DEM. The uncertainties associated with the lidar and 

photogrammetric datasets were estimated by comparing the elevations of points between individual 

surveys within fiducial areas that we are confident have not changed over the course of this study. 

Four primary metrics are used to quantify uncertainty in the topographic and bathymetric 

datasets. These metrics are mean error in elevation (MEz), mean absolute error in elevation (MAEz), the 

root-mean-square error in elevation at the 68-percent confidence level (RMSEz), and root-mean-square 

error in elevation at the 95-percent confidence level (RMSEz 95%). These statistics are computed as 

follows: 

 

where ΔEHi is the ellipsoid-height difference between corresponding points in two datasets. The 

standard deviation and skewness for each ellipsoid-height difference (ΔEH) distribution are also 

reported. 
18

The primary intended use for the DEMs described in this study is to determine the net change in 

volume between different time periods. The MAEz metric represents the spatially distributed uncertainty 

for each DEM. The RMSEz and RMSEz 95-percent metrics are the elevation errors that are not 

expected to be exceeded at the 68- and 95-percent levels of confidence, respectively, and provide an 

estimate of the level of confidence in the elevation for each grid cell in the mapped area for each survey 

date. However, resolution of uncertainty at the level of each grid cell is more conservative than required 

when the primary interest is net change in storage over a large area. The RMSE metric uses the sum of 

squared difference values and, as a result, a relatively few large errors have a much greater influence on 

the RMSE value than do the dominant, smaller errors. The RMSE metric also varies in ways not related 

to the average error of a population (Willmott and Matsuura, 2005). The MEz represents the mean 

difference in elevation, or bias between surveys. However, because comparisons are pooled for different 

time periods for the multibeam data, if some surveys were high and other surveys low, the MEz may be 

near zero and not a measure of potential bias for any single survey (see section on Multibeam 

Uncertainty below). The MAEz metric provides a good estimate of the average uncertainty associated 

with repeat measurements that includes any potential bias, and it is this metric that best describes the 

uncertainties associated with the different data collection methods used to generate the DEMs presented 

in this report. 

Bathymetry

Surface roughness or texture affects uncertainty in grid-cell elevations, regardless of survey 

method. For rough-textured surfaces, small errors in position can result in large errors in elevation, 

whereas for smoother surfaces, errors in position may result in very little error in elevation. Therefore, 

areas that have a high surface roughness, such as rocky shorelines, will inherently have higher 

uncertainties than areas that are relatively smooth, such as sand-bedded areas and shallow gravel bars 

(Wheaton and others, 2010). To more accurately represent the vertical uncertainty in the multibeam 

bathymetric topography, the surface roughness (or bed texture) within each surveyed surface was 

quantitatively classified into smooth and rough surface elements.

Bed-Texture Classification

Bed texture was classified into smooth and rough categories based on statistical analysis of the 

bathymetric data. High-resolution (0.25-m grid spacing) multibeam bathymetric data were used to 

generate hillshade raster images of the surfaces using an illumination angle of 90°, which is directly 

overhead (fig. 6A). A hillshade raster image scales the image intensity between 0 and 255 for each cell 

in the raster image. From the hillshade-image intensity values, the focal standard deviation (FSD) was 

calculated for each image cell using a 3×3-m moving window. The FSD grid values were then classified 

into rough (FSD less than 10) and smooth (FSD greater than or equal to 10) categories. The FSD 

separation value (10) was selected by trial and error and visual inspection. The selected FSD value 

resulted in a classification that best matched appearance in the hillshade images. The FSD separation 

value corresponds to adjacent-cell elevation differences of approximately 0.25 to 0.36 m. Within the 

smooth textural class, ellipsoid height differences ranged from 0.0 to 0.25 m, and within the rough 

textural class, ellipsoid height differences ranged from 0.36 to 0.9 m. The results from this hillshadeFSD classification were converted to polygons, restricting the minimum polygon area to be 25 m2

 (fig. 

6B), which were, in turn, converted to 1-m grids that were coincident with the 1-m DEM (fig. 6C). 

Multibeam Uncertainty

DEM uncertainty was estimated on smooth and rough channel beds by examining the ΔEH in the 

1-m DEMs within fiducial areas (that is, areas that did not change appreciably in elevation within the 4-
19

year period of this study). The fiducial surfaces, which were at least 100 m2 in area, were created as 1-m 

DEMs using the 1-m multibeam bathymetric data. Fiducial surfaces were identified in both smooth and 

rough bed-texture map classes. A total of 12 fiducial areas were selected in smooth areas, seven in rough 

areas, with at least one fiducial area defined in each reach (reaches 2 through 7 only). Figure 7 shows 

examples of rough and smooth fiducial polygons within reach 6. 

Figure 6. Maps of a part of reach 4 in Grand Canyon, Arizona, showing stages in the bed-texture classification 

process using the December 2004 survey data. A, 0.25-meter (m) digital elevation model (DEM) and hillshade 

derived from high-resolution mulitbeam bathymetric data. B, Bed-texture classification polygons superposed on 

the 0.25 m DEM and hillshade. For each cell in the hillshade grid, the focal standard deviation (FSD) was 

calculated using a 3×3-m picture-element array. Cells with FSD values greater than or equal to 10 were 

classified as rough, cells with FSD less than 10 were classified as smooth. Rough and smooth cells were 

aggregated into polygons with an area greater than 25 square meters (m2) and converted into a 1-m grid. C, 

Final 1-m bed-texture classification grid superposed on the 0.25-m hillshade. 
20

Figure 7. Map of a part of reach 6 in Grand Canyon, Arizona, showing examples of rough and smooth fiducial 

areas on a shaded-relief image derived from the May 2002 digital elevation model (DEM) superposed on the 

May 2002 orthophotography. Fiducial areas are assumed to not have changed in elevation over the course of 

the study and, as such, were used to generate uncertainty estimates for the multibeam data.

For smooth areas, the fiducial surfaces were defined on large gravel bars and relatively flat 

bedrock outcrops. For rough areas, fiducial surfaces were defined on steep talus slopes and boulderdominated debris fans. For each survey date, every fiducial DEM grid cell was compared to its 

corresponding grid cells for all the other survey dates, which resulted in five temporal ΔEH comparisons 

for each grid cell. All grid cells from each fiducial area and temporal comparison were combined, or 

pooled, to derive one uncertainty estimate for each survey date (table 6). For example, the summary 

statistics for the August 2000 smooth bed classification were derived from a dataset that included ΔEH

values from all 12 fiducial areas and all five temporal comparisons. The ΔEH populations all have 

skewness values that are less than 0.5, which indicates a fairly normal distribution. MAEz values 

average 0.07 m for smooth areas and 0.27 m for rough areas. Kaplinski and others (2009) used a crossline analysis on the raw multibeam soundings to estimate uncertainty (precision) in the raw multibeam 

datasets; their results were similar to the results obtained for the DEM datasets, where the MAEz values 

ranged from 0.04 to 0.08 m. One advantage of using the fiducial-surface method is that the resulting 

uncertainties account for a number of sources of error involved in DEM production, which otherwise 

would need to be formulated and determined individually and summed. This technique provides a 

reasonable, standardized procedure for estimating uncertainty, where fiducial areas can be reliably 

established. 
21

Table 6. Summary statistics of multibeam bathymetry uncertainty used in this study along the Colorado River 

corridor within Glen, Marble, and Grand Canyons, Arizona. [MEz, mean error in elevation; MAEz, mean absolute error in elevation; RMSEz, root-mean-square error in elevation at the 

68-percent confidence level; RMSEz 95%, root-mean-square error in elevation at the 95-percent confidence level; m, meters; 

n, number of observations]

Survey date Bed class n MEz (m)

MAEz 

(m)

RMSEz 

(m)

RMSEz 95% 

(m)

Std. dev. 

(m) Skewness

August 2000 smooth 95,905 -0.04 0.08 0.10 0.19 0.09 0.22

August 2000 rough 23,320 -0.02 0.34 0.45 0.89 0.45 0.05

September 

2000

smooth 99,904 -0.01 0.08 0.10 0.20 0.10 0.07

September 

2000

rough 30,098 0.00 0.33 0.44 0.86 0.44 0.07

May 2002 smooth 169,773 0.01 0.06 0.08 0.15 0.08 0.07

May 2002 rough 35,099 0.00 0.25 0.33 0.64 0.33 0.00

May 2004 smooth 169,958 0.00 0.07 0.09 0.17 0.09 -0.13

May 2004 rough 35,036 0.01 0.24 0.32 0.63 0.32 -0.03

November

2004

smooth 169,702 0.00 0.06 0.08 0.15 0.08 -0.10

November

2004

rough 35,062 0.01 0.22 0.29 0.57 0.29 -0.04

December 

2004

smooth 163,647 0.01 0.06 0.08 0.15 0.08 0.04

December 

2004

rough 44,053 0.02 0.23 0.32 0.62 0.31 -0.01

Singlebeam Uncertainty

Uncertainty analysis of singlebeam data requires a different approach because of interpolation 

uncertainty associated with generating a continuous surface from gridded transect lines. Uncertainty for 

the parts of the DEMs created from singlebeam surveys was estimated by partitioning the uncertainty 

into a component associated with survey precision and a component associated with DEM interpolation 

of the singlebeam data. Survey precision was estimated using cross-line checks (U.S. Army Corps of 

Engineers [USACE], 2002). A cross-line check compares the elevation (or depth) of intersection points 

from separate intersecting survey lines. Cross-line checks were conducted on eight individual 

singlebeam transects for each survey trip by selecting pairs of points that were within a 1-m radius. For 

each pair of points, the ΔEH was calculated. The ΔEH values from all cross-line checks were combined 

for each survey trip to derive an estimate of measurement uncertainty. The results of the cross-line 

analyses (table 7) show that both the August and September surveys were of good quality with a MEz

less than 0.01 m ( indicating minimal bias) and a RMSEz 95% less than 0.25 m, which exceed both 

USACE and International Hydrographic Organization standards for “special order” and surveys 

(USACE, 2002). 

Table 7. Summary statistics of singlebeam bathymetry cross line check uncertainty used in this study along the 

Colorado River corridor within Glen, Marble, and Grand Canyons, Arizona. [MEz, mean error in elevation; MAEz, mean absolute error in elevation; RMSEz, root-mean-square error in elevation at the 

68-percent confidence level; RMSEz 95%, root-mean-square error in elevation at the 95-percent confidence level; m, meters; 

n, number of observations] 

Survey date n MEz (m) MAEz (m) RMSE (m) RMSE 95% (m) Std. dev. (m) Skewness

August 2000 545 0.00 0.07 0.10 0.19 0.10 0.33

September 2000 858 -0.01 0.07 0.10 0.19 0.10 0.10
22

The uncertainty associated with interpolating singlebeam-transect grids to a continuous surface 

was estimated by using a bootstrapping technique on surveys at one site (River Mile 32 in reach 4) with 

singlebeam surveys in both August and September 2000 (Efron and Tibshirani, 1998). The process 

involved partitioning the sorted singlebeam points into test and training subsets. The test subset 

consisted of a random sample of 10 percent of the original dataset that was withheld from the 

interpolation process (that is, DEM construction). DEMs were constructed with the remaining 90 

percent of the original dataset and the resulting DEM cells were compared to the test subset to derive 

ΔEH values. The results of the comparison show MAEz interpolation errors of 0.13 and 0.07 m for the 

August and September surveys, respectively (table 8).

Table 8. Summary statistics of singlebeam interpolation uncertainty used in this study along the Colorado River 

corridor within Glen, Marble, and Grand Canyons, Arizona. [MEz, mean error in elevation; MAEz, mean absolute error in elevation; RMSEz, root-mean-square error in elevation at the 

68-percent confidence level; RMSEz 95%, root-mean-square error in elevation at the 95-percent confidence level; m, meters; 

n, number of observations] 

Survey date n MEz (m) MAEz (m) RMSE (m) RMSE 95% (m) Std. dev. (m) Skewness

August 2000 159 -0.01 0.13 0.24 0.47 0.24 -0.09

September 2000 210 0.01 0.07 0.09 0.17 0.09 -0.20

The total uncertainty applied to regions of the DEMs constructed from singlebeam surveys was

obtained by computing the quadratic sum of the individual error components (Taylor, 1997) using the 

following equation: 

 

Using the MAEz statistic from tables 7 and 8, the total uncertainty for singlebeam data is 0.15 m 

for the August 2000 surveys and 0.10 m for the September 2000 surveys. 

Lidar and Photogrammetry Uncertainty

Estimates of lidar and photogrammetric vertical uncertainties were derived from the ΔEH

between the different temporal airborne data collections for fiducial areas within reach 5 (table 9). 

Fiducial points were selected using the following criteria: (1) the bare, smooth land-cover units above 

the 1,274-m3

/s stage elevation, (2) slopes of less than 12 degrees, (3) points more than 1 m from dense 

or sparse vegetation landform classifications, and (4) points not in the vicinity of abrupt changes in slope 

(Maune and others, 2007). In addition, the points were visually inspected with imagery to exclude areas 

that appeared to have changed. The results of the comparison show that MAEz values range from 0.17 

to 0.21 m. 

Table 9. Summary statistics of lidar and Photogrammetry uncertainty used in this study along the Colorado River 

corridor within Glen, Marble, and Grand Canyons, Arizona. [MEz, mean error in elevation; MAEz, mean absolute error in elevation; RMSEz, root-mean-square error in elevation at the 

68-percent confidence level; RMSEz 95%, root-mean-square error in elevation at the 95-percent confidence level; m, meters; 

n, number of observations] 

Survey date n MEz (m) MAEz (m) RMSEz (m) RMSEz 95% (m) Std. dev. (m) Skewness

August 2000 754590 -0.02 0.18 0.26 0.51 0.26 -0.71

September 2000 755694 -0.02 0.18 0.26 0.50 0.26 -0.72

May 2002 824240 -0.02 0.21 0.28 0.56 0.28 -0.49

November 2004 829324 0.00 0.17 0.23 0.45 0.23 -0.44

December 2004 825070 -0.05 0.17 0.23 0.46 0.23 -0.39
23

Uncertainty Surfaces

For each DEM, a map was created that depicts uncertainty for each cell within each DEM. 

Assignment of each cell’s uncertainty was based on the type of data that was used to determine the 

elevation for that cell in the final DEM (fig. 8A). Owing to the multiple sources of data used to generate 

the final DEM, this required generating a grid that identified the data source or method of interpolation 

for each cell (fig. 8B). Inclusion of all data sources and interpolation methods results in nine data-source 

categories—(1) lidar, (2) photogrammetry, (3) multibeam over rough bed, (4) multibeam over smooth 

bed, (5) singlebeam, (6) TS points above the 227-m3/s stage elevation, (7) TS points below the 227-m3/s 

stage elevation, (8) interpolated areas above the 227-m3

/s stage elevation, and (9) interpolated areas 

below the 227-m3/s stage elevation. MAEz values were assigned to each cell based on the data source 

category (fig. 8C); table 10). Lidar and (or) photogrammetry uncertainty values were assigned to TS 

points and interpolated areas above the 227-m3/s stage elevation (classes 6 and 8), and multibeam 

smooth bed uncertainties were assigned to TS points and interpolated areas below the 227-m3/s stage 

elevation (classes 7 and 9). Interpolated areas constitute less than 10 percent of the total DEM area, and 

the majority of these areas are sufficiently well constrained by flanking data points that it was deemed 

appropriate to apply the calculated uncertainty of the surrounding data points. For example, the majority 

of interpolated areas occur below the 227-m3

/s stage elevation in shallow sandbar and gravel-bar areas

with low surface roughness and slope (fig. 8A). Within these areas, the TIN model creates surface area 

between data points (either total station or multibeam) that sufficiently captures the topography 

surrounding the data point. A small part of the interpolated areas undoubtedly incur uncertainty beyond 

that of the surrounding data points. Future studies should consider investigating methods for applying an 

additional interpolation term to the uncertainty in these areas. 
24

Figure 8. Maps of a part of reach 5 in Grand Canyon, Arizona, showing the stages involved in assigning 

uncertainty values using the November 2004 survey data—A, data points; B, raster image of input data 

sources; and C, uncertainty surface generated for the November 2004 digital elevation model (DEM). M, 

meters; m3/s, cubic meters per second; MAEz, mean absolute error in elevation. 
25

Table 10. Uncertainty estimates assigned to each data source category in final digital elevation models (DEMs) for 

the Colorado River corridor within Glen, Marble, and Grand Canyons, Arizona. [m3

/s, cubic meters per second; n.a., not applicable]

Data source category1 August 2000

September 

2000 May 2002 May 2004

November 

2004

December 

2004

Lidar 0.18 0.18 n.a. n.a. 0.17 0.17

Photogrammetry n.a. n.a. 0.21 n.a. n.a. n.a.

Multibeam—smooth 0.08 0.08 0.06 0.07 0.06 0.06

Multibeam—rough 0.34 0.33 0.25 0.24 0.22 0.23

Singlebeam 0.15 0.10 n.a. n.a. n.a. n.a.

Total station above 227 m3/s 0.18 0.18 0.21 0.10 0.17 0.17

Total station below 227 m3/s 0.08 0.08 0.06 0.07 0.06 0.06

Interpolated above 227 m3/s 0.18 0.18 0.21 0.10 0.17 0.17

Interpolated below 227 m3/s 0.08 0.08 0.06 0.07 0.06 0.06

1

MAEz (root-mean-square error in elevation at the 68-percent confidence level) statistics from tables 5 through 8 were used 

for each data source category.

Summary 

One meter DEMs were constructed for six study reaches along the Colorado River in Grand 

Canyon. The DEMs combine elevations determined from ground-based total station surveys, airborne 

remote-sensing missions, and sonar bathymetric surveys collected in in August 2000, September 2000, 

May–June 2002, May–June 2004, November 2004, and December 2004. 

The general approach to DEM construction was to create a TIN model from the input datasets, 

then interpolate a 1-m raster DEM from the TIN model. Lidar and photogrammetry points were 

processed to eliminate anomalous spikes, vertical offsets, planimetric shifts, regional tilts, and to 

exclude points on or near vegetated areas, standing water, and for points higher than the 2,746-m3

/s 

stage elevation. Bathymetry surveys excluded rapids and riffles and shallow areas along the shoreline, 

where depths were less than about 1.5 m. In areas along the shoreline lacking bathymetric point data, TS 

points collected by total station were used constrain the TIN model. Clipping polygons were generated 

that outlined the perimeter of the combined datasets and internal spatial gaps in the point datasets. The 

TIN models were formed and then clipped with the internal and external (perimeter) clipping polygons. 

The final TIN model was used to create a 1-m resolution DEM for each survey. All DEMs were 

derived to be coincident with each other. That is, they share the same cell resolution, and cell centers, 

and bounding northing and easting coordinates. The end result is a set of coincident DEMs. This step 

ensures that no resampling errors are introduced during change detection between surveys.

Statistics were used to construct uncertainty grids that are coincident with the DEMs. For each 

survey period, the vertical component of uncertainty was estimated for each data type and for two 

different areas of bed-surface texture. These estimates of uncertainty were applied regionally to the 

uncertainty grid, depending on which data type was used in DEM construction. Even though the 

uncertainty estimates were spatially uniform by method, because the DEMs were produced by hybrid 

data sources the resulting uncertainty estimates varied spatially. Interpolated areas, or areas not 

constrained by data points, constituted less than 10 percent of the DEM area and were assigned 

uncertainty estimates from surrounding areas where the uncertainty was defined. Vertical uncertainty 

estimates range from 0.17 to 0.21 m within the lidar and photogrammetry parts of the DEMs, from 0.06 

to 0.08 m within areas classified as multibeam smooth, and between 0.22 to 0.34 m within areas 

classified as mulitbeam rough (table 10). Therefore, the range of vertical change that can be reasonably 

detected (that is, change above the quadratic sum of the uncertainty estimates from the surfaces being 

compared) varies from 0.08 to 0.01 m for regions within the multibeam smooth classification, 0.24 to 

0.28 m from regions within the lidar and photogrammetry classification, and 0.32 to 0.47 m for regions 

within the multibeam rough classification.
26

The resulting DEMs from this study will provide valuable information to the ongoing efforts to 

assess the effects of GCD operations on the CRE. The DEMs can be used by researchers to map the 

spatial characteristics of the geomorphic change within the study reaches and to estimate sediment 

budgets for different time periods by calculating the difference in volume between surveys. In addition, 

the DEMs provide valuable boundary conditions for numerical models of sediment transport and 

deposition, as well as help define the spatial distribution of habitat for fisheries investigations.

Acknowledgments

 This study was funded by the Bureau of Reclamation as part of the Glen Canyon Dam Adaptive 

Management Program. The authors wish to thank the multitudes of people involved in the data 

collection and processing. 

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