1 USDA Forest Service Res. Note PSW-RN-414-WEB. 1993.

E xperienced hydrologists and geomorphologists can estimate the relative mobility of a streambed by

looking at indicators of bedload transport,

such as the freshness of bed-surface material. Another such indicator is the amount

of fine sediment in pools. Pools in gravelbed streams commonly contain deposits of

fine sediment (mostly sand and gravel) that

overlie a coarser substrate of coarse gravel,

cobbles, or boulders. In such channels, the

fraction of pool volume filled with fine

sediment can be used as an index of the

supply of mobile sediment. This fraction

(V*) is the ratio of fine-sediment volume to

pool water volume plus fine-sediment volume. In a previous paper, we investigated

the relationship of V*w, the weighted mean

value of V* for a reach, to qualitative evaluations of sediment yield in eight tributary

basins of the Trinity River in northwestern

California.1 This study suggested that V*w

could be used to evaluate sediment supply

in gravel-bed channels without directly measuring sediment transport or sediment delivery from hillslopes. In one channel, V*

increased abruptly downstream of a sediment source, suggesting that V* could be

used to identify significant sediment

sources.

We are conducting ongoing research on

the relationship between V*w, sediment

supply, and basin characteristics and are

attempting to link V* to habitat suitability

for aquatic organisms. If this is successful,

V* could be used to simultaneously evaluate sediment supply and its effects on aquatic

ecosystems. These relationships could then

provide a needed link between watershed

condition and fish habitat.

This paper describes a method to measure V* and discusses factors affecting the

accuracy of estimates of V* and V*w.

APPLICATIONS

AND LIMITATIONS

V* can be used to evaluate and monitor

channel condition and to identify and quantify effects of discrete sediment sources.

There are, however, limits to the types of

channels where it can be used, and care

must be taken in interpreting differences in

V* between channels.

The usefulness of V* is limited to channels in which significant volumes of fine

sediment can be deposited in pools. To

date, we have found that V* can be accurately measured and results consistently

interpreted in channels that have:

• a wide range in particle size between

armor layers and fine sediment in pools.

Sediment supply needs to include at least

moderate proportions of sand and fine

gravel. We have found V* to be very low

and insensitive to sediment supply in basins that are formed in basalt or competent,

fine-grained metamorphic or sedimentary

rocks, for example.

• stable banks of densely rooted alluvium, bedrock, or armored colluvium.

• a single thread. In braided channels,

the volume and proportion of fine sediment

can vary widely between anabranches and

thus create wide variations in V*.

• gradients less than about 5 percent. We

Measuring the Fraction of Pool

Volume Filled with Fine Sediment

Sue Hilton Thomas E. Lisle

United States

Department of

Agriculture

Forest Service

Pacific Southwest

Research Station

P.O. Box 245

Berkeley

California 94701

Research Note

PSW–RN-414-WEB

July 1993

Hilton, Sue; Lisle, Thomas E. 1993. Measuring the fraction of pool volume filled

with fine sediment. Res. Note PSW-RN414. Albany, CA: Pacific Southwest Research Station, Forest Service, U.S. Department of Agriculture; 11 p.

The fraction of pool volume filled with fine

sediment (usually fine sand to medium gravel) can

be a useful index of the sediment supply and

substrate habitat of gravel-bed channels. It can be

used to evaluate and monitor channel condition

and to detect and evaluate sediment sources. This

fraction (V*) is the ratio of fine-sediment volume

to pool water volume plus fine-sediment volume.

These volumes are computed for the residual portion of the pool that lies below the elevation of the

downstream riffle crest. Fine-sediment thickness

is measured by driving a graduated metal probe

into a fine-grained deposit until the underlying

coarser substrate is felt. Water depth and finesediment thickness are measured across transects,

and volumes are computed by summing products

of cross-sectional areas and distances between

transects. Replicate measurements of V* were

made in 20 pools, and the variability of V*w, the

weighted mean value of V* for a reach, was

analyzed in 12 reaches. The largest source of

variability in V* was the measurement of fine

sediment volume. Topographic irregularities in

pools and on riffle crests and effects of variation in

discharge on measurement of riffle crest elevation

also affected V*. Ten to 20 pools are needed to

estimate V*w in a reach, depending on acceptable

error and variability between pools.

Retrieval Terms: fine sediment, pools, monitoring, sedimentation, fish habitat
2 USDA Forest Service Res. Note PSW-RN-414-WEB. 1993.

are uncertain about how V* varies inherently between step pools, which are associated with steep slopes, and bar pools, which

are commonly associated with gentle slopes.

Care should be taken in interpreting

differences in V*w between different stream

channels. Knowledge of variations of V*

between streams with different geologies

and stream types is needed to interpret

variations in V* with respect to sediment

supply. For example, a value of V*w of

0.15 would be expected to represent high

sediment supplies in basins underlain by

competent metamorphic rocks, but would

be considered low for basins in weathered

granite. V* values can be expected to be

associated with substrate conditions important to aquatic organisms, such as

embeddedness or infiltration, but specific

responses will depend on the community

present, which will in turn depend on the

natural range and variability of substrate

conditions in the channel.

These problems are not encountered

when monitoring changes in V*w over time

or in using V* to evaluate sediment sources.

Volumes of sediment from landslides, for

example, can be easily measured from air

photos or in the field, but evaluating the

intensity, extent, and duration of their impacts on channels has been problematical.

V*w measurements upstream and downstream of such sources can potentially be

used to evaluate and monitor their mobile

sediment inputs.

Measuring V* in large rivers has practical limitations, although pools can be

sounded and fine sediments probed from

tethered rafts. We have measured V* in

pools as wide as 30 m and 2000 m3 in

volume. Small pools create no logistical

problems, but measurement precision may

need to be increased in very small pools (<1

m3 in volume). We have measured V* in

second- through fifth-order channels.

METHODS

V*w is estimated in a section of a stream

channel by measuring the water and fine

sediment volume in the residual pool in all

of the pools in a study reach and then

calculating the weighted average value of

V* for the reach.

Time and Equipment

Two or three experienced people can

measure a wadable pool in half an hour to

an hour, but accurate measurement of large

pools requires a raft, which takes more

people and more time. The minimum equipment required is two tapes, chaining pins,

and a graduated rod. The rod must be long

enough to measure water depth plus fines

depth in the deepest part of the pool. A rod

made of one-half inch diameter stainless

steel probes fine sediment deposits well

without bending. Systematic sampling also

requires a calculator with a random number

generator or a random number table. We

use a palmtop computer with a spreadsheet

to choose transect locations, enter the data,

and calculate V*. This reduces data processing time and provides an opportunity to

catch and correct errors in the field.

Choosing a Study Reach and

Identifying Pools

The general location of a study reach is

set by the purpose of the study. Reaches

may be located upstream and downstream

of a sediment source or downstream of a

watershed rehabilitation project, for example. The specific location is chosen to

avoid complicating factors which might

affect V* within the reach, such as intrareach sediment inputs, braided sections, or

tributaries. A reach should include enough

pools to provide an accurate estimate of

V*w for the stream segment. The number of

pools needed depends on the variability of

V* between pools and on the desired accuracy of the estimate of V*w. In channels

where V* does not vary greatly between

pools, 10 to 15 pools are often sufficient

(see Discussion).

After a study reach has been selected,

the length of the reach is surveyed to identify pools to measure and determine what

constitutes fine sediment in this channel.

For our purposes, a measurable pool is an

area of channel which (1) has a significant

residual depth2,3 (the deepest part of the

pool must be at least twice as deep as the

water flowing out of the pool at the downstream end); (2) has an essentially flat water surface during low flow (water surface

slope <0.05 percent); and (3) includes most

of the channel (it must include the thalweg

and occupy at least half of the width of the

low-flow channel). The specific criteria

can vary, as long as they are repeatable and

consistent across all reaches compared. We

allow for possible variation in depositional

patterns between different types of pools by

measuring all pools in a reach, regardless of

origin, but pool type could be a selection

factor if enough pools are available. One

should avoid measuring potential pools with

unclear boundaries, such as long glides

containing small deep areas or small deep

areas in rocky channels, because it is difficult to measure such pools consistently.

What constitutes fine sediment in a channel is determined by the distribution of

particle sizes and patterns of fine-sediment

deposition in the channel. Fine sediment is

defined as the material forming the matrix

among the gravel framework of the bed

material.4 This material is commonly winnowed from areas of high shear stress, such

as riffles, and deposited in pools.1 Fine

sediment in a reach is defined as material

which (1) is distinctly finer than the bed

surface (median particle size (D50) of fine

sediment approximately one tenth or less

of the D50 of the bed surface) and (2) can be

distinguished from underlying coarser sediment by probing with the rod. Deposits of

fine sediment that are armored (covered by

a layer of larger sediment) or densely occupied by roots of riparian plants are not

considered available for transport and are

not measured. In most channels, fine sediment is defined for working purposes as

deposits with a D50 of 11 mm or less, but

deposits with a D50 of 16 mm (medium

gravel) can be measured in channels with

large surface particle sizes and high transport energy.

Measuring Riffle-Crest Depth and

Defining Pool Boundaries

Calculation of V* requires measuring

the volume of water and fine sediment in the

“residual” pool. The residual pool is defined as the portion of the pool that is deeper

than the riffle crest forming the downstream

lip of the pool, that is, the pool that would

remain if there were negligible surface flow

(figure 1A).3 The riffle crest is a high point

on a longitudinal profile and usually the

shallowest place at the downstream end of a

pool. During low flows, when the water

surface in pools is nearly flat, the riffle crest

can be identified by the beginning of the

riffled, more sloping water surface.
3 USDA Forest Service Res. Note PSW-RN-414-WEB. 1993.

the upstream ends of many pools, the boundary is where a plane at the elevation of the

riffle crest would intersect the streambed

with fine sediment removed (see figure

1A). In a few situations, we exclude sections of stream channel which would be

included in this definition. For example, a

long glide extending into a pool may be

excluded, even if the glide is deeper than

the riffle-crest depth. Similarly, if the upstream end of the pool is a riffle that is

deeper than the riffle crest, the upstream

boundary of the pool is defined as where the

nearly horizontal water surface would begin at a minimum flow.

Measuring Water and Fine Sediment

Volume

Volumes of water and fine sediment in

the residual pool are calculated from measurements of water and fine-sediment depth

along a series of cross sections in the pool.

The basic technique is essentially a systematic sample, with cross sections spaced

evenly along the length of the pool. Zeroarea cross sections are assumed at the ends

of the pool. Depth-measurement points are

spaced evenly across each cross section and

at either end. The locations of both the cross

sections and the depth-measurement points

are determined from a random start. The

basic system is modified in some cases to

improve the accuracy of the estimate. The

basic systematic sample will be described

first, followed by examples of modifications for specific situations.

Basic systematic sample (figure 2).

1. Stretch a tape along the length of the

pool, from the upstream end to the furthest

point on the riffle crest or along the longest

dimension of the pool. This tape must be

straight, since bends will distort the volume

calculations. If the pool is so irregular that

a bend cannot be avoided, divide the pool

into sections and measure each separately

(figure 3).

2. Draw a sketch map of the pool, showing locations of the upstream end of the

pool, riffle crest, areas of fine-sediment

deposition, and major features of the pool,

such as logs and outcrops.

3. Decide on the number of cross sections and the distance between depth-measurement points. The appropriate sampling

intensity depends on the complexity of the

pool and on the accuracy required. We take

from 4 to 10 cross sections in each pool and

The first step in calculating V* is to

measure the riffle-crest depth and define

the pool boundaries. Water depth at the

riffle crest is measured by taking the median of several depth measurements taken

across the thalweg at the riffle crest (figure

2). Because the riffle-crest depth defines

the residual pool, it is important to measure

it consistently. Near the riffle crest, the

water surface may break in several places,

discontinuously, or gradually over a distance. The riffle crest is identified as the

shallowest continuous line (usually not

straight) across the channel close to where

the water surface becomes continuously

riffled. Depths are measured across the

deepest part of the flow at 5-20 evenly

spaced locations along this line, depending

on the width and irregularity of the measured section. To consistently measure the

same section of the riffle crest, measurements are taken where we expect water to

flow at minimum discharge. Thus the measured section occupies a smaller proportion

of the total wetted width at high flows than

at low flows. Defining and measuring the

riffle crest can be confusing. Survey teams

should discuss measurement locations and

periodically take duplicate measurements

to maintain consistency.

Water depths and fine-sediment depths

are measured within the “scoured residual

pool,” which is the residual pool that would

result if all of the fine sediment in the pool

were removed. If the water surface over the

pool is essentially horizontal, the boundary

of the scoured residual pool is where water

depth plus fine-sediment depth equals rifflecrest depth (figure 1B). Where the water

surface is not completely horizontal, as at

{

{

Graduated Rod

Buried Armor


Layer

Water Depth

Water Surface

Riffle Crest Depth

Residual Pool

Scoured Residual Pool

B. CROSS SECTION

Fine Sed.


Depth

Riffle Crest Depth

A. LONGITUDINAL PROFILE

Water Surface

Riffle Crest

Residual Pool

Figure 1—(A) Longitudinal profile of a pool, showing the riffle crest and the area included in the

residual pool volume. (B) Cross section of a pool, showing measurement of water and fine sediment

depth and volume of water and fine sediment in the scoured residual pool.
4 USDA Forest Service Res. Note PSW-RN-414-WEB. 1993.

Figure 2—Pool #21, Horse Linto Creek, showing location of the longitudinal tape, transects, measurement points for water and fine sediment depth,

the riffle crest, and measurement points for riffle crest depth.

basic sample can be modified in a variety of

ways, from decreasing the distance between

cross sections or depth-measurement points

at some locations to dropping the systematic

sample entirely and deliberately choosing

cross-section or depth-measurement

locations or both. Because deliberately

chosen locations introduce potential bias,

locations are chosen only when it will clearly

improve the accuracy of the estimate. These

are some common situations in which

modifications can improve accuracy:

• In most pools, fines occupy less than

one-half of the substrate area. To measure

fines volume more accurately, the distance

between depth measurement points is usually reduced over fines deposits, and points

are added at their edges. Also, cross sections are often added to measure an area of

fines more intensely or to define its upstream or downstream limits.

with the rod until a change in resistance is

felt as it strikes coarser material (figure 1B).

A small sledge may be useful for probing

deep deposits. The cross section begins at

the edge of the scoured residual pool, where

water depth plus fines depth becomes greater

than riffle-crest depth (figure 1B). Record

total water depth and fines depth at both

edges of the pool, and at regular intervals

across the pool as determined in step 4. If a

fines deposit deep enough to be included in

the scoured pool extends above the water

surface, record height above the water surface as a negative water depth.

Modifications. The advantage of the

basic systematic sample is that it is simple,

repeatable, and statistically unbiased. The

main disadvantage is that it does not use

information about the pool (such as the

location of fines deposits) that is available

to the people taking the measurements. The

set the distance between depth locations to

provide 7 to 16 points across the widest

cross section.

4. Determine the locations of cross sections and depth-measurement points. Divide the total length of the pool by the

number of cross sections to find the distance between sections. Choose a random

number between zero and this distance to

locate the first cross section, and add the

chosen spacing to locate the remaining sections. Choose random numbers between

zero and the distance between depth-measurement points to locate the first point in

from the edge of each cross section.

5. Run a tape perpendicular to the lengthwise tape at each cross-section location.

Measure water depth and the thickness of

any fine sediment present at each measurement point with a graduated rod. Finesediment depth is determined by probing
5 USDA Forest Service Res. Note PSW-RN-414-WEB. 1993.

Calculating V* and V*w

V* is calculated as follows:

1. Calculate the residual cross-sectional

area (the area deeper than the depth at

the riffle crest) of fines and water in

each cross section.

2. Set a zero-area cross section at the

upstream and downstream ends of the

pool.

3. Calculate the average residual crosssectional area of fines and water

between each pair of adjacent cross

sections.

4. Multiply the average cross-sectional

area for each pair by the distance

between them.

5. Add the volumes of the water and fine

sediment in all the segments to find

the totals for the pool.

6. Calculate V* for the pool:

V* = residual fines volume

scoured residual pool volume

where scoured residual pool volume = residual

fines volume + residual water volume.

A sample data set with detailed instructions

and examples of the calculations is shown

in appendix A. Worksheets are available to

do these calculations in Lotus 1-2-3 and in

SQL*Calc.

V*w is the average of the V*’s for all the

pools in a reach weighted by the scoured

pool volume of each pool. Because V* is

the ratio of fines volume to scoured pool

volume, the weighted mean for the reach

can be simply calculated as:

Vw

* = Σ

Σ

 (residual fines volume)

 (scoured residual pool volume)

The variance of the estimated residual

water volume, fines volume, and V* for

individual pools may be assessed by

remeasuring a sample of the pools and treating each measurement as a random sample of

all possible measurements of that pool. The

variability of V*w for the reach can also be

estimated, but since V* is a ratio of two

estimates (fines volume and water volume),

calculating the variability of the weighted

Figure 3—Measuring a pool with a bend. The longitudinal tape is strung in two straight segments, transects are located systematically

along the tape, and a zero-area cross section is recorded at the location of the bend in the tape.

• If a pool has a deep, complex segment

and another segment that is fairly long,

simple, and shallow, the pool may be divided into two segments and the more complex segment sampled more intensely. A

cross section at the boundary between segments makes the volume estimates for each

more accurate.

• Cross sections or depth-measurement

points or both may be added to adjust for

irregularities in pool shape, such as large

rocks, holes, or shoals.

• If most or all of the fines in a pool are

in a few discrete deposits, their volume can

be measured separately. The pool volume

is measured using the basic systematic technique, as though fines in the discrete deposits were absent (fines depth measurements

in the deposits are recorded as zero). The

residual-pool volume of fine sediment in

the deposits is then measured more intensively, and the volumes of the discrete

deposits are added to the fine sediment

volume measured in the rest of the pool.

Longitudinal Tape

Transect

Depth Measurement Point

Boundary between Sections
6 USDA Forest Service Res. Note PSW-RN-414-WEB. 1993.

mean is complex. A formula for estimating

the variability of V*w is in appendix B, along

with a process for testing for significant

differences in V*w between reaches.

ACCURACY OF THE ESTIMATES

The accuracy of the estimated value of

V*w for a reach depends on the accuracy of

the estimates of V* for each pool and on the

variability of V* between pools in the reach.

To find out how precise our individual pool

volume measurements were, we measured

variability due to sampling and measurement

error by repeating measurements of several

pools. We also investigated how discharge at

the time of measurement affected the measured surface elevation of the residual pool

and consequent values of V*. To find out

how variability between pools affected V*w,

we studied the relationship between the estimated value of V*w and the variability of the

estimate of V*w in 12 reaches, eight in the

Trinity River watershed and four others in

northern California.

Individual Pool Estimates

Nine pools in Trinity River tributaries

were measured three times each in 1990,

and six of these were remeasured two or

three times each in 1991. For these duplicate measurements, we kept riffle-crest

depth and pool length constant and varied

the starting point for the systematic sample.

The standard deviation of V* ranged from

0.00 to 0.08, and increased slightly with

V*. Coefficients of variation ranged from 0

to 170 percent, with the higher values concentrated at very low values of V* (figure

4). The coefficient of variation of V* in a

pool was highly correlated to that of the fine

sediment volume in that pool (r = 0.995).

Figure 4 also includes the coefficients of

variation for five pools in the Salmon River,

California, which were measured three times

each in 1991. These measurements were

taken a week apart, by different people, and

riffle-crest depth and pool length varied

somewhat between measurements. The

standard deviations and coefficients of

variation of those pools were similar to

those of the other replicate measurements.

Effect of Discharge on V*

Because we measure only within residual

pools, the measured water and fine-sediment

volumes (and thus V*) should not vary with

discharge. If the riffle crest is always measured in the same place, the riffle-crest depth

will increase exactly as much as the water

surface of the pool rises, the elevation of the

surface of the residual pool (riffle-crest elevation) will be constant, and the same volume will be measured at any discharge. However, because locating the riffle crest and

selecting the section to measure are somewhat subjective, there is some potential for

error. Systematic errors could occur if the

measured riffle-crest elevation is consistently

affected by discharge and if V* is consistently affected by riffle-crest elevation. To

determine whether discharge affects rifflecrest elevation, we measured riffle-crest elevation (water-surface elevation minus the

measured riffle-crest depth) at three pools in

Jacoby Creek at four different flow levels.

Elevations were measured at extremely low

base flows, normal summer base flows, and

flows significantly above summer base flows.

To find out whether riffle-crest elevation

affects V*, V*’s calculated at different rifflecrest depths were compared for sample pools

from five creeks in northern California.

Measured riffle-crest elevations in Jacoby

Creek tended to be higher at low flows than

at high flows, possibly because the width of

the minimum flow channel was underestimated at high flows. Riffle-crest elevations

did change less than water-surface elevations, however. Maximum changes in watersurface elevation ranged from 0.10 to 0.20 m,

whereas changes in riffle-crest elevation

ranged from 0.01 to 0.07 m. Maximum

changes in residual elevation were equivalent to 10 percent, 25 percent, and 70 percent

of the riffle-crest depth of the respective

pools at moderately low flows.

To evaluate the effect of an error of this

magnitude in riffle-crest elevation on V*,

we calculated V* using a riffle-crest depth

equivalent to 150 percent of the original

value (measured at moderately low flows)

in 19 pools. Original values of V* ranged

from 0.01 to 0.62. The deeper riffle-crest

depths resulted in smaller residual pools,

which had higher V* values in 18 of the 19

cases. The mean percent change in V* was

13 percent (16 percent if the negative change

was omitted), which corresponded to a mean

absolute change in V* of 0.05.

Variability in V*w

We calculated the standard error of the

estimate of V*w for all of the reaches we

measured using the formula in appendix B.

We then modified the formula to predict the

number of samples (pools) required to

Figure 4—Variability of the estimate of V*, from multiple measurements of V* on pools in Trinity River

tributaries in 1990 and 1991 and in the South Fork Salmon River in 1991. The coefficient of variation

is the percentage ratio of the standard error of the mean to the mean value of V* for each set of

measurements.

200

160

120

80

40

0

0 0.1 0.2 0.3 0.4 0.5 0.6

Coefficient of Variation of V*, percent

Mean V* of Pool

Trinity Basin '90

Trinity Basin '91

Salmon River
7 USDA Forest Service Res. Note PSW-RN-414-WEB. 1993.

would probably have been enough in most

reaches. The calculated sample size (figure

5) is not necessarily the number of pools

that should be measured in each reach,

since the percent error in V*w needed to

distinguish between reaches will depend on

both the value of V*w (a 20 percent error is

a large range of V*w values when V*w is

high and a small range when V*w is small)

and on the closeness of the values being

compared. The sample size calculation does,

however, indicate the relative sampling intensity required to be able to measure reaches

with high standard errors at the same precision as reaches with lower variability between pools. We recommend evaluating

the irregularity of the pools and the variation in V* before and during data collection

in a reach. If all of the pools in a reach have

similar values of V*, then differences between the estimates of V* caused by measurement error could have a significant

effect on the variance of the estimate of

V*w, and V*w can be best estimated by

measuring a few (6-10) pools accurately.

For most reaches we recommend measuring 10-15 pools, and if the value of V*

varies widely between pools, the best strategy might be to measure as many pools as

possible (20 or more), perhaps with less

sampling intensity on each. If V* is highly

variable but the number of pools available

the potential to bias V*w. We recommend

measuring at moderately low flows. Rifflecrest depths can be difficult to measure

accurately at very low flows when the pattern of the flow is affected by surface rocks.

At moderately high flows the water surface

over a pool is likely to slope appreciably

and affect pool volume measurements. For

monitoring over time, comparisons will be

more accurate if V*w is measured at a

consistent stage or discharge. Similarly,

comparisons between reaches will be more

reliable if all reaches are measured at nearly

the same relative flow. If this is not possible, allowance should be made for the

possibility that values of V*w measured at

high base flow could be elevated relative to

those measured at low flow.

Our estimates of the variability of V*w

include the effects of measurement errors

in V* but do not include any possible bias

due to variations in discharge, since all

pools in a reach were measured at approximately the same discharge. The desired

standard error of V*w depends on the precision required to detect changes in a reach,

deviations from a reference value, or differences between reaches. We found that the

standard errors from measuring 10-20 pools

per reach enabled us to distinguish fairly

well between reaches, and the sample size

calculations indicated that fewer pools

achieve a standard error of 20 percent of

V*w for each reach. The standard errors of

our reaches, each of which included 10 to

20 pools, ranged from 0.01 to 0.06 and

averaged 17 percent of the value of V*w.

The calculated sample size necessary to

obtain a 20 percent error in V*w ranged

from 4 to 26 pools and generally decreased

as V*w increased. Exceptions were reaches

in Grouse Creek, which had extremely irregular pools due to the presence of very

large boulders, and in North Fork Caspar

Creek, which had irregular pools caused by

large woody debris. These two reaches had

high standard errors and required higher

sample sizes.

DISCUSSION

The main factor affecting the variability

of the estimate of V* for a pool seems to be

the amount of fines in the pool. In pools

with moderate to high values of V* (V*

>0.10), most (80 percent) of the standard

deviations were less than 20 percent of the

mean V* for the pool. In pools with lower

V* values, the standard deviations ranged

up to 170 percent of V*. Although it is not

practical to expect the same percent errors

in these pools as in those with higher V*

values (because a small percent of a small

number is a very small number), it may still

be important to measure V* in these pools

more precisely than in pools with a higher

proportion of fine sediment. Error in V*

was strongly correlated with error in finesvolume measurement, and fine sediment

does tend to be measured less intensively

when it occupies a small proportion of the

area of the pool. Therefore, we strongly

recommend increasing sampling intensity

in areas of fines or measuring fine-sediment deposits separately, or both, particularly where fine-sediment deposits occupy

a small proportion of the surface area of the

pool or when it is important to measure low

values of V* accurately.

Estimates of the maximum possible error in V* due to variations in discharge (13-

16 percent of V* measured at moderately

low flow) were slightly less than the 18

percent average measurement error for replicate measurements at a constant discharge.

However, measurement error from systematic samples with a random start is random,

whereas errors due to changes in water

depth appear to be consistent and thus have

Figure 5—Predicted sample sizes necessary to limit the error in V*w to 20 percent of the value of V*w

for that reach, calculated for 12 reaches. Our estimate of V*w for each reach is shown with our

standard error of the estimate for that reach, which was based on 10-20 pools.

0

5

20

25

30

w V*

0

5

0 0.1 0.2 0.3 0.4 0.5 0.6

s.e. V* w

V* w
8 USDA Forest Service Res. Note PSW-RN-414-WEB. 1993.

Sample Size

• If all pools in a reach have similar

values of V*, measure 6-10 pools relatively

intensively.

• If V* varies somewhat (V* for all

pools is within 20-30 percent of the mean),

measure 10-15 pools.

• If V* is highly variable (some V*’s of

0.4 or more and others 0.1 or less), measure

as many pools as possible, up to 20 or so.

• If the objective is to monitor changes

over time in a single reach, and if the pools

in the reach are structurally stable, intensive measurement of a few pools (4-5 minimum) may minimize variability and provide additional information about changes

in individual pools.

Fine Sediment Measurements

• When fine-sediment deposits occupy

a third or less of the pool substrate area,

increase measurement intensity in finesediment deposits, either by decreasing

the distance between depth-measurement

points or by making separate measurements

of deposits.

Discharge Levels

• Measure all pools at moderately low

flows.

• If a reach is being monitored over time,

measure at approximately the same discharge each year.

• If reaches are being compared, measure all reaches at approximately the same

relative flow.

in the reach is limited (by sediment sources,

changes in slope, etc.), putting more effort

into sampling each pool will at least reduce

the measurement-error component of the

total variability. If the objective is to monitor a reach over time, and if the structure of

the pools in a reach is fairly stable, accurate

measurements of a few major pools at approximately the same discharge each year

may give the best information.

SUMMARY OF

RECOMMENDATIONS

To minimize variability of the estimates

and eliminate potential bias, we make the

following recommendations:
9 USDA Forest Service Res. Note PSW-RN-414-WEB. 1993.

APPENDIX A

Calculating Residual Pool Water Volume, Fine-Sediment Volume, and V*

Follow these basic steps to compute residual-water and fine-sediment volumes for a pool:

1. Calculate cross-sectional areas of the water and fine sediment in the residual pool at each cross section.

2. Assume a zero-area cross section at the beginning and end of the pool. Calculate water and sediment volumes in cells between

each pair of adjacent cross sections, including the zero-area cross sections at the endpoints.

3. Sum residual-water and fine-sediment volumes for all of the cells to compute total volumes.

The following example of the calculations uses the data from a very small pool. In this example, d = water depth, drc = riffle-crest

depth, and yf = fine-sediment thickness. These are the data:

riffle-crest depth (drc) = 0.10 m; total length of pool = 12.0 m

cross section #1 at 2.4 m

distance (m) 0 0.5 1.5 2.5 2.7

d (m) 0.10 0.50 0.88 0.40 0.10

yf (m) 0 0 0.02 0.02 0

cross section #2 at 6.4 m

distance (m) 0 1 2 3 4 5 6 6.2

d (m) 0.06 0.62 0.74 1.12 0.96 0.70 0.56 0.10

yf (m) 0.04 0.10 0.02 0.01 0 0 0 0

cross section #3 at 10.4 m

distance (m) 0 0.8 1.8 2.8 3.8 4.6

d (m) -0.02 0.08 1.08 1.14 0.94 0.10

yf (m) 0.12 0.10 0.14 0.06 0.04 0

The first step is to compute depths of the water and fines in the residual pool. The residual water depth, dr, is the water depth minus

the riffle crest depth. The residual fine-sediment thickness, yrf, is the thickness of the fine sediment below the riffle crest (figure 1).

If the water depth at any location is less than the riffle crest depth, the fines thickness at that location is reduced by a corresponding

amount. That is, dr = d - drc and IF d < drc, THEN yrf = yf - (drc - d), ELSE yrf = yf. After these calculations, the data look like this:

cross section #1

distance (m) 0 0.5 1.5 2.5 2.7

dr (m) 0 0.40 0.78 0.30 0

yrf (m) 0 0 0.02 0.02 0

cross section #2

distance (m) 0 1 2 3 4 5 6 6.2

dr (m) -0.04 0.52 0.64 1.02 0.86 0.60 0.46 0

yrf (m) 0 0.10 0.02 0.01 0 0 0 0

cross section #3

distance (m) 0 0.8 1.8 2.8 3.8 4.6

dr (m) -0.12 -0.02 0.98 1.04 0.84 0

yrf (m) 0 0.08 0.14 0.06 0.04 0

The next step is to compute cross-sectional areas of water and fine sediment. We start by calculating the width wi, average residual

depth (dr)i, and average fine-sediment thickness (yrf)i of each segment of the cross section (between two adjacent measurement points).

cross section #1

segment number 1 2 3 4

wi (m) 0.5 1 1 0.2

(dr)i (m) 0.20 0.59 0.54 0.15

(yrf)i (m) 0 0.01 0.02 0.01
10 USDA Forest Service Res. Note PSW-RN-414-WEB. 1993.

cross section #2

segment number 1 2 3 4 5 6 7

wi (m) 1 1 1 1 1 1 0.2

(dr)i (m) 0.24 0.58 0.83 0.94 0.73 0.53 0.23

(yrf)i (m) 0.05 0.06 0.015 0.005 0 0 0

cross section #3

segment number 1 2 3 4 5

wi (m) 0.8 1 1 1 0.8

(dr)i (m) -0.07 0.48 1.01 0.94 0.42

(yrf)i (m) 0.04 0.11 0.10 0.05 0.02

In each segment, the cross-sectional area of residual water (ar)i equals (dr)i × wi, and cross-sectional area of fine sediment (arf)i

equals (yrf) i × wi. Negative average water depths are set equal to zero. This gives us:

cross section #1

segment number 1 2 3 4

(ar)i (m2) 0.10 0.59 0.54 0.03

(arf)i (m2) 0 0.01 0.02 0.002

cross section #2

segment number 1 2 3 4 5 6 7

(ar)i (m2) 0.24 0.58 0.83 0.94 0.73 0.53 0.046

(arf)i (m2) 0.05 0.06 0.015 0.005 0 0 0

cross section #3

segment number 1 2 3 4 5

(ar)i (m2) 0 0.48 1.01 0.94 0.336

(arf)i (m2) 0.032 0.11 0.10 0.05 0.016

The total cross-sectional area of residual water, Ar, and fine sediment, Arf, of each cross section equals the sum of the corresponding

segment areas. Cross sections are added to upstream and downstream ends of the pool and given areas of zero.

cross-section # 0 1 2 3 4

location (m downstream) 0 2.4 6.4 10.4 12

Ar (m2) 0 1.26 3.90 2.77 0

Arf (m2) 0 0.032 0.130 0.308 0

To compute the water and fine sediment volume in each cell of the pool, between each two adjacent cross sections, we calculate

the average cross-sectional areas of residual water (Ar)j and fine sediment (Arf)j and the length (lj) for each cell. The cell in the upstream

end of the pool, for example, has an average residual area equal to one-half of the area of the first cross section downstream.

cell number 1 2 3 4

lj (m) 2.4 4.0 4.0 1.6

(Ar)j (m2) 0.63 2.58 3.33 1.38

(Arf)j (m2) 0.016 0.081 0.219 0.154

The volumes for each cell, (Vr)j and (Vrf)j, are the average areas times the length, and the total for the pool is the sum of the volumes

of all the cells.

cell number 1 2 3 4 total

(Vr)j (m3) 1.5 10.3 13.3 2.2 27.4

(Vrf)j (m3) 0.04 0.32 0.88 0.25 1.48

Finally we calculate V* as: 

total fines volume

(total fines + total residual pool volume) = 0 051 .

and we’re done!
11 USDA Forest Service Res. Note PSW-RN-414-WEB. 1993.

APPENDIX B

Estimating the Variance of the Estimate of V*w

The formula we used for estimating the variance of V*w was developed using the Delta method5 for estimating the variance of a

variable that is a function of other variables. The variance of V*w for a reach is calculated as:

Var V n f w f w f w fw w i

i

n

i

i

n

i

i

n

w i

i

n

f i

i

n

i

i

n

* ( ) ≅ + cov ,























 +





























− ( ) ( )



















 = =

−

= = ==

∑ ∑ ∑ ∑ ∑∑

11 1

2

2

1

2

2

1 1

2

4

σ σ

where fi is the fines volume and wi is the residual pool water volume of the ith pool in the reach, and cov (f,w) is the covariance of the

fines volume and the water volume in the reach. The covariance is calculated as:

covv f w, f fw w

n

i i i

n

( ) = ( ) − ( ) −

−

∑ =1

1

The covariance can be obtained from many statistical programs by printing a variance-covariance matrix.

The calculated variance can be used to test for significant differences in V*w between two reaches by assuming that the test statistic,

V V

Var V Var V

w w

w w

1 2

1 2

* *

* *

−

( ) + ( ) ,

has a standard normal distribution.

3Lisle, Thomas E. 1987. Using “residual depths”

to monitor pool depths independently of discharge.

Res. Note PSW-394. Berkeley, CA: Pacific Southwest Forest and Range Experiment Station, Forest

Service, U.S. Department of Agriculture; 4 p.

4Carling, Paul A.; Reader, N.A. 1982. Structure,

composition and bulk properties of upland stream

gravels. Earth Surface Processes and Landforms 7:349-

365.

5Bishop, Yvonne M.M.; Feinberg, S.E.; Holland,

P.W. 1975. Discrete multivariate analysis: theory and

practice. Cambridge, MA: The M.I.T. Press, p. 487.

The Authors:

Sue Hilton and Thomas E. Lisle are hydrologic

technician and hydrologist, respectively, with the

Station’s Hillslope Processes, Fishery Resources, and

Stream Environment Research Work Unit in Arcata

(1700 Bayview Drive, Arcata, CA 95521-6098).

ACKNOWLEDGMENTS

Research leading to the development of this

method was funded by the Trinity River Basin Fish

and Wildlife Restoration Grant Program and the

California Department of Forestry and Fire Protection. Meredith Manning, Lex Rohn, and Scott Bowman spent many hours measuring pools and have

contributed greatly to improving the technique.

END NOTES AND REFERENCES

1Lisle, Thomas E.; Hilton, S. 1992. The volume of

fine sediment in pools: an index of sediment supply in

gravel-bed streams. Water Resources Bulletin 28(2):

371-383.

2Bathurst, James C. 1981. Discussion of “Bar

Resistance of Gravel-bed Streams” by G. Parker and

A.W. Peterson. Journal of the Hydraulics Division,

American Society of Civil Engineers 107(HY10):

1276-1278.

Var Var
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