U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2015–5179

Prepared in cooperation with the Bureau of Land Management

Quantifying the Eroded Volume of Mercury-Contaminated 

Sediment Using Terrestrial Laser Scanning at Stocking Flat, 

Deer Creek, Nevada County, California, 2010–13

Terrestrial

laser scanner

Eroding cutbank of

mercury-contaminated

sediment

Deer Creek
Cover.

Front image—A FARO Focus3D laser scanner on top of eroding cutbank at Stocking Flat study site, February 4, 2013.

Back top image—Oblique image for a selected 4-meter-wide area of the cutbank showing retreat of the cutbank surface

between January 2011 and February 2013. The oblique perspective is looking downstream and the selected area is the

foreground of the cutbank shown in the cover photo, just beyond the tripod and laser scanner.

Back bottom image—Color-coded difference plot showing the horizontal change, in meters, from January 2011 to 

February 2013 for the selected area shown in the above image.
Quantifying the Eroded Volume of MercuryContaminated Sediment Using Terrestrial 

Laser Scanning at Stocking Flat, Deer 

Creek, Nevada County, California, 2010–13

By James F. Howle, Charles N. Alpers, Gerald W. Bawden, and Sandra Bond

Prepared in cooperation with the Bureau of Land Management

Scientific Investigations Report 2015–5179

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

SALLY JEWELL, Secretary

U.S. Geological Survey

Suzette M. Kimball, Director

U.S. Geological Survey, Reston, Virginia: 2016

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Suggested citation:

Howle, J.F., Alpers, C.N., Bawden, G.W., and Bond, Sandra, 2016, Quantifying the eroded volume of mercurycontaminated sediment using terrestrial laser scanning at Stocking Flat, Deer Creek, Nevada County, California, 

2010–13: U.S. Geological Survey Scientific Investigations Report 2015–5179, 23 p., http://dx.doi.org/10.3133/

SIR20155179.

ISSN 2328-0328 (online)
iii

Contents

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

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

Purpose and Scope ..............................................................................................................................3

Study Area Description........................................................................................................................3

Methods...........................................................................................................................................................3

Data Collection......................................................................................................................................4

Point-Cloud Alignment .........................................................................................................................5

Geometric Benchmarks..............................................................................................................5

Reference Points .........................................................................................................................5

Alignment of Sequential Surveys..............................................................................................7

Quality Assurance of Alignments.......................................................................................................8

Volumetric Determination....................................................................................................................8

Data-Point Removal.....................................................................................................................8

Creating Surfaces........................................................................................................................8

Defining a Common Boundary...................................................................................................9

Calculating Volumetric Changes ...............................................................................................9

Results of Volume Calculations .................................................................................................................10

Visualization of Changes.............................................................................................................................14

Shaded-Relief Images........................................................................................................................14

Two-Dimensional Change Maps ......................................................................................................16

Three-Dimensional Anaglyphs .........................................................................................................20

Summary........................................................................................................................................................20

References Cited..........................................................................................................................................21

Glossary.........................................................................................................................................................23

Figures

1. Maps and photographs showing location of Deer Creek in the Yuba River drainage 

basin of northern California ........................................................................................................2

2. Photographs showing an Optech ILRIS 36D laser scanner deployed in two locations 

at Stocking Flat, Deer Creek, Nevada County, California.......................................................4

3. Graphics output from PolyWorks® software package showing an example of 

alignment and comparison of overlapping point-cloud data ................................................6

4. Photograph showing a FARO Focus3D laser scanner on top of eroding cutbank at 

Stocking Flat study site, February 4, 2013 ................................................................................6

5. Images showing sequence for defining reference points from geometric 

benchmarks ...................................................................................................................................7

6. Graphics output from PolyWorks® software showing the sequence for calculating 

volume ..........................................................................................................................................10

7. Graphics output from PolyWorks® software showing lidar point cloud of the cutbank 

surface..........................................................................................................................................13

8. Images showing shaded-relief oblique views of Stocking Flat cutbank study site 

near Nevada City, California, for the four surveys between December 2010 and 

February 2013 ..............................................................................................................................15
iv

9. Photograph showing the central part of the cutbank on March 17, 2011, high 

streamflow and the near-vertical fluvial scarp......................................................................16

10. Graphics output from PolyWorks® software showing difference maps of horizontal 

change across the cutbank surface for four periods between December 1, 2010, and 

February 4, 2013 ..........................................................................................................................17

11. Images showing three-dimensional anaglyphs and two-dimensional difference 

maps showing changes from December 2010 to February 2013 for selected areas 

of the cutbank..............................................................................................................................18

12. Images showing three-dimensional anaglyph and two-dimensional difference 

maps showing changes from January 2011 to February 2013 for a selected area of 

the cutbank ..................................................................................................................................19

Figures—Continued

Tables

1. Calculated volumes between the cutbank surface and reference planes for 

surveys 1, 2, 3, and 4...................................................................................................................11

2. Measured volumes of mercury-contaminated sediment (in cubic meters) eroded 

from the Stocking Flat cutbank study site for various periods between December 1, 

2010, and February 4, 2013.........................................................................................................14

Conversion Factors

International System of Units to Inch/Pound

Multiply By To obtain

Length

centimeter (cm) 0.3937 inch (in.)

millimeter (mm) 0.03937 inch (in.)

meter (m) 3.281 foot (ft)

kilometer (km) 0.6214 mile (mi)

meter (m) 1.094 yard (yd)

Area

square meter (m2

) 10.76 square foot (ft2) 

square centimeter (cm2

) 0.1550 square inch (in2) 

Volume

cubic meter (m3

) 35.31 cubic foot (ft3)

Mass

kilogram (kg) 2.205 pound avoirdupois (lb)

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

°F = (1.8 × °C) + 32.

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

°C = (°F – 32) / 1.8.
v

Abbreviations and Acronyms

2-D two dimensional

3-D three dimensional

ASL above sea level

BLM Bureau of Land Management

Hg mercury 

lidar light detection and ranging (or LiDAR)

PVC polyvinyl chloride

RMSE root-mean-square error

TIN triangulated irregular network

TLS terrestrial laser scanning

USGS United States Geological Survey

VR virtual reality

Vrui Virtual reality user interface

WY water year

Selected technical terms are defined in the glossary. These terms are indicated in bold font the 

first time they are used in the main body of the report.
vi
Quantifying the Eroded Volume of Mercury-Contaminated 

Sediment Using Terrestrial Laser Scanning at Stocking 

Flat, Deer Creek, Nevada County, California, 2010–13

By James F. Howle, Charles N. Alpers, Gerald W. Bawden, and Sandra Bond

Abstract 

High-resolution ground-based light detection and ranging 

(lidar), also known as terrestrial laser scanning, was used 

to quantify the volume of mercury-contaminated sediment 

eroded from a stream cutbank at Stocking Flat along Deer 

Creek in the Sierra Nevada foothills, about 3 kilometers west 

of Nevada City, California. Terrestrial laser scanning was used 

to collect sub-centimeter, three-dimensional images of the 

complex cutbank surface, which could not be mapped nondestructively or in sufficient detail with traditional surveying 

techniques.

The stream cutbank, which is approximately 50 meters 

long and 8 meters high, was surveyed on four occasions: 

December 1, 2010; January 20, 2011; May 12, 2011; and 

February 4, 2013. Volumetric changes were determined 

between the sequential, three-dimensional lidar surveys. 

Volume was calculated by two methods, and the average 

value is reported. Between the first and second surveys 

(December 1, 2010, to January 20, 2011), a volume of 143 

plus or minus 15 cubic meters of sediment was eroded from 

the cutbank and mobilized by Deer Creek. Between the second 

and third surveys (January 20, 2011, to May 12, 2011), a 

volume of 207 plus or minus 24 cubic meters of sediment was 

eroded from the cutbank and mobilized by the stream. Total 

volumetric change during the winter and spring of 2010–11 

was 350 plus or minus 28 cubic meters. Between the third 

and fourth surveys (May 12, 2011, to February 4, 2013), the 

differencing of the three-dimensional lidar data indicated that 

a volume of 18 plus or minus 10 cubic meters of sediment was 

eroded from the cutbank. The total volume of sediment eroded 

from the cutbank between the first and fourth surveys was 368 

plus or minus 30 cubic meters.

Introduction

On the western slope of the Sierra Nevada, historical 

hard-rock (lode) and placer (gravel) mines produced large 

volumes of mercury (Hg)-contaminated mining debris

(Gilbert, 1917; James, 1989). Elemental Hg was used 

extensively to enhance gold recovery during the mid-tolate 1800s and the early 1900s (Alpers and others, 2005a), 

which resulted in Hg contamination of sediment in many 

areas throughout the Sierra Nevada, including the Yuba River 

drainage basin, Deer Creek subbasin, and the Stocking Flat 

study site (fig. 1). Although Hg was used both in hard-rock and 

in placer gold-mining operations, historical records indicated 

that much more Hg was used and lost to the environment from 

placer gold-mining activities in the Sierra Nevada than from 

hard-rock mines and associated mills (Churchill, 2000; Alpers 

and others, 2005a).

To identify Hg “hot spots” for remediation targets in 

the Deer Creek drainage basin and other areas in the Sierra 

Nevada, the U.S. Geological Survey (USGS) has been 

working in cooperation with the Bureau of Land Management 

(BLM) and other federal, state, and local agencies on 

regional and detailed studies since 1999 (Hunerlach and 

others, 1999, 2004; May and others, 2000; Alpers and others, 

2005a, 2005b, 2006, 2012; Fleck and others, 2011; MarvinDiPasquale and others, 2011). In the Deer Creek drainage 

basin, methylmercury concentrations in water, sediment, fish 

(primarily brown trout and largemouth bass), and predatory 

invertebrates (larval dragonflies, mayflies, stoneflies, and 

adult water striders) were monitored during 2010 and 2011 to 

assess temporal and spatial variability in stream environments 

upstream and downstream from suspected mercury sources 

(Jacob Fleck and others, U.S. Geological Survey, written 

commun., 2015).

The Stocking Flat study site lies along Deer Creek about 

3 kilometers (km) west of Nevada City, California (figs. 1B,

C). Several large historical hard-rock gold mines (Champion, 

Providence, and Mountaineer) and associated mills are less 

than 2.5 km upstream from Stocking Flat. In addition to 

these hard-rock mines, there were small-to-medium sized 

hydraulic gold mines in the areas that are now Hirschman’s 

Pond and Scotts Flat Reservoir (fig. 1B). During the late 19th 

and early 20th centuries, the Deer Creek drainage at Stocking 

Flat became filled with sediment consisting largely of mining 

debris from upstream hard-rock and placer mines (fig. 1C). 
2 Quantifying Mercury-Contaminated Sediment at Stocking Flat, Deer Creek, Nevada County, Calif., 2010–13

Sac15-0571_fig 01

A

Area of 

figure 1A

Sierra Nevada

California

N

S N

EXPLANATION

Water

Urban

Barren

Forest

Shrubland

Herbaceous

Planted/cultivated

Watershed boundary

Yuba River

Deer Creek

City

Gold mine

Champion/Providence Mine

Nevada City

The Stocking Flat study site is in an alluvial plain composed of 

historical hard-rock and placer-mining debris

Cutbank

study site

Stocking Flat

Deer Creek

Historical

mining

debris

Nevada City

Grass Valley

Grass Valley

Marysville

North Yuba RiverNorth Yuba River

Middle Yuba River Middle Yuba River

South Yuba River South Yuba River

Deer Creek Deer Creek Yuba River Yuba River

Scotts Flat 

Reservoir

Lake

Wildwood

Hirchsman’s Pond

Mountaineer Mine

Stocking Flat study

site. Area of figure 1C

Deer Creek near

Smartsville, Calif.,

streamgage

Champion/Providence Mine

South Yuba River

M

South Yuba River

iddle Yuba River

Middle Yuba River

Deer Creek

B

C D

39° 40’

39° 30’

39° 20’

39° 10’

39°19’30”

121°03’

39°15’18.0”

39°15’16.0”

121°02’55.0”

121°10’ 121° 120°50’

39°9’

121° 30’ 121° 120° 30’

0 10 20 MILES 5

0 10 20 KILOMETERS 5

0 10 20 KILOMETERS

0 5 10 15 20 MILES

5 15

50 METERS

Photo credit: Photo from Friends of Deer Creek and Sierra Streams Institute, 2011.

Figure 1. A, Location of Deer Creek in the Yuba River drainage basin of northern California; B, the Deer Creek drainage basin showing 

geographic locations discussed in text; C, undated historical photo showing the Deer Creek drainage looking west, downstream from 

Nevada City; and D, aerial photograph of Stocking Flat, with an arrow showing the direction of streamflow in Deer Creek.
Methods 3

Deer Creek, a major tributary to the Yuba River (fig. 1A), 

has incised into these contaminated sediments for many 

years, thus increasing the potential for mobilization of Hg to 

downstream areas.

Terrestrial laser scanning (TLS) is a remote-sensing 

technology that can collect high-resolution (sub-centimeter), 

three-dimensional (3-D) measurements of the land surface 

that cannot be achieved with traditional surveying techniques 

(Heritage and Large, 2009). Sometimes TLS is referred to 

as terrestrial lidar or tripod-mounted lidar (T-lidar). A laser 

scanner or lidar scanner emits pulses of near-infrared laser 

light that are timed to measure the distance (range) from 

the laser scanner to the reflecting surface. Laser ranges are 

combined with angular orientation data to generate a dense 

and detailed set of x, y, and z points (locations of individual 

laser returns) referred to as a point cloud. The non-destructive 

sampling of the unconsolidated cutbank sediments and the 

sub-centimeter precision of the point cloud allows for a 

spatially detailed assessment of change across the cutbank 

surface.

In this study, four sequential TLS surveys of the stream 

cutbank were completed. Each survey period was composed 

of multiple TLS scans collected from different vantages 

that were combined into a composite 3-D point cloud of the 

stream cutbank. The sequential surveys were co-registered, 

or ‘aligned,’ into a common 3-D reference frame so that 

volumetric comparisons between the surveys could be made. 

The difference in volume between sequential surveys is the 

amount of sediment removed from the cutbank by erosion 

and mobilized by the stream. Volume was calculated by two 

methods, and the average value was reported.

Purpose and Scope

The purpose of this report is (1) to document the methods 

used to quantify the volume of Hg-contaminated sediment 

eroded from a discrete section of stream cutbank along Deer 

Creek at Stocking Flat (fig. 1D), an area managed by the 

BLM, and (2) to quantify the volume of eroded sediment 

(incremental and total) for three periods between December 1, 

2010, and February 4, 2013.

The results of this study have been combined with 

laboratory determinations of Hg concentration and grain-size 

distribution (Jabob Fleck and others, U.S. Geological Survey, 

written commun., 2015) to quantify the amount of Hg eroded 

into Deer Creek downstream from the cutbank. Results from 

these investigations are to be used by the BLM to determine 

whether removal or stabilization of Hg-contaminated sediment 

is needed at the Stocking Flat study site.

The TLS approach also provides information regarding 

the physical processes of cutbank erosion, such as stream 

under-cutting and slumping. This information could be useful 

to the BLM for stabilizing Hg-contaminated sediment at 

Stocking Flat and similar sites elsewhere. A suite of innovative 

visualization graphics, including 3-D images, is included in 

this report to facilitate understanding of the physical processes.

Study Area Description

The Stocking Flat study site is along Deer Creek in the 

foothills of the Sierra Nevada (fig. 1), where the topographic 

relief is approximately 200 meters (m) from the valley floor 

to surrounding ridge lines. The cutbank-study site at Stocking 

Flat is at an elevation of 650 m above sea level (ASL) and is on 

an alluvial plain largely composed of mining debris fluvially 

transported from upstream historical hard-rock and placer 

gold mines (fig. 1C). The Deer Creek drainage basin, a major 

tributary in the Yuba River drainage basin (fig. 1A), ranges 

in elevation from approximately 90 m ASL at the confluence 

with the main stem of the Yuba River to more than 1,500-m 

ASL at the headwaters. The stream cutbank at Stocking Flat 

is approximately 50 m long and 8 m high and covers about 

400 square meters (m2).

The climate in the study area is Mediterranean, with 

warm-to-hot, dry summers and cool, rainy winters. The longterm precipitation gage nearest to the Stocking Flat study 

site is approximately 4.5 km to the south-southwest, at Grass 

Valley, California (fig. 1). The average annual water-year

(WY) precipitation at Grass Valley, California, is 1.34 m 

(or 52.80 inches, in.). For WY 2011 (October 2010 through 

September 2011), the total precipitation of 1.85 m (72.81 in.) 

was 138 percent of the long-term average, and the WY 2012 

total of 1.19 m (46.74 in.) was 88 percent of the long-term 

average. Similarly, total precipitation in WY 2013 of 1.20 m 

(47.21 in.) was 89 percent of the long-term average. Daily 

precipitation data for this gage for WY 1967 through 2013 

are available at http://www.ncdc.noaa.gov/cdo-web/search

(National Weather Service Station GHCND: USC00043573, 

GRASS VALLEY NUMBER 2, CA US, last accessed 

August 28, 2014).

The closest USGS streamgage (11418500) is at the lower 

end of the Deer Creek drainage near Smartsville, California, 

approximately 20 km west-southwest (downstream) of the 

Stocking Flat study site (fig. 1B). It was not feasible to use the 

data from this streamgage to estimate stream discharge at the 

Stocking Flat study site because a reservoir (Lake Wildwood) 

between Stocking Flat and the streamgage (fig. 1B) retained 

storm-water runoff during periods of heavy precipitation.

Methods

This section contains information on methods of TLS data 

collection, point-cloud alignment, and volumetric calculations. 

Information on quality assurance is included to explain how 

uncertainties in volume calculations were quantified.
4 Quantifying Mercury-Contaminated Sediment at Stocking Flat, Deer Creek, Nevada County, Calif., 2010–13

Data Collection

The cutbank and the terrace above it were surveyed 

on four occasions: December 1, 2010; January 20, 2011; 

May 12, 2011; and February 4, 2013. These surveys were 

used to determine the volume of sediment eroded between the 

surveys by assessing the 3-D difference in the cutbank surfaces 

from one survey to another. 

Data from the first three TLS surveys (during 2010 and 

2011) were collected with an Optech ILRIS-36D laser scanner 

(Optech Inc., West Henrietta, New York; fig. 2). The laser 

returns from the Optech scanner have an x-y-z positional 

accuracy of plus or minus 4 millimeters (mm) at a distance of 

100 m (according to manufacturer specifications). The target 

area for this study was less than 50 m from the scanner. The 

laser scanner, mounted on a rotating base (fig. 2A), panned 

the target area and collected a composite color image that 

was displayed on a tablet personal computer (PC). On the 

tablet PC, the area to be scanned was defined, and the laser 

spot spacing was set to 7–9 mm, which yielded an average 

data density of more than 15,000 points for each square meter 

across the cutbank. Detailed inset areas of geometric bench 

marks, described later in this section, were defined to increase 

the data density of those targets to a laser spot spacing 

of 4 to 5 mm. During each survey, the laser scanner was 

deployed in two locations so the entire cutbank surface and the 

geometric benchmarks could be imaged by the laser scanner: 

(1) on the right bank of the stream across from the cutbank 

(fig. 2A) and (2) on the terrace above the cutbank (fig. 2B).

When the Optech scanner was used with the pan-and-tilt 

base (fig. 2A), the scanner systematically scanned the target 

area with a series of overlapping 40-degree by 40-degree 

scans. Each 40-degree-wide scan was collected with 8-degree 

(or 20-percent) overlap with the adjoining scan to ensure 

that the scans could be accurately aligned or combined into 

a composite point cloud by using the PolyWorks® software 

package (Version 12.0.15, InnovMetric Software Inc., Quebec 

City, Quebec, Canada). Figure 3A shows overlapping scans 

of the upstream part of the cutbank. The first light detection 

and ranging (lidar) scan (on left side of fig. 3A) is slightly in 

front of the second scan (on right side of fig. 3A). The sharp 

color change marks the downstream limit of the first scan. The 

two scans are slightly misaligned because the laser scanner 

was in a slightly different position for the second scan. This 

misalignment was corrected with an iterative algorithm that 

computed an optimal alignment by minimizing the distance 

between the overlapping 3-D point clouds. Through a series of 

rotations and translations, the overlapping point clouds were 

adjusted until a user-defined convergence, (here, 10–7 or less), 

between the two scans was achieved. A lesser convergence 

value represents a better 3-D alignment. The alignment is 

visually evident by the melding of the different color point 

clouds in the area of overlap (fig. 3B). The two-standarddeviation error (or 95-percent confidence interval) of the 

iterative alignments was typically on the order of 4–6 mm. In 

figure 3C, the darkest color in the area of overlap indicates 

that the separation of the two aligned point clouds was less 

than 5 mm.

The fourth survey (February 4, 2013) was collected 

with a FARO Focus3D laser scanner, which had less scatter 

in the point-cloud data than in previous surveys, leading 

to improved 3-D definition of the cutbank surface. Laser 

returns from the FARO scanner have positional accuracy of 

plus or minus 0.5 mm at a distance of 25 m (according to 

manufacturer specifications). Inspection of the FARO data 

in a fully immersive 3-D environment (Kellogg and others, 

2008; Kreylos and others, 2008) showed that the positional 

accuracies across the cutbank surface were improved by 

using the FARO scanner compared to the point-cloud data 

collected with the Optech scanner for the first three surveys. 

Figure 2. An Optech ILRIS 36D laser scanner deployed in two 

locations at Stocking Flat, Deer Creek, Nevada County, California: 

A, laser scanner mounted on pan-and-tilt base with cutbank in the 

background, view to the southwest, and B, laser scanner without 

pan-and-tilt base on top of cutbank terrace, with view to the 

north-northwest.

Eroding cutbank

Permanent ‘T’ style

geometric benchmark 

Reference spheres

mounted on 

permanent

monuments

Stream flow

Optech ILRIS 36D

laser scanner

mounted on pan 

and tilt base

Stream flow

Eroding cutbank

of contaminated 

mining debris

A

B

Tablet computer

controller

Photographs by James F. Howle
Methods 5

The improved positional accuracy of the FARO laser returns 

was achieved by averaging six laser pulses to determine 

each recorded point compared to the single pulse used by the 

Optech scanner. The FARO scanner, mounted on a standard 

survey tripod (fig. 4), rotated about the vertical axis, collecting 

a full 360-degree point cloud, except for a 60-degree-wide 

cone directly beneath the scanner. A pre-set laser spot spacing 

of 6.7 mm at a distance 10 m from the scanner origin was 

used. The cutbank and terrace areas were scanned from four 

different vantages (two setups from the right bank of the creek, 

facing the cutbank, and two setups on the left-bank terrace, 

above the cutbank). The combined data density from the four 

scans was more than 11,400 points per square meter, which is 

equivalent to a laser-spot spacing of approximately 9 mm.

The alignment of the four scans in the fourth (February 4, 

2013) survey was accomplished with the software package 

SCENE (Version 4.0, FARO Technologies, Lake Mary, 

Florida). For each scan, the SCENE software automatically 

identified the 0.2-m-diameter reference spheres (fig. 4) and 

determined the relative positions of these spheres. The SCENE 

software then locked the position of the scan that had the 

greatest number of reference spheres, while the remaining 

scans were rotated and translated until the reference spheres 

were best fit in 3-D space relative to the locked scan. For the 

purpose of assessing the quality of the alignment, the SCENE 

software also calculated a root-mean-square error (RMSE, 

or one standard deviation) of the alignment. This error was 

computed from the spatial variations of the reference sphere 

center points for each unlocked scan relative to the locked 

scan. The 95-percent confidence interval of the alignment 

(two-standard-deviation error) was plus or minus 4.4 mm for 

the fourth survey.

Point-Cloud Alignment

To make comparisons between the different surveys, 

there must be stable and common benchmarks in each survey. 

For this study, two types of geometric benchmarks were 

used to register the surveys. The first benchmark type was 

a stable monument to which a removable reference sphere 

was attached, and the second benchmark type was a ‘T’ form 

constructed from polyvinyl chloride (PVC) pipe (fig. 5A). The 

following section describes the construction of the two types 

of geometric benchmarks that were installed on the terrace 

above the cutbank (fig. 5A).

Geometric Benchmarks

Three reference-sphere benchmarks were constructed by 

digging holes, approximately 0.3 m wide and 0.5 m deep, into 

the alluvium. Then, 1.2-m-long, 16-mm-diameter sections of 

threaded steel rod were driven into the alluvium at the center 

of the holes until 0.2 m of rod was left exposed above the 

ground surface. Each hole was backfilled to the land surface 

with about 30 kilograms (kg) of concrete. Approximately 

0.15 m of the protruding rod was cased with 0.1-m-diameter 

PVC pipe and filled with concrete, leaving about 0.05 

m (5 centimeters, cm) of threaded rod exposed (fig. 5A). 

Commercially available plastic spheres (0.45-m diameter) 

were fitted with threaded couplings. Each sphere was screwed 

onto a stable monument until the coupling bottomed out 

against the threaded rod of the monument. Linear reference 

marks on the sphere, coupling, and PVC casing were aligned 

so that each sphere could be repositioned on the corresponding 

monument to within plus or minus 4 mm.

Four reference ‘T’ benchmarks were constructed from 

readily available PVC pipe (with an outer diameter of 60 mm) 

and a PVC ‘T’ coupling. The constructed PVC ‘T’ benchmarks 

measured approximately 0.6 m wide by 1.0 m high. To anchor 

each ‘T,’ a hole approximately 0.3 m wide and 0.3 m deep 

was dug into the alluvium and anchored with about 20 kg of 

concrete.

Reference Points

After the scans for a given period were combined into 

a composite 3-D point cloud, reference points were defined 

from the point clouds of the geometric benchmarks by using 

the PolyWorks® software package. The spherical point clouds 

(more than 10.9 x 103 points per sphere, fig. 5B) were isolated 

in a 3-D environment and modeled as perfect spheres of a 

known radius (fig. 5C). From these “best-fit” spheres, the 

center points were mathematically derived as unique (x, y, z) 

points in 3-D space at millimeter resolution (fig. 5D). The 

repeatability of defining these points for any given sphere 

was plus or minus 0.4 mm (maximum variance along 

x, y, or z axis).

By using the point clouds of the PVC ‘T’s, reference 

points were defined at the intersection of perpendicular 

cylinder axes. In a 3-D visualization environment, the lidar 

point clouds of the PVC pipes (more than 6.5 x 103

 points per 

‘T’ excluding points on the ‘T’ couplings) were isolated and 

modeled as “best-fit” cylinders of a known radius (fig. 5C). 

The intersection of the perpendicular cylinder axes define (x, 

y, z) points in space at millimeter resolution (fig. 5D). The 

repeatability of defining these points in 3-D space was plus or 

minus 0.7 mm (maximum variance along an x, y, or z axis).
6 Quantifying Mercury-Contaminated Sediment at Stocking Flat, Deer Creek, Nevada County, Calif., 2010–13

S N

Orange point cloud 

of second scan

0 1 2 3 4 5 METERS

A B

C

Purple point cloud 

for first scan is slightly in 

front of second scan Cutbank crest

Downstream edge

of first scan Waterline

Stream flow

Area of overlapping

scans

For the area of overlap,

the distance between the

first and second scan is 

less than 5 millimeters

 Vegetation 

 data shadows

Purple and orange 

point clouds are melded 

together after alignment

Sparse data density along waterline

Figure 3. An example of alignment and comparison 

of overlapping point-cloud data: A, overlapping and 

slightly misaligned scans of the upstream part of 

cutbank; B, same scans shown in A after alignment; 

and C, difference plot for the area of overlapping scans 

shown in B.

Figure 4. A FARO Focus3D laser scanner on top of eroding cutbank at Stocking Flat study site, February 4, 2013.

FARO Focus 3D

laser scanner

0.2-meter-diameter 

FARO reference 

spheres

Eroding cutbank

Cutbank crest

Deer Creek

Stream

flow

Permanent 

reference ‘T’s 

Photograph by James F. Howle
Methods 7

Alignment of Sequential Surveys

The process of defining reference points was repeated for 

the seven geometric benchmarks in each survey. The seven 

reference points had the same spatial (geometric) relation, 

but the coordinate systems differed because the laser scanner 

was placed in a slightly different x, y, and z location during 

each survey. The alignment was accomplished by using the 

PolyWorks® software package, which rotates and translates 

the coordinate system of reference points from repeat surveys 

to that of the baseline survey. Errors associated with aligning 

arise from (1) minor misalignments in the baseline and 

repeat surveys, on the order of 4 to 6 mm; (2) variability in 

repositioning the reference spheres on the monuments, on the 

order of 2 to 4 mm; (3) variability in modeling the reference 

points for multiple study periods, on the order of less than 

1 mm; and (4) monument instability, assumed to be negligible 

on the basis of physical inspections of the monuments, which 

remained stable and undisturbed during the entire study 

period.

Once a repeat survey was aligned to the baseline survey, 

an assessment of the alignment (quantitative error) was 

determined. This assessment accounts for the cumulative error 

from the various sources that were previously described. For 

each geometric benchmark (sphere or ‘T’) in the baseline 

and subsequent scans, the corresponding reference-point 

coordinates along the x, y, and z axes were tabulated and 

differenced. The variance along each axis, for each reference 

point, was used to calculate the RMSE of the alignment. 

The alignment of the second (January 2011) survey, relative 

to the baseline survey (the first survey, December 2010), 

Figure 5. Sequence for defining reference points from geometric benchmarks. A, Photograph of removable reference spheres and 

semi-permanent reference ‘T’s. B, Graphics output from PolyWorks® software package showing point-cloud image of cutbank and 

geometric benchmarks. C, “Best-fit” sphere and cylinders. D, Reference points derived from the sphere center and the intersection of 

the cylinder axes.

• •

Cutbank crest

Photograph by James F. Howle

A B

C D

Cutbank

 crest

Removable reference 

spheres mounted on 

permanent monuments

Permanent

reference ‘T’s

Point cloud of

reference `T ́

Point cloud of

0.45-meter reference

sphere

Best-fit sphere and cylinders Reference points with unique x, y, z 

coordinates at millimeter resolution
8 Quantifying Mercury-Contaminated Sediment at Stocking Flat, Deer Creek, Nevada County, Calif., 2010–13

produced a RMSE of 5.1 mm. For the third survey 

(May 2011), the RMSE was 5.7 mm, and for the fourth 

survey, the RMSE was 2.8 mm. The reference-point alignment 

technique used in this study resulted in a RMSE of the 

alignment (one-standard-deviation errors) on the order of 3 

to 6 mm, which meant a 95-percent confidence interval, or a 

two-standard-deviation error, was equal to or less than 12 mm 

for these alignments. Precise 3-D measurements, discussed in 

the next section, comparing the stable geometric benchmarks 

in each survey confirmed the calculated 95-percent confidence 

interval of about 6- to 12-mm uncertainty in the alignment of 

sequential surveys.

Quality Assurance of Alignments

This study utilized the University of California, 

Davis (UCD) KeckCAVES (W.M. Keck Center for Active 

Visualization in the Earth Sciences) and the Virtual Reality 

User Interface (Vrui) LiDAR Viewer software (Kreylos and 

others, 2008) to visually inspect the lidar point-cloud data 

for the purpose of quality assurance (QA) of the alignment 

of overlapping scans from a single survey as well as the 

alignments of sequential surveys.

Immersion within lidar point-cloud data by utilizing 

3-D virtual reality (VR) technologies offers a unique and 

powerful tool to visualize complex 3-D data sets that cannot 

be seen with a conventional two-dimensional (2-D) computer 

screen. At the UCD KeckCAVES, lidar point-cloud data are 

stereoscopically projected (with four projectors) onto the 

floor, back wall, and side walls of a square room (or “cave”), 

3 m on each side. The projectors are linked to a head-tracked 

pair of eye glasses that enables 3-D visualization of the lidar 

point-cloud data in a virtual reality (VR), or fully immersive 

visualization environment. Using a hand-held controller, a 

user can move through the 3-D data, which can be enlarged 

to a scale greater than 1:1. The interactivity with the 3-D 

data enables the inspection and isolation of features more 

intuitively, quickly, and accurately than previously possible 

with non-immersive 2-D environments, such as desktop 

computers (Kellogg and others, 2008; Kreylos and others, 

2008).

To verify the alignment of overlapping scans for a 

single survey, the data from each scan were color coded so 

that one scan could be easily differentiated from another. 

Within the area of overlap, features such as planar surfaces, 

distinctly shaped cobbles, and geometric benchmarks were 

isolated at a scale greater than or equal to 1:1. By clicking 

on common points with the hand-held controller, precise 

distances between overlapping scans were measured. These 

measurements were compared with the previously discussed 

statistical uncertainties generated by the alignment software to 

verify those values. Similarly, for the alignments of sequential 

surveys, each survey was color coded and distances between 

distinct points on the stable geometric benchmarks were 

measured, and the measured differences were compared to the 

previously discussed RMSE to verify those values.

Volumetric Determination

The PolyWorks® software package was used to determine 

the volume of cutbank erosion between sequential surveys: 

Surveys 1 and 2 (December 1, 2010, to January 20, 2011), 

Surveys 2 and 3 (January 20, 2011, to May 12, 2011), and 

Surveys 3 and 4 (May 12, 2011, to February 4, 2013). Before 

volumes could be determined between the surveys, additional 

steps were needed to remove unwanted points, to create 

surfaces from the remaining points, and to define a common 

perimeter.

Data-Point Removal

Areas of vegetation, scattered along the base and across 

the surface of the cutbank, were scanned during each survey 

(fig. 2B). Small clusters of vegetation (typically 0.5 m2 in area) 

can create laser returns in front of the cutbank surface and 

also create “shadows” of missing data on the cutbank (blank 

areas in fig. 3C). Laser returns from vegetation were removed 

from the composite point cloud by using the software package 

TerraScan® (Version 12.020; Terrasolid, Helsinki, Finland), 

thus creating a bare-earth model of the cutbank surface. After 

the TerraScan® vegetation filter was applied to each survey, 

the data were subdivided into 2-m2 areas. Each area was then 

individually inspected for stray laser returns that were not 

removed by the vegetation filter. Systematically inspecting 

the 2-m2 areas ensured that points representing vegetation and 

other errant multipath laser returns were not included in the 

volume calculations.

Creating Surfaces

To calculate volume using the PolyWorks® software 

package requires that a continuous 3-D surface is generated 

from the land-surface points. Areas of missing data, caused 

by shadows from vegetation, protruding cobbles, or both, 

were interpolated by using two different techniques. The 

first technique, performed in PolyWorks®, transformed the 

lidar point cloud into a continuous 3-D surface by creating 

a triangulated irregular network (TIN) of nearest-neighbor 

points. A kriging algorithm (SurferTM version 11.0, Golden 

Software, Inc., Golden, Colorado) was also used to generate 

a best-fit surface through the point cloud and to interpolate 

across areas of missing data. For each survey, volumes were 

calculated by using both types of surface (TIN and kriged) 

to assess differences in calculated volumes between the two 

techniques. The differences were less than 1 percent, and 

thus, either technique for this study was acceptable. Given 

the faster computational speed of generating a TIN surface 

(several minutes) compared to generating a kriged surface 

(tens of minutes), the TIN method for surface generation was 

preferred.
Methods 9

Defining a Common Boundary

Prior to calculating volume changes, the area of the data 

common to all surveys is needed. This step eliminates any 

effect of areal sampling bias on the calculated volume changes 

caused by a different extent of data among the surveys.

From a plan-view perspective, a common data boundary 

for the four surveys was defined across the upper terrace and 

along the upstream and downstream margins. Along these 

boundaries, data for the four surveys were trimmed to match 

the survey that had the least extent. Additional trimming along 

the water surface was also necessary because the stream’s 

water-surface elevation was different during each of the 

surveys. The surveys with lower water surface were trimmed 

to that of the higher, so the lower data were not included 

in the volume calculation. The stream stage of the second 

survey was approximately 0.4 m lower than the stage of the 

first survey. Consequently, along the length of the cutbank, 

an area corresponding to the 0.4-m elevation difference was 

trimmed from the lower extent of the second survey to match 

the water-surface profile from the first survey. Similarly, for 

the second and third surveys, the stream stage of the second 

survey was approximately 0.2 m lower than the stage of the 

third survey, so the lowest 0.2 m of the second survey were 

excluded from the volume calculation. The fourth survey 

extended approximately 0.15 m lower than the third survey, so 

the lowest 0.15 m of the fourth survey were not included in the 

volume calculation.

This process normalizes the cutbank area to allow 

for a consistent comparison between the surveys. This 

normalization caused the subsequent volume-change 

calculations to be minima, because the volume of cutbank 

erosion below the higher of the two water-surface profiles was 

excluded in the erosion measurements.

The areal normalization of the sequential 3-D data 

sets was a straightforward process along the upper terrace, 

upstream margin, and downstream margin, and along the 

water-surface profile. Sparse point-cloud data directly next to 

the stream, however, required an interpretation of the lateral 

extent of the cutbank surface from a plan-view perspective. 

The sparse data density near the stream edge was caused 

by vegetation along the edge of the stream, which created 

irregular data shadows (fig. 3C). Also, the wet alluvium along 

and above the creek’s water surface attenuated the laser energy 

and prevented some of the laser pulses from returning to the 

scanner. 

Two interpretive approaches were used to define the 

boundary (extent) of the data for each survey. In the first 

boundary approach, the landward extent of the data was used 

to define the edge of the cutbank, which created numerous 

apparent cavities in the cutbank along the edge of the stream. 

This first approach can underestimate the streamward extent 

of the cutbank if an apparent cavity was caused by a data 

shadow or attenuated laser returns. In the second boundary 

approach, the apparent cavities were bridged, which created 

a smoother edge along the cutbank and stream interface. This 

second approach can overestimate the streamward extent of 

the cutbank if an apparent cavity was actually a recess in the 

cutbank surface. For each survey, volumes were calculated 

by using both approaches with techniques described in the 

following section.

Calculating Volumetric Changes

The PolyWorks® software package was used to calculate 

the volume between a user-defined reference plane and a 3-D 

surface of the cutbank for each survey (fig. 6). The volume 

calculations for each survey were made relative to the same 

fixed-reference plane. The volumetric changes were computed 

by differencing the calculated volumes between sequential 

surveys. Because the PolyWorks® software calculates the 

volume perpendicular to the reference plane (fig. 6), the 

orientation of the reference plane was chosen to minimize 

volume ”shadows” that could be created by the overhanging 

crest of the cutbank and by protruding cobbles. For this study, 

the reference plane was oriented approximately parallel to the 

length and slope of the cutbank and faced the concave side of 

the cutbank (fig. 6B). If a reference plane, for example, was 

set horizontally above the cutbank, the volume underneath the 

overhanging crest of the cutbank or under protruding cobbles 

would be missed. Because most Geographic Information 

System (GIS) software packages project data onto a horizontal 

plane, volumes would not be accurately calculated without an 

inclined reference plane.
10 Quantifying Mercury-Contaminated Sediment at Stocking Flat, Deer Creek, Nevada County, Calif., 2010–13

Results of Volume Calculations

The previously discussed RMSE of the sequential 

alignments relative to the baseline survey (5.1 mm in 

January 2011, 5.7 mm in May 2011, and 2.8 mm in 

February 2013) were used to assess potential volumetric errors 

for the sequential alignments. The assessment was made by 

translating the reference plane along an axis perpendicular 

to the reference plane by plus or minus the RMSE value and 

calculating surface-to-plane volumes that bracket the volume 

calculated with the fixed-reference plane (table 1). Translating 

the reference plane by one RMSE in the positive direction 

(toward the cutbank surface) resulted in a smaller calculated 

volume (fig. 7; table 1). Conversely, translating the reference 

plane by one RMSE in the negative direction (away from the 

cutbank) resulted in a larger calculated volume. Note that 

alignment errors parallel to the reference plane did not change 

the calculated volume and that the largest potential errors 

were generated from misalignments that are perpendicular to 

the reference plane. The calculated volumes (plus or minus 

one RMSE) spanned a range equivalent to the 95-percent 

confidence interval (two standard deviation error) for each 

sequential alignment. These volumetric error assessments 

were made both for the first and for the second boundaryapproach data sets (table 1). Note that for any given survey, 

the first boundary approach, or interpretation, of the stream 

edge with cavities yielded a larger surface-to-plane volume 

than the second boundary approach, or interpretation, which 

had a smoother stream edge (fig. 7).

Figure 6. The sequence for calculating 

volume: A, oblique perspective, with view 

to west-northwest, showing kriged threedimensional (3-D) surface of cutbank; 

horizontal distance along waterline is 

approximately 50 meters; B, reference plane 

used in volume calculation; C, perimeter 

of lidar (light detection and ranging) data 

projected onto the reference plane; and 

D, green polygon is the calculated volume 

between the surface of the cutbank and the 

reference plane.

The volume between 

 the 3-D surface and 

 the reference 

 plane is

 computed 

 perpen-

 dicular to 

 the 

 reference 

 plane at 

 1.0 squarecentimeter increments

Perimeter of lidar 

 data is projected 

 onto the 

 reference 

 plane

Inclined reference

 plane oriented 

 parallel to the

 length and 

 slope of the 

 cutbank

 surface

N

E

A

B

C

D

Waterline

Cutbank crest

Direction of stream flow

Kriged 3-D surface generated from 

5,327,926 bare-earth lidar returns
Results of Volume Calculations 11

By using data sets with the first and second boundary 

approaches and reference planes adjusted for potential 

alignment error, volumes for each period were calculated 

by using a discretization interval of 1.0 square centimeter 

(cm2). This discretization interval was integrated across the 

entire area of the cutbank surface (fig. 6D), which produced 

a high-resolution surface-to-plane volume measurement 

(table 1). The volume changes (erosion measurements) for 

each period (December 2010 to January 2011, January 2011 to 

May 2011, and May 2011 to February 2013), were computed 

by differencing the calculated volumes for the two surveys 

that bracket a given period. The calculated volume of eroded 

sediment for each period represented the 3-D space between 

the cutbank surfaces for the surveys bracketing that period.

For each period, a range of volume changes were 

calculated by differencing end-member values derived 

from the first and second boundary-approach data sets and 

associated alignment errors (table 1). For example, to estimate 

the maximum amount of erosion for the January 2011 to 

May 2011 period, the second boundary-approach January 

data (with a positive reference-plane error) were subtracted 

from the first boundary-approach May data (with a negative 

reference-plane error). Conversely, to estimate the minimum 

amount of erosion for the January 2011 to May 2011 period, 

the first boundary-approach January data (with a negative 

reference-plane error) were subtracted from the second 

boundary-approach May data (with a positive reference-plane 

error). Averaged results of these combinations and the range of 

uncertainties are discussed in the following paragraphs.

Table 1. Calculated volumes between the cutbank surface and reference planes for surveys 1, 2, 3, and 4.

[Volumes were calculated using both the first (Model A) and second (Model B) boundary interpretations of the stream edge, the fixed reference plane, and 

reference planes adjusted plus and minus (±) one root mean square error (RMSE) relative to the fixed reference plane. Abbreviations: m3, cubic meters; 

Survey 1, December 1, 2010; Survey 2, January 20, 2011; Survey 3, May 12, 2011; Survey 4, February 4, 2013; —, no data]

Survey and streamedge interpretation 

(Model A or 

Model B)

Volume between fixed 

reference plane and 

cutbank surface 

(m3

)

Volume between reference 

plane (adjusted plus one 

RMSE) and cutbank surface 

(m3

)

Volume between reference 

plane (adjusted minus one 

RMSE) and cutbank surface 

(m3

)

Range in 

volume from 

± RMSE

(m3)

Erosion volume 

from Dec. 1, 2010, 

to Jan. 20, 2011

(m3)

Model A1

Survey 1 2,008 22,008 22,008 0 —

Survey 2 2,146 3, 42,144 3, 52,148 ±2 —

Model B6

Survey 1 1,990 21,990 21,990 0 —

Survey 2 2,138 3

2,136 32,139 ±2 —

Maximum erosion — — — — 7

158

Minimum erosion — — — — 8

128

Average erosion 

and range of 

uncertainty

— — — — 143 ±15

Survey and streamedge interpretation 

(Model A or 

Model B)

Volume between fixed 

reference plane and 

cutbank surface 

(m3

)

Volume between reference 

plane (adjusted plus one 

RMSE) and cutbank surface 

(m3

)

Volume between reference 

plane (adjusted minus one 

RMSE) and cutbank surface 

(m3

)

 Range in 

volume from 

± RMSE

(m3

)

Erosion volume 

from Jan. 20, 2011, 

to May 12, 2011

(m3

)

Model A1

—Continued

Survey 2 9

2,382 32,380 32,384 ±2 —

Survey 3 2,582 102,580 102,584 ±2 —

Model B6

—Continued

Survey 2 9

2,355 32,353 32,357 ±2 —

Survey 3 2,569 102,567 102,571 ±2 —

Maximum erosion — — — — 11231

Minimum erosion — — — — 12183

Average erosion 

and range of 

uncertainty

— — — — 207 ±24
12 Quantifying Mercury-Contaminated Sediment at Stocking Flat, Deer Creek, Nevada County, Calif., 2010–13

Survey and streamedge interpretation 

(Model A or

Model B)

Volume between fixed 

reference plane and 

cutbank surface 

(m3

)

Volume between reference 

plane (adjusted plus one 

RMSE) and cutbank surface 

(m3

)

Volume between reference 

plane (adjusted minus one 

RMSE) and cutbank surface 

(m3

)

Range in 

volume from 

± RMSE

(m3)

Erosion volume 

from May 12, 2011, 

to Feb. 4, 2013

(m3)

Model A1

—Continued

Survey 3 2,582 102,580 102,584 ±2 —

Survey 4 2,594 132,593 132,595 ±1 —

Model B6

—Continued

Survey 3 2,569 102,567 102,571 ±2 —

Survey 4 2,593 132,592 132,594 ±1 —

Maximum erosion — — — — 1428

Minimum erosion — — — — 158

Average erosion 

and range of 

uncertainty

— — — — 18 ±10

1

The calculated volume of the “Model A” data set (first boundary approach or interpretation of the stream edge), for any given timeframe, is larger than the 

calculated volume of the “Model B” data set (second boundary approach) for the same timeframe, because the cavities along the waterline create a larger volume 

between the cutbank surface and the reference plane. See discussion in Defining a Common Boundary section of report and figure 7.

2

The baseline survey on December 1, 2010, was held fixed; reference plane adjustments were only made for subsequent surveys, which were compared to the 

baseline survey. See discussion in Alignment of Sequential Surveys section of report.

3

The root mean square alignment error (RMSE) of the January 2011 survey relative to the baseline survey was 5.1 millimeters (mm). See discussion in 

Alignment of Sequential Surveys section of report.

4

Translating the reference plane by one RMSE in the positive direction (toward the cutbank surface) resulted in a smaller calculated volume. See discussion in 

Calculating Volumetric Changes section of report and figure 7.

5

Translating the reference plane by one RMSE in the negative direction (away from cutbank surface) resulted in a larger calculated volume. See discussion in 

Calculating Volumetric Changes section of report and figure 7.

6

The calculated volume of a “Model B” data set, for any given timeframe, was smaller than the calculated volume of the “Model A” data set for the same 

timeframe, because the apparent cavities along the waterline were bridged creating less volume between the cutbank surface and the reference plane. See 

discussion in Defining a Common Boundary section of report and figure 7.

7

The maximum erosion from December 2010 to January 2011 is the difference between the January 2011 “Model A” (minus one RMSE) volume and the 

December 2010 “Model B” (plus one RMSE) volume. See discussion in Calculating Volumetric Changes section of report and figure 7.

8

The minimum erosion from December 2010 to January 2011 is the difference between the January 2011 “Model B” (plus one RMSE) volume and the 

December 2010 “Model A” (minus one RMSE) volume. See discussion in Calculating Volumetric Changes section of report and figure 7.

9

The calculated volume for January 2011 that was compared to May 2011 was larger than the January 2011 volume that was compared to December 2010, 

because the May 2011 water profile was lower than the December 2010 water profile, which allowed for a greater extent of the January 2011 data to be used for 

comparison. See discussion in Defining a Common Boundary section of report.

10The RMSE of the May 2011 survey relative to the baseline survey was 5.7 mm. See discussion in Alignment of Sequential Surveys section of report.

11The maximum erosion from January 2011 to May 2011 is the difference between the May 2011 “Model A” (minus one RMSE) volume and the January 2011 

“Model B” (plus one RMSE) volume.

12The minimum erosion from January 2011 to May 2011 is the difference between the May 2011 “Model B” (plus one RMSE) volume and the January 2011 

“Model A” (minus one RMSE) volume.

13The RMSE of the February 2013 survey relative to the baseline survey was 2.8 mm. See discussion in Alignment of Sequential Surveys section of report.

14The maximum erosion from May 2011 to February 2013 is the difference between the February 2013 “Model A” (minus one RMSE) volume and the 

May 2011 “Model B” (plus one RMSE) volume. 

15The minimum erosion from May 2011 to February 2013 is the difference between the February 2013 “Model B” (plus one RMSE) volume and the 

May 2011 “Model A” (minus one RMSE) volume.

Table 1. Calculated volumes between the cutbank surface and reference planes for surveys 1, 2, 3, and 4.—Continued

[Volumes were calculated using both the first (Model A) and second (Model B) boundary interpretations of the stream edge, the fixed reference plane, and 

reference planes adjusted plus and minus (±) one root mean square error (RMSE) relative to the fixed reference plane. Abbreviations: m3, cubic meters; 

Survey 1, December 1, 2010; Survey 2, January 20, 2011; Survey 3, May 12, 2011; Survey 4, February 4, 2013; —, no data]
Results of Volume Calculations 13

For the three periods, the range in the uncertainty values, 

plus or minus relative to the average (plus or minus 15 m3, 

plus or minus 24 m3, and plus or minus 10 m3), reflected 

the range of values likely to contain the average value 

(tables 1, 2). The range of values for each period was derived 

by combining subjective interpretations (first and second 

boundary approaches to define the edge of the cutbank along 

the waterline) coupled with objective error assessments of the 

sequential alignments. Although the objective volumetric error 

associated with sequential alignments can be quantified in 

terms of a 95-percent confidence interval, the subjective error 

cannot be quantified in terms of a confidence interval.

Between the first survey (December 1, 2010) and 

second survey (January 20, 2011), a minimum of 143 plus or 

minus 15 m3

 of Hg-contaminated sediment was eroded from 

the Stocking Flat cutbank study site. Between the second 

survey (January 20, 2011) and third survey (May 12, 2011), at 

least 207 plus or minus 24 m3

 of sediment were eroded from 

the cutbank. Adding these two estimates, the total estimated 

volume of Hg-contaminated sediment eroded by Deer Creek 

for the period from December 1, 2010, to May 12, 2011, was 

greater than 350 plus or minus 28 m3 (table 2). Between the 

third and fourth surveys (May 12, 2011, to February 4, 2013), 

an additional 18 plus or minus 10 m3 of Hg-contaminated 

sediment was eroded.

For the three periods during the study (December 2010 

to January 2011, January 2011 to May 2011, and May 2011 to 

February 2013), the total average volume of eroded material 

was at least 368 plus or minus 30 m3 (table 2). This erosion 

volume is a minimum, because during each period, the volume 

of cutbank erosion below the higher of the two water-surface 

profiles was excluded from the erosion measurements, as 

Sac15-0571_fig 07 previously discussed.

Fixed-reference plane parallel to the length 

and slope of the cutbank surface (see figure 6B)

Direction of stream flow

Waterline or

cutbank-stream interface Area shown in B

Area enlarged in C

N Lidar point cloud of cutbank surface

Apparent cavities 

 along waterline

0 1 2 3 4 5 6 7 8 9 10 METERS

First approach, or interpretation, of the apparent 

cavities along the cutbank and stream interface

Second approach, or interpretation, of the apparent 

cavities along the cutbank and stream interface

Fixed-reference plane

Reference plane translated one RMSE in the positive

direction (toward the cutbank) yields a smaller 

surface-to-plane volume

Reference plane translated one RMSE in the negative

 direction (away from the cutbank) yields a larger 

 surface-to-plane volume

Not to scale

A

B C

0 1 2 METERS

Figure 7. Lidar point cloud of the cutbank surface: A, oblique view, parallel to the fixed-reference plane, showing areas of apparent 

cavities along the waterline; B, first and second boundary approaches, or interpretations, of the apparent cavities along the cutbank 

and stream interface; and C, positions of reference planes translated plus and minus one root-mean-square alignment error (RMSE) 

value relative to the fixed-reference plane.
14 Quantifying Mercury-Contaminated Sediment at Stocking Flat, Deer Creek, Nevada County, Calif., 2010–13

Visualization of Changes

The purpose of this section is to demonstrate that 

visualization can reveal important insights into the data. Tufte 

(1983) stated, “Graphics are instruments for reasoning about 

quantitative information. Often the most effective way to 

describe, explore, and summarize a set of numbers—especially 

a very large set—is to look at pictures of those numbers.” 

Also, Kellogg and others (2008) noted, “The human brain 

excels at visually identifying patterns, and as a result, the best 

interpretations arise when scientists can fully visualize their 

data.”

In this section, the three dimensionality of the lidar 

data used in this study is demonstrated by a combination of 

shaded-relief images, 2-D change maps, and 3-D anaglyphs. 

The various techniques allowed for the visualization of where, 

when, and how much the cutbank changed. The graphics 

can also provide insights regarding the interpretation of the 

processes responsible for the observed changes and where 

mitigation measures can be most effective.

Shaded-Relief Images

The first visualization technique is a shaded-relief 

image with color-coded elevation and artificial illumination 

(fig. 8), which was generated by using the Quick Terrain 

ModelerTM software (QT Modeler, Version 7.0.2, Applied 

Imagery, Silver Spring, Maryland). This technique was 

performed on each of the four surveys. An oblique view was 

used to permit a view of the entire cutbank and upper terrace. 

This oblique perspective was maintained for all surveys to 

allow one to easily see changes from one image to the next. 

Artificial illumination was also used to highlight subtle 

geomorphic features that provide insight to the slope processes 

at work.

The first survey (December 1, 2010) showed a generally 

uniform slope across the cutbank surface at or near the 

angle of repose (fig. 8A). The artificial illumination cast a 

Table 2. Measured volumes of mercury-contaminated sediment (in cubic meters) eroded from the Stocking Flat cutbank study site for 

various periods between December 1, 2010, and February 4, 2013.

[±, plus or minus]

Surveys Time span Days Minimum erosion volume

(cubic meters)

Uncertainty

(cubic meters)

1–2 December 1, 2010, to January 20, 2011 50 143 ±15

2–3 January 20, 2011, to May 12, 2011 112 207 ±24

Sub-total (1–3) Erosion from December 1, 2010, to May 12, 2011 162 350 1

±28

3–4 May 12, 2011, to February 4, 2013 634 18 ±10

Total (1–4) Total erosion from December 1, 2010, to February 4, 2013 796 368 2

±30

1

The cumulative uncertainty of the erosion volume, in cubic meters (m3), for the December 2010 to May 2011 subtotal was calculated with the following 

equation: Cumulative Error (CE) = √ (Survey 1–2 uncertainty)2 + (Survey 2–3 uncertainty)2 or CE = √ (15)2 + (24)2 = 28 m3.

2

The cumulative uncertainty of the erosion volume (in cubic meters) for the December 2010 to February 2013 total was calculated with the following 

equation: CE = √ (Surveys 1–2 uncertainty)2

 + (Surveys 2–3 uncertainty)2 + (Surveys 3–4 uncertainty)2 or CE = √ (15)2 + (24)2 + (10)2 = 30 m3.

dark shadow where an over-hanging free face had formed 

at the upstream end of the cutbank crest. Also, a lobe of 

colluvium protruded along the waterline of the stream near the 

downstream end of the cutbank.

By January 20, 2011 (second survey), the protruding lobe 

of colluvium was eroded by the stream (fig. 8B). This erosion, 

which took place between the first and second surveys, 

was primarily along the down-stream half of the cutbank, 

where arcuate head scarps also formed in the unconsolidated 

sediment. The head scarps were interpreted to be the product 

of rotational slumping, which was most likely induced by 

stream under-cutting of water-saturated sediment. Also, 

between the first and second surveys, erosion of the cutbank 

crest caused the over-hanging free face to become less steep 

(near vertical), which is evident by the brighter illumination of 

the free face shown in figure 8B compared with figure 8A.

During March 2011, a period of high streamflow (fig. 9) 

caused substantial erosion along the entire lower part of the 

cutbank. This erosion formed a near-vertical fluvial scarp 

along the length of the cutbank (fig. 8C), which destabilized 

the unconsolidated sediment on the upper part of the cutbank 

and initiated the down-slope transport of sediment (fig. 9). By 

the time of the third survey (May 12, 2011), the near-vertical 

fluvial scarp had been partially buried by the down-slope 

movement of sediment (fig. 8C). The down-slope transport 

of sediment caused localized lowering of the cutbank crest 

and also caused the enlargement and over-steepening of the 

previously mentioned free face near the upstream end of 

the cutbank (fig. 8C). Most of the down-slope transport of 

sediment, from the destabilized upper part of the cutbank, 

likely was accomplished by gravity-driven dry ravel. Near the 

downstream end of the cutbank, however, a translational slope 

failure also appears to have occurred; this interpretation was 

based on a shallow and arcuate head scarp near the crest of the 

cutbank, a relatively smooth and flat surface directly below it, 

and an irregular and chaotic accumulation of sediment farther 

down the slope (fig. 8C).
Visualization of Changes 15

Figure 8. Shaded-relief oblique views of Stocking Flat cutbank study site near Nevada City, California, for the four surveys between 

December 2010 and February 2013. The images were created with Quick Terrain ModelerTM software (QT Modeler, Version 7.0.2, Applied 

Imagery, Silver Spring, Maryland). Points of equal elevation are color coded. The hand icon shows artificial illumination direction from 

the southwest. The upper terrace (bright gray) is approximately 8 meters above the waterline. The oblique perspective and illumination 

are the same for all images. A, Survey 1: December 1, 2010; B, Survey 2: January 20, 2011; C, Survey 3: May 12, 2011; and D, Survey 4: 

Sac15-0571_fig 08 February 4, 2013.

Continued lowering 

of cutbank crest

Continued erosion of the crest and slope below caused the free face to expand, 

delivering sediment down-slope, which buried the previous head scarp

Fluvial scarps mostly buried by colluvium

From May 2011 to February 2013, only minor erosion 

occurred along the cutbank at the waterline; see figure 10C

Upper head scarp degraded 

by dry-ravel erosion

Down-slope transport caused 

aggradation on the lower

part of the cutbank; see figure 10C

Area of figures 11C,

E, F, G and H

Cutbank crest lowered 

by slope degradation

Erosion of the slope, below the free face, caused the 

free face to enlarge 

Near-vertical fluvial scarps

From January 2011 to May 2011, the entire length of the cutbank was 

substantially eroded; see figure 10B 

Protruding lobe

of colluvium;

see figure 10B

Head

scarp

High stream flow in March of 2011 eroded a 

near-vertical fluival scarp across the cutbank. The 

removal of sediment below the fluvial scarp destabilized the upper part of the cutbank and initiated the 

down-slope transport of sediment, which partially 

buried the fluvial scarp.

Translational 

failure and 

down-slope 

 transport of 

sediment 

Erosion of the crest caused the free face to become slightly less steep 

(near-vertical) Arcuate head scarps associated with 

rotational slumping of cutbank

From December 2010 to January 2011, erosion at the waterline was 

primarily along the down-stream half of the cutbank; see figure 10A 

Degraded

game trail

Near-vertical free face

Area of figures 11A, B,

C, D, and G Colluvial 

apron 

Area of figure 12 

A. Survey 1, December 2010

C. Survey 3, May 2011

D. Survey 4, February 2013

B. Survey 2, January 2011

N

E

Stream flow

Crest of cutbank

Over-hanging free face

Upper terrace

Waterline

0 5 10 METERS

Game trail

Cutbank

Protruding lobe

of colluvium
16 Quantifying Mercury-Contaminated Sediment at Stocking Flat, Deer Creek, Nevada County, Calif., 2010–13

Between the third and fourth surveys (from May 12, 

2011, to February 4, 2013), the unsupported upper part of 

the cutbank, above the partially buried fluvial scarps shown 

in figure 8C, continued to erode and deliver sediment down 

slope. This down-slope transport of sediment mostly buried 

the remaining fluvial scarps formed during March of 2011 

(fig. 8D). The continued down-slope transport caused further 

lowering of the cutbank crest and the expansion of the nearvertical free face at the upstream end of the cutbank (fig. 8D). 

During this final period, there was only minor erosion along 

the waterline at the base of the cutbank.

Two-Dimensional Change Maps

The second visualization technique uses color-coded, 2-D 

change maps, which were created by using the PolyWorks®

software package to measure the distance between the 

sequential data along the horizontal axis, perpendicular 

to the image. These images show the amount and spatial 

variability of change across the entire cutbank surface 

between sequential surveys (fig. 10) and for discrete areas of 

the cutbank (figs. 11B, D, F, H, 12B–D). These images also 

demonstrate the centimeter-scale resolution of the TLS data. 

By comparing the oblique-perspective shaded-relief images to 

the color-coded change maps for the same period, the viewer 

can acquire a more comprehensive picture of where and how 

much changed during a given period.

For example, the protruding lobe of colluvium shown 

in the first survey (fig. 8A; December 1, 2010) had been 

removed by stream erosion by the time of the second survey 

(fig. 8B; January 20, 2011). The amount of horizontal change 

Stream flow

Near-vertical fluvial scarp

Destabilized slope above

near-vertical fluvial scarp

Coarse colluvium derived from 

destabilized slope above the 

near-vertical fluvial scarp

Photograph by Carrie Monohan

(erosion) during the period varied from approximately 2 m to 

approximately 3.5 m along the section of the waterline where 

the apron of colluvium was eroded (fig. 10A).

Between the second and third surveys (from January 20, 

2011, to May 12, 2011), high streamflow during March 2011 

(fig. 9) resulted in substantial erosion along the entire lower 

part of the cutbank (fig. 10B) and the formation of a fluvial 

scarp (fig. 8C). The broad area of yellow to orange across the 

lower half of the cutbank in figure 10B represents horizontal 

erosion ranging from approximately 2 to 2.5 m between the 

second and third surveys. The upper extent of the yellow to 

orange areas generally correlates with the top of the fluvial 

scarp eroded in March of 2011. In figure 10B, the upper part 

of the cutbank has a green to yellow color gradation that 

represents horizontal erosion of approximately 0.5 to 1.5 m. 

This erosion across the upper part of the cutbank was caused 

by down-slope transport of sediment (dry ravel) after the 

formation of the fluvial scarp, which destabilized the upper 

part of the cutbank.

Figure 10C shows the horizontal change between the 

third and fourth surveys (from May 12, 2011, to February 4, 

2013). During this period, erosion continued across the upper 

part of the cutbank, while there was generally deposition 

across the lower part. This was most notable at the upstream 

end of the cutbank, where an area of erosion that exceeded 

1.0 m into the slope resulted in down-slope transport of 

sediment and deposition over a similar-sized area as was 

eroded (fig. 10C). The erosion on the upper part of the slope 

caused the free face to expand in size, and the down-slope 

transport of the sediment buried the fluvial scarp that was 

visible in May of 2011 with colluvium (figs. 8C, D).

Figure 9. The central part of the cutbank on March 17, 2011, high streamflow and the near-vertical fluvial scarp.
Visualization of Changes 17

Figure 10. Difference maps of horizontal change across the cutbank surface for four periods between December 1, 2010, and 

February 4, 2013. All images are from a horizontal perspective, with a view to the west-southwest, and the distance along the base of 

the cutbank was approximately 50 meters. Changes, in meters, were measured perpendicular to the image. A, December 1, 2010, to 

January 20, 2011; B, January 20, 2011, to May 12, 2011; C, May 12, 2011, to February 4, 2013; and D, December 1, 2010, to February 4, 2013.

0

-1.00

-1.50

-2.00

-2.50

-3.00

-0.50

-3.50

Erosion at waterline of about 3.5 meters

Areas of blue to purple color represent localized 

aggradation of less than or equal to 0.15 meter

Stream flow

METERS

0.10

0.05

0.15

0.20

0

0 0

-1.00

-1.50

-2.00

-2.50

-3.00

-0.50

-3.50

0.10

0.05

0.15

0.20 Areas of green color 

represent erosion of about 1.0 meter

Aggradation of colluvium

at the waterline;

see figure 8C

Areas of yellow color represent

erosion of about 2.0 meters up to and below

the fluvial scarp shown in figure 8C

METERS

The upper limit of significant horizontal

 erosion coincides with the top of the 

 fluvial scarp shown in figure 8C 

0.25

1.25

1.00

0.50

-0.75

-1.00

-1.25

0

-0.25

-0.50

0.75

Erosion of greater than 1.0 meter

Deposition of about 1.0 meter

METERS

From May 2011 to February 2013, erosion generally

occurred on the upper half of the cutbank, which 

resulted in deposition across the lower half

0.00

0.00

0.20

 0.10

-3.00

-4.00

 0.00

-1.00

-2.00

0.30

0.40

Areas of green color represent 

bank erosion of about 1.0 meter Locailzed deposition greater than

or equal to 0.3 meter

METERS

Yellow color represents areas of 

horizontal bank erosion of about 2.0 meters

A. Horizontal change from December 2010 to January 2011

D. Horizontal change from December 2010 to February 2013

C. Horizontal change from May 2011 to February 2013

B. Horizontal change from Januray 2011 to May 2011
18 Quantifying Mercury-Contaminated Sediment at Stocking Flat, Deer Creek, Nevada County, Calif., 2010–13

Backside of

arcuate head scarp

shown in figure 8B

Cutbank crest

Surface of cutbank 

in December 2010

Eroded surface of cutbank 

in January 2011

Perpendicular to

cutbank surface

Parallel to

cutbank surface

Surface of cutbank

in January 2011

Surface of cutbank

in May 2011

Near-vertical fluvial scarp

eroded into cutbank;

see figure 8C

Cutbank crest 

lowered 0.25 meter Arcuate head 

scarp

Destabilized slope

above fluvial scarp

Near-vertical fluvial

scarp in May 2011 

Erosion of the fluvial scarp 

and destabilized slope above 

caused deposition on the lower 

part of the cutbank from May 2011 

to February 2013 

Cutbank slope in

February 2013

at or near the angle 

 of repose

Surface of cutbank

in December 2010

Cutbank slope at or

near the angle of repose 

in February 2013

Cutbank crest

lowered 0.45 meter

between December 

2010 and February 2013 

0.00

0.10

0.05

 0.00

-0.50

-1.00

-1.50

Arcuate 

head scarp

shown in

figure 8B

Localized

aggradation

on cutbank

slope

Cutbank crest

Waterline

3 m

0.00

-0.50

-1.00

-1.50

Cutbank crest lowered

by bank erosion

Near-vertical fluvial

scarp eroded into 

cutbank; see figure 8C

METERS

0.00 0.00

-0.50

0.50

Area shown in B

and D above

Erosion

Deposition

METERS

8.2 m

-1.00

-1.50

-0.60

-1.90

Area shown in B

and D above

METERS

A. December 2010 and January 2011 B. Change from December 2010 to January 2011

C. January 2011 and May 2011 D. Change from January 2011 to May 2011

E. May 2011 and February 2013 F. Change from May 2011 to February 2013

G. December 2010 and February 2013 H. Change from December 2010 to February 2013

METERS
Visualization of Changes 19

Figure 11. Three-dimensional (3-D) anaglyphs and two-dimensional (2-D) difference maps showing changes from December 2010 to 

February 2013 for selected areas of the cutbank. Inset images A, C, E, and G are oblique-perspective 3-D anaglyphs showing a sequence 

of the retreating cutbank. The oblique perspective, looking downstream, is the same for all images. Red-blue glasses (with the red lens 

on the right side) are needed for enhanced 3-D viewing. Anaglyphs were generated with Vrui LiDAR Viewer software. Inset images B, D, 

F, and H are graphics from PolyWorks® software showing 2-D color-coded difference maps of the same areas and time frames shown in 

the neighboring anaglyphs. Changes, in meters, were measured perpendicular to the image. A, Oblique anaglyph comparing a selected 

area of the cutbank from December 2010 and January 2011. See figure 8B for location of selected area. B, Difference map of data shown 

in A. C, Oblique anaglyph comparing selected areas of the cutbank in January 2011 and May 2011. See figure 8D for areal extent and 

location of May 2011 data. D, Difference map of data shown in C. This difference map only covers the areal extent of the January 2011 

data. E, Oblique anaglyph comparing selected areas of the cutbank in May 2011 and February 2013. See figure 8D for extent and location 

of selected area. F, Difference map of data shown in E. G, Oblique anaglyph comparing selected areas of the cutbank in December 2010 

and February 2013. See figure 8D for extent and location of selected area. H, Difference map of data shown in G. This difference map 

only covers the area of union for the December 2010 and February 2013 data.

Figure 12. Three-dimensional (3-D) anaglyph and two-dimensional (2-D) difference maps showing changes from January 2011 to 

February 2013 for a selected area of the cutbank. See figure 8B for location of the selected area. A, Oblique-perspective 3-D anaglyph, 

looking downstream, shows a sequence of the retreating cutbank from January 2011, May 2011, and February 2013. Red-blue glasses

(with the red lens on the right side) are needed for enhanced 3-D viewing. Anaglyphs were generated with Vrui LiDAR Viewer software. 

B, Graphic output from PolyWorks® software showing 2-D difference map for the period January 2011 to May 2011 for the area shown 

in A. Changes, in meters, were measured perpendicular to the image. Note that the color scales are different for figures B, C, and D. C,

Difference map of data shown in A for the period May 2011 to February 2013. D, Difference map of data shown in A for the period 

January 2011 to February 2013.

Cutbank slope in

January 2011 at the

 angle of repose

Base of near-vertical fluvial 

scarp in May 2011; see figure 8C 

February 2013

Cutbank crest

Perpendicular to

cutbank surface

Parallel to

cutbank surface

-0.20

-2.00

0.00

METERS

-0.60

-0.80

-1.00

-1.20

-1.40

-1.60

-1.80

-0.40

Little to no erosion

near scarp crest

Up to 2 meters of 

erosion near the 

base of the fluvial

scarp shown in 

figure 8C 

4 m

1.00

-0.60

1.20

METERS

0.60

0.40

0.20

0.00

-0.20

-0.30

-0.40

0.80

-0.50

-0.10

0.00

Erosion of the

vertical free face below

the cutbank crest

caused deposition on

the lower half of the 

cutbank, which buried 

the previous fluvial 

scarp; see figures 8C

and 8D

-0.10

-1.00

0.00

METERS

-0.30

-0.40

-0.50

-0.60

-0.70

-0.80

-0.90

-0.20

-1.10

-1.20

Slope erosion of 

about 0.9 meters

A

C. Horizontal change from May 2011 to February 2013 D. Horizontal change from January 2011 to February 2013

B. Horizontal change from January 2011 to May 2011
20 Quantifying Mercury-Contaminated Sediment at Stocking Flat, Deer Creek, Nevada County, Calif., 2010–13

Figure 10D shows the overall horizontal change 

between the first and last surveys (from December 1, 2010, 

to February 4, 2013). During the study period, the greatest 

amount of erosion was near the downstream end of the 

cutbank, where the horizontal change approached 4.0 m. This 

area of greatest erosion along the waterline corresponded in 

space with the greatest amount of cutbank-crest lowering 

(figs. 8A, D, 10A, C) as a result of the undermining of the 

slope base by stream erosion.

Three-Dimensional Anaglyphs

The third technique used to visualize 3-D changes of 

the sequential data is oblique-perspective anaglyphs. An 

anaglyph image is a stereoscopic 3-D effect that provides the 

viewer with the perception of depth (figs. 11A, C, E, G, 12A). 

By using Vrui LiDAR Viewer software (Kreylos and others, 

2008), the 3-D effect is achieved by encoding images with 

different colors for each eye. When viewed through the colorcoded anaglyph glasses (red and blue lens glasses), each of the 

images reaches one eye, giving perception of a 3-D scene. The 

oblique perspective of selected areas of the cutbank allows the 

viewer to visualize the space between sequential lidar data. By 

comparing an oblique-perspective anaglyph to the 2-D colorcoded change map (for example, figs. 11A, B), the viewer 

can see the relative positions of the cutbank at different times 

in the anaglyph and also see a quantitative measure of the 

intervening space in the 2-D color-coded change map.

Figure 11A shows an oblique-perspective anaglyph, 

looking downstream, for a selected 3-m-wide swath of the 

cutbank on December 1, 2010, and January 20, 2011 (see 

fig. 8B for location of the selected area). Between the first 

and second surveys, there were only minor localized changes 

across the upper part of the cutbank (fig. 11B). At the base of 

the cutbank, however, an arcuate-shaped head scarp formed in 

the unconsolidated sediment (figs. 8B, 11A). The head scarp, 

a product of rotational slumping, caused localized erosion of 

1.5 m into the cutbank (fig. 11B).

The 3-D anaglyph in figure 11C has the same oblique 

perspective and data from January 2011 as figure 11A, as well 

as an 8-m-wide area of data from May of 2011 (see fig. 8D

for the location and extent of the May 2011 data). Between 

the January 20, 2011, and May 12, 2011, surveys, a period of 

high streamflow during mid-March (fig. 9) caused substantial 

erosion of the cutbank and formed a near-vertical fluvial scarp 

(fig. 11C, D). After the near-vertical fluvial scarp formed, the 

slope above it became destabilized, which initiated the downslope transport of sediment. From May 2011 to February 

2013, the unsupported fluvial scarp and upper part of the 

cutbank locally eroded as much as 0.5 m, resulting in localized 

deposition of 0.5 m on the lower half of the cutbank (fig. 11F).

From December 2010 to February 2013, the 

maximum horizontal erosion at the base of the cutbank was 

approximately 1.9 m within the area of data overlap (fig. 11H). 

Near the top of the cutbank, the horizontal erosion totaled 

approximately 1.0 m (fig. 11H), which resulted in the crest of 

the cutbank being lowered approximately 0.45 m (fig. 11G).

Figure 12A shows an oblique perspective anaglyph, 

looking downstream, for a selected 4-m-wide swath of the 

cutbank for three dates: January 20, 2011; May 12, 2011; and 

February 4, 2013 (see fig. 8B for the location of the selected 

area). In January 2011, the cutbank slope was at or near the 

angle of repose, with a slightly over-steepened section below 

the crest (fig. 12A). The high streamflow in March 2011 

(fig. 9) cut a near-vertical fluvial scarp and caused horizontal 

erosion of approximately 2.0 m near the base of fluvial scarp 

(fig. 12B). After the formation of the fluvial scarp, the slope 

above it became destabilized, which initiated the downslope transport of sediment. Between January 20, 2011, 

and May 12, 2011, the slope above the fluvial scarp eroded 

about 0.7 m (fig. 12B). This erosion undermined the crest of 

the cutbank and formed a near-vertical free face (fig. 12A). 

From May 2011 to February 2013, the top of the fluvial scarp 

and upper part of the cutbank continued to erode and shed 

sediment down slope. Horizontal erosion of greater than 

0.5 m at the upper part of the cutbank caused the free face to 

further enlarge (figs. 12A, C). The simultaneous down-slope 

transport of colluvium accumulated horizontally up to 1.0 m 

on the lower part of the cutbank (figs. 12A, C). The erosion on 

the upper half of the cutbank and deposition below returned 

the slope angle to a value at, or near, the angle of repose 

(fig. 12A). For the 4-m-wide swath shown in figure 12, the 

net horizontal change (bank retreat) from January 2011 to 

February 2013 was generally on the order of 0.9 plus or minus 

0.3 m (fig. 12D). A notable exception to this was near the top 

of the cutbank, where the net effect of the bank retreat was a 

steepening of the slope angle and horizontal erosion of about 

0.3 m (figs. 12A, D).

Summary

The purpose of this report is to document the methods 

used to quantify the volume of mercury (Hg)-contaminated 

sediment eroded from a discrete section of stream cutbank 

along Deer Creek at Stocking Flat, an area which is managed 

by the Bureau of Land Management (BLM), and to report the 

eroded volume results for three periods between December 1, 

2010, and February 4, 2013 (incremental and total volume). 

The sequential terrestrial laser scanning (TLS) data also 

provide information regarding the physical processes of 

cutbank erosion. This latter information could be useful to the 

BLM for the purpose of the stabilizing of Hg-contaminated 

sediment at Stocking Flat and similar sites elsewhere. A 

suite of innovative visualization graphics, including twodimensional (2-D) maps and three-dimensional (3-D) images, 

are also included.
References Cited 21

Sequential TLS has proven to be an effective tool to 

quantify volumetric changes of a complex, eroding surface 

that could not have been mapped non-destructively or in 

sufficient detail using traditional surveying techniques. The 

non-destructive scanning of the unconsolidated cutbank 

sediments and the sub-centimeter precision of the resulting 

point clouds allowed for a spatially detailed assessment 

of change across the cutbank surface. In this study, four 

sequential TLS surveys of the stream cutbank were carried 

out. Each survey was composed of multiple TLS scans 

collected from different vantages, which were combined 

into a composite 3-D point cloud of the stream cutbank. The 

sequential surveys were co-registered, or ‘aligned,’ into a 

common 3-D reference frame so that volumetric comparisons 

between the surveys could be made. The utilization of 

virtual-reality technology to inspect the alignment of the 

light detection and ranging (lidar) point-cloud data enabled 

the isolation of features more intuitively, quickly, and 

accurately than previously possible with non-immersive 2-D 

environments and greatly improved the level of confidence 

in data quality prior to analysis. The differences between 

sequential surveys indicated the amount (volume) of sediment 

removed from the cutbank by erosion.

From December 1, 2010, to January 20, 2011, a minimum 

of 143 plus or minus 15 cubic meters (m3

) of Hg-contaminated 

sediment was eroded from the Stocking Flat cutbank study 

site. From January 20, 2011, to May 12, 2011, an additional 

207 plus or minus 24 m3 or more of sediment was eroded from 

the cutbank. Combining these two measurements, the total 

minimum volume of Hg-contaminated sediment eroded by 

Deer Creek during the period from December 1, 2010, through 

May 12, 2011, was 350 plus or minus 28 m3. From May 12, 

2011, to February 4, 2013, an additional 18 plus or minus 

10 m3

 or more of Hg-contaminated sediment was eroded. The 

total volume of eroded sediment from December 1, 2010, 

through February 4, 2013, was at least 368 plus or minus 

30 m3

 (table 2).

The analysis of sequential TLS data by using 2-D 

visualization techniques, such as oblique-perspective, shadedrelief imagery, and color-coded change maps, as well as 

stereoscopic 3-D anaglyphs, can enhance the understanding of 

complex 3-D data sets, aid with the interpretation of physical 

processes, and help with the design of remediation and 

mitigation measures.

The results of this study are to be used in combination 

with laboratory data for Hg concentration and grain-size 

distribution (Jacob Fleck and others, U.S. Geological 

Survey, written commun., 2015) to quantify the amount of 

Hg eroded into Deer Creek during this period. Results from 

these investigations are for use by the BLM, in consultation 

with other federal, state, and local agencies, as well as 

other interested parties, to determine whether removal or 

stabilization of Hg-contaminated sediment is needed at the 

Stocking Flat site. These results can be used by the BLM to 

prioritize future remediation activities related to abandoned 

mines and mine wastes in the Deer Creek drainage basin.

References Cited

Alpers, C.N., Hunerlach, M.P., May, J.T., and Hothem, R.L., 

2005a, Mercury contamination from historical gold mining 

in California: U.S. Geological Survey Fact Sheet 2005–

3014, 6 p., available at http://pubs.usgs.gov/fs/2005/3014/.

Alpers, C.N., Hunerlach, M.P., May, J.T., Hothem, R.L., 

Taylor, H.E., Antweiler, R.C., De Wild, J.F., and 

Lawler, D.A., 2005b, Geochemical characterization 

of water, sediment, and biota affected by mercury 

contamination and acidic drainage from historical gold 

mining, Greenhorn Creek, Nevada County, California, 

1999–2001: U.S. Geological Survey Scientific 

Investigations Report 2004–5251, 278 p., available at 

http://pubs.usgs.gov/sir/2004/5251/.

Alpers, C.N., Hunerlach, M.P., Marvin-DiPasquale, M.C., 

Antweiler, R.C., Lasorsa, B.K., De Wild, J.F., and 

Snyder, N.P., 2006, Geochemical data for mercury, 

methylmercury, and other constituents in sediments from 

Englebright Lake, California, 2002: U.S. Geological Survey 

Data Series 151, 95 p., available at http://pubs.usgs.gov/

ds/2006/151/.

Alpers, C.N., Fleck, J.A., Beaulieu, Elizabeth, Hothem, 

R.L., May, J.T., Marvin-DiPasquale, M.C., Blum, A.E., 

and Graves, P.G., 2012, Characterization of mercury 

and methylmercury contamination in stream and pond 

environments and provenance of mine waste from 

historical gold mining in the Sierra Nevada, California 

[abs.]: U.S. Environmental Protection Agency Hard-rock 

Mining Conference, April 3–5, 2012, Denver, Colorado, 

Advancing solutions for a new legacy, p. 103–104, available 

at https://clu-in.org/download/issues/mining/Hard_Rock/

ConferenceHandout/HRM_2012_Handout.pdf.

Churchill, R.K., 2000, Contributions of mercury to 

California’s environment from mercury and gold mining 

activities: Insights from the historical record, in Extended 

abstracts for the U.S. Environmental Protection Agency 

sponsored meeting, Assessing and Managing Mercury 

from Historic and Current Mining Activities, November 

28−30, 2000, San Francisco, Calif., EPA/325/R-04/102; p. 

33−36 and S35−S48, available at https://cfpub.epa.gov/si/

si_public_record_Report.cfm?dirEntryId=96732&CFID=15

005568&CFTOKEN=17523643.

Fleck, J.A., Alpers, C.N., Marvin-DiPasquale, M.C., 

Hothem, R.L., Wright, S.A., Ellett, Kevin, 

Beaulieu, Elizabeth., Agee, J.L., Kakouros, Evangelos, 

Kieu, L.H., Eberl, D.D., Blum, A.E., and May, J.T., 2011, 

The effects of sediment and mercury mobilization in the 

South Yuba River and Humbug Creek confluence area, 

Nevada County, California: Concentrations, speciation, 

and environmental fate—Part 1: Field characterization: 

U.S. Geological Survey Open-File Report 2010–1325A, 

104 p., available at http://pubs.usgs.gov/of/2010/1325A.
22 Quantifying Mercury-Contaminated Sediment at Stocking Flat, Deer Creek, Nevada County, Calif., 2010–13

Gilbert, G.K., 1917, Hydraulic-mining débris in the Sierra 

Nevada: U.S. Geological Survey Professional Paper 105, 

154 p., available at: https://pubs.er.usgs.gov/publication/

pp105.

Heritage, G.L. and Large, A.R.G., 2009, Laser scanning for 

the environmental sciences, Wiley-Blackwell Publishing, 

ISBN 978-1-4051-5717-9, 278 p.

Hunerlach, M.P., Rytuba, J.J., and Alpers, C.N., 1999, 

Mercury contamination from hydraulic placer-gold 

mining in the Dutch Flat mining district, California, 

in Morganwalp, D.W., and Buxton, H.T. (eds.), U.S. 

Geological Survey Toxic Substances Hydrology Program 

– Proceedings of the Technical Meeting, Charleston, South 

Carolina, March 8–12, 1999, U.S. Geological Survey WaterResources Investigations Report 99–4018B, p. 179–189, 

available at http://ca.water.usgs.gov/mercury/dutch/

wrir994018b.pdf.

Hunerlach, M.P., Alpers, C.N., Marvin-DiPasquale, M.C., 

Taylor, H.E., and De Wild, J.F., 2004, Geochemistry 

of mercury and other trace elements in fluvial tailings 

upstream of Daguerre Point Dam, Yuba River, California: 

U.S. Geological Survey Scientific Investigations Report 

2004–5165, 66 p., available at 

http://pubs.usgs.gov/sir/2004/5165/.

James, L.A., 1989, Sustained storage and transport of 

hydraulic mining sediment in the Bear River, California: 

Annals Association of American Geographers, v. 79, no. 4, 

p. 570–592.

Kellogg, L.H., Bawden, G.W., Bernardin, Tony, 

Billen, Magali, Cowgill, Eric, Hamann, Bernd, 

Jadamec, Margarete, Kreylos, Oliver, Staadt, Oliver, 

and Sumner, Dawn, 2008, Interactive visualization 

to advance earthquake simulation: Pure and Applied 

Geophysics, v. 165, no. 3, p. 621–633. DOI 10.1007/

s00024-008-0317-9.

Kreylos, Oliver, Bawden, G.W., and Kellogg, L.H., 2008, 

Immersive visualization and analysis of LiDAR data, in

Bebis, G., and others, Advances in Visual Computing, 

Proceedings Part I, 4th International Symposium on Visual 

Computing, December 1–3, 2008, Las Vegas, Nevada: 

Lecture Notes in Computer Science, v. 5358, p. 846–855, 

available at http://link.springer.com/book/10.1007/978-3-

540-89639-5/page/5.

Marvin-DiPasquale, Mark, Agee, J.L., Kakouros, Evangelos, 

Kieu, L.H., Fleck, J.A., and Alpers, C.N., 2011, The effects 

of sediment and mercury mobilization in the South Yuba 

River and Humbug Creek confluence area, Nevada County, 

California: Concentrations, speciation and environmental 

fate—Part 2: Laboratory Experiments: U.S. Geological 

Survey, Open-File Report 2010–1325B, 53 p., available at 

http://pubs.usgs.gov/of/2010/1325B.

May, J.T., Hothem, R.L., Alpers, C.N., and Law, M.A., 2000, 

Mercury bioaccumulation in fish in a region affected 

by historic gold mining: The South Yuba River, Deer 

Creek, and Bear River watersheds, California, 1999: 

U.S. Geological Survey Open-File Report 00–367, 30 p., 

available at http://ca.water.usgs.gov/archive/reports/

ofr00367/index.html.

Tufte, E.R., 1983, The visual display of quantitative 

information, second edition: Cheshire, Connecticut, 

Graphics Press, 193 p.
Glossary 23

Glossary

Anaglyph image: A stereoscopic three-dimensional (3-D) 

effect achieved by encoding images with chromatically 

different colors (typically red and blue) for each eye. When 

viewed through the color-coded anaglyph glasses (red and 

blue lens glasses), each of the images reaches one eye, 

giving the depth perception of a 3-D scene.

Angle of repose: The maximum angle, relative to the 

horizontal plane, at which sediment of a given particle size 

and degree of rounding will remain stable without sliding 

down slope.

Colluvium: A general term for loose, unconsolidated 

sediments that have been eroded from a higher slope 

position (typically a steeper slope) and deposited down 

slope (typically on a lower angle slope) by gravity-driven 

processes.

Dry ravel: A general term that describes the gravity-driven 

rolling, bouncing, and sliding of sediment particles down a 

slope.

Hard-rock mining: A general term that refers to various 

methods used to excavate hard minerals, typically those 

containing precious and base metals such as gold, silver, 

copper, zinc, and lead. In the Sierra Nevada of California, 

hard-rock mining of low-sulfide gold-quartz vein deposits 

was primarily done by underground methods.

Hydraulic gold mine: A type of surface mine where a 

high-pressure jet of water (emitted from a water cannon, 

or monitor) is used to dislodge or erode gold-bearing 

sedimentary deposits exposed on a hillside or cliff face. The 

practice was largely banned in California starting in 1884.

Kriging: A weighted statistical technique used to interpolate 

a value based on the spatial covariance of surrounding data 

points. In this study, the kriged or interpolated values are 

points on the surface of the cutbank between existing lidar 

data points.

Lidar: Light detection and ranging is a remote-sensing 

technology used to make precise three-dimensional “point 

clouds” of the land surface. Sometimes lidar is referred to 

as terrestrial laser scanning (TLS). Pulses of near-infrared 

laser light are timed to measure the distance (range) from 

the lidar scanner to the reflecting surface. Laser ranges 

are combined with angular orientation data to generate a 

dense and detailed set of points (locations of individual laser 

returns) referred to as a point cloud.

Mining debris: Waste materials from mining (including 

hydraulic mining) and mineral processing, including 

waste rock and mill tailings from hard-rock mines. Waste 

rock is material below ore grade that is separated from 

economically viable ore. Waste rock typically is not milled, 

so it consists of material including large clasts or cobbles. 

Mill tailings are what remain after the milling process has 

separated out the valuable fraction of an ore, leaving waste 

material that is typically sand-sized or smaller particles.

Placer mining: Mining of an unconsolidated alluvial 

or colluvial deposit (placer deposit). Typically, placer 

deposits are mined by surface methods (hydraulic mining 

or dredging); in some cases, underground methods (drift 

mining) are used. Metallic clasts and mineral grains 

are gravity separated by means of hydraulic saturation, 

mechanical agitation, or both.

Point cloud: A point cloud is a set of vertices in a threedimensional coordinate system. These vertices are usually 

defined by x, y, and z coordinates and typically represent the 

external surface of an object.

Terrestrial laser scanning (TLS): Sometimes referred to as 

terrestrial lidar or tripod-mounted lidar (T-lidar). ‘Terrestrial’ 

refers to the laser scanner being used near the Earth’s 

surface (stationary on a tripod) as opposed to airborne laser 

scanning (ALS).

Water year: A 12-month period, offset from the calendar 

year, that brackets seasonal precipitation typically 

associated with the winter and spring months. The 

U.S. Geological Survey water year (WY) starts on October 1 

and ends on September 30 of the following year; for 

example, WY 2011 started October 1, 2010, and ended 

September 30, 2011. 

Prepared by the Sacramento Publishing Service Center.

For more information concerning this report, contact:

Director

U.S. Geological Survey

California Water Science Center

6000 J Street, Placer Hall

Sacramento, CA 95819

dc_ca@usgs.gov

or visit our Web site at:

http://ca.water.usgs.gov

Red-blue glasses (with the red lens on the right side) are needed for 

enhanced 3-D viewing of the following figures in this report: 11A, 11C, 

11E, 11G, and 12A. To request red-blue glasses, please contact James 

Howle by phone (530-587-0910, ext. 2017) or by email (jfhowle@usgs.

gov).
Creek, Nevada County, California, 2010–13—

By James F. Howle and others—Quantifying the Eroded Volume of Mercury-Contaminated Sediment Using Terrestrial Laser Scanning at Stocking Flat, Deer 

Series Name 2015–5179

ISSN 2328-0328 (online)

ISSN 2328-031X (print)

http://dx.doi.org/10.3133/SIR20155179

Horizontal slope erosion 

of ~ 1.2 meters from 

January 2011 to February 2013

Cutbank surface in

January 2011 Cutbank surface in

February 2013

Horizontal change from Jan. 2011 to Feb. 2013 

-0.10

-1.00

0.00

Meters

-0.30

-0.40

-0.50

-0.60

-0.70

-0.80

-0.90

-0.20

-1.10

-1.20

Slope erosion of 

~ 1.2 meters