U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2006–5168

A Comparison of Approaches for 

Estimating Bottom-Sediment Mass in 

Large Reservoirs

1,010

1,000

0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500 5,000 5,500 6,000

1,020

1,030

1,040

1,050

1,060

1,070

1,080

1,090

1,100

1,110

1,120

1,130

1,140

1,150

1,160

1,170

1,180

Elevation, in feet above sea level

Distance along range line 3, in feet

1962 U.S. Army Corps of Engineers bathymetric data

1999 U.S. Geological Survey bathymetric data Big Blue River channel

Northeast Range line 3

Northeast

Southwest

Southwest

Sediment deposition

Range line 3

T u t t l e C r e e k L a k e
A Comparison of Approaches for 

Estimating Bottom-Sediment Mass in Large 

Reservoirs

By Kyle E. Juracek

Scientific Investigations Report 2006–5168

U.S. Department of the Interior

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

DIRK KEMPTHORNE, Secretary

U.S. Geological Survey

P. Patrick Leahy, Acting Director

U.S. Geological Survey, Reston, Virginia: 2006

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Suggested citation:

Juracek, K.E., 2006, A comparison of approaches for estimating bottom-sediment mass in large reservoirs: 

U.S. Geological Survey Scientific Investigations Report 2006–5168, 13 p.
iii

Contents

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

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

Description of Study Areas ..........................................................................................................................2

Methods...........................................................................................................................................................2

Comparison of Sediment Mass Estimates...............................................................................................10

Summary and Conclusions.........................................................................................................................11

Acknowledgment.........................................................................................................................................12

References Cited..........................................................................................................................................12

Figures

1. Map showing location of reservoirs in Kansas used in study..............................................3

 2–5. Maps showing location of bathymetric range lines, sediment-coring sites, estimated 

 bulk densities, and boundaries of reservoir components for: 

2. Cheney Reservoir.................................................................................................................5

3. Hillsdale Lake. ......................................................................................................................6

4. Perry Lake. ............................................................................................................................7

5. Tuttle Creek Lake. ................................................................................................................8

Tables

1. Year of completion, basin size, original water-storage capacity, and original surface 

area for selected reservoirs in Kansas.....................................................................................4

2. Sediment volumes, number of reservoir components, bulk densities, and computed 

sediment masses for selected reservoirs in Kansas..............................................................9

3. Coring-site combinations, mean bulk densities, and computed sediment masses using 

the midpoint approach for Tuttle Creek Lake, northeastern Kansas. ................................11

4. Coring-site combinations, mean bulk densities, and computed sediment masses using 

the strategic approach for Tuttle Creek Lake, northeastern Kansas.................................12
iv

Conversion Factors, Abbreviations, and Datum

Multiply By To obtain

Length

centimeter (cm) 0.3937 inch (in.)

meter (m) 3.281 foot (ft) 

kilometer (km) 0.6214 mile (mi)

Area

square kilometer (km2) 247.1 acre

square kilometer (km2) 0.3861 square mile (mi2)

Volume

cubic meter (m3) 35.31 cubic foot (ft3)

Mass

kilogram (kg) 2.205 pound (lb)

Density

kilogram per cubic meter (kg/m3) 0.06243 pound per cubic foot (lb/ft3) 

Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83).
Abstract

Estimates of sediment and sediment-associated constituent loads and yields from drainage basins are necessary for the 

management of reservoir-basin systems to address important 

issues such as reservoir sedimentation and eutrophication. 

One method for the estimation of loads and yields requires 

a determination of the total mass of sediment deposited in a 

reservoir. This method involves a sediment volume-to-mass 

conversion using bulk-density information. A comparison of 

four computational approaches (partition, mean, midpoint, 

strategic) for using bulk-density information to estimate total 

bottom-sediment mass in four large reservoirs indicated that 

the differences among the approaches were not statistically 

significant. However, the lack of statistical significance may 

be a result of the small sample size. Compared to the partition 

approach, which was presumed to provide the most accurate 

estimates of bottom-sediment mass, the results achieved using 

the strategic, mean, and midpoint approaches differed by as 

much as ±4, ±20, and ±44 percent, respectively. It was concluded that the strategic approach may merit further investigation as a less time consuming and less costly alternative to the 

partition approach. 

Introduction

Estimates of sediment and sediment-associated constituent loads and yields from drainage basins are important for 

the management of lakes and reservoirs (Morris and Fan, 

1998; Umbanhowar and others, 2003). Together, sediment and 

constituent loads and yields provide baseline information that 

may be used to assess the effectiveness of implemented management practices intended to reduce sedimentation in, and 

improve the water quality of, a lake or reservoir. For example, 

such information is useful in the development, implementation, evaluation, and revision of total maximum daily loads 

designed to control reservoir sedimentation and eutrophication 

(Juracek and Stiles, 2003). For reservoirs, one method for the 

estimation of loads and yields involves a determination of the 

total mass of deposited sediment (Vanoni, 1975; Rausch and 

Heinemann, 1984; Annandale, 1987). 

A primary factor that affects the accuracy of bottomsediment mass determination, and associated load and yield 

estimates, is the spatial representativeness of available bulkdensity information that is used to convert sediment volume 

to mass (Foster and others, 1990; Butcher and others, 1993; 

Verstraeten and Poesen, 2001). Sediment bulk density varies 

among reservoirs (Dendy and Champion, 1978; Rausch and 

Heinemann, 1984; Butcher and others, 1993) as well as horizontally and vertically within a reservoir (Heinemann, 1962; 

Lara and Pemberton, 1965; Foster and Charlesworth, 1994). 

For example, bulk density tends to be lowest downstream 

near the dam where the fine sediment is deposited and highest 

in the upstream part of the reservoir where the coarse delta 

deposits are located. This upstream-to-downstream gradation is the result of the relation between particle size, settling 

velocity, and flow velocity as the sediment-laden water enters 

and moves through a reservoir. Localized deviations from this 

gradation can be caused by several factors including an influx 

of relatively coarse-grained sediment from tributary and shore 

sources, and compaction (Morris and Fan, 1998). Given such 

spatial variability, the bulk density determined for a single site 

typically is not representative of the reservoir as a whole. 

In this report, the results of a study to compare several 

approaches to using bulk-density information for the estimation of bottom-sediment mass in large reservoirs are presented. 

Although considerable research has addressed various aspects 

of reservoir sedimentation (for example, see Vanoni, 1975; 

Morris and Fan, 1998), a search of the literature uncovered 

no previous studies that provide a comparison of approaches 

for estimating bottom-sediment mass using reservoir surveys 

and bulk-density information. Because of the fundamental 

importance of bottom-sediment mass, an understanding of the 

comparability of approaches for its estimation is needed. The 

objective of the study described herein was to determine, for 

four large reservoirs, the differences in estimated bottom-sediment mass using four approaches. The approaches selected 

provide a set of alternatives that have been, or potentially may 

be, used for the purpose of estimating bottom-sediment mass. 

The approaches represent a range in terms of complexity and 

data-collection requirements. 

The first two approaches, referred to as the partition and 

mean approaches, have been used in previous reservoir sediment studies (for example, White and others, 1997; Juracek, 

A Comparison of Approaches for Estimating BottomSediment Mass in Large Reservoirs

By Kyle E. Juracek
1998). Optimally, both of these approaches require relatively 

extensive data collection to provide sufficiently detailed bulkdensity information for a reservoir. In the partition approach, 

a reservoir is partitioned into a number of discrete in-channel 

and out-of-channel components. One or more bulk-density 

values are used to compute sediment mass for each of the 

individual components, which then are summed to provide 

an estimate of the total bottom-sediment mass for a reservoir. 

Because it best accounts for the variability in bulk density, the 

partition approach is presumed to provide the most accurate 

estimate of total bottom-sediment mass for a reservoir. However, this approach may not always be possible or feasible. In 

the mean approach, total bottom-sediment mass is computed 

in one step using the mean bulk-density value for a reservoir. 

This approach is simpler than the partition approach. 

The second two approaches, referred to as the midpoint 

and strategic approaches, also are simpler than the partition approach and, more importantly, require less-extensive 

data collection. No published examples of the second two 

approaches were found in the literature. Given the variability 

of sediment deposition and bulk density within a reservoir, the 

appropriateness of these two approaches is questionable. Nevertheless, they are included as possible alternatives to assess 

their comparability to the partition approach. In the midpoint 

approach, total bottom-sediment mass is computed in one step 

using the mean bulk-density value for an area located near the 

middle of each reservoir. In the strategic approach, the bulkdensity values determined for the upstream- and downstreammost areas of each reservoir are averaged and used to estimate 

total bottom-sediment mass. Both of these approaches are 

based on the assumption of a relatively uniform upstream-todownstream gradation of bulk density within a reservoir. The 

validity of this assumption will vary among reservoirs. 

In sum, the primary purpose of this report is to document 

whether or not less time consuming and less costly alternative 

approaches for estimating total bottom-sediment mass could 

provide results that are comparable to the partition approach. 

The findings presented herein could have implications for 

present and future reservoir and basin management, especially as related to decisions regarding data collection and the 

estimation of sediment and associated constituent mass, load, 

and yield. 

Description of Study Areas

The reservoirs selected for this study were Cheney Reservoir in south-central Kansas, Hillsdale Lake in east-central 

Kansas, and Perry and Tuttle Creek Lakes in northeast Kansas 

(fig. 1). Cheney Reservoir is an impoundment on the North 

Fork Ninnescah River that was completed in 1964. Hillsdale 

Lake, completed in 1981, is an impoundment on Big Bull 

Creek. Perry Lake is an impoundment on the Delaware River 

that was completed in 1969. Tuttle Creek Lake, completed 

in 1962, is an impoundment on the Big Blue River. Basin 

sizes range from 373 km2 for Hillsdale Lake to 24,900 km2

for Tuttle Creek Lake. The original water-storage capacities 

at conservation-pool elevation ranged from 84 million m3 for 

Hillsdale Lake to 524 million m3 for Tuttle Creek Lake. The 

original surface areas of the reservoirs at conservation-pool 

elevation ranged from 18 km2 for Hillsdale Lake to 64 km2

for Tuttle Creek Lake (table 1). Land use in all four basins is 

predominantly an agricultural mix of cropland and grassland. 

Methods

Available information from previously completed reservoir sediment studies of Cheney Reservoir (Pope, 1998; Mau, 

2001), Hillsdale Lake (Juracek, 1997), Perry Lake (Juracek, 

2003), and Tuttle Creek Lake (Juracek and Mau, 2002) was 

used for the purposes of this study. The information available 

from these studies was not collected with the present study 

objective in mind and, therefore, does not provide an ideal 

data set in terms of completeness. However, the information is 

believed to be representative of what is typically collected for 

reservoir sediment studies and is considered to be sufficiently 

comprehensive for the purposes of this study. 

In the previously completed studies, total bottom-sediment volume for each of the reservoirs was determined by 

bathymetric survey. Each reservoir was resurveyed along 

bathymetric range lines that were established at the time of 

reservoir construction (figs. 2–5). Using the bathymetric 

range lines as boundaries (Rausch and Heinemann, 1984), the 

original conservation-pool surface area of each reservoir was 

partitioned into in-channel (that is, the pre-reservoir stream 

or river channel) and out-of-channel (that is, the pre-reservoir 

flood plain) components to improve the precision of the bottom-sediment volume estimates. For example, in Cheney Reservoir, the availability of five range lines enabled the partitioning of the reservoir into six in-channel and six out-of-channel 

components (fig. 2). The bottom-sediment volume for each 

component was computed as the total surface area multiplied 

by the mean thickness of the sediment. With one exception, 

mean sediment thickness for each component was computed 

as the average of the sediment thicknesses determined using 

the range lines that defined the component. In the case of 

Hillsdale Lake, the thickness of the relatively thin out-ofchannel sediment deposits (generally, less than 0.3 m) was 

estimated using coring data. Total bottom-sediment volume for 

each reservoir was computed as the sum of the components. 

At each reservoir, sediment cores for bulk-density determination were collected to provide a spatially representative 

sample of conditions upstream to downstream as well as in 

and out of the submerged channels. The sediment cores were 

collected using a gravity corer mounted on a pontoon boat. 

The liner used in the corer was cellulose acetate butyrate 

transparent tubing with a 6.67-cm inside diameter. The cores 

ranged in length from less than 0.5 to about 4 m. Respectively, 

the number of cores collected (and the approximate density of 

 A Comparison of Approaches for Estimating Bottom-Sediment Mass in Large Reservoirs
Figure 1. Location of reservoirs in Kansas used in study.

cores per km2 of reservoir surface area) for Cheney Reservoir, 

Hillsdale Lake, Perry Lake, and Tuttle Creek Lake were 10 

(0.3 cores/km2), 30 (1.7 cores/km2), 18 (0.4 cores/km2), and 22 

(0.3 cores/km2). The location of the coring sites for the four 

reservoirs is provided in figures 2 through 5. 

To account for the variability of bulk density with depth 

in the sediment profile, the cores were divided into multiple 

intervals, which then were sampled for bulk-density determinations. Typically, a 2.5-cm thick sample was removed from 

each interval. Depending on the length of the recovered core, 

the number of intervals per core ranged from 1 to 17 with a 

typical range of 5 to 10. Bulk density was determined using 

standard methods (Guy, 1969; Gordon and others, 1992). The 

interval-specific bulk densities were averaged to determine a 

representative mean bulk density for each coring site. 

The conversion of total sediment volume to total sediment mass was accomplished using four approaches in this 

report. The partition approach was presumed to provide the 

most accurate estimates of bottom-sediment mass as it best 

accounts for the spatial variability of bulk density in the bottom sediment of each reservoir. In this approach, each reservoir was partitioned into a number of in-channel and out-ofchannel components to improve the precision of the sediment 

mass estimates. Typically, the boundaries for the components 

corresponded to the established bathymetric range lines 

(figs. 2–5). An exception was the out-of-channel area for 

Hillsdale Lake, which was partitioned into only three components as dictated by the limited thickness and spatial distribution of sediment (Juracek, 1997). The total number of reservoir components used ranged from 12 for Cheney Reservoir to 

37 for Tuttle Creek Lake (table 2). 

Sediment mass for each reservoir component was computed as the total sediment volume for the component multiplied by the representative mean bulk density for the compoTuttle

Creek

Lake

North Fork

Ninnescah River

Delaware River

Big Bull

Creek

Big Blue River

KANSAS

NEBRASKA

COLORADO

MISSOURI

OKLAHOMA

80°

KANSAS

Index map

MISSOURI

K

RIVER

ansas River

Arkansas River

Arkansas River Hillsdale

Lake

Perry

Lake

102°

40°

39°

38°

37°

101° 100° 99° 98° 97° 96°

95°

Cheney

Reservoir

0 20 40 60 80 KILOMETERS

0 20 40 MILES

Methods 
nent. As dictated by the location of the coring sites in relation 

to the boundaries of the reservoir components, a bulk-density 

value was assigned to each component using available values 

outright (if the component had a single coring site) or averaged (if the component had multiple coring sites) to provide 

what was believed to be the most representative value. In some 

cases, a lack of bulk-density information for a particular component necessitated the use of bulk-density information from 

a nearby component (that is, the nearest coring site for which 

a bulk-density value was available). Total sediment mass for 

each reservoir was computed as the sum of the masses determined for the individual reservoir components. 

In the mean approach, the total sediment mass for each 

reservoir was computed as the total sediment volume (previously determined) multiplied by the mean bulk density for 

the reservoir. The mean bulk density was computed as the 

average of the representative mean bulk densities determined 

for the individual coring sites. Both the partition and mean 

approaches used all available bulk-density information for 

each reservoir. 

For the midpoint approach, the total sediment mass for 

each reservoir was computed as the total sediment volume 

(previously determined) multiplied by the midpoint bulk density for the reservoir. The midpoint bulk density was computed 

as the average of the representative mean bulk densities determined for an in-channel and out-of-channel core collected near 

the middle of each reservoir. At Tuttle Creek Lake there were 

two out-of-channel cores collected at the selected reservoir 

midpoint. Thus, the average bulk density for the two sites was 

used as the out-of-channel value in the midpoint approach. 

Because Hillsdale Lake has two primary arms (fig. 3), the 

midpoint bulk density was computed as the average of the 

representative mean bulk densities determined for an in-channel and out-of-channel core collected near the middle of both 

arms. The coring sites used to compute the midpoint bulk 

density for each reservoir are identified in figures 2 through 5. 

The strategic approach involved the use of bulk densities 

determined for two coring sites (that is, one in-channel and 

one out-of-channel) near both the upstream and downstream 

limits of each reservoir. For consistency, the in- and out-ofchannel coring sites located farthest upstream and downstream 

were selected. The coring sites used in the strategic approach 

for each reservoir are identified in figures 2 through 5. Total 

sediment mass was computed as the total sediment volume 

(previously determined) multiplied by the mean bulk density 

for the four coring sites. 

Because Hillsdale Lake has two primary arms (fig. 3), 

the farthest upstream and downstream coring sites for the inchannel and out-of-channel locations were included for both 

arms. Thus, a total of eight bulk-density values were used to 

compute the mean for Hillsdale Lake. It should be noted that 

the upstream, out-of-channel value for the Big Bull Creek arm 

was estimated on the basis of a regression relation (R2 = 0.89) 

between bulk density and percent moisture content. Also, due 

to insufficient sediment volume, the downstream, out-of-channel values for both arms were estimated on the basis of the 

relation between the in- and out-of-channel values determined 

for upstream areas of the reservoir (Juracek, 1997). 

At Tuttle Creek Lake, there were two out-of-channel coring sites located near the dam (fig. 5). Thus, the average bulk 

density for the two sites was used as the out-of-channel value 

in the strategic approach. 

To determine whether or not the differences among the 

four approaches were statistically significant, the nonparametric Friedman two-way analysis of variance by ranks test 

(Siegel and Castellan, 1988) was performed. In this test, the 

results for each reservoir (that is, the sediment mass estimates) 

were ranked from smallest (rank of 1) to largest (rank of 4). 

Then, the sum of the ranks for each approach was used in 

the computation of the test statistic Fr. At the 0.05 level of 

significance, the critical value Fcrit is 7.8. If Fr > Fcrit, then the 

null hypothesis (that is, equivalence among the approaches) 

Table 1. Year of completion, basin size, original water-storage capacity, and original surface area for selected reservoirs in Kansas.

[km2, square kilometers; m3, cubic meters]

Reservoir

(stream or river)

Year of 

completion

Basin size

(km2)

Original water-storage 

capacity1

(million m3)

Original surface 

area1

(km2)

Cheney Reservoir 

(North Fork 

Ninnescah River)

1964 2,420 187 39

Hillsdale Lake (Big 

Bull Creek)

1981 373 84 18

Perry Lake (Delaware 

River)

1969 2,890 300 49

Tuttle Creek Lake (Big 

Blue River)

1962 24,900 524 64

1

At conservation-pool elevation (data from the U.S. Army Corps of Engineers and the Bureau of Reclamation, written com­mun., various dates).

 A Comparison of Approaches for Estimating Bottom-Sediment Mass in Large Reservoirs
Cheney Dam

North Fork

Ninnescah River

97°54'

37°50'

52' 50' 97°48'

48'

46'

37°44'

0

0

1

1 2 3 4 KILOMETERS

2 MILES

Base from U.S. Geological Survey digital data, 1:100,000, 1995

U.S. Geological Survey, Castleton 1:24,000, 1965;

Cheney 1:24,000, 1964 (photorevised 1982);

Haven SE 1:24,000, 1965 

Universal Transverse Mercator projection, Zone 14

Bulk-density values from Pope (1998) and Mau (2001)

1

7

10

1

Cheney Reservoir

Approximate extent of Cheney Reservoir at

 conservation-pool elevation 

 

Bathymetric range line and number—Established

 by Bureau of Reclamation

Pre-reservoir stream or river channel

In-channel sediment-coring site and number—

 Number in parentheses ( ) is mean bulk density, in 

 kilograms per cubic meter

Out-of-channel sediment-coring site and number—

 Number in parentheses ( ) is mean bulk density, in 

 kilograms per cubic meter

Coring site used for midpoint approach

Coring site used for strategic approach

P2

(326.8)

**P2

(326.8)

P13

(430.9)

*P6

(1662.9)

P11

(677.6)

P7

(1041.3)

P9

(1669.3)

**P8

(833.0)

**P10

(1659.7)

*P4

(632.8)

P1

(381.3)

**P1

(381.3)

EXPLANATION

8

9

1

*

**

Figure 2. Location of bathymetric range lines, sediment-coring sites, estimated bulk densities, and boundaries 

of reservoir components for Cheney Reservoir.

Methods 
Hillsdale

Lake

Hillsdale 

Dam 

41' 

43' 

38°39'

38°45'

95°01' 59' 57' 55' 53' 94°51'

7 

2 

9 

10 

8 

6 

5 

4 13 

14 

15 

16 

3 

18 

12 

1 

1 

0

0

1 2 3 4 KILOMETERS

1 2 MILES

Approximate extent of Hillsdale Lake at

 conservation-pool elevation 

 

Bathymetric range line and number—Established

 by U.S. Army Corps of Engineers

Pre-reservoir stream or river channel

In-channel sediment-coring site and number—

 Number in parentheses ( ) is mean bulk density, in 

 kilograms per cubic meter

Out-of-channel sediment-coring site and number—

 Number in parentheses ( ) is mean bulk density, in 

 kilograms per cubic meter

Coring site used for midpoint approach

Coring site used for strategic approach

Base from U.S. Geological Survey digital data, 1:24,000, 1973

Lambert Conformal Conic projection

Standard parallels 33° and 45°, central meridian 98°15'

Big Bull

Creek

Little Bull

Creek

EXPLANATION

SC–3

(769.0)

**D–4

(461.4)

**D–2

(448.6)

BB–4*

(959.6)

BB–4

(959.6)

*

**

BB–6

(863.5)

BB–15

(698.5)

BB–14

(778.6)

**BB–13

(791.4)

BB–13

(791.4)

BB–18

(717.7)

**BB–1

(914.7)

SB–1

(751.3)

LB–14

(584.7)

LB–13

(554.3)

LB–16*

(458.2)

LB–2

(853.9)

LB–15*

(788.2)

LB–6

(495.0)

LB–10

LB–11

(554.3)

LB–1

(932.4)

**LB–7

(770.6)

LB–8

(575.1)

**LB–9

(720.9)

BB–9

(571.9) BB–12

(475.8)

BB–2

(682.5)

RC–2

(794.6)

*BB–10

BB–11

(605.6)

WB–2

(653.6)

Bulk-density values from Juracek (1997)

Figure 3. Location of bathymetric range lines, sediment-coring sites, estimated bulk densities, and boundaries of reservoir 

components for Hillsdale Lake.

 A Comparison of Approaches for Estimating Bottom-Sediment Mass in Large Reservoirs
8 

7 

6 

5 

4 

30 

3 

25 

24 2 

29 

28 

1 

26 

Perry Dam 

Perry Lake

Delaware River

0

0 1 2 MILES

1 2 3 4 5 KILOMETERS

8'

10'

12'

14'

16'

18'

39°20'

39°6'

U.S. Geological Survey, Holton SE 1:24,000, 1951 (photorevised 1979); 

Valley Falls 1:24,000, 1959 (photorevised 1979); 

Winchester 1:24,000, 1949 (photorevised 1979); 

Meriden 1:24,000, 1952 (photorevised 1982); 

Ozawkie 1:24,000, 1951 (photorevised 1970 and 1975); 

Oskaloosa 1;24,000, 1951 (photorevised 1979); 

Grantville 1:24,000, 1983; 

Perry 1;24,000, 1951 (photorevised 1970 and 1975); 

Williamstown 1:24,000, 1959 (photorevised 1979) 

95°32' 30' 28' 26' 24' 22' 95°20'

1 

Approximate extent of Perry Lake at

 conservation-pool elevation 

 

Bathymetric range line and number—Established

 by U.S. Army Corps of Engineers

Pre-reservoir stream or river channel

In-channel sediment-coring site and number—

 Number in parentheses ( ) is mean bulk density, in 

 kilograms per cubic meter

Out-of-channel sediment-coring site and number— 

 Number in parentheses ( ) is mean bulk density, in 

 kilograms per cubic meter 

Coring site used for midpoint approach 

Coring site used for strategic approach 

POC−1

(418.1)

**POC−2

(294.8)

POC−1

(418.1)

POC−7

(301.2)

POC−6

(416.5)

*POC−5 (455.0)

POC−9

(491.8)

**POC−4

(741.7)

POC−8

(523.9)

 PIC−2

(563.9)

**PIC−11

(461.4)

PIC−10

(456.6)

PIC−12

(559.1)

PIC−1

(406.9)

PIC−8

(959.6)

PIC−7

(714.5)

PIC−6

(850.7)

**PIC−4

(940.4)

*PIC−9

(493.4)

PIC−2

(563.9)

EXPLANATION

* 

** 

Bulk-density values from Juracek (2003)

Figure 4. Location of bathymetric range lines, sediment-coring sites, estimated bulk densities, and 

boundaries of reservoir components for Perry Lake.

Methods 
Figure 5. Location of bathymetric range lines, sediment-coring sites, estimated bulk 

densities, and boundaries of reservoir components for Tuttle Creek Lake.

1

Approximate extent of Tuttle Creek Lake at

 conservation-pool elevation 

 

Bathymetric range line and number—Established

 by U.S. Army Corps of Engineers

Pre-reservoir stream or river channel

In-channel sediment-coring site and number—

 Number in parentheses ( ) is mean bulk density, in

 kilograms per cubic meter

Out-of-channel sediment-coring site and number—

 Number in parentheses ( ) is mean bulk density, in

 kilograms per cubic meter

Coring site used for midpoint approach

Coring site used for strategic approach

**TOC−1 (520.7)

TOC−1 (520.7)

**TOC−1A

(445.4)

EXPLANATION

*

**

U.S. Geological Survey, Riley 1:24,000, 1964 (photorevised 1978); Bulk-density values from Juracek and Mau (2002)

Tuttle Creek Dam 1:24,000, 1964 (photorevised 1978);

Olsburg SW 1:24,000, 1964 (photorevised 1978);

Olsburg NW 1:24,000, 1964 (photorevised 1978);

Olsburg 1:24,000, 1964 (photorevised 1978);

Randolph 1:24,000, 1964 (photorevised 1983);

Blue Rapids SW 1:24,000, 1964 (photorevised 1983);

Blue Rapids SE 1:24,000, 1968

Universal Transverse Mercator projection, Zone 14

0

0

1 2 3 4 5 6 KILOMETERS

1 2 4 MILES

96o46' 44' 42' 40' 38' 36' 34' 96o32'

39o34'

32'

30'

28'

26'

24'

22'

20'

18'

39o16'

5

6

7

8

9

10

13

14

15

16 17

18

19

20

21

4

3

1

2

Tuttle Creek Lake

Big Blue River

Tuttle Creek Dam

**TIC−1

(586.3)

TIC−1

(586.3)

TIC−2 (608.8)

TIC−3 (644.0)

TIC−4

(512.6)

*TIC−5

(604.0)

TOC−2A

(299.6)

TOC−2 (669.6)

TOC−3 (370.1)

TOC−4

(499.8)

*TOC−5

(610.4)

TOC−3A

(379.7)

TOC−4A

(429.3)

*TOC−5A

(400.5)

TOC−7A

(600.8)

TOC−7

(560.7)

**TOC−13 (1030.1)

TIC−13 (879.5)

**TIC−16 (974.0)

TIC−9

(927.6)

TOC−9

(909.9)

 A Comparison of Approaches for Estimating Bottom-Sediment Mass in Large Reservoirs
Table 2. Sediment volumes, number of reservoir components, bulk densities, and computed sediment masses for selected reservoirs in Kansas.

[m3, cubic meters; I, in-channel; O, out-of-channel; kg/m3, kilograms per cubic meter; kg, kilograms; %, percent]

Reservoir (fig. 1)

Sediment 

volume 

(millions 

of m3)

Number of 

reservoir 

components 

(I,O)

Number of 

bulk 

density 

estimates 

(I,O)

Bulk density1 (kg/m3)

Computed sediment mass

 [millions of kg (percentage difference from partition 

approach)]

Minimum Maximum Mean Standard deviation Partition approach Mean approach Midpoint approach2 Strategic approach3

Cheney 

Reservoir4

8.75 12

(6, 6)

10

(5, 5)

326.8 1,669.3 931.6 548.1 6,990 8,150

(+16.6%)

10,000

(+43.1%)

7,000 

(+0.1%)

Hillsdale Lake5 2.59 21

(18, 3)

30

(18, 12)

448.6 959.6 686.6 152.4 1,800 1,780

(-1.1%)

1,820

(+1.1%)

1,730

(-3.9%)

Perry Lake6 70.0 26

(14, 12)

18

(10, 8)

294.8 959.6 558.3 201.3 44,100 39,100

(-11.3%)

33,200

(-24.7%)

42,700

(-3.2%)

Tuttle Creek 

Lake7

175 37

(19, 18)

22

(8, 14)

299.6 1,030.1 612.0 209.3 133,000 107,000 

(-19.5%)

97,100 

(-27.0%)

134,000

(+0.8%)

1Computed using all coring sites for which representative bulk-density information was available.2Mean bulk densities computed using the midpoint approach for Cheney Reservoir, Hillsdale Lake, Perry Lake, and Tuttle Creek Lake were 1,147.9, 702.9, 474.2, and 554.8 kg/m3, respectively.3Mean bulk densities computed using the strategic approach for Cheney Reservoir, Hillsdale Lake, Perry Lake, and Tuttle Creek Lake were 800.2, 668.8, 610.4, and 768.4 kg/m3, respectively.4Sources of data: Pope (1998) and Mau (2001).5Source of data: Juracek (1997).6Source of data: Juracek (2003).7Source of data: Juracek and Mau (2002).

Methods 
is rejected and the differences among the approaches may be 

considered statistically significant. 

Comparison of Sediment Mass 

Estimates

Compared to the partition approach, which was presumed 

to provide the most accurate estimates of total bottom-sediment mass, the results achieved using the strategic, mean, and 

midpoint approaches differed by as much as +4, +20, and 

+44 percent, respectively. Table 2 provides a summary of 

the sediment volume, bulk densities, and estimated sediment 

masses for each of the four reservoirs. Estimates of sediment 

and sediment-associated constituent loads and yields would 

exhibit similar differences among the four approaches. 

Despite some relatively large percentage differences 

among the estimated sediment masses, especially between the 

midpoint and partition approaches (table 2), the Friedman test 

indicated no statistically significant differences among the four 

approaches at the 0.05 level of significance. The value of the 

test statistic Fr was 0.3. Because Fr < Fcrit, the null hypothesis 

could not be rejected. However, the lack of statistical significance may be a result of the small sample size. 

Differences between the partition approach and the three 

alternative approaches were expected, although it was not 

known in advance what to expect in terms of the magnitude of 

the differences. Of the three alternatives, it was anticipated that 

the mean approach might perform best (that is, provide sediment-mass estimates closest to the estimates obtained using 

the partition approach) because it used all available bulk-density information (albeit averaged), whereas the midpoint and 

strategic approaches used a limited subset of the available 

information. With the exception of Hillsdale Lake, the mean 

approach did perform better than the midpoint approach. However, with the exception of Hillsdale Lake, the mean approach 

did not perform better than the strategic approach (table 2). 

The excellent agreement between the partition and strategic 

approaches was surprising and may, in part, be a result of the 

small sample size (that is, four reservoirs).

The results also indicated that the differences between 

the partition and mean approaches may be directly related to 

the range in bulk density within each reservoir. That is, as the 

range in bulk density increases, the difference between the partition and mean approaches increases (table 2). In addition, the 

differences between the partition and mean approaches may be 

inversely related to the density of coring within the reservoirs. 

The difference is relatively small for Hillsdale Lake 

(1.7 cores/km2), relatively moderate for Perry Lake 

(0.4 cores/km2), and relatively large for Cheney Reservoir 

(0.3 cores/km2) and Tuttle Creek Lake (0.3 cores/km2). The 

differences between the partition and all three alternative 

approaches were small for Hillsdale Lake.

The sediment-mass estimates obtained represent one 

possible set of outcomes for each reservoir using the midpoint 

and strategic approaches. Because the bulk density of bottom 

sediment varies throughout a reservoir, the results for both 

approaches will vary depending on the location of the coring 

sites used. The available information for the four reservoirs 

does not allow for a comprehensive evaluation of the variability in sediment-mass estimates using the two approaches. 

However, a limited assessment was possible. 

Tuttle Creek Lake was selected to provide an assessment 

of variability because the reservoir has a predominantly linear 

(that is, relatively simple) shape and a reasonably good number and distribution of coring sites (fig. 5). For the midpoint 

approach, 12 unique combinations of coring sites were used 

to assess variability in sediment-mass estimates (table 3). The 

estimates computed using the midpoint approach ranged from 

79,900 to 106,000 million kg with a mean of 91,300 million 

kg and a standard deviation of 7,400 million kg (+ 8 percent). 

Depending on the combination of coring sites selected for 

Tuttle Creek Lake, the sediment-mass estimate obtained using 

the midpoint approach differed from the partition-based estimate by as little as 20 percent or as much as 40 percent. The 

average difference was 31 percent. 

Twelve unique combinations of coring sites also were 

used to assess variability for the strategic approach (table 4). 

The estimates computed using the strategic approach ranged 

from 110,000 to 136,000 million kg with a mean of 

120,000 million kg and a standard deviation of 10,000 million 

kg (+9 percent). Depending on the combination of coring sites 

selected for Tuttle Creek Lake, the sediment-mass estimate 

obtained using the strategic approach differed from the partition-based estimate by as little as 1 percent or as much as 

17 percent. The average difference was 10 percent. Thus, 

regardless of the combination of coring sites selected, the strategic approach performed better than the midpoint approach 

for Tuttle Creek Lake. 

Additional research, using more detailed data sets, is 

needed to improve understanding of the spatial variability of 

bulk density in reservoir bottom sediment. For example, data 

sets are needed to determine the variability of bulk density 

over relatively short distances (for example, less than 

0.5 km), between in-channel and out-of-channel locations, 

and with proximity to shore. Once assembled, such data sets 

can be used to better define the variability within and among 

approaches used to estimate total bottom-sediment mass for 

reservoirs. Moreover, such data sets may be used to provide 

guidance for determining the optimal number and location of 

coring sites needed to provide the representative bulk-density 

information required for the estimation of total bottom-sediment mass. 

As evidenced in figures 2 through 5, bulk density varied 

substantially both upstream to downstream and laterally within 

the reservoirs and sometimes over relatively short distances. 

The expected upstream-to-downstream decrease in bulk 

density was generally evident for the in-channel coring sites 

in all four reservoirs and for the out-of-channel coring sites in 

Perry and Tuttle Creek Lakes. In these cases, the bulk density 

determined for the upstream-most coring site was always 

10 A Comparison of Approaches for Estimating Bottom-Sediment Mass in Large Reservoirs
substantially larger than the bulk density determined for the 

downstream-most coring site. However, the bulk densities 

determined for the intermediate coring sites did not necessarily grade uniformly from one endmember to the other. For 

Cheney Reservoir and Hillsdale Lake, a pattern of bulk-density values for the out-of-channel coring sites was not discernible. In the case of Cheney Reservoir, the absence of a discernible pattern for bulk density may be caused, in part, by limited 

out-of-channel sampling. The deviation of bulk density from a 

uniform upstream-to-downstream gradation within reservoirs 

can be attributed to several factors including tributary and 

shore inputs, and compaction. Results for the four approaches 

to estimating total bottom-sediment mass will vary in response 

to the variability of bulk density within the reservoir bottom 

sediment and the number and location of coring sites used for 

bulk-density determinations. 

The absence of a discernible upstream-to-downstream 

gradation in the out-of-channel bulk-density values for at least 

one of the reservoirs (Hillsdale Lake), combined with the 

finding that the variability of the representative bulk densities 

for the out-of-channel coring sites was larger than the variability for the in-channel coring sites for three of four reservoirs 

(Perry Lake being the exception), indicated the possibility that 

the out-of-channel areas may be more important as a cause 

of variability in sediment-mass estimation. More spatially 

detailed bulk-density information is needed to confirm this 

observation. The implication is that out-of-channel areas of 

reservoirs may require more extensive sampling to provide 

representative bulk-density information. 

Finally, on the basis of an analysis of the deviation from 

the mean, it was determined that the vertical (within-core) 

variability in bulk density typically was less than the horizontal variability in representative bulk density among the 

coring sites. This finding is consistent with that of Foster and 

Charlesworth (1994) who found that the spatial variability of 

bulk density for surface sediment was generally similar to, 

or greater than, the vertical variability for four reservoirs in 

England. 

Summary and Conclusions

In this study, a comparison of four computational 

approaches (partition, mean, midpoint, strategic) for using 

bulk-density information to estimate total bottom-sediment 

mass in four large reservoirs indicated that the differences 

among the approaches were not statistically significant. However, the lack of statistical significance may be a result of the 

small sample size. Percentage-wise, some of the differences 

were substantial.

Table 3. Coring-site combinations, mean bulk densities, and computed sediment masses using the midpoint approach for Tuttle 

Creek Lake, northeastern Kansas.

[kg/m3, kilograms per cubic meter; kg, kilograms]

Combination Coring sites used 

(fig. 5)

Mean bulk 

density1

(kg/m3)

Computed 

sediment mass 

(millions of kg)

Percentage

difference from 

partition-based 

estimate

Original TIC–5, TOC–5, TOC–5A 554.8 97,100 -27.0

Option A TIC–4, TOC–4, TOC–4A 488.6 85,500 -35.7

Option B TIC–5, TOC–4, TOC–4A 534.3 93,500 -29.7

Option C TIC–4, TOC–5, TOC–5A 509.1 89,100 -33.0

Option D TIC–5, TOC–5 607.2 106,000 -20.3

Option E TIC–5, TOC–5A 502.3 87,900 -33.9

Option F TIC–4, TOC–4 506.2 88,600 -33.4

Option G TIC–4, TOC–4A 471.0 82,400 -38.0

Option H TIC–5, TOC–4 551.9 96,600 -27.4

Option I TIC–5, TOC–4A 516.7 90,400 -32.0

Option J TIC–4, TOC–5 561.5 98,300 -26.1

Option K TIC–4, TOC–5A 456.6 79,900 -39.9

1

For the combinations having two out-of-channel coring sites (that is, Original, Option A, Option B, and Option C), the two sites were averaged to 

provide a single out-of-channel bulk-density value. Then, the out-of-channel value and the in-channel value were averaged to provide the mean bulk 

density used in the computation of the sediment mass.

Comparison of Sediment Mass Estimates 11
Overall, the strategic approach provided total bottomsediment mass estimates that were the most similar to the 

partition approach. This result, which was unexpected given 

the limited amount of bulk-density information used, indicated 

that the strategic approach may merit further investigation as a 

less time consuming and less costly alternative to the partition approach. Potentially, the strategic approach may offer a 

viable alternative when the partition approach is not possible 

or feasible. 

Acknowledgment

This study was made possible in part by data collected 

through cooperative studies between the U.S. Geological 

Survey and the Johnson County Environmental Department, 

the Johnson County Unified Wastewater Districts, the Kansas 

Department of Health and Environment, the Kansas Water 

Office, the U.S. Environmental Protection Agency, and the 

city of Wichita, Kansas. 

References Cited

Annandale, G.W., 1987, Reservoir sedimentation: New York, 

Elsevier, 221 p. 

Butcher, D.P., Labadz, J.C., Potter, A.W.R., and White, P., 

1993, Reservoir sedimentation rates in the Southern Pennine 

Region, UK, chap. 6, in McManus, J., and Duck, R.W., eds., 

Geomorphology and sedimentology of lakes and reservoirs: 

New York, John Wiley and Sons, p. 73–92. 

Dendy, F.E., and Champion, W.A., 1978, Sediment deposition 

in U.S. reservoirs—summary of data reported through 1975: 

U.S. Department of Agriculture Miscellaneous Publication 

No. 1362, 82 p. 

Foster, I.D.L., and Charlesworth, S.M., 1994, Variability in 

the physical, chemical and magnetic properties of reservoir 

sediments—implications for sediment source tracing, in

Olive, L.J., Loughran, R.J., and Kesby, J.A., eds., Variability in stream erosion and sediment transport: International 

Association of Hydrological Sciences (IAHS) Publication 

No. 224, p. 153–160. 

12  A Comparison of Approaches for Estimating Bottom-Sediment Mass in Large Reservoirs

Table 4. Coring-site combinations, mean bulk densities, and computed sediment masses using the strategic approach for 

Tuttle Creek Lake, northeastern Kansas.

[kg/m3, kilograms per cubic meter; kg, kilograms]

Combination Coring sites used 

(fig. 5)

Mean bulk 

density1

(kg/m3)

Computed 

sediment mass 

(millions of kg)

Percentage 

difference from 

partition-based 

estimate

Original TIC–1, TOC–1, TOC–1A, TIC–16, TOC–13 768.4 134,000 +0.8

Option A TIC–1, TOC–1, TOC–1A, TIC–16, TOC–7 651.0 114,000 -14.3

Option B TIC–1, TOC–1, TOC–1A, TIC–16, TOC–7A 661.1 116,000 -12.8

Option C TIC–1, TOC–1, TOC–1A, TIC–13, TOC–13 744.8 130,000 -2.3

Option D TIC–1, TOC–1, TOC–1A, TIC–13, TOC–7 627.4 110,000 -17.3

Option E TIC–1, TOC–1, TOC–1A, TIC–13, TOC–7A 637.4 112,000 -15.8

Option F TIC–2, TOC–2, TOC–2A, TIC–16, TOC–13 774.4 136,000 +2.3

Option G TIC–2, TOC–2, TOC–2A, TIC–16, TOC–7 657.0 115,000 -13.5

Option H TIC–2, TOC–2, TOC–2A, TIC–16, TOC–7A 667.1 117,000 -12.0

Option I TIC–2, TOC–2, TOC–2A, TIC–13, TOC–13 750.8 131,000 -1.5

Option J TIC–2, TOC–2, TOC–2A, TIC–13, TOC–7 633.4 111,000 -16.5

Option K TIC–2, TOC–2, TOC–2A, TIC–13, TOC–7A 643.4 113,000 -15.0

1

All combinations used two out-of-channel coring sites at the downstream location. The two sites were averaged to provide a single out-of-channel bulk-density value. The resultant out-of-channel value then was averaged with the other coring sites to provide the mean bulk density used in the 

computation of the sediment mass.
Foster, I.D.L., Dearing, J.A., Grew, R., and Orend, K., 1990, 

The sedimentary data base—an appraisal of lake and reservoir sediment based studies of sediment yield, in Walling, 

D.E., Yair, A., and Berkowicz, S., eds., Erosion, transport 

and deposition processes: International Association of 

Hydrological Sciences (IAHS) Publication No. 189, 

p. 19–43. 

Gordon, N.D., McMahon, T.A., and Finlayson, B.L., 1992, 

Stream hydrology—an introduction for ecologists: New 

York, John Wiley and Sons, 526 p. 

Guy, H.P., 1969, Laboratory theory and methods for sediment 

analysis: U.S. Geological Survey Techniques of WaterResources Investigations, book 5, chap. C1, 58 p. 

Heinemann, H.G., 1962, Volume-weight of reservoir sediment: Journal of the Hydraulics Division, Proceedings of 

the American Society of Civil Engineers, v. 95, p. 181–197. 

Juracek, K.E., 1997, Analysis of bottom sediment to estimate 

nonpoint-source phosphorus loads for 1981–96 in Hillsdale 

Lake, northeast Kansas: U.S. Geological Survey WaterResources Investigations Report 97–4235, 55 p. 

Juracek, K.E., 1998, Analysis of lake-bottom sediment to estimate historical nonpoint-source phosphorus loads: Journal 

of the American Water Resources Association, v. 34, 

p. 1449–1463. 

Juracek, K.E., 2003, Sediment deposition and occurrence of 

selected nutrients, other chemical constituents, and diatoms 

in bottom sediment, Perry Lake, northeast Kansas, 1969–

2001: U.S. Geological Survey Water-Resources Investigations Report 03–4025, 56 p. 

Juracek, K.E., and Mau, D.P., 2002, Sediment deposition and 

occurrence of selected nutrients and other chemical constituents in bottom sediment, Tuttle Creek Lake, northeast 

Kansas, 1962–99: U.S. Geological Survey Water-Resources 

Investigations Report 02–4048, 73 p. 

Juracek, K.E., and Stiles, T.C., 2003, The role of reservoir 

sediment studies in the TMDL process in Kansas, in

Proceedings, TMDL 2003 Specialty Conference, November16–18, 2003, Chicago, Illinois: Alexandria, Virginia, 

Water Environment Federation, 12 p., CD-ROM.

Lara, J.M., and Pemberton, E.L., 1965, Initial unit weight of 

deposited sediments, in Proceedings, Federal Interagency 

Sedimentation Conference, 1963: U.S. Department of Agriculture Miscellaneous Publication 970, p. 818–845. 

Mau, D.P., 2001, Sediment deposition and trends and transport 

of phosphorus and other chemical constituents, Cheney 

Reservoir watershed, south-central Kansas: U.S. Geological 

Survey Water-Resources Investigations Report 01–4085, 

40 p. 

Morris, G.L., and Fan, Jiahua, 1998, Reservoir sedimentation 

handbook: New York, McGraw-Hill, various pagination. 

Pope, L.M., 1998, Watershed trend analysis and water-quality assessment using bottom-sediment cores from Cheney 

Reservoir, south-central Kansas: U.S. Geological Survey 

Water-Resources Investigations Report 98–4227, 24 p. 

Rausch, D.L., and Heinemann, H.G., 1984, Measurement of 

reservoir sedimentation, chap. 7, in Hadley, R.F., and Walling, D.E., eds., Erosion and sediment yield—some methods 

of measurement and modeling: Norwich, United Kingdom, 

GeoBooks, p. 179–200. 

Siegel, Sidney, and Castellan, N.J., 1988, Nonparametric statistics for the behavioral sciences: New York, McGraw-Hill, 

399 p. 

Umbanhowar, C.E., Jr., Engstrom, D.R., and Bergman, E.C., 

2003, Reconstructing eutrophication and phosphorus loading for Lake Volney, Minnesota—combining lake sediments 

and land-use history to establish ‘natural’ baselines for 

management and restoration: Lake and Reservoir Management, v. 19, p. 364–372. 

Vanoni, V.A., 1975, Sedimentation engineering: New York, 

American Society of Civil Engineers, 745 p. 

Verstraeten, Gert, and Poesen, Jean, 2001, Variability of dry 

sediment bulk density between and within retention ponds 

and its impact on the calculation of sediment yields: Earth 

Surface Processes and Landforms, v. 26, p. 375–394. 

White, P., Butcher, D.P., and Labadz, J.C., 1997, Reservoir 

sedimentation and catchment sediment yield in the Strines 

Catchment, U.K.: Physics and Chemistry of the Earth, v. 22, 

p. 321–328. 

References Cited 13
Prepared by Lawrence Publishing Service Center.

Edited by Lanna Combs.

Graphics by Jeff Hartley.

Layout by Lyn Osburn.

For more information concerning the research 

described in this report, contact: 

U.S. Geological Survey

4821 Quail Crest Place 

Lawrence, KS 66049

(785) 842-9909 

http://ks.water.usgs.gov/
Printed on recycled paper

Juracek—A Comparison of Approaches for Estimating Bottom-Sediment Mass in Large Reservoirs—Scientific Investigations Report 2006–5168

**TOC-1

(520.7)

**TOC-1A

(445.4)

EXPLANATION

*

**

Bulk-density values from Juracek and Mau (2002)

00 1 2 3 4 KILOMETERS1 2 3 4 MILES

96o46' 44' 42' 40' 38' 36' 34' 96o32'

39o34'

32'

30'

28'

26'

24'

22'

20'

18'

39o16'

5

6

7

8

9

10

13

14

15

16 17

18

19

20

21

4

3

1

2

Tuttle Creek Lake

Big

Blue

River

Tuttle Creek Dam

**TIC1 (586.3)

TIC2 (608.8)

TIC3 (644.0)

TIC4 (512.6)

*TIC5 (604.0)

TOC-2A

(299.6)

TOC2 (669.6)

TOC3 (370.1)

TOC4 (499.8)

*TOC-5

(610.4)

TOC-3A

(379.7)

TOC-4A

(429.3)

*TOC-5A

(400.5)

TOC-7A

(600.8)

TOC7 (560.7)

**TOC-13

(1030.1)

TIC-13

(879.5)

**TIC-16

(974.0)

TIC9 (927.6)

TOC9 (909.9)

TOC1 (520.7)

TIC1 (586.3) 1

Approximate extent of Tuttle Creek Lake at

 conservation-pool elevation 

 

Bathymetric range line and number

—Establishe

d

 by U.S. Army Corps of Engineers

Pre-reservoir stream or river channel

In-channel sediment-coring site and number—

 Number in parentheses ( ) is mean bulk density, in 

 kilograms per cubic meter

Out-of-channel sediment-coring site and number—

 Number in parentheses ( ) is mean bulk density, in 

 kilograms per cubic meter

Coring site used for midpoint approach

Coring site used for strategic approach