Radioactive Waste 

Dilution in the 

Clinch River 

Eastern Tennessee

GEOLOGICAL SURVEY PROFESSIONAL PAPER 433-G

Prepared in cooperation with the U.S. 

Atomic Energy Commission and the Oak 

Ridge National Laboratory
Radioactive Waste 

Dilution in the 

Clinch River 

Eastern Tennessee

By P. H. CARRIGAN, JR.

TRANSPORT OF R AD IONUCL I D E S BY STREAMS

GEOLOGICAL SURVEY PROFESSIONAL PAPER 433-G

Prepared in cooperation with the U.S. 

Atomic Energy Commission and the Oak 

Ridge National Laboratory

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1968
UNITED STATES DEPARTMENT OF THE INTERIOR 

STEWART L. UDALL, Secretary

GEOLOGICAL SURVEY 

William T. Pecora, Director

For sale by the Superintendent of Documents, U.S. Government Printing Office 

Washington, D.C. 20402 - Price 25 cents (paper cover)
CONTENTS

Page

Abstract ___________________________ Gl 

Introduction _ _______________________ 1 

Acknowledgments ______________________ 3 

Streamflow characteristics of Whiteoak Creek and the

Clinch River _______________________ 3 

Dilution factor _______________________ 4 

Computation of dilution factors ____________ 4

Selected period of record ______________ 4

Extension of discharge records for 

Whiteoak Creek ___________________ 4

Page

Results of statistical analyses G5 

Minimum, mean, and maximum daily dilution

factors 5 

Probability of equaling or exceeding

specified dilution factors 5

Seasonal variations in dilution _ 6

Frequency studies of minimum dilution factors 7

Effects of diffusion in the Clinch River on dilution __ 7

Conclusions ___ _ ___ _ 8

References ____ ___ _ 9

ILLUSTRATIONS

Page

FIGURE 1. Index map of lower Clinch River basin ______________________________ _ G2

2. Graph showing flows in Whiteoak Creek and Clinch River during 1951, indicating variations in the river's

dilution of radioactive releases ___________________________________ _ 3

3. Graph showing periods of records available for streamflow stations in Whiteoak Creek basin 4

4. Graph showing relationships between monthly discharges for two streamflow stations in Whiteoak Creek

basin __________________________.________________________ ___ 5

5. Graph showing duration curve of daily dilution factors __________ ___ 6

6. Graph showing seasonal variations in dilution factors _________ _ __ 6

7. Graph showing annual minimum dilution factor frequency curves ____ _____ 7

8. Graph showing variation in flow of the Clinch River during a day, due to power releases from Norris

Lake ___________________________.___________________________________ 7

9. Graph showing estimate of variation in concentration of radioactivity in the Clinch Raver at the mouth of

Whiteoak Creek during a 24-hour period ______________________________-____ 8 

10. Graph showing effects of power releases from Norris Lake on the variation in concentration of radioactivity during a 24-hour period __________._______________________ _ 8

III

TRANSPORT OF RADIONUCLIDES BY STREAMS

RADIOACTIVE WASTE DILUTION IN THE CLINCH RIVER, EASTERN TENNESSEE

By P. H. CARRIGAN, JR.

Abstract

A convenient, direct measure of simple volumetric dilution 

of low-level radioactive liquid wastes released from the Oak 

Ridge National Laboratory by waters of the Clinch River 

has been defined. This measure of dilution is called the 

dilution factor. The dilution factor is the ratio of flow in the 

Clinch River to flow of the radioactive liquid waste stream 

(Whiteoak Creek) for concurrent periods of time.

Dilution characteristics of the Clinch River and Whiteoak 

Creek have been described by means of several types of 

statistical analyses: central tendencies, extremes, cumulative 

frequency distribution, seasonal trends, and magnitudeduration-frequency curves of minimum dilution factors.

In order to apply results of these statistical analyses, 

complete and steady mixing of the waters of the Clinch 

River and Whiteoak Creek must be assumed. Exploratory 

diffusion tests indicate that complete mixing in the cross 

section has occurred within a reasonable distance downstream from the mouth of Whiteoak Creek.

Flows in the Clinch River in the vicinity of Whiteoak 

Creek have been affected considerably by releases from 

Morris Lake for peak-demand hydroelectric power. Other 

exploratory tests indicate that the effects of the variation 

in flow of the Clinch River were almost completely evened 

out through processes of turbulent diffusion.

INTRODUCTION

This report describes a contribution of the U.S. 

Geological Survey to the Clinch River Study. The 

Clinch River Study was a multiagency effort to evaluate the past, present, and future use of the Clinch 

River for disposal of low-level radioactive liquid 

waste from the Oak Ridge National Laboratory, 

operated by Union Carbide Corp. for the U.S. 

Atomic Energy Commission, in eastern Tennessee 

(Morton, 1961, 1962, 1963). The agencies that participated in the study are: Oak Ridge National 

Laboratory; Tennessee Game and Fish Commission; 

Tennessee State Department of Public Health, 

Stream Pollution Control Board; Tennessee Valley 

Authority; U.S. Atomic Energy Commission; U.S. 

Geological Survey; and U.S. Public Health Service.

When the study was begun in 1960, the Clinch 

River Study Steering Committee, an advisory group 

composed of representatives of each of the participating agencies (Morton, 1963, p. 1), established 

the following objectives: (1) To determine the fate 

of radioactive materials currently being discharged 

to the Clinch River, (2) to determine and understand 

the mechanisms of dispersion of radionuclides released to the river, (3) to evaluate the direct and 

indirect hazards of current disposal practices in 

the river, (4) to evaluate the overall usefulness of 

the river for radioactive waste disposal purposes, 

and (5) to provide appropriate conclusions regarding long-term monitoring procedures.

Work described in this report was part of a cooperative program with the Health Physics Division, 

Oak Ridge National Laboratory; the Oak Ridge 

Operations Office, U.S. Atomic Energy Commission; 

and the Division of Reactor Development and 

Technology, U.S. Atomic Energy Commission.

The release of low-level radioactive liquid waste 

to the basin of Whiteoak Creek, which drains the 

Oak Ridge National Laboratory (ORNL) area, was 

begun soon after establishment of ORNL in 

1943 for the processing of radioactive materials. 

Radioactive liquids have entered Whiteoak Creek 

as a result of direct releases of processed waste 

water from ORNL, seepage from liquid-waste 

holdup pits, and drainage from solid-waste disposal 

trenches (Browder, 1959).

Throughout most of ORNL's history, the waters 

of Whiteoak Creek have been impounded in Whiteoak Lake by Whiteoak Dam, which is located 0.6 

mile upstream from the mouth of the creek. The 

lake was created as a holdup facility for the radioactive waste carried in the creek water. Radioactive 

waste waters in Whiteoak Creek flow into the Clinch 

River at a point 3.3 miles downstream from the 

ORNL area. The diluted wastes in the Clinch River 

flow into the Tennessee River 20.8 miles downstream 

from the entry of Whiteoak Creek.

The continuous release of radioactivity to the 

Clinch River during nearly 20 years of ORNL operations has provided a unique opportunity for studying

Gl
G2 TRANSPORT OF RADIONUCLIDES BY STREAMS

the effects of such releases on the river and the 

effects of the physical, chemical, hydrologic, and 

biological characteristics of the river on the fate of 

the radioactivity.

Dilution of radioactive waters, which are released 

to the Clinch River through Whiteoak Dam (fig. 1, 

inset), by flow in the river has been an integral part 

of waste water treatment at ORNL. Concentrations 

of low-level radioactivity in these releases have been 

greater than desirable levels in the creek. Through 

dilution afforded by the river, concentrations have 

been reduced to very acceptable levels in the river 

(see Morgan, 1959a, p. 447).

Various estimates of average dilution afforded by 

the river have been made; estimated dilution has 

ranged from 450 to 1,000 times the average discharge in Whiteoak Creek (for example, see Morton, 

1962, p. 106, and Feige and others, 1960, p. 25). 

Variations in estimates stem from using different 

bases of flow comparisons: different periods of record, different streamflow measuring sites.

Other statistical measures of available dilution 

such as the median and the frequency of occurrence 

of minimums had not been estimated until this work 

was undertaken.

7'30" 84-00'

TENNESSEE

--^NORTH 

J CAROLINA

S SOUTH 

^CAROLINA

A Streamflow stations 

1 Clinch River near Scarboro, Tenn.

2 Whiteoak Creek at Whiteoak Dam, 

near Oak Ridge Tenn.

3 Whiteoak Creek below ORNL, 

near Oak Ridge, Tenn.

4 Whiteoak Creek at ORNL,

near Oak Ridge, Tenn. 

O Water-sampling station at mile 5.5

Enlargement

at right MELTON HILL 

DAM

5 0

I I I

10 MILES

FIGURE 1. Lower Clinch River basin from Norris Lake to river mouth.
RADIOACTIVE WASTE DILUTION, CLINCH RIVER, EASTERN TENNESSEE G3

Three of the principal radionuclides, strontium-90, 

ruthenium-106, and cobalt-60, released continuously 

into the river, are transported downstream into the 

Tennessee River without substantial uptake by bottom sediments or biota. (See Churchill and others, 

1965; Carrigan and Pickering, 1967, p. 63.) These 

radionuclides are moving in the water as solutes 

or as finely divided, nonsettleable, particulate matter. 

Hence, reduction of concentration of the three radionuclides, once complete mixing of waters from 

Whiteoak Creek with those of the Clinch River 

takes place rapidly, occurs within 4 to 6 miles 

downstream from the creek mouth (Morton, 1963, 

p. 70).

Dilution of releases from Whiteoak Creek by 

waters of the Clinch River is not constant, variation 

in dilution being a function of variations in flows of 

both streams. Because of the complexity in relationship in flows of the two streams, description of the 

influence of dilution on the fate of radioactive materials is best attacked through statistical analyses.

Various types of statistical analyses are presented 

in this report to characterize the dilution afforded 

by the river: central tendency, extremes, cumulative 

frequency distribution, seasonal trends, and magnitude-duration-frequency curves.

Techniques of statistical analyses employed are 

those commonly utilized in statistical descriptions of 

variations in streamflow. Extension of these techniques to consideration of simultaneous variation in 

flows of two streams is new and unusual and demonstrates another useful interpretation of streamflow 

data.

Consistency in analysis is maintained by using a 

selected base period of record and by limiting streamflow data to that obtained at one streamflow observation station on Whiteoak Creek and to one on the 

Clinch River.

ACKNOWLEDGMENTS

The efforts of Shirley A. Wilson and Harold 

Erickson of the U.S. Geological Survey in completing 

the initial computations of the mass of data leading 

to the statistical analyses of dilution factors are 

gratefully acknowledged. The help of personnel of 

the. Waste Disposal Research Section, Health 

Physics Division, ORNL, under the direction of E. G. 

Struxness, in conducting the turbulent diffusion 

tests in August 1961, including radiochemical 

analyses, is also acknowledged. Records of discharge 

in the Clinch River near Scarboro, Tenn., were obtained through the cooperation of the Tennessee 

Valley Authority. Figures 1 and 5 were prepared in 

the Graphic Arts Department, ORNL.

STREAMFLOW CHARACTERISTICS OF WHITEOAK 

CREEK AND THE CLINCH RIVER

Variations in flow of Whiteoak Creek reflect, almost completely, variations in natural runoff in its 

basin. Flows through Whiteoak Dam normally are 

uncontrolled, the lake serving only for emergency 

storage needs.

Average flow in Whiteoak Creek at Whiteoak Dam, 

near Oak Ridge, Tenn. (fig. 1, sta. 2), for the period 

of record, 1953-55, 1960-63, is 13.5 cfs (cubic feet 

per second); drainage area at this station is 6.01 

square miles (U.S. Geological Survey, unpub. data, 

1963, p. 71).

Accretions to the flow in the creek (imported 

water) from various waste streams in ORNL are 

28 percent of the average flow (from data furnished 

by ORNL and streamflow records).

Flow in the lower Clinch River is highly regulated 

in contrast to the virtually natural flow in Whiteoak 

Creek. For purposes of this report, only effects of 

regulation by Norris Lake require description.

Norris Dam, at mile 79.8, is a multipurpose structure used in the generation of peak-demand electric 

power and for flood control. Once or twice daily, 

releases are commonly made from Norris Lake to 

meet peak-power demands. Often on weekends either 

no release or diminished releases are made because 

of decreased power demands. During storm periods, 

floodflows are attenuated by temporary storage in 

Norris Lake. As soon as the flood threat has abated 

in the Tennessee Valley, sustained high releases 

(15,000-20,000 cfs) are made from the lake for 

several days.

The mouth of Whiteoak Creek is at mile 20.8 on 

the Clinch River. The streamflow gaging station in 

operation furthest downstream on the Clinch River 

prior to 1962 was at mile 39.0 near Scarboro, Tenn. 

(fig. 1, sta. 1); the station was 18.2 miles upstream 

from the mouth of the creek. Average flow for the 

period of record at this station, 1936-62, was 4,612

10,000 

5000

0 1000

a 500 

in

£ 100

jij 20 

10 

5

 

Mor

Mont

thlyc

ily di;

ischa

icharg e, Cli ich River (<

rge, Whiteoak Creek (

 : 

tatior

itatio

1)

i2)

Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec

FIGURE 2. Comparison of flows in Whiteoak Creek and the Clinch River 

during 1951. Distances between the two curves indicate variations in 

the river's dilution of radioactive releases from the creek.
G4 TRANSPORT OF RADIONUCLIDES BY STREAMS

cfs. Drainage area of the Clinch River at this site is 

3,300 square miles (U.S. Geological Survey, unpub. 

data, 1962, p. 66).

DILUTION FACTOR

In figure 2, variations in monthly flows during 

1951 are shown for the Clinch River near Scarboro, 

Tenn. (fig. 1, sta. 1), and for Whiteoak Creek at 

Whiteoak Dam, near Oak Ridge, Tenn. (fig. 1, inset, 

sta. 2). Linear differences between the curves for 

the two streams, which is the difference in logarithms of flows, are a direct measure of the relative 

dilution. Changes in the distances between curves, 

in figure 2, indicate that an appreciable variation in 

dilution occurs during the year.

One method of describing variations in dilution 

factors would be to establish, first, the relationship 

between discharges of the Clinch River and Whiteoak Creek by methods of correlation analyses. After 

the relationship between discharges for a selected 

period of record had been established, variation in 

dilution factor could be completely described by 

variation in discharge of one stream.

A correlation of the logarithms of concurrent 

flows in Whiteoak Creek and in Clinch River was 

attempted, but as can be surmised from study of 

figure 2 the results were unsatisfactory. The index 

of correlation was 0.363 (Ezekiel and Fox, 1959, 

p. 131), and the standard error of estimate was 

±0.182 log units (equivalent to +52, 34 percent) 

(Ezekiel and Fox, 1959, p. 65).

Because of lack of good correlation between discharges of the two streams, some other method of 

describing the relationship of discharges is needed.

Another measure which can be used to describe 

the dilution of releases afforded by the Clinch River 

is the ratio of flows in the two streams, called the 

dilution factor. The dilution factor is defined as the 

ratio of flow in Clinch River near Scarboro, Tenn. 

(mile 39.0), to that in Whiteoak Creek at Whiteoak 

Dam, near Oak Ridge, Tenn. for concurrent periods 

of time.

COMPUTATION OF DILUTION FACTORS

SELECTED PERIOD OF RECORD

The base period of record selected for statistical 

studies of dilution factors is from October 1, 1950, 

to September 30, 1960, 10 water years (1951-60). 

This period was selected for two reasons: (1) during 

the period, cumulative departure of precipitation 

from average precipitation for the long-term meteorological station at Clinton, Tenn. (fig. 1), was near 

zero and (2) no streamflow records for Whiteoak 

Creek basin were available for the period prior to 

1950.

Records of discharge in the Clinch River at the 

gaging station near Scarboro, Tenn. are available 

for the entire base period. Records of discharge in 

Whiteoak Creek at the gaging station at Whiteoak 

Dam, near Oak Ridge, Tenn., are available for July 

10, 1953, to October 14, 1956, and for August 1 to 

September 30, 1960.

EXTENSION OF DISCHARGE RECORDS FOR WHITEOAK CREEK

Discharges in Whiteoak Creek at Whiteoak Dam 

were estimated for the periods of missing record on 

the basis of records for the gaging station Whiteoak 

Creek below ORNL, near Oak Ridge, Tenn. (fig. 1, 

inset, sta. 3). The latter station was operated from 

June 1950 to July 1953 and from July 1955 to 

September 1960.

Statistical correlation is a means by which shortterm records for a station such as that on Whiteoak 

Creek at Whiteoak Dam are adjusted to represent a 

long-term record (Searcy, 1960, p. 68). Virtually no 

concurrent periods of record were available to develop a suitable relation between discharges for the 

two stations, Whiteoak Creek at Whiteoak Dam and 

Whiteoak Creek below ORNL, through correlation 

analysis. However, discharge records at a third station, Whiteoak Creek at ORNL, near Oak Ridge, 

Tenn. (fig. 1, sta. 4), were available for the period 

June 1, 1950, to July 14, 1955. Periods of records 

available for streamflow stations in Whiteoak Creek 

basin are shown in figure 3.

STATION

4 1 ^8fe&^fe28^:&:S8^$fe^S8^ T

i 1 1

'%$*%f88y&

2 \

r ........................ ii i

1950 1952 1954 

CALENDAR

ijffijftjfl

S$:$:$::S *§?£

1

1956 1958 1960 

YEAR

FIGURE 3. Periods of records available for streamflow stations in 

Whiteoak Creek basin. (See fig. 1.)

Availability of discharge records for the station 

Whiteoak Creek at ORNL made possible definition 

of a relationship between discharges for two pairs 

of stations on Whiteoak Creek: (1) for the stations 

at ORNL and at Whiteoak Dam and (2) for the 

stations at ORNL and below ORNL. Statistical correlations, using graphical techniques described by 

Searcy (1960), were used to develop the two relationships. Indices of correlation were 0.995 and 

0.993, respectively, and standard errors of estimate 

were 0.0624 log units (equivalent to +15, 13 percent) and 0.034 log units (equivalent to +8, 5 

percent), respectively.

The relationships in discharge for the above two 

pairs of stations were used to develop through
RADIOACTIVE WASTE DILUTION, CLINCH RIVER, EASTERN TENNESSEE G5

cross-plotting technique the relation between discharges for the stations below ORNL and at Whiteoak Dam. Although the index of correlation for the 

latter pair of stations cannot be computed, it can 

be safely implied that the coefficient is about 98 percent and that the standard error of estimate is about 

+ 18, 15 percent.

The relationship used to estimate daily discharges 

in Whiteoak Creek at Whiteoak Dam for the missing 

periods of record is curve 1 in figure 4.

50

8 40

£30

a.

o 20

00

o

<v

4 5 6 8 10 20 30 40 50 

DISCHARGE AT STATION 3, IN CUBIC FEET PER SECOND

FIGURE 4. Relationships between monthly discharges for two streamflow 

stations in Whiteoak Creek basin: Whiteoak Creek at Whiteoak Dam 

(sta. 2) and Whiteoak Creek below ORNL (sta. 3).

A primary requisite for correlation, that homogeneity in the hydrologic environment exist (H. C. 

Riggs, written commun., 1962), seems to be partially 

satisfied because the two stations are in close proximity at either end of Whiteoak Lake. Another 

requirement to satisfy completely the criteria for 

homogeneity is the development of correlations for 

each month in the year, rather than a single correlation that includes all monthly data. Some divergence from this latter requirement would seem 

permissible. The period of concurrent records for 

any of the stations in Whiteoak Creek basin was 

certainly too short to permit development of monthly 

correlations.

Study of methods of correlation analyses in the 

Water Resources Division, U.S. Geological Survey, 

subsequent to the time the daily dilution factors 

for this report were computed, has indicated that 

algebraic methods of correlation are preferable to 

graphical techniques (Walter Hoffman, written 

commun., 1962). When discharge records for the

1963 water year were available, postdating analytical record leading to this report, statistical correlation was made of monthly discharges for Whiteoak 

Creek below ORNL and Whiteoak Creek at Whiteoak 

Dam using algebraic methods described by Ezekiel 

and Fox (1959). The data for this correlation and 

the resultant regression curve (curve 2) are superposed on the original regression curve (curve 1) in 

figure 4. For the algebraically determined curve, the 

index of correlation is 0.993 and the standard error 

of estimate is ±0.0321 log units (equivalent to +8, 

 7 percent). The standard error of estimate for 

curve 1 in figure 4 is 0.0595 log units ( + 15, 13 

percent), and the index of correlation is 0.976 

(determined by techniques described by Arkin and 

Colton, 1950, p. 76, 80).

RESULTS OF STATISTICAL ANALYSES

MINIMUM, MEAN, AND MAXIMUM DAILY DILUTION FACTORS

The mean daily dilution factor for the 10-year 

base period, 1951-60, was 670. This factor was computed as the sum of the daily dilution factors divided by the number of days in the 10-year period. 

For the same period the mean dilution factor, computed as the ratios of average discharges for the 

base period, was 390. For shorter periods of record, 

mean dilution factor, based on the ratio of average 

discharges for the shorter period, had been about 

450. The mean dilution factor, based on the ratio of 

daily flows, is greater because the sum of quotients 

is greater than the quotient of the sums.

Minimum daily dilution factor during the base 

period was 5.1, occurring on February 6, 1955. 

Maximum daily dilution factor was 4,330, occurring 

on January 4, 1955.

PROBABILITY OF EQUALING OR EXCEEDING SPECIFIED 

DILUTION FACTORS

The cumulative-frequency curve showing probability of equaling or exceeding specified dilution 

factors is called a dilution-factor-duration curve. 

This curve is the integral of the frequency distribution curve for the daily dilution factors, with integration proceeding from the highest to the lowest 

daily dilution factor.

Probability of equaling or exceeding any specified 

daily dilution, within the range of experience, may 

be determined from the duration curve shown in 

figure 5. For example, daily dilution factors of 1,400 

and 87 are equaled or exceeded 10 and 90 percent 

of the time, respectively. Median daily dilution factor for the base period was 570.

Methods used to define the dilution-factor-duration 

curve (fig. 5) are the same as those described by 

Searcy (1959) to define flow-duration curves.
G6 TRANSPORT OF RADIONUCLIDES BY STREAMS

5000

1000 

500

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z 100

o

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:D

20 

10 

5

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)1 0.1 125 10 20 30 40 50 60 70 80 90 95 98 99 99.5 99.8 99.9 99.99

PERCENTAGE OF TIME INDICATED DILUTION FACTOR WAS EQUALED OR EXCEEDED 

FIGURE 5. Duration curve of daily dilution factors for the period 1951-60.

1000

0 500

fc

<

LJO

h3 200

Q

100 

t;n

M iximi m^

Mea n^

Mi nimi m^

Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec

FIGURE 6. Seasonal variations in dilution factors showing 

maximum, mean, and minimum monthly factors during the 

period 1951-60.

SEASONAL VARIATIONS IN DILUTION

As shown in figure 6, mean monthly dilution factors vary during the year in a somewhat sinusoidal

manner. Magnitudes of monthly factors are less 

than the mean daily dilution factor in 6 successive 

months, December through May. Lowest monthly 

dilution factors occur in March; the highest may 

occur in August or October.

Variation in minimum or maximum monthly dilution factors follow the same general seasonal pattern 

as that for mean monthly dilution factors. Minimum 

mean monthly dilution factors have been found to 

be 320 or less in all months of the year.

Dilution factors, computed for use in figure 6, are 

ratios of concurrent mean monthly flows in the 

Clinch River to those in Whiteoak Creek during the 

10-year base period.

The individual influence on the dilution factor of 

flow in the Clinch River and of flow in Whiteoak 

Creek was statistically tested. Results of the test 

did not indicate that variation in creek flow, or in 

river flow, exerted a dominant influence on variation 

in the dilution factors.
RADIOACTIVE WASTE DILUTION, CLINCH RIVER, EASTERN TENNESSEE G7

FREQUENCY STUDIES OF MINIMUM DILUTION FACTORS

Results of frequency studies of minimum dilution 

factors which occur annually for durations of 1, 3, 

7,15, 30, 60, and 90 days are shown in figure 7.

500

1.4 1.6 2 34568 

RECURRENCE INTERVAL, IN YEARS

10 15

FIGURE 7. Annual minimum dilution factor frequency curves for durations from 1 to 90 days during the period 1951-60.

The number of occurrences of an event of given 

magnitude in a given period of time is expressed in 

terms of a recurrence interval. In this context the 

recurrence interval (fig. 7, abscissa) is the average 

interval of time within which the dilution factor 

will, at least once, be equal to or less than a given 

magnitude. The recurrence interval also can be considered as the reciprocal of the probability of a 

dilution factor of given magnitude occurring in any 

year; for instance, the dilution factor with recurrence interval of 2 years is one that has a 50-percent 

chance of occurring in any year; the factor with 

5-year recurrence interval has a 20-percent chance of 

occurring in each year; the factor with a 10-year 

recurrence interval has a 10-percent chance of occurring in each year.

In the following table, minimum dilution factors 

of specified duration are listed for recurrence intervals of 2 and 10 years.

Duration 

(days)

1 ______ .

3 ____ .

7 __ __ .

15

30 ___ _.

60 ____ .

90 ____ .

Recurrence intervals

2 years

. ____ 20

. ____ 44

58

. _ __ 94

. ____ 140

. ____ 234

. __ _ _ 302

10 years

6

20 

27 

41 

75 

123 

163

Methods to define the magnitude-durationfrequency curves are those described by Furness 

(1960, p. 5-19) in his work concerned with low-flow 

frequency curves.

EFFECTS OF DIFFUSION IN THE CLINCH RIVER 

ON DILUTION

Waters draining from Whiteoak Creek do not immediately mix with waters of the Clinch River. 

Through the process of turbulent diffusion, waters 

of the two streams do mix vertically, laterally, and 

longitudinally as they move downstream. Unless 

the mixing process occurring in the river is completed within a reasonable distance downstream 

from the mouth of Whiteoak Creek application of 

information on dilution factors would not be useful 

to other phases of the Clinch River Study.

In exploratory steady-flow diffusion tests, the 

author and B. J. Frederick, U.S. Geological Survey, 

found, as had F. L. Parker, ORNL (in Morgan, 

1959b, p. 9), that vertical and lateral mixing of 

Whiteoak Creek waters with the Clinch River 

waters was virtually complete within a distance of 

4 to 6 miles downstream from the mouth of Whit&- 

oak Creek for flows of 6,000 to 20,000 cfs. The region 

of the river channel in which cross-sectional mixing 

is first complete is upstream from any point of 

major water use and upstream from water-sampling 

stations established for studying the fate of the 

waterborne radioactive wastes. (See Churchill and 

others, 1965.)

For purposes of exploring effects of diffusion on

10,000

8000

6000

0 4000

5 5 2000

1000

Ohr 0600 1200 1800 2400 hr

FIGURE 8. The typical variation in flow of the Clinch River during a 

day in the vicinity of Whiteoak Creek, due to power releases from 

Norris Lake during Aug. 14-19, 1961. (Same variation in flow observed 

at mile 5,5 except for timelag of 40 min.)
G8 TRANSPORT OF RADIONUCLIDES BY STREAMS

dilution, release of water from Whiteoak Creek into 

the Clinch River may be considered to vary so slowly 

that virtually a steady flow condition exists. Flow 

in the river cannot be considered steady, however. 

Variations in flow due to hydroelectric operations at 

Norris Dam may cause 4- or 5-fold variations in the 

dilution of creek waters at its mouth within a day. 

An example of variation in flow of the Clinch River 

from the vicinity of Whiteoak Creek to the mouth of 

the Emory River during a day is shown in figure 8.

During the period August 14-19, 1961, a test was 

conducted to determine effects of power releases 

from Norris Lake on diffusion of radioactive releases 

from Whiteoak Lake in the Clinch River. Records of 

Flow at Whiteoak Dam, records of radioactivity 

(gross beta radioactivity) released from Whiteoak 

Lake, time of travel from Whiteoak Dam to the 

mouth of Whiteoak Creek, and variation in flow of 

the Clinch River (fig. 8) were used in determining 

variation in concentration of radioactivity in the 

Clinch River as shown in figure 9.

3.0

2.0

2 O

z z 

o < 

o ^ 0.8

0.6

0.4

1200 hr 1800 2400 

August 15, 1961

0600 1200 

August 16, 1961

1800 hr

FIGURE 9. Estimate of variation in concentration of radioactivity in the 

Clinch River at the mouth of Whiteoak Creek during a 24-hour period, 

based on records of radioactive releases and of flow in Whiteoak Creek 

at Whiteoak Dam and of flow in Clinch River at mile 5.5, assuming 

complete and instantaneous mixing.

Owing to turbulent diffusion, the variations in the 

concentration of radioactivity of the continuous releases from Whiteoak Creek are attenuated as the 

waters move downstream in the river from the 

creek mouth. The effect of this attenuation on the 

concentration of radioactivity in the Clinch River 

was observed for 24 hours at a water-sampling station at mile 5.5 (fig. 1), 15.3 miles downstream from 

the mouth of Whiteoak Creek. Results of these 

observations of the variation in radioactivity are 

shown in figure 10. Variations in radioactivity released from Whiteoak Creek on August 15-16, 1961, 

which were created by effects of power releases

RADIOACTIVITY CONCENTRA" 

MILLILI" PER PICOCURIES i_i*-*-|sj O ^ 

ohoj^btboo §5 bot o

o

«-° cr

e oo

0 0

00 hr 1200 1800 2400 0600 1200 

August 17, 1961 August 18, 1961

(fig. 9), have been completely attenuated through 

turbulent diffusion.

FIGURE 10. Effects of power releases from Norris Lake on the variation 

in concentration of radioactivity in the Clinch River at mile 5.5 during 

a 24-hour period.

For most of the year (years prior to 1962) the 

variation in dilution within a day is the result of 

steady flow from Whiteoak Creek and cyclic flow, 

due to power releases, in the Clinch River. Rapid 

variations in flow in Whiteoak Creek due to storm 

runoff do occur and would cause variations in the 

concentration of radioactivity released to the Clinch 

River. The concentrations in the radioactive release 

would vary in a pattern somewhat like that shown in 

figure 9. Hence, fluctuations in the concentrations of 

release of radioactivity due to storm runoff from 

the creek should be effectively damped in a flow distance of 15 miles. The variation in flow during a day 

in the Clinch River is greatly diminished from that 

shown in figure 8 if the flow is greater than 10,000 

cfs. Releases from Norris Reservoir greater than 

10,000 cfs are flood-control releases and are nearly 

steady. Steady flows in the river would enhance 

damping due to diffusion.

CONCLUSIONS

The daily dilution factor is a simple measure of 

dilution afforded by the Clinch River. Flows in the 

Clinch River dilute radionuclide concentrations of 

Whiteoak Creek waters 670 times on the average 

(1951-60). The extreme range in dilution factor is 

from 4,330 to 5.1. The factor ranges for 10 to 90 

percent of the time from 1,400 to 83. A seasonal 

trend in dilution is apparent, the monthly dilution 

being less than average from December through 

May. Minimum dilution factors for durations of 1 

to 90 days range from 20 to 302 and 6 to 163 for 

recurrence intervals of 2 to 10 years.

Two restrictions on indiscriminate application of 

results of the analyses should be recognized. First, 

the results are a historic presentation of data rather
RADIOACTIVE WASTE DILUTION, CLINCH RIVER, EASTERN TENNESSEE G9

than a useful predictive tool, because of controlled 

flow conditions in the Clinch River. Flow in the 

Clinch River was regulated by Norris Lake until 

1962; in May 1962, further regulation of the river 

occurred after closure of Melton Hill Dam took 

place. (See fig. 1.) Peak-power releases from Melton 

Hill Lake will significantly change flow variations 

and diffusion of low-level radioactive waters in the 

lower Clinch River from those experienced when 

regulation was solely by Norris Lake. (See Morton, 

1965, p. 108-129.) Second, derivation of daily dilution factors for periods of missing record is not as 

statistically rigorous as would be desired.

Information in this report is no longer applicable 

to estimation of short-term variations in dilution 

because of effects of power releases from Melton 

Hill Lake on radionuclide transport. The information provides, however, a valuable base for comparative evaluations of these power releases on dilution.

Studies of the kind in this report are useful to 

waste management. Measures of central tendency 

(mean or median) indicate whether present means 

of disposal are adequate. Cumulative frequency 

curves and magnitude-duration-frequency curves aid 

in determining storage capacity for temporary holdup of waste. Advantageous times for release of 

stored wastes may be selected from information on 

seasonal trends.

REFERENCES

Arkin, Herbert, and Colton, R. R., 1950, Statistical methods 

[4th ed., revised]: New York, Barnes and Noble, Inc., 

224 p.

Browder, F. N., 1959, Radioactive waste management at 

Oak Ridge National Laboratory, in Hearings on industrial radioactive waste disposal before the Special Subcommittee on Radiation of Joint Committee on Atomic 

Energy: U.S. 86th Gong., 1st sess., v. 1, p. 461-514.

Carrigan, P. H., Jr., and Pickering, R. J., 1967, Radioactive 

materials in bottom sediment of Clinch River, Part B, 

Inventory and vertical distribution of radionuclides in 

undisturbed cores: Oak Ridge National Laboratory, 

ORNL-3721, Supp. 2B, 80 p.

Churchill, M. A., Cragwall, J. S., Jr., Andrew, R. W., and 

Jones, S. L., 1965, Concentrations, total stream loads, 

and mass transport of radionuclides in the Clinch and 

Tennessee Rivers, Supplement No. 1 to Status report 

No. 5 on Clinch River Study: Oak Ridge National 

Laboratory, ORNL-3721, Supp. 1, 78 p.

Ezekiel, Mordecai, and Fox, K. A., 1959, Methods of correlation and regression analysis [3d ed.]: New York, John 

Wiley & Sons, Inc., 548 p.

Feige, Yehuda, Parker, F. L., and Struxness, E. G., 1960, 

Analysis of waste disposal practice and control at 

ORNL: Oak Ridge National Laboratory, ORNL CF 

60-8-72, 50 p.

Furness, L. W., 1960, Kansas streamflow characteristics; 

Kansas Water Resources Board Tech. Rept. No. 2, pt. 2, 

179 p.

Morgan, K. Z., 1959a, Waste management at Oak Ridge National Laboratory, in Hearings on industrial radioactive 

waste disposal before the Special Subcommittee on 

Radiation of Joint Committee on Atomic Eneregy: U.S. 

86th Gong., 1st sess., v. 1, p. 445-460.

 1959b, Health Physics Division annual progress report

for period ending July 31, 1959: Oak Ridge National

Laboratory, ORNL-2806, 220 p. 

Morton, R. J., ed., 1961, Status report No. 1 on Clinch River

Study: Oak Ridge National Laboratory, ORNL-3119,

81 p.

 1962, Status report No. 3 on Clinch River Study: Oak 

Ridge National Laboratory, ORNL-3370, 123 p.

 1963, Status report No. 4 on Clinch River Study: 

Oak Ridge National Laboratory, ORNL-3409, 115 p. 

-1965, Status report No. 5 on Clinch River Study: Oak

Ridge National Laboratory, ORNL-3721, 149 p. 

Searcy, J. K., 1959, Flow-duration curves: U.S. Geological

Survey Water-Supply Paper 1542-A, 33 p. 

 1960, Graphical correlation of gaging-station records:

U.S. Geol. Survey Water-Supply Paper 1541-C, p. 67-100.

O