REGIONALIZATION OF 

LOW-FLOW CHARACTERISTICS 

OF TENNESSEE STREAMS 

U.S. GEOLOGICAL SURVEY 

Water-Resources Investigations Report 85-4191 

Prepared in cooperation with the 

TENNESSEE DEPARTMENT OF HEALTH AND ENVIRONMENT, 

DIVISION OF WATER MANAGEMENT 
REGIONALIZATION OF LOW-FLOW CHARACTERISTICS 

OF TENNESSEE STREAMS 

R. H Bingham 

U. S. GEOLOGICAL SURVEY 

Water-Resources Investigations Report 85-4 19 1 

Prepared in cooperation with the 

TENNESSEE DEPARTMENT OF HEALTH AND ENVIRONMENT, 

DIVISION OF WATER MANAGEMENT 

Nashville, Tennessee 

1986 
UNITED STATES DEPARTMENT OF THE INTERIOR 

DONALD PAUL HODEL, Secretary 

GEOLOGICAL SURVEY 

Dallas L Peck, Director 

For additional information Copies of this report can be 

write to: purchased from: 

District Chief 

U.S. Geological Survey 

A-413 Federal Building 

U.S. Courthouse 

Nashville, Tennessee 37203 

Open-File Services Section 

Western Distribution Branch 

U.S. Geological Survey 

Box 25425, Federal Center 

Lakewood, Colorado 80225 
CONTENTS 

Abstract 1 

Introduction 1 

Application of regional equations to estimate low-flow characteristics 3 

Limitations and accuracy of equations 3 

Estimates for low flow at ungaged sites 5 

Verification of regression equations at partial-record sites 5 

Procedures for regionalizing low-flow characteristics 14 

Ground water-surface water relations 14 

Streamflow recession 18 

Multiple aquifer contributions to streamflow 19 

Graphical computation method 21 

Weighted-average method 21 

Mapping streamflow-recession indexes 24 

Regression analyses 27 

Summary 33 

References cited 33 

Supplement A 

Examples of estimating low flow for ungaged sites 36 

SUPP lement 6 

SUPP 

Comparison of low-flow estimates for low-flow 

partial-record stations in west Tennessee 41 

lement C 

Comparison of low-flow estimates for low-flow 

partial-record stations in central and east Tennessee 45 

Supplement 0 

Low-flow values estimated from observed streamflow 

records and regression equations, and data used 

to derive the equations for Tennessee streams 58 

PLATES 

Plate 1. Map showing streamflow-recession index areas 

and boundaries, and locations of stations 

used in the regression analysis in pocket 

2. Map showing location of low-flow partial-record 

stations used to test the regression equations in pocket 

ILLUSTRATIONS 

Figures l-4. Graphical solutions for west Tennessee of: 

1. 3-day Z-year low-flow equation 6 

2. 3-day lo-year low-flow equation 7 

3. 3-day ZO-year low-flow equation 8 

4. 7-day lo-year low-flow equation 9 

iii 
Figures 5-8. Graphical solutions for central and east Tennessee of: 

5. 3-day 2-year low-flow equation 10 

5: 

3-day lo-year low-flow equation 11 

3-day 20-year low-flow equation 12 

8. 7-day lo-year low-flow equation 13 

9. Plots showing comparison of 3-day 20-year low 

flow from correlation methods with 3-day 

20-year low flow from regression equation 

for partial-record stations in west Tennessee 15 

10. Plots showing comparison of 3-day 20-year 

low flow from correlation methods 

with 3-day 20-year low flow from 

regression equation for partial-record 

stations in central and east Tennessee 16 

11. Generalized cross section of a stream 

basin showing ground-water movement 17 

12-14. Graphs showing: 

12. Baseflow recessions for South Fork 

Forked Deer River which drains mostly sand 20 

13. Baseflow recessions for Sewee Creek 

which drains mostly limestone and dolomite 22 

14. Three rates of baseflow recessions 

for Sequatchie River which drains 

mostly limestone and dolomite 23 

15. Generalized sketch of Sequatchie 

River basin and aquifer boundaries 25 

16. Plots showing comparison of 3-day 20-year 

low flow from measured streamflow 

with 3-day 20-year low flow from regression 

equation for gaging stations in west Tennessee 30 

17. Plots showing comparison of 3-day 20-year 

low flow from measured streamflow 

with 3-day ZO-year low flow from regression 

equation for gaging stations in central and east Tennessee 31 

CONVERSION FACTORS 

Analyses and compilations used in this report are in inch-pound units of 

measurements. Factors for converting inch-pound units to metric (SI) units 

are listed below. 

Multiply 

mile (mi) 

square mile (mi2) 

cubic foot per second (ft3/s) 

BY To obtain - 

1.609 kilometer (km) 

2.59 square kilometer (km2) 

0.0283 cubic meter per second W/s) 

iv 
REGIONALIZATION OF LOW-FLOW CHARACTERISTICS 

OF TENNESSEE STREAMS 

R. H Bingham 

ABSTRACT 

Procedures for estimating 3-day Z-year, 3-day lo-year, 3-day 20-year, and 

-/-day lo-year low flows at ungaged stream sites in Tennessee are based on surface geology and drainage area size. One set of equations applies to west 

Tennessee streams, and another set applies to central and east Tennessee 

streams. The equations do not apply to streams where flow is significantly 

altered by activities of man. Standard errors of estimate of equations for 

west Tennessee are 24 to 32 percent and for central and east Tennessee 31 to 

35 percent. 

Streamflow-recession indexes, in days per log cycle, are used to account 

for effects of geology of the drainage basin on low flow of streams. The 

indexes in Tennessee range from 32 days per log cycle for clay and shale to 

350 days per log cycle for gravel and sand, indicating different aquifer characteristics of the geologic units that sustain streamflows during periods of no 

surface runoff. Streamflow-recession rate depends primarily on transmissivity 

and storage characteristics of the aquifers, and the average distance from 

stream channels to basin divides. Geology and drainage basin size are the most 

significant variables affecting low flow in Tennessee streams according to 

regression analyses. 

INTRODUCTION 

Low-flow information is essential to surface-water quality and watersupply management. The amount of available water in a stream for dilution and 

transport of waste is a critical factor in determining the load capacity of 

the stream and withdrawal rates for water supply. With the current emphasis 

on water quality, low-flow information is important to regulatory agencies 

concerned with waste disposal into streams. The permissible rate of waste 

disposal into Tennessee streams, for example, is based on the 3-day 20-year 

low flow. Needs for low-flow estimates will increase throughout the State, 

therefore improved techniques to analyze the available data are needed. Immediate applications of the results of this project are to: (1) update the 

low-flow characteristics of gaged streams, and (2) derive new methods with 

improved reliability for estimating low-flow of ungaged stream sites. 

In response to the expected increase for low-flow information, the U.S. 

Geological Survey, in cooperation with the Tennessee Department of Health and 
Environment, began a study in 1981 to estimate low flow of streams in Tennessee. The study was divided into two phases. During the first phase, statistical analyses of daily streamflow data for continuous-record gaging stations 

were performed to calculate low flow for selected recurrence intervals and 

duration of streamflow. Low-flow for continuous-gaging stations were then used 

to estimate low flow at partial-record stations by methods of correlation. 

Descriptions of procedures used in the analyses and results of the first phase 

of the study are presented in a report by Bingham (1985). 

During the second phase of the study, equations were derived by multiple 

regression techniques to estimate four low-flow characteristics of ungaged 

streams in Tennessee. The four characteristics are the 3-day Z-year (3Q2), 

3-day lo-year (3QlO), 3-day 20-year (3Q20), and 'I-day lo-year (7410) low 

flow. The 342, 3410, and 3420 are the discharges at 2-, lo-, and 20-year 

recurrence intervals taken from a frequency curve of annual values of the 

lowest mean discharge for 3 consecutive days (the 3-day low flow). The 7410 

is the discharge at the lo-year recurrence interval taken from a frequency 

curve of annual values of the lowest mean discharge for 7 consecutive days (the 

7-day low flow). In Tennessee, low flow at ungaged stream sites can be estimated by substituting values for drainage area size and mapped streamflowrecession indexes into the regression equations. 

This report summarizes results of the second phase of the study and 

describes methods to estimate low flows in Tennessee streams. The report is 

based on low-flow data collected as part of programs with the Tennessee Department of Health and Environment and other state and federal agencies. Low-flow 

data for some streams in the Cumberland River basin were furnished by the U.S. 

Army Corps of Engineers. Data for some streams in the Tennessee River basin 

were furnished by the Tennessee Valley Authority. 

Five previous reports describe low flow, and flow duration of Tennessee 

streams: Eaton (1958), Wood and Johnson (1965), May and others (1970), Gold 

(1981), and Bingham (1985). The report by Bingham is based on streamflow data 

through 1981. 

APPLICATION OF REGIONAL EQUATIONS TO ESTIMATE LOW-FLOW CHARACTERISTICS 

The methods for estimating low flows in Tennessee streams consist of two 

sets of regression equations that are based on an index of streamflow recession 

and size of the drainage basin. One set of equations can be used to estimate 

low flow of streams in west Tennessee which have drainage areas between 25 and 

1,940 mi*. The other set of equations can be used to estimate low flow of 

streams in central and east Tennessee which have drainage areas between 2.68 

and 2,557 mi2. Areas where the separate sets of equations apply are shown 

on plate 1 (in pocket). 

The following four equations can be used for estimating low flows in 

ungaged streams in west Tennessee. 

2 
Standard error 

of estimate, 

in percent 

3Qz = 1.17 x lO-4 A'*'* (G-3O)'*43 29 

3Q1Cl = 7.83 x lO-6 Aloo (G-3O)1*86 25 

3Q20 = 3.28 x lO-6 Aloo (G-30)'*" 32 

7Q10 = 1.16 x lO-5 Aloo (G-3O)1*7g 24 

The following four equations can be used for estimating low flows in 

ungaged streams in central and east Tennessee. 

3Q2 = 2.95 x 10'~ Aoegg (G-3O)1'o' 

3Q10 = 5.33 x ,o-4 &o1 (G-3O)1*3o 

3Q20 = 3.15 x 

10-4 Al.01 (G-309.39 

7Ql, = 7.08 x lO-4 A'*" (G-3O)'o25 

where 

Standard error 

of estimate, 

in percent 

35 

32 

33 

31 

342 = 

3410 = 

estimated 3-day Z-year low flow, in cubic feet per second; 

estimated 3-day lo-year low flow, in cubic feet per second; 

3420 = estimated 3-day ZO-year low flow, in cubic feet per second; 

7Q10 = estimated 7-day lo-year low flow, in cubic feet per second; 

A = contributing drainage area, in square miles; and 

G= streamflow-recession index, in days per log cycle of decrease in 

discharge, determined from plate 1. 

Limitations and Accuracy of Equations 

Accuracy of the regression equations is expressed as standard error of 

estimate in percent. Standara error is computed from the difference between 

estimates of low flow from station data and estimates of low flow from the 

regression equations. Standard error of estimate is the range of error to 

be expected about two-thirds of the time. The standard error of estimate 

listed above is based on regression analyses using a streamflow-recession 

index determined from mapped values on plate 1. 

342, 

The regression equations in this report are limited to estimating the 

3410, 34209 and 7410 low flow in natural flow streams in 

Tennessee. In deriving the equations, drainage areas ranged from 25 to 
1,940 mi2 for west Tennessee streams, and streamflow-recession indexes ranged 

from 32 to 350. The following table gives the ranges in low-flow characteristics for stations in west Tennessee. 

Low-flow 

characteristic 

Range of flow, in 

cubic feet per second 

From To 

3Q10 261 

3Q20 .l 241 

7Qlo .l 266 

Drainage areas ranged from 2.68 to 2,557 mi2 for central and east Tennessee 

streams, and streamflow-recession indexes ranged from 32 to 175. The following 

table gives the ranges in low-flow characteristics for stations in central and 

east Tennessee. 

Low-flow 

characteristic 

Range of flow, in 

cubic feet per second 

From To 

3Q2 0.2 854 

3Qlo .l 511 

3Q20 . I 434 

7410 .2 541 

Use of the equations should be limited to the range in low flow, drainage area, 

and streamflow-recession indexes used to derive the equations. 

The regression equations should not be used on streams where the flow is 

significantly affected by regulation or other activities of man. Caution 

should be used when applying the equations to streams where a significant 

amount of the low flow is contributed by springs. Definition of the contributing drainage area, in such cases, is uncertain; some of the spring flow 

might be from adjacent basins. Caution also should be used in applying the 

equations to streams where most of the formation at or near land surface is 

limestone. Solution cavities in the limestone may alter the rate of flow considerably within short reaches of the stream channel. For example, a stream 

channel in limestone can have low flow of several cubic feet per second at one 

site and have zero flow at another site downstream. This commonly occurs in 

Overton, Putnam, White, Warren, Rutherford, and Williamson Counties of central 

Tennessee, and may occur locally in other counties. 

4 
Standard errors of the regression equations were determined using map 

values (plate 1, in pocket) of streamflow-recession indexes in the analyses. 

Those errors apply only to the stations used in the regression analyses. The 

average errors associated with use of the equations to estimate low flows in 

ungaged streams are unknown, but are probably slightly larger than the standard 

errors of the equations. 

ESTIMATES FOR LOW FLOW AT UNGAGED SITES 

The following procedures can be used to estimate the 342, 3410, 

3420, and 7Q10 low flows for ungaged sites on streams with natural flow in 

Tennessee. From topographic maps, determine the size of drainage area upstream 

from the site. From plate 1, determine the streamflow-recession index for the 

stream basin. Low flows for the site can be estimated by substituting the 

values of drainage area size and strea,nflow-recession index into the appropriate regression equations and performing the indicated mathematical operations or by graphical determination using figures 1 through 8. Low-flow 

values, computed by the equations or estimated from the graphs, of less than 

0.05 ft3/s for 3410, 3Q20, and 7410 should be considered zero. Lowflow values less than 0.15 ft3/s for 392 should be considered zero. 

Examples using the regression equations to estimate low flow in ungaged 

streams are given in Supplement A of this report. 

The estimating methods are modified for a stream basin draining two or 

more areas of different streamflow recession indexes. Drainage area is determined as described in the preceding paragraph. However, discharge from each of 

two or more streamflow-recession index areas must be computed separately using 

the equations, and the results weighted based on an estimate of the percentage 

of the basin draining each streamflow-recession index area. 

VERIFICATION OF REGRESSION EQUATIONS AT PARTIAL-RECORD SITES 

Tne regression equations were used to estimate 3420 for 600 low-flow 

partial-record stations within the State (plate 2) and the results were compared with low-flow estimates obtained from correlation methods. The 600 

stations exclude those used in the regression analyses. Estimated low flows, 

drainage area, mapped streamflow recession index (plate 1), and identification 

number for the stations are given in Supplement B for west Tennessee and in 

Supplement C for central and east Tennessee. 

Many of the stations in the supplements represent flow affected by man's 

activity, and many stations have drainage areas and low-flow values outside the 

limitations of data used to derive the equations for 3Q20. Those stations, 

and stations where large springs are known to occur upstream from the site, 

were omitted from the computation of the standard error of estimate. Partialrecord stations used to compute the standard errors are flagged with an asterisk in supplements 6 and C. 

The standard error of estimate was approximated by assuming the correlation values of low flow to be accurate. Regression equations were used to 

5 
0 

S3llW 3klvflos NI ‘Pi) Eltlv 30VNIVtla 
lllll I I I llllII I I I Q 

S3llW 3klVflOS NI ‘(VI V3W 3E)VNlVtla 

7 
l- I I 1111II I I I llllIl I I I 

% 

% 

% 

OS 

S3llW 3HVfKX NI ‘(VI V3HV 3E)VNlVHCl 

8 
8 

9 

0 

STIIW 3HVfKX NI ‘(VI V3HV 3WNIVklCl 
1000 - 

ic 

!!I 

5 

W 

% 

i 

z 

I3 

100 - 

5 

% 

-3 1.01 3~2 = 2.95 x 10 A 0.99[G - 301 

1 I I Illllll I I I Ill111 I I Illllll 

.1 1 10 100 1000 

DISCHARGE OQ21, IN CUBIC FEET PER SECOND 

Figure B.--Graphical solution of 3day P-year low-flow equation for central and east Tennessee. 

10 
-4 1.01 

3Q10- 5.33x 10 A CG - 30) 1.30 

I I IlltIlt’ I I I111111 I I I111111 I I 11111t 

1 10 100 loo0 

DlSCHAFtGE C3010 I, IN CUBIC FEET PEFI SECOND 

Figure 6.-Graphical solution of 3-day lO-year lowflow equation for central and east Tennessee. 

11 
-4 1.01 (G _ 30)1.39 

3~2~’ 3.15 x 10 A 

t I I 

I 

I I Illllll I I I Illll 

1 I I lllll~rl I I I I11111 

.I 1 10 100 1000 

DlSCHARGE (3Q2d. IN CUBtC FEET PER SECOND 

Figure it.-Graphical solution of 3-day 20-year low-flow equation for central and east Tennessee. 

12 
10,000 r I I lllllll I I I Illlll I I I I11111 I I llIII’- 

7Q 

-4 

,o = 7.08 x 10 A 1 .oo (G _ SOIL25 

I I1111111 I 

1 I I I lllll I, I I IllIll I I I IIIII 

.l 1 10 100 1000 

DISCHARGE(7QlgI, IN CUBIC FEET PER SECOND 

Figure &-Graphical solution of 7-day lo-year low-flow equation for central and east Tennessee. 

13 
estimate 3420 for partial-record stations and the results compared with estimates obtained from correlation methods. Residuals, in log units, were determined as the difference in logarithms of low flows from regression equations 

and from correlation methods. The error was computed by the root-mean-square 

procedure using the equation: 

where RMS = root mean square, in log units, 

z = mean of the residuals, and 

S = standard deviation of the residuals. 

Computed RMS values were transformed to 45 percent for 33 partial-record stations in west Tennessee and to 41 percent for 223 partial+ecord stations in 

central and east Tennessee. A two-sided student's t test indicated no bias in 

low flows determined by the regression equations. 

Other comparisons of the low-flow estimates were made with graphical 

plots. The 3020 low flows from correlation methods for the partial-record 

stations were plotted against 3420 low flows estimated with the regression 

equations. Plots of low-flow data for the 33 stations in west Tennessee are 

illustrated in figure 9. Plots for the 223 stations in central and east 

Tennessee are illustrated in figure 10. According to visual inspection, the 

plots indicate no bias, however, the largest errors appear to be associated 

with the smallest low-flow values used for the comparison. Although these 

comparisons between low-flow estimates from regression equations and from 

correlation are not completely independent, they do support confidence in the 

equations. 

PROCEOURES FOR REGIONALIZING LOW-FLOW CHARACTERISTICS 

Analyses of basin and climatic characteristics that influence the rate of 

low flow were performed to regionalize methods of estimating low flow in 

ungaged streams statewide. The most significant result of these analyses is to 

relate the effects of geology to the rate of low flow. The relation is defined 

by streamflow recession indexes for various rock types and combinations of rock 

types. Streamflow-recession indexes are strongly influenced by aquifers within 

the geologic framework underlying the stream basin. Thus, the streamflowrecession indexes used in these analyses reflect the effects of geology on the 

rate of low flow. The recession index area boundaries were delineated based 

on geologic maps. 

Ground Water-Surface Water Relations 

Low flow in a stream is usually ground water discharged from the aquifer 

system to the stream. During the wet period in the spring, most rocks underlying the stream basin are recharged by precipitation in excess of the amount 

of water that can move through the rocks. After the wet season, water in the 

rocks drains slowly into the adjacent stream and provides flow during the 

summer and fall. Such drainage, in combination with evapotranspiration, causes 

the ground-water level to decline to a point below the local streambed and 

14 
.1 

1 IO 100 

LOW FLOW FROM REGRESSION EQUATION. IN CUBIC FEET PER SECOND 

Figure Q.-Plots showing comparison of a-day ZO-year low flow fromcorrelation methods with 

3day 20-year low flow from regression equation for partial-record stations in west Temessee 

15 
\ 

0 Equal discharge line 

0 

0 0 

0 / 0 

10 - 

-3‘points 

saints 

0 

/d 

6 ~20p~l”ts 

j points 

3 points 

.l $ 1 I111111 I I I111111 I I I llllll 1 I I111111 

.l 1 10 100 1000 

LOW FLOW FROM REGRESSION EQUATION, IN CUBIC FEET PER SECOND 

Figure 1 O.-Plots showing comparison of 3-day 20-year low flow from correlation methods wlth 3-day 

2Ll-year low flow from regression equation for partial-record stations in central and east Tennessee. 

16 
water stops flowing into some streams. Consequently, streams in some areas of 

the State have zero flow for a period during most years. A generalized cross 

section of a stream basin illustrating the movement of ground water from the 

aquifer system to the stream is shown in figure 11. 

Sandstone 

Sandstone Arrows indicate general direction 

of ground-water movement 

Figure 1 l.--Generalized cross section of a stream basin showing ground-water movement. 

The interactions between the aquifer or groups of aquifers and the streams 

are extremely complex. The rate of ground-water discharge to a stream is a 

function of the capacity of the aquifer to store and transmit water, aquifer 

thickness and area1 extent, slope of the water level within the aquifer, amount 

of precipitation to recharge the aquifer, size of the stream basin, and time. 

Most streams used in these analyses receive water from two or more rock types 

or geologic units each having different effects on low flow of the streams. 

For example, sand yields more water to a stream than does clay, and sandstone 

yields more water to a stream than does shale. Area1 and vertical differences 

can also occur in aquifer characteristics within a given rock type. 

Rorabaugh and others (1966) investigated methods of relating ground water 

to surface water in the Columbia River basin. In their work, ground-water discharge to selected streams was related to the physical characteristics of the 

aquifer system as evidenced by the recession pattern of the water level in the 

aquifer system during a period of no recharge. The report also indicates that 

streamflow recession for continuous-record gaging stations on unregulated 

streams can be used to estimate streamflow characteristics. 

Trainer and Watkins (1975) used streamflow-recession indexes to estimate 

average values of aquifer transmissivity and storage in the upper Potomac River 

17 
basin. Their work shows a direct relation between streamflow recession and 

the transmissivity of the aquifers. For example, stream basins underlain by 

aquifers with large transmissivity values had higher indexes of streamflow 

recession than basins underlain by aquifers with small transmissivity values. 

By applying that relation, Bingham (1982) used streamflow-recession indexes and 

surface geology to regionalize low-flow characteristics of unregulated streams 

in Alabama. For Tennessee, the same relation was used along with information 

on surface geology to regionalize low flow for selected frequencies statewide. 

Streamflow recession 

The rate of streamflow recession during base flow is controlled by the 

hydraulic characteristics of the aquifers. The streamflow-recession index can 

be estimated by the equation (Rorabaugh and others 1966): 

a25 t=T, 

Where t = time in days per log cycle, 

= distance from the stream to the hydrologic divide, 

s" = storage coefficient of the aquifer or aquifers, and 

T = transmissivity of the aquifer or aquifers. 

For this report, these characteristics are not necessary as streamflow data 

were used to estimate the streamflow-recession indexes graphically. However, 

according to Trainer and Watkins, (1975, p. 31-32) three factors which affect 

the streamflow-recession index complicate its definition and interpretation 

from a graph. Those factors are: (1) the brevity of most recession episodes 

in a humid region makes the recession curve difficult to establish precisely, 

(2) losses from ground water and from streamflow through evapotranspiration 

distort the ideal recession curve during much of the year, and (3) many recession curves are complex because of nonhomogeneity of the aquifers or the 

presence of multiple aquifers. 

Records from approximately 150 continuous-record gaging stations were 

examined in an attempt to define the streamflow-recession index areas across 

the State. Streamflow-recession indexes were defined for 109 of those sites. 

Streamflow at the remaining stations was significantly affected by activities 

of man, or the record was too short to define the streamflow-recession indexes. 

For stations where the length of record was adequate, 20 years of streamflow 

hydrograph plots were examined to determine periods of record to use in estimating the streamflow-recession indexes. Approximately 6 to 10 recessions 

were plotted for each of the stations to assure consistency in the recession 

index definition. For some stations, however, only two to three recessions 

could be used for various reasons to estimate the index. The streamflow recessions, for each station, were plotted on semilog graph paper, daily streamflow 

on the log scale, and time, in days, on the arithmetic scale. The index of 

streamflow recession for each station was defined in days per log cycle, that 

is, the number of days required for the flow to decrease one complete log 

cycle. The base flow recession of a stream is nearly straight on a semilog 

plot. 

Streamflow records for periods during November through March were generally used for defining the streamflow-recession indexes. During that time, 

interferences from evaporation and transpiration are least, and the recession 

18 
probably reflects the geohydrologic control on base runoff and low flow of 

streams. ilowever, the recession slope is difficult to determine from streamflow in the winter because of interruptions from precipitation. Many of the 

interruptions are brief, and the recession slope may become nearly straight a 

few days after the streamflow peak. 

The peak discharge during a period of rainfall is used as the first 

plotting point for the streamflow-recession curve. The plotting of stream 

discharge for each successive day is continued until the streamflow-recession 

curve approximates a straight line. The number of days required for the 

straight-line condition to occur is a function of the basin geometry and the 

properties of the basin material (Rorabaugh and others, 1966) and is defined 

as the critical-time factor. The critical-time factor is expressed by the 

equation: 

O.Za*S 

tc= T . 

Each variable is defined on a previous page of this report. The straight-line 

part of the curve is used to define the index of streamflow recession. The 

streamflow recession for South Fork Forked Deer River at Jackson, Tennessee 

(station 221, pl. 1) is illustrated in figure 12. The straight-line part of 

the curve for South Fork Forked Deer River indicates a recession index of about 

235 days per log cycle, and a critical-time factor of 47 days. 

Definition of the streamflow-recession index, for numerous stations, can 

be aided or verified by the critical-time factor. After the days per log 

cycle have been estimated from the recession plot, multiply the number of days 

by the critical-time factor (0.2) to determine the number of days for the 

recession curve to become an apparent straight line. The critical-time procedure works fairly well when the first plotting point on the recession curve 

represents medium to high discharge. For low to medium discharge, the curves 

represent increments or additions to the composite of all past events, and, in 

many cases, the critical-time factor may be as low as 0.1 and may not be conclusive (Daniel, 1976). In many stream basins in Tennessee, the geometry and 

aquifer characteristics are such that the critical-time factor may represent 

weeks or months. 

Great care is required in estimating the streamflow-recession index from 

hydrographs because precipitation falls frequently during the winter, and 

periods of streamflow recession between flood peaks are relatively short. 

Recession curves that become straight-line segments on semilog plots within 6 

to 10 days after flood peaks can be determined readily through inspection of 

several years of hydrographs for each stream. By contrast, the straight-line 

segment of a recession curve that would become linear after 50 days or more of 

uninterrupted recession can be determined only approximately. 

Multiple Aquifer Contributions To Streamflow 

On a statewide basis, the variation of aquifer hydraulic characteristics 

and interaction of the aquifers and streamflow is extremely complex. Trainer 

19 
Drainage 

- 20 days - 

100 TIME. IN DAYS 

Figure 12.--Base flow recessions for South Fork Forked Deer 

River which drains mostly sand (station 221 on plate 11. 

20 
and Watkins (1975, p. 34) indicate in their report that both area1 and vertical 

differences in hydraulic characteristics of aquifers probably contribute to the 

complexity of streamflow-recession curves. In many Tennessee streams the flow 

represents the effects of several aquifers, each having different hydraulic 

characteristics. 

For the purposes of developing the regression equations, no simple method 

exists for assigning fractions of low flows to parts of a basin draining two or 

more unlike aquifers. In the case of naturally integrated recessions, such 

might not be possible while at the same time preserving the statistical validity of the data. 

Graphical Computation Method 

The streamflow-recession indexes, as determined graphically, for most of 

the streams in these analyses represent naturally integrated effects of the 

different aquifers within the basin. For example, flow of Sewee Creek near 

Decatur, in Meigs County (Station 120 pl. l), represents naturally integrated 

effects of two aquifers. One aquifer has a streamflow-recession index of 65 

days per log cycle and the other aquifer has a streamflow-recession index of 

120 days per log cycle (pl. 1). However, the naturally integrated effects of 

both aquifers result in a streamflow-recession index of about 85 days per log 

cycle (fig. 13). 

Significantly different streamflow recessions were estimated for several 

streams used in these analyses by separate straight line segments for different periods on the same streams. Riggs (1964, p. 353-354) describes how 

runoff from two very unlike aquifers in the same drainage basin might produce 

two very distinct regions or straight-line segments in the streamflow-recession curve. When two significantly different indexes are observed, it seems 

reasonable that the flatter one (more days per log cycle) would control longer 

frequency low flows. For example, a streamflow-recession index of 50 days per 

log cycle would deplete 99.999 percent of a beginning streamflow during the 

same period that an index of 250 days per log cycle would aeplete only 90 percent of the same beginning streamflow. When different indexes are observed in 

a single basin, the resulting streamflow is the sum of the contributions from 

each part of the drainage area and the separate effects are relatively easily 

distinguished. The streamflow recessions for Sequatchie River near Whitwell, 

in Marion County (station 145, plate l), illustrate two indexes representing 

two unlike aquifers (fig. 14). The recessions also indicate that the naturally 

integrated effects of the two unlike aquifers (32 and 100 days per log cycle) 

result in a streamflow-recession index of about 85 days per log cycle. However, for some streams where two or more only slightly different indexes might 

be expected on the basis of geologic formations, a single observed index can 

be a naturally integrated effect, and the separate effects from each part of 

the drainage area may be indistinguishable. 

Weighted-Average Method 

The weighted-average streamflow-recession index procedure was applied in 

mapping the index areas as shown on plate 1; 

slightly from values obta 

thus the values shown may differ 

ined by the graphical computat ion method for the same 

21 
10,000 , 

1000 - 

100 - 

Drainage area (AI = 117 square miles 

-20 daysTIME, IN DAYS 

Figure 13.--Base flow recessions for Sewee Creek which drains 

mostly limestone and dolomite (station 120 on plate 1). 

22 
Drainage area [Al = 402 square miles 

co b 

3, 24 

&I ch 

-20 daysTIME, IN DAYS 

Figure 14.--Three rates of base flow recessions for Sequatchie River 

whichdrains mostly limestone and dolomite (station 145 on plate 1) 

23 
stations. For the purposes of application of the regressions, however, the 

effect of contributions from different parts of a basin can be accounted for by 

the procedure described in Supplement A of this report. 

The weighted-average procedure was based on an estimate of the percentage 

of a stream basin draining each of two or more different aquifers. Sequatchie 

River at station 145 on plate 1 provides an example of the averaging procedure. 

A generalized sketch of Sequatchie River basin is shown in figure 15. Approximately 75 percent of the basin drains a limestone and dolomite aquifer which has 

a streamflow-recession index of 100 days per log cycle (fig. 14). Twenty-five 

percent of the basin drains the overlying shale and sandstone aquifer which has 

a streamflow-recession index of 32 days per log cycle. The weighted-average 

streamflow-recession index is computed by summing 75 percent of 100 days per 

log cycle and 25 percent of 32 days per log cycle. Thus, the weighted-average 

streamflow-recession index of the two aquifers is 83 days per log cycle for 

Sequatchie River at station 145 (pl. 1) near Whitwell. The weighted-average 

streamflow-recession index is the best estimate of the combined effects of the 

two aquifers on low flow of Sequatchie River at station 145. 

Mapping Streamflow-Recession Indexes 

Streamflow-recession index areas (plate 1) were delineated based on streamflow hydrographs, contacts between geologic formations, and the types of geologic formations at land surface in the basin. The types of formations include 

gravel, sand, clay, and silt in west Tennessee and limestone, chert, shale, 

sandstone, dolomite, and conglomerate in Central and east Tennessee. In the 

mountainous areas of extreme east Tennessee, the surface formations also include 

siltstone, quartzite, and slate. Streamflow data have not been obtained for all 

the formations contributing water to streamflow within the State. However, the 

entire State was mapped based on the assumption that similar types of formations 

contribute similar amounts of water to streamflow, and that ground-water divides 

on the shallow aquifers correspond to topographic divides. 

Boundaries between areas of streamflow-recession indexes on plate 1 follow 

the same general pattern as the contact lines between formations or groups of 

formations with major differences in rock type and water-bearing properties. 

However, the quantitative significance of the several geologic factors that 

influence low flow in streams cannot be determined precisely. 

The streamflow-recession indexes defined for each of the 109 continuous 

gaging stations were used to represent the relative effects of surface formations on low flow. Effects of the formations on low-flow characteristics were 

evaluated by plotting gaging station locations and listing their respective 

streamflow-recession indexes on a map of the State (pl. 1). The data on plate 

1 were compared with that on a geologic map of the State (Hardeman and others, 

1966) to delineate areas where formation effects on low flow are similar. 

Adequate descriptions of the surface formations are essential in determining the position of streamflow-recession index boundaries. In many separate areas, several formations with similar rock types and water-bearing 

properties were grouped together in a single streamflow-recession area (pl. 1). 

24 
Limestone and dolomite aquifer. 

Recession index, !OO days per 

log cycle 

Shale and sandstone aquifer. 

Recession index, 32 days 

per log cycle 

ii 

. 

. 

I Basin boundary 

‘Y Aquifer boundary 

Not to scale l \ rt 

JrJ 

2’ Streamflow station 0357100 Sequatchie River 

near Whitwell (station 145 on plate 11 

Figure 15.--Generalized sketch of Sequatchie River basin and aquifer boundaries. 

25 
For example, in the Sequatchie River Valley near Chattanooga several dolomite 

and limestone formations are at the surface along the floor and walls of the 

valley. Those formations have similar rock types and were assumed to have 

similar water-bearing properties within the Sequatchie Valley, consequently, 

they were mapped together in a single streamflow-recession index area for the 

entire length of the valley. Similarly, sand formations in west Tennessee 

which have essentially the same descriptions were assumed to have the same 

water-bearing properties and mapped together in a single streamflow-recession 

index area. 

Formations with contrasting rock types and water-bearing properties were 

separated on plate 1 by streamflow-recession index boundaries. Formations consisting primarily of clay were separated from formations consisting primarily 

of sand and other geologic units. Formations consisting primarily of shale 

were separated from formations consisting primarily of sandstone and other 

geologic units. The streamflow-recession index areas on plate 1 represent the 

relative capacity of the formations to release water to streams during low 

flow. A large number of days per log cycle represent slower depletion of water 

from the formations and a large capacity o f the formations to release water, 

whereas, a small number of days per log cycle represent faster depletion of 

water from the formations and a small capacity to release water. 

The State geologic map (Hardernan and others, 1966) was inadequate in many 

areas to delineate streamflow-recession index boundaries. In those areas, 

7%-minute geologic map quadrangles were used as an aid in delineating the 

boundaries. For example, the boundaries for Crooked Creek basin and for Beaver 

Creek basin (station number 212, pl. 1) near Huntingdon, in Carroll County were 

based on a geologic map of the Huntingdon quadrangle (Ferguson, 1970) and the 

Palmer Shelter quadrangle (Parks, 1974). The maps were used to define areas 

of fluvial deposits in the Crooked Creek and Beaver Creek basins. Because of 

higher-yielding fluvial deposits, the streamflow-recession index area of 350 

days per log cycle was extended to include those stream basins. The fluvial 

deposits are not apparent on the state geologic map. 

For three areas in west Tennessee, a mineral resources map of the Tennessee Valley Region (TVA, 1970) was used to delineate streamflow-recession index 

boundaries for local clay deposits near Lexington, Henderson, and Bolivar. 

The clay in these three areas have an effect on low flow. The capacity of the 

clay to release water to streams is much smaller than the surrounding sand 

formation. Perhaps the effects of other clay deposits on low flow of west 

Tennessee streams should be accounted for, but streamflow records are not 

available to determine such effects. 

The boundary between streamf low-recession index areas of 100 days and 175 

days per log cycle in Polk, Monroe, Blount, and Sevier Counties in east Tennessee was delineated based on reports by McMaster and Hubbard (1970) and King 

(1964). 

Although descriptions of formations are some of the criteria used in 

delineating streamflow-recession index areas on plate 1, local variations in 

rock type may result in indexes considerably different than the areas indicate. 

The areas on plate 1 represent approximately average streamflow-recession 

26 
indexes; the index may vary slightly from stream to stream within each area. 

The map is limited to 10 categories of index areas for practical application in 

estimating low flows. Approximately 15 to 20 categories could be delineated, 

but the map would be too cumbersome and difficult to use. The procedures used 

to delineate streamflow-recession index areas on plate 1 are highly subjective 

to interpretation of formation descriptions and to a lack of adequate information for precise positioning of the index boundaries. 

Regression Analyses 

Low flows at gaging stations were related to various basin and climatic 

characteristics by using regression techniques. Low-flow data used in the 

final regression analyses are tabulated in Supplement D. Characteristics 

tested were streamflow-recession index, drainage area, main channel slope, 

length of main channel , mean basin elevation, percent forest cover within the 

basin, and mean annual precipitation. Streamflow-recession index and drainage 

area were the only characteristics significant at the 5 percent level of 

significance. 

In Tennessee the most widely used low-flow data are the 3420. Thus, the 

first regression analyses were performed for the 3420 low flow. Analyses for 

the 3Q2, 3410, and 7Q10 were performed after completion of the analyses 

for 3@0. Low-flow values for the respective frequencies were substituted 

into the analyses. Estimating equations derived from the regression analyses 

are of the same general form for 342, 3410, 3420, and 7410 low flows. 

The first several regression attempts used streamflow-recession index 

determined from streamflow hydrographs. The regressions included 109 continuous-record gaging stations randomly located across the State. Those stations appear to represent low flows without significant effects from activities 

of man. Attempts were made to derive one set of equations to apply statewide. 

However, because of differences in the hydraulic characteristics of aquifers 

in west Tennessee and aquifers in the rest of the State, the standard error of 

estimate of the regression was about 73 percent for 3420 low flow. The 

equation over estimated 3420 for all continuous-record stations in west Tennessee. For subsequent regressions the State was separated into (1) west 

Tennessee and (2) central and east Tennessee. 

The separation was based primarily on geology and topography. In west 

Tennessee the aquifers that yield significant amounts of water to streams are 

in unconsolidated sand and gravel; aquifers in central and east Tennessee are 

mostly in sandstone, limestone, and dolomite. The land surface in west Tennessee slopes gently, and consequently, the surface of the water table also slopes 

gently. The gently sloping water table surface in west Tennessee has less 

hydraulic head than the steeper sloping water table in aquifers in central and 

east Tennessee. Because of the contrasting difference in water-table slopes, 

the amount of water contributed to low flow in west Tennessee streams is less 

per unit area of aquifer. This is probably the principal reason the statewide 

3420 equation overestimated low flow in west Tennessee streams. 

In subsequent regression analyses for west Tennessee streams, 22 continuous-record stations were used to derive an equation to estimate 3420 low 

27 
flow. Variables used in the equation were drainage area and streamflowrecession index determined from station hydrographs. Standard error of estimate for the regression was about 33 percent. The next regression used mapped 

streamflow-recession index values estimated from plate 1 for each of the 22 

continuous-record stations. Standard error of estimate for that regression 

was about 32 percent. In the final regression analyses to derive an equation 

to estimate 3420 low flow for west Tennessee streams, information for 15 

low-flow partial-record stations was added to the data set. The partialrecord stations were selected randomly for geographic and geologic distribution. The final regression analysis using 22 continuous-record stations and 15 

partial-record stations has a standard error of estimate of about 32 percent. 

Additional regression analyses were performed for west Tennessee streams 

to derive equations to estimate 392, 3410, and 7410 low flows. The 

standard error of estimates for those equations are 29, 25, and 24 percent, 

respectively. All the equations for west Tennessee streams are of the same 

format; the regression constant and variable exponents are different. 

In regression analyses for central and east Tennessee streams, 59 continuous-record stations were used to derive an equation to estimate 3420 low 

flow. Variables used in the equation were drainage area and streamflowrecession index determined from station hydrographs. Standard error of 

estimate for the regression was about 28 percent. The next regression used 

streamflow-recession indexes estimated from plate 1 for each of the 59 continuous-record stations. Standard error of estimate for that regression was 

about 32 percent. In the final regression analyses for central and east 

Tennessee streams, streamflow-recession indexes were estimated from plate 1 

for 28 additional continuous-record stations and for 116 low-flow partialrecord stations. Information for those stations was added to the data set and 

the regression rerun. The partial-record stations were selected randomly for 

geographic and geologic distribution. The final regression using 87 continuous-record stations and 116 partial-record stations has a standard error of 

estimate of about 33 percent. 

Additional regression analyses were performed for streams in central and 

east Tennessee to derive equations to estimate 302, 3Ql0, and 7410 low 

flows. Standard error of estimates for those equations are 35, 32, and 31 

percent, respectively. All the equations for central and east Tennessee 

streams are of the same format; the regression constant and variable exponents 

are different. 

Equations were derived to estimate low flows based on drainage area size 

as the only independent variable. Those equations are unacceptable because 

the standard errors of estimate associated with the equations are too large. 

For west Tennessee streams, the errors ranged from 100 percent for 342 to 

153 percent for 3420. For central and east Tennessee streams, the errors 

ranged from 108 percent for 3Q2 to 158 percent for 3420. These large 

errors indicate the importance of geologic effects on low flow. Geologic 

effects are accounted for, to some degree, by the mapped index of streamflow 

recession. After adding the streamflow-recession index variable to the equation for estimating 3420 in west Tennessee streams, the standard error of 

estimate was decreased from 153 to 32 percent. For central and east Tennessee 

streams, the standard error of estimate was decreased from 158 to 33 percent. 

28 
During the regression analyses a value of 30 was subtracted from the 

streamflow-recession index to increase the equation constant and to reduce 

exponents of the variables. In addition, the value of 30 is related to the 

streamflow-recession rate of zero low-flow areas. The streamflow-recession 

index for the zero low-flow areas is 32 days per log cycle. Thus, a value of 

30 is the feasible maximum value that can be subtracted from the index because 

of logarithmic transformations used in the regression analyses. However, subtracting a large value from one of the variables in regression equations can 

affect the linearity of those equations. 

The linearity of the low-flow equations in this report was checked with 

graphical plots. The graphs include plots of regression residuals versus log 

of the streamflow-recession index, and residuals versus log of drainage area. 

According to visual inspection, the group of plotting points on each graph 

forms a straight line. In addition, the 3420 low flows from observed streamflow data for gaging stations were plotted against predicted 3420 low flows 

estimated with the regression equations. Plots for stations used to derive the 

3420 low flow equation for west Tennessee streams are illustrated in figure 

16. Plots for stations used to derive the 3920 low-flow equation for central 

and east Tennessee streams are illustrated in figure 17. 

Drainage areas for gaging stations used in the regression analyses for 

west Tennessee streams ranged from 25.0 to 1,940 rni2. However, the distribution of drainage areas vary considerably within that range. For example, 

only four stations have a drainage area larger than 1,000 mi2, and only two 

stations have a drainage area larger than 1,500 mi2. The following table 

summarizes the distribution of drainage areas used in the regression analyses 

for west Tennessee streams. 

Range in drainage Number of stations 

area, (mi*) in analyses 

25-50 9 

50-100 

100-250 5" 

250-500 5 

500-1,000 5 

l,OOO-1,500 2 

1,500-1,940 2 

Total stations 37 

The streamflow-recession indexes used in the regression analyses for west 

Tennessee streams ranged from 65 to 350 days per log cycle. The following 

table summarizes distribution of indexes for gaging stations used in the 

regression analyses. 

Range in streamflowrecession indexes 

60-100 

101-150 

151-200 

201-250 

251-300 

301-350 

Total stations 

Number of stations 

in analyses 

5 

6 

i: 

2 

1 

37 

29 
1000 - I 11111111 I I I I11111 I I I I11111 I I Illll ? 

-6 1.07 

3020 = 3.28 X 10 A (G - 3012.00 

.1v; ’ ’ ’ I”lll I I 1111111 I I I I11111 I I IllI 

.l 1 10 100 

LOW FLOW FROM MEASURED STREAMFLOW, IN CUBIC FEET PER SECOND 

I 

1000 

Figure lg.---plots showing comparison of 3day 20-year low flow from measured streamflow 

with 3day 20-year low flow from regession equation for gaQng stations in west Temessee. 

33 
1000 I I I I , , , I , I I I I11111 I I I I11111 I I lllll 

3020 = 3.15 x 10-4A’.o’tG - 301”3g / 

1 -o- 0 

00 o\o 0 

0 0 O 2 points 

2 points 0 o-2 Points 

2 points 

\, O \b o” “,” 

I// 

3 pointZ’ 

\ 

2 points 

0 a. 

Point 

I 

line 

.lK I ,A I I11111 I ,1111111 I I I I Illll 

.l 

LiW FLOW FROM MEASURED STREAMFLOW. IN CUBIC FEET PER SECOND 

I I I I1111, 

10 100 1000 

Figure 17.-Plots showing comparison of 3-day 20-year low flow from measured streamflow with 3-day 

20-year low flow from regression equation for gaging stations in central and east Tennessee. 

31 
Drainage areas for gaging stations used in the regression analyses for 

central and east Tennessee streams ranged from 2.68 to 2,557 mi2. The 

following table summarizes the distribution of drainage areas used in the 

regression analyses. 

Range in drainage 

area (mi') 

2.68-10 

10-25 

25-50 

50-100 

loo-250 

250-500 

soo-1,000 

l,OOO-2,000 

2,000-2,557 

Total stations 

Number of stations 

in analyses 

:: 

37 

36 

32 

11 

17 

5 

1 

203 

Streamflow-recession indexes used in the regression analyses for central 

and east Tennessee streams ranged from 32 to 240 days per log cycle. The 

following table summarizes distribution of indexes for gaging stations used in 

the regression analyses. 

Range in streamflow- Number of stations 

recession indexes in analyses 

32-40 

41-50 

51-65 

66-80 

81-100 

101-120 

121-140 

141-175 

Total stations 

12 

26 

:; 

38 

31 

28 

A partial analysis of the sensitivity of the regression equations to 

the streamflow-recession index G was performed for one set of conditions for 

the variable G. Results of sensitivity of the equations for west Tennessee 

streams for G equal 50, 100, and 200 are as follows: 

A= 100 mi2, and 

G = 50, then a 10 percent error in G results in about 34 to 38 percent 

difference in 342, 40 to 50 percent for 3Ql0, 44 to 55 

percent for 3420, and 40 to 49 percent for 7Q10; 

for G=lOO, then a 10 percent error in G results in about 20 to 21 percent 

difference in 342, 25 to 28 percent for 3410, 27 to 31 

percent for 3420, and 24 to 27 percent for 7410; and 

for G=200, then a 10 percent error in G results in about 16 to 17 percent 

difference in 342, 21 to 23 percent for 3410, 22 to 25 

percent for 3420, and 20 to 22 percent for 7410. 

32 
Results for sensitivity of the equations for central and east Tennessee 

streams for G = 50, 100, and 200 are as follows: 

A= 100 mi2, and 

G= 50, then a 10 percent error in G results in about 14 percent 

difference in 392, 31 to 34 percent for 3410, 33 to 36 

percent for 3Q20, and 30 to 32 percent for 7410; 

for G=lOO, then a 10 percent error in G results in about 14 percent 

difference in 3Q2, 18 to 19 percent for 3410, 19 to 20 

percent for 3420, and 18 percent for 7419; and 

for G=200, then a 10 percent error in G results in about 12 percent 

difference in 342, 15 to 16 percent for 3410, 16 to 17 

percent for 3420, and 14 to 15 percent for 7910. 

The sensitivity analyses indicate that the sensitivity of the variable 

G in each equation decreases as the value of G increases. 

SUMMARY 

The permissible rate of waste disposal into Tennessee streams is based 

on the 3-day 20-year low flow. Thus, estimates of low flow are very important for waste-disposal regulation, and for determining withdrawal rates for 

water supply. 

Regression equations derived from observed streamflow data at 241 gaging 

stations can be used with streamflow-recession index and drainage area to 

estimate 3-day 2-year, 3-day lo-year, 3-day 20-year, and 7-day lo-year low 

flow in ungaged streams in Tennessee. One set of equations apply to streams 

in west Tennessee, and one set applies to streams in central and east Tennessee. Standard errors of the regression estimates ranged from 24 to 32 

percent for west Tennessee, and from 31 to 35 percent for central and east 

Tennessee. The standard errors apply only to the 241 stations used in the 

regression analyses. 

The relative effects of different rock types and geologic units on low 

flow were accounted for by a streamflow-recession index expressed in days per 

log cycle. Streamflow recession is controlled by the hydraulic characteristics of aquifers within the stream basin. The streamflow-recession index is 

defined as the number of days required for base flow of the stream to recede 

one complete log cycle. These indexes for gaging stations are related to 

the geology of the State. Area1 distribution of the indexes is shown on 

plate 1. 

REFERENCES CITED 

Bingham, R. H., 1982, Low-flow characteristics of Alabama streams: U.S. Geological Survey Water-Supply Paper 2083, 27 p. 

1985, Low flows and flow duration of Tennessee streams through 1981: 

U.S. Geological Survey Water Resources Investigations Report 84-4347, 

32i p. 

33 
Cragwall, J. S., Jr., 1966, Low-flow analysis of streamflow data: Vanderbilt 

University Department of Civil Engineering, Technical Report no. 9, 242 p. 

Daniel, J. F., 1976, Estimating ground-water evapotranspiration from streamflow 

records: Water Resources Research, v. 12, no. 3, p. 360-364. 

Eaton, W. R., 1958, Sumnary of flow duration and low flow at stream gaging stations in Tennessee: U.S. Geological Survey open-file report, 137 p. 

Ferguson, C. C., 1970, Geologic map of the Huntingdon quadrangle, Tennessee: 

Tennessee Department of Conservation, Division of Geology, Map GM g-SW, 

scale 1:24,000. 

Gold, R. L., 1981, Low-flow frequency and fJow duration of Tennessee streams: 

U.S. Geological Survey Open-File Report 78-807, 361 p. 

Hardernan, W. D., Miller, R. A., and Swingle G. D., compilers, 1966, Geologic 

map of Tennessee: Tennessee Department of Conservation, Division of Geology, 4 sheets, scale 1:250,000. 

King, Philip B., 1964, Geology of the Central Great Smoky Mountains Tennessee: 

U.S. Geological Survey Professional Paper 349-C, 148 p., 13 Plates. 

May, V. J., Wood, G. H., and Rima, D. R., 1970, A proposed streamflow data program for Tennessee: U.S. Geological Survey open-file report, 108 p. 

McMaster, W. M., and Hubbard, E.F., 1970, Water resources of the Great Smoky 

Mountains National Park, Tennessee and North Carolina: U.S. Geological 

Survey Hydrologic Investigations Atlas, HA-420, 2 sheets, Scale 1:125,000. 

Parks, W. S., 1974, Geologic map of the Palmer Shelter quadrangle, Tennessee: 

Tennessee Department of Conservation, Division of Geology, Map GM lo-NW, 

scale 1:24,000. 

Riggs, H. C., 1964, The base-flow recession curve as an indicator of ground 

water: International Association of Scientific Hydrology Publication 63, 

p. 352-363. 

Rorabaugh, M. I ., Simons, W. D., Garrett, A. A., and McMurtrey, R. G., 1966, 

Exploration of methods of relating ground water to surface water-Columbia 

River basin first phase, with a section on Direct computation of groundwater outflow by electric analog by B. H. Bermes: U.S. Geological Survey 

open-file report, 124 p. 

Tennessee Valley Authority, 1970, Mineral resources of the Tennessee Valley 

Region: Tennessee Valley Authority, Division of Water Control Planning, 

GeoJogic Branch, map report. 

Trainer, F. W., and Watkins, F. A., Jr., 1975, Geohydrologic reconnaissance of 

the upper Potomac River basin: U.S. Geological Survey Water-Supply Paper 

2035, 68 p. 

34 
Wood, G. H., and Johnson, A. M. F., 1965, Flow characteristics of Tennessee 

streams, part A, Summaries of flow duration and of low and high flows at 

gaging stations in Tennessee: Tennessee Division of Water Resources, 

326 p. 

35 
SUPPLEMENT A 

Examples of Estimating Low Flow for Ungaged Streams 

The following computations demonstrate the application of regression 

equations for estimating low flow in ungaged streams in Tennessee. For the 

first example, assume a stream site is in west Tennessee and that the entire 

basin has a single streamflow recession index. Assume a 30 mi2 basin lying 

within a region having a streamflow-recession index (plate 1) of 140. Esti- 

{mates of low flows for the site are computed in the following manner. 

3Qz = 1.17 x 1~)'~ A'*'* (G-3O)'*43 

342 = .000117 (30)1*02 (140-30)"43 

34, = .000117 (32.1) (830) 

3Q2 = 3.1 ft3/s 

3Q10 = 7.83 x lO-6 A1*06 (G-3O)"86 

3Q,, = .00000783 (30)1*06 (140-30)"86 

3Q,, = .00000783 (36.8) (6,266) 

3Qlo = 1.8 ft3/s 

3QZ0 = 3.28 x lO-6 Aloo (G-3O)2*oo 

3Q2, = .OOOQO328 (30)1*07 (140-30)2'00 

3Q2, = .00000328 (38.1) (12,100) 

3Q20 = 1.5 ft3/s 

74 ,* = 1.16 x lO-5 Aloo (G-30)Ta7' 

7Q,, = .0000116 (30)'*06 (140-30)"" 

7Qlo = .0000116 (36.8) (4,509) 

7Q,, = 1.9 ft3/, 

36 
For the second example, assume a stream site in central Tennessee is 

draining a basin having two streamflow-recession index areas. Seventy percent 

of the basin is in an area with an index of 50, and 30 percent of the basin 

has an index of 140. The entire basin has a drainage area of 80 mi2. The 

estimating equations are used for the entire basin using each of the two 

streamflow-recession indexes, then a weighted average low flow is computed 

based on the percentage of the basin draining each streamflow-recession index 

area on plate 1. Estimates of low flows are computed with the regression 

equations in the following manner. First, assume the entire basin is draining an area having a streamflow recession index of 50. 

3Qz = 2.95 x lO-3 A'*'9 (G-3O)'oo' 

392 = .00295 (80)'*" (50-30)""' 

392 = .00295 (76.6) (20.6) 

392 = 4.7 ft3/s 

Then assume the entire oasin is draining an area having a streamflow-recession 

inaex of 140. 

3Q2 = 2.95 x 1O-3 A'*'9 (G-30)'*" 

39, = .00295 (80)'*" (140-30)""' 

342 = .00295 (76.6) (115.3) 

3Q2 = 26 ft3/s 

The estimated low flows of 4.7 ft3/s and 26 ft3/s for 342 are weighted 

based on the 70 and 30 percent of the basin draining areas of each streamflowrecession index. 

4.7 ft3/s (0.7) = 3.3 ft3/s 

26 ft3/s (0.3) 

weighted average low flow 

The 11.1 ft3/s is rounded 

= 7.8 ft3/s 

= 11.1 ft3/s 

to the nearest whole number, thus, 11 ft3/s is 

the estimated 3Q2 for tne stream site in the second example. 

The same procedure applies for estimating the 3410 low flow. First 

assume the entire basin is draining an area having a streamflow-recession 

index of 50. 

34 1o = 5.33 x lO-4 Aloo1 (G-3O)'*3o 

39'0 = .000533 (80)1*01 (50-30)"3" 

3Qlo = .000533 (83.6) (49.1) 

3Q lo = 2.2 ft3/s 

37 
Then assume the entire basin is draining an area hav ing a streamf 

index of 140. 

3Q'0 = 5.33 x 'O-4 A'*" (G-3O)"3o 

3Q,, = .000533 (80)'*" ('40-30)"30 

3Q,, = .000533 (83.6) (450.6) 

3Q’o = 20 ft3/s 

low-recession 

The estimated low flows of 2.2 ft3/s and 20 ft3/s for 34'0 are weighted 

based on the 70 and 30 percent of the basin draining areas of each streamflowrecession index. 

2.2 ft3/s (0.7) = 1.5 ft3/s 

20 ft3/s (0.3) = 6.0 ft3/s 

weighted average low flow = 7.5 ft3/s 

The 7.5 ft3/s is the estimated 34'0 low flow for the stream site in the 

second example. 

The same procedure applies for estimating 3420 and 74'0 low flows for 

the stream site in the second example. The appropriate equation for estimating 

3920 and for estimating 7Q'O is used for each index area and a weighted 

average low flow is computed based on the percent of the basin draining each 

index area. The estimated 3420 low flow for the stream site in the second 

example is 6.6 ft3/s. The estimated 74'0 low flow for the stream in the 

second example is 7.7 ft3/s. 

For the third example, assume a stream site in east Tennessee. Assume 

the stream is draining a basin having three streamflow-recession index areas 

and 50 percent of the basin has an index of 65, 30 percent has an index of 100, 

and 20 percent has an index of 50. Drainage area of the basin is 125 mi2. 

The estimating equations are used by applying each of the three streamflowrecession indexes to the entire basin, then a weighted average low flow is 

computed based on the percent of the basin in each index area. Estimates of 

low flows for this example are computed in the following manner. First, assume 

the entire basin has a streamflow recession index of 65. 

34, = 2.95 x 'O-3 A'*" (G-30)'*" 

39, = .00295 ('25)"'gg (65-30)"" 

3Q2 = .00295 ("9.1) (36.27) 

3Q2 = '3 ft3/s 

38 
Next, assume the entire basin has a streamflow-recession 

3Q2 = 2.95 x 103 A'*" (G-3O)'*o' 

3Q, = .00295 (125)0'99 (loo-30)'*0' 

3Q; = .00295 (119.1) (73.04) 

3Q2 = 26 ft3/s 

Finally, assume the entire basin has a streamf low-recess ion index of 50. 

39, = 2.95 x lO-3 A"" (G-3O)1*o' 

3Q2 = .00295 (125)0'99 (50-30)1'o' 

34, = .00295 (11%') (20.61) 

34, = 7.2 ft3/s 

index of 100. 

The estimatea low flows of 13 ft3/s, 26 ft3/s, and 7.2 ft3/s are weighted 

based on 50, 30, and 20 percent of the basin draining areas of each streamflowrecession index. 

13 ft3/s (0.5) = 6.5 ft3/s 

26 ft3/s (0.3) = 7.8 ft3/s 

7.2 ft3/s (0.2) = 1.4 ft3,'s 

weighted average low flow = 15.7 ft3/s 

The 15.7 ft3/s is rounded to the nearest whole number, thus, 16 ft3/s is 

the estimated 3Q2 for the stream site in the third example. 

The same procedure applies for estimating 3410, 3420, and 7410 for 

the stream site in the third example. The appropriate equation for estimating 

3Q10, 3420, and 7410 is used for each index area and a weighted average 

low flow computed based on the percent of the basin drainin 

s 

each area. For 

the stream site in the third example, the 3Q10 is 9.7 ft /s, 3420 is 7.9 

ft3/s, and 7Q10 is 9.9 ft3/s. 

The weighted average low flow procedure should be used for all ungaged 

stream sites within the State where the basin is draining more than one 

streamflow recession index area. 

Graphical solutions for the equations for estimating low flows in 

Tennessee streams are presented in figures 1 tnrough 8. The dashed line and 

arrows on figures 1 through 4 indicate the procedure to follow for the 

following example. 

A = 100 mi2 

G = 80, determined from plate 1 

39 
Enter the figures with drainage area (100 mi2) along the vertical scale. 

Move horizontally to the line for a streamflow-recession index of 80, then 

move down to the discharge scale. The following results for west Tennessee 

streams were obtained from figures 1 through 4 for this example: 

from figure 1, 34, = 3.4 ft3/s, 

from figure 2, 34,, = 1.5 ft3/s, 

from figure 3, 3Q,, = 1.1 ft3/s, and 

from figure 4, 7Qlo = 1.7 ft3/s. 

The following results for central and east Tennessee streams were obtained 

using the same methods as described above except figures 5 through 8 were 

used for the following example: 

A = 100 mi2 

G = 40 

from figure 5, 3Q, = 2.9 ft3/s, 

from figure 6, 3Q,, = 1.1 ft3/s, 

from figure 7, 3Q,, = 0.8 ft3/s, and 

from figure 8, 7Q,, = 1.3 ft3/s. 

40 
SUPPLEMENT 6 

Comparison of Low-Flow Estimates for Low-Flow 

Partial-Record Stations in West Tennessee 

[OBS = map index numbers which correspond to those on plate 2; STAN = downstream order station number; DA = drainage area, in square miles; INDEX = 

mapped (plate 1) streamflow recession index number, in days per log cycle 

(index value is a weighted average for basin where the basin lies in multiple 

streamflow-recession index areas); COR3Q20 = estimated 3-day, ZO-year low flow, 

in cubic feet per second, from correlation method; and COM3Q20 = estimated 

3-day, 20-year low flow, in cubic feet per second, from regression equation; 

* = stations used to compute standard error of estimate of the equation for 

partial-record stations assuming low-flow values from the correlation method 

are accurate] 

41 
SUPPLEMENT B 

Comparison of Low-Flow Estimates for Low-Flow 

Partial-Record Stations in West Tennessee 

OBS STAN DA INDEX COR3Q20 COM3Q20 

373 03593295 10.8 

374 03593520 3.06 

376 03594122 7.17 

377 03594123 10.5 

381* 03594422 49.5 

382 03594424 2.50 

383 03594453 7.96 

384 03594467 1.91 

385 03594479 1.22 

387 03594560 20.2 

493 03605060 17.6 65 0 

494 03605062 18.1 65 0 

495 03605067 4.13 65 0 

496 03605070 5.63 65 0 

497 03605073 2.49 65 0 

498 03605076 27.3 65 0 

499 03606230 8.76 195 0 

500 03606250 10.4 250 1.62 

501* 03606300 88.2 230 15.6 

502 03606305 11.3 250 2.40 

503 03606502 13.2 250 1.27 

504 03606530 9.10 245 0 

505 03606535 6.67 175 0 

506 03606537 9.46 75 0 

507 03606542 4.03 250 0 

508 03607265 14.3 265 6.60 

509 07024182 1.43 350 0 

510* 07024200 26.5 350 7.80 

511 07024330 9.99 300 1.00 

512* 07024350 204 315 55.0 

513* 07024400 55.7 275 3.50 

514 07024600 6.37 340 0 

515* 07024700 67.6 320 25.0 

516 07024710 18.6 140 0 

517* 07024730 156 245 44.0 

518* 07024750 34.2 300 9.00 

519* 07024760 93.4 190 10.0 

52ok 07024770 286 210 56.0 

521" 07024800 752 175 145 

522* 07024900 110 215 10.0 

65 0 0.1 

65 0 0 

65 0 0 

65 0 0 

250 12.4 10.3 

250 .lO .4 

65 0 0 

5"; 0" : 

70 0 .2 

.l 

.l 

0 

0 

0 

.l 

.9 

1x 

2:1 

2.5 

1.6 

.5 

.l 

.7 

3.1 

.5 

11.2 

72s:: 

14.5 

2.3 

25.0 

33:; 

10.5 

10.8 

45.2 

82.4 

17.2 

42 
SUPPLEMENT B--Continued 

OBS STAN DA INDEX COK3Q.20 COM3Q20 

523 07024910 23.3 140 0 

524 0 7024920 24.0 140 0 

525* 07025050 238 145 13.5 

526* 07025100 268 135 15.0 

527 07025180 8.44 35 0 

528 07025190 45.6 35 0 

529 07025200 73.8 35 .90 

530 07025219 4.98 32 0 

531 07025220 6.79 32 0 

532 07025222 3.77 32 0 

533 07025460 9.27 32 0 

534 07025640 .14 32 0 

535 07025642 .12 32 0 

536* 0 7025900 1736 180 248 

537 07026030 17.7 32 .52 

538 07026380 62.5 32 0 

539 07026400 38.6 32 0 

540 07027100 14.8 32 .25 

541* 07027290 39.9 70 .lO 

542 07027352 19.8 140 .60 

543 07027400 21.5 250 

544 07027495 4.85 350 

545 07027600 32.3 180 

546* 07927680 687 220 

547 07027900 27.3 32 

548 07027970 11.0 32 

549 07027971 13.6 32 

550 07027980 28.5 32 

551 07028010 1.24 32 

552* 07028200 1048 175 

553 07028600 .95 

554 07028710 16.6 

555* 07028920 173 

556 0 7028950 13.3 

557 07029050 7.23 

558 07029070 53.9 

559 07029090 25.5 

560 0 7029200 16.3 

561* 07029275 310 

562* 07029350 329 

32 

55 

210 

140 

32 

32 

32 

1:; 

90 

9.40 

.92 

.40 

132 

0 

0 

0 

0" 

118 

0 

0 

31.0 

0" 

0 

0 

.28 

28.5 

6.00 

1.2 

1.2 

15.1 

14.3 

0 

0 

0 

0" 

0 

0 

: 

216 

0 

0 

i 

.3 

1.0 

4.2 

1.8 

12;:: 

i 

0 

0" 

117.6 

0 

0 

26.4 

.6 

0 

0 

0 

0 

31.9 

5.8 

43 
SUPPLEMENT B--Continued 

OBS STAN DA INDEX COR3Q20 COM3Q20 

563* 07029370 44.1 240 8.00 

564* 07029373 55.9 200 8.00 

565* 07029374 56.0 200 8.00 

566 07029390 48.3 65 0 

567* 07029480 121 350 30.0 

568* 07029490 122 350 30.0 

569 07029600 24.7 335 12.0 

570* 07029675 51.4 155 3.30 

571 07029680 1.95 350 .60 

572 07029685 4.20 350 .80 

573 07029950 2.16 140 0 

574 07029960 3.24 140 0 

575 07030030 39.4 32 0 

576* 07030050 2308 170 285 

577 07030100 33.9 32 .lO 

578 07030110 10.1 32 0 

579 07030140 83.8 32 0 

580 07030145 9.04 32 0 

581* 07030210 78.7 165 14.0 

582* 07030212 80.6 165 14.0 

583 07030220 15.5 

584 07030260 34.7 

585 07030350 18.2 

586 07030352 91.0 

587 07030355 153 

588* 07030357 726 

589 07030375 24.0 

590* 07030600 597 

591 07030900 7.79 

592 07030910 11.8 

593 07031100 1.68 32 

594* 07031650 699 215 

595 07032185 .90 32 

596 07032210 75.7 35 

597 07032222 9.47 32 

598 07032232 116 32 

599 07032250 182 32 

600 07032310 49.4 32 

140 

32 

32 

32 

13420 

350 

225 

32 

32 

0 

0 

0 

2.90 

3.50 

72.0 

11.3 

150 

0 

0 

0 

135 

0 

i 

0 

0 

.50 

8.3 

7.0 

7.0 

.3 

56.9 

57.4 

::"5 

1:; 

.l 

.l 

0 

255.1 

0 

i 

0 

6.4 

6.6 

.7 

0 

iii 

0 

45.7 

10.1 

116.5 

0 

0 

0 

124.1 

0 

0 

0 

0 

0 

0 

44 
SUPPLEMENT C 

Comparison of Low-Flow Estimates for Low-Flow Partial-Record 

Stations in Central and East Tennessee 

[OBS = map index numbers which correspond to those on plate 2; STAN = downstream order station number; DA = drainage area, in square miles; INDEX = 

mapped (plate 1) streamflow recession index number, in days per log cycle 

(index value is a weighted average for basin where the basin lies in multiple 

streamflow recession-index areas); COR3Q20 = estimated 3-day, ZO-year low flow, 

in cubic feet per second, from correlation method; and COM3Q20 = estimated 

3-day, 20-year low flow, in cubic feet per second, from regression equation; 

* = stations used to compute standard error of estimate of the equation for 

partial-record stations assuming low-flow values from the correlation method 

are accurate] 

45 
1 

2 

3* 

5 

6 

7 

8 

1:* 

11 

12 

13 

14" 

15* 

16* 

17* 

18 

19 

20 

OBS STAN DA INDEX COR3Q20 COM3Q20 

03312300 1.85 50 0.54 0 

03313820 .59 50 0 0 

03313871 .92 50 0 0 

03403750 240 32 .lO .2 

03403800 51.1 32 .lO 0 

03407879 32.8 

03407990 300 32' 

0 0 

.lO .3 

03410000 1.21 0 

03410010 5.27 3322 ii 0 

03410050 712 35 2.90 2.2 

03414340 34.6 33 0 .l 

03414350 33.7 32 0 0 

03414470 

03414680 23.4 70.8 50 0 1.50 1:: 

03417695 15.3 65 1.10 

03417850 40.3 65 .80 1:: 

03418030 13.8 65 1.60 .6 

03418060 74.2 60 2.8 

03418189 11.2 45 

ii 

.2 

03418520 14.8 32 0 0 

03419000 101 32 0 .l 

03419140 9.80 70 i .5 

03419170 

03419178 3.09 2232 

03419182 6.67 

3322 0 00 

0 0 

03419270 37.7 60 4.50 1.4 

03420125 29.0 35 .lO .I 

03420165 

03420180 6.52 .20 50 32 : i 

03420185 157 32 0 .l 

297 140 44.0 68.1 

31.1 120 5.00 5.3 

30.2 120 4.20 5.1 

2.92 120 0 

3.01 120 1.00 :; 

2.20 120 0 

18.5 120 5.70 3:: 

5.07 

8605 

.lO 

21.1 1.30 1:: 

6.36 80 .64 .5 

21 

22 

23 

24 

25 

26* 

27* 

28 

29 

30 

;;z 

33* 

34 

35* 

:;* 

g: 

40* 

03420880 

03421200 

03422600 

03422610 

03422620 

03422649 

03422700 

03422802 

03422900 

03422950 

SUPPLEMENT C 

Comparison of Low-Flow Estimates for Low-Flow Partial-Record 

Stations in Central and East Tennessee 

46 
SUPPLEMENT C--Continued 

OBS STAN DA INDEX COR3Q20 CObl3QZO 

41* 03423100 6.96 80 0.44 

42* 03423200 7.37 80 .50 

43* 03423250 17.4 80 1.10 

44* 03423400 34.2 65 1.50 

45* 03424520 29.8 60 2.00 

46* 03424600 31.1 35 .13 

47 03424620 9.53 35 .17 

48" 03424640 38.0 42 .70 

49 03424650 92.1 35 0 

50 03424680 41.2 63 0 

51 03424700 12.9 35 

52" 03424750 227 43 

53 03424790 10.4 35 

54 03424800 12.0 35 

55 03424850 43.0 35 

56* 03424900 26.9 35 

57 03425060 14.6 32 

58 03425080 50.9 32 

59 03425200 19.1 36 

60 03425290 64.0 36 

0 

2.7 

0 

0 

0 

61 03425300 74.2 

62 03425350 22.3 

63 03425355 25.4 

64 03425360 106 

65 03425580 15.6 

66 03425600 11.0 

67 03425610 32.4 

68 03425618 22.9 

69 03425622 55.i3 

70 03425624 97.3 

36 

3366 

37 

32 

32 

32 

40 

38 

37 

71 03425645 4.74 35 

72 03425698 2.35 32 

73 03425700 3.32 32 

74 03425775 2.28 32 

75 03425800 .86 32 

76 03425850 32.4 32 

77 03425851 1.39 32 

78 03426000 19.2 46 

79 03426030 38.1 40 

80 03426390 31.2 36 

0' 

10 

0 

0 

0 

0 

i 

0 

0 

0 

: 

i 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0.5 

.5 

E 

1.10 

.l 

0 

.4 

1:: 

0 

2.7 

0 

0 

.l 

.l 

0 

0 

.l 

.3 

.3 

11' 

.5 

i 

0 

.2 

:; 

0 

0 

0 

0 

0 

0 

0 

.3 

.3 

.l 

47 
SUPPLEMENT C--Continued 

OBS STAN DA INDEX COR3Q20 COM3Q20 

81 03426400 46.0 36 

82* 03426700 7.03 55 

83 03426840 5.42 42 

84 03426860 28.5 47 

85* 03426900 125 51 

86 03426920 10.9 32 

87 03426950 30.7 33 

88 03426960 48.2 33 

89 03427000 37.0 32 

90 03427700 10.5 32 

91 03427720 10.3 32 

92 03427800 56.3 32 

93 03427820 12.4 33 

94 03428050 24.5 32 

95 03428100 165 32 

96 03428190 5.85 32 

97 03428200 177 32 

98 03428400 49.9 32 

99 03428410 51.3 32 

100 03428490 2.58 32 

101 03429050 50.8 32 

102 03429500 69.7 32 

103 03429900 11.1 32 

104 03430020 35.6 32 

105 03430130 5.23 32 

106 03430145 .53 35 

107 03430150 29.4 33 

108 03430400 12.0 33 

109 03430700 3.86 35 

110 03430900 58.3 33 

111 03431060 93.4 34 

112 03431070 101 34 

113 03431085 107 34 

114 03431100 1.51 35 

115 03431120 3.30 35 

116 03431200 7.42 35 

117 03431350 14.2 35 

118 03431580 13.3 35 

119 03431599 51.3 35 

120 03431610 5.29 35 

0 

.35 

0 

0 

3.20 

0 

0 

i 

0 

0 

0 

0 

0 

0 

0 

2.10 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0.2 

.2 

.l 

.5 

2.8 

0 

0 

.l 

0 

0 

0 

0 

0 

0 

.l 

0 

.2 

0 

0 

0 

0 

.l 

0 

0 

0" 

0" 

0 

.l 

.2 

.2 

.2 

0 

0 

i 

0 

.2 

0 

48 
SUPPLEMENT C--Continued 

OBS STAN DA INDEX COK3920 COM3Q20 

121 03431630 

122 03431640 

123 03431660 

124 03431668 

125 03431680 

126 03431900 

127 03432000 

128 03432200 

129 03432250 

130 03432300 

2.21 

1.25 

1.43 

12.0 

1::: 

64.6 

25.7 

11.4 

15.9 

35 

35 

35 

35 

35 

33 

33 

33 

34 

34 

131 03432310 6.85 33 

132 03432320 138 33 

133 03432330 10.2 34 

134 03432335 9.55 34 

135 03432350 191 33 

136 03432360 194 33 

137 03432400 210 34 

138 03432420 3.65 35 

139 03432500 66.9 36 

140 03432900 17.6 35 

141 03432950 27.2 

142 03432960 5.06 

143" 03433720 80.2 

144* 03433810 27.2 

145* 03433910 66.2 

146* 03434580 727 

147* 03434585 5.05 

148 03434590 13.3 

149* 03434595 13.8 

150* 03434640 107 

35 

9"; 

80 

100 

55 

80 

80 

80 

90 

151* 03434700 

152 03435002 

153* 03435044 

154* 03435110 

155* 03435120 

156" 03435300 

157 03435580 

158 03435602 

159 03435604 

843 

27.3 

78.4 

19.7 

69.2 

547 

.43 

.48 

17 

183 

60 33.0 

50 .lO 

52 1.90 

50 .35 

53 1.00 

70 27.0 

50 0 

50 0 

50 0 

160 03435705 50 0 

i 

0 

0 

.lO 

.lO 

.lO 

0 

i 

0 

0 

4.00 

2.30 

6.00 

21.2 

.40 

.20 

.60 

7.20 

0 

0 

i 

00 

.l 

0 

0 

0 

0 

.2 

i 

.3 

.3 

.5 

0 

:: 

.1 

0 

27:; 

8.0 

21.5 

.4 

1.0 

1.0 

10.5 

32.1 

.6 

1.9 

1:; 

30.9 

0 

0 

0 

0 

49 
SUPPLEMENT C--Continued 

06s STAN DA INDEX COR3Q20 COM3Q20 

161 03435727 3.09 

162 03435772 1.65 

163 03435791 2.22 

164 03435805 1.54 

165 03435808 .43 

166 03435950 1.32 

167* 03436130 20.5 

168* 03436300 69.3 

169* 03436440 179 

170* 03436490 455 

171* 03436655 52.2 120 

172* 03436930 55.7 120 

173 03437060 11.4 120 

174 03437080 2.37 120 

175 03437090 1.95 120 

176 03437196 2.85 80 

177* 03454790 32.6 100 

178* 03461260 5.22 100 

179 03461508 12.5 50 

180 03461510 13.5 50 

181 

182* 

183" 

184* 

E 

187 

188* 

189* 

190 

191* 03468196 3.48 120 .56 

192* 03469100 46.1 140 8.60 

193* 03469105 3.74 100 .20 

194" 03469119 18.0 100 1.90 

195* 03469130 110 105 12.4 

196* 03469230 20.0 135 3.20 

197* 03469253 31.8 125 4.70 

198f 03469282 7.23 130 1.25 

199 03469290 3.89 100 .ll 

200* 03469400 59.9 125 7.70 

03464915 6.32 100 2.45 

03465220 57.3 100 5.0 

03465610 23.1 120 3.40 

03465631 4.21 120 .96 

03466234 15.5 120 2.25 

03466910 18.7 65 0 

03467470 9.30 65 0 

03467895 9.30 82 .74 

03468050 30.8 70 1.95 

03468085 1.90 65 0 

50 

50 

50 

50 

50 

50 

80 

:o" 

77 

0 

0" 

0 

0 

0 

1.40 

5.60 

9.10 

94.0 

0.1 

0 

0 

0 

0 

0 

1.5 

1;:: 

104 

10.0 8.9 

6.00 9.5 

0 1.9 

0" ::: 

0 .2 

3.10 3.9 

.21 .6 

1.02 .3 

1.05 .3 

.7 

6.9 

3.9 

2:; 

.8 

.4 

.7 

1.7 

.l 

.6 

10.4 

.4 

2.1 

14.7 

4.2 

5.8 

1.4 

11:; 

50 
SUPPLEMENT C--Continued 

OBS STAN DA INDEX COR3Q20 COM3Q20 

201* 03469620 50.2 65 3.30 

202* 03470330 28.3 80 2.40 

203* 03478550 48.0 120 10.4 

204* 03478590 a.32 115 1.70 

205 034 78639 2.98 120 0 

206* 03481700 6.77 75 .63 

207" 03481800 24.4 75 1.38 

2oa* 03451815 70.0 75 4.44 

209* 03484200 57.8 105 6.20 

210* 03484797 32.6 100 7.10 

211* 03486230 39.0 

212* 03486488 6.78 

213 03486660 a.74 

214* 03486860 9.06 

215* 03487100 20.3 

216* 03487548 36.3 

217* 03487562 43.2 

218 03490300 9.22 

219* 03491800 32.3 

220 03491900 2.60 

221* 03492005 3.13 100 .44 

222* 03492995 30.6 80 2.50 

223 03494695 7.91 80 .20 

224* 03494800 58.8 50 1.70 

225* 03494955 3.62 80 .50 

226* 03497113 6.36 80 1.08 

227" 03497200 60.1 165 19.5 

228* 03498715 17.9 120 4.00 

229* 03499000 13.5 120 2.30 

230* 03499053 11 .a 120 1 .a0 

231* 03499055 30.6 

232* 03499062 32.0 

233* 03499110 352 

234 03499160 2.49 

235" 03499290 5.00 

236* 03499412 10.5 

237* 03518130 60.3 

238* 03518456 59.9 

239* 03518470 21.7 

240* 03518750 25.2 

100 

70 

120 

120 

120 

110 

100 

80 

1% 

120 

120 

105 

80 

120 

1;: 

105 

175 

57 

2.3 

2.1 

a.2 

1.3 

.5 

1:: 

4.6 

::; 

4.40 4.7 

.32 .4 

4.10 1.5 

1.40 1.5 

3.40 3.4 

4.10 5.2 

4.50 5.2 

2.50 .7 

.60 .7 

.5o .4 

.4 

2.3 

1:; 

:i 

la.0 

3.0 

2.3 

2.0 

8.10 5.2 

7.20 5.4 

66.0 47.5 

0 .2 

.60 .a 

1 .oo 1.0 

9.90 9.5 

9.40 7.9 

a.00 7.1 

1.50 .a 

51 
SUPPLEMENT C--Continued I 

OBS STAN DA INDEX COR3Q20 COM3Q20 

241" 03519000 271 105 46.0 36.5 

242* 03519600 11.2 120 1.20 1.9 

243* 03519660 43.4 120 8.40 7.4 

244 03519682 2.62 120 .30 .4 

245* 03519700 30.7 110 5.40 4.4 

246* 03527700 4.83 50 .11 .l 

247* 03528200 21.7 50 .30 .5 

248 03528240 8.50 65 1.90 .4 

249f 03531700 23.9 105 3.50 3.1 

250* 03531800 4.65 65 .30 .2 

251* 03534200 39.3 65 2.40 

252 03534400 4.98 65 0 

253* 03534500 9.45 67 .30 

254* 03534509 11.4 70 .65 

255* 03535055 103 87 8.40 

256" 03535183 7.12 82 1.10 

257" 03535187 36.4 70 2.50 

258* 03535195 52.5 76 3.60 

259* 03535200 56.1 79 4.20 

260* 03535400 86.8 82 6.20 

261 03538000 6.01 

262 03538200 55.9 

263* 03538215 18.4 

264 03538243 1.78 

265* 03538244 12.4 

266 03538247 2.40 

267 03538296 13.8 

268 03538398 31.2 

269 03538600 12.0 

270 03539750 153 

271 03539860 50.3 

272 03540793 19.5 

273 03541303 34.3 

274 03541487 19.0 

275 03541990 3.48 

276* 03541995 11.8 

27?* 03542000 108 

278 03542500 95.9 

279 03542503 6.69 

280* 03542505 3.03 

87 

46 

35 

65 

;"5 

34 

35 

32 

32 

0 

4.10 

15 

:11 

1.00 

0' 

10 

0 

0 

0 

33 0 

32 0 

34 0 

5382 0" 

62 1.85 

35 .44 

32 0 

65 .64 

65 .20 

1.8 

.2 

.5 

.6 

9.4 

.6 

Z:i 

4.1 

6.9 

.5 

.9 

1 

11 

.7 

0' 

1 

.l 

0 

. 1 

.l 

0 

.l 

0 

.l 

.5 

.3 

.l 

.3 

. 1 

52 
SUPPLEMENT C--Continued 

OBS STAN DA INDEX COR3Q20 COM3Q20 

281* 03543300 32.3 

282-k 03544220 6.48 

283 03556560 4.39 

284* 03556700 3.82 

285* 03557200 9.90 

286* 03557300 101 

287* 03564920 7.40 

288" 03565087 33.5 

289 03565130 2.90 

290 03565405 2.04 

291* 03565410 24.3 140 3.10 

292" 03565437 22.1 140 7.80 

293* 03565444 26.8 140 10.0 

294* 03565730 69.3 140 19.5 

295* 03566050 15.6 100 1.70 

296* 03566102 21.2 100 2.00 

297* 03566106 25.2 100 2.50 

298* 03566112 35.1 100 3.80 

299* 03566117 2.87 120 .16 

300* 03566123 2.81 120 .52 

301* 03566128 42.1 120 8.20 

302* 03566137 11.6 120 1.80 

303* 03566235 65.9 120 6.00 

304 03566253 3.12 84 0 

305 03566271 5.84 65 0 

306 03566292 57.2 32 0 

307 03566319 17.6 40 0 

308 03566400 49.0 35 0 

309 03566410 18.1 65 1.75 

310* 03566430 10.8 65 .30 

311 03566530 62.6 

312 03566533 5.05 

313* 03566550 6.68 

314* 03566625 108 

315 03566985 2.63 

316 03566990 4.55 

317 03566996 12.1 

318* 03567400 153 

319* 03567494 14.2 

320* 03567496 19.3 

105 

65 

50 

57 

76 

170" 

120 

140 

120 

35 

65 

65 

25" 

65 

66 

120 

120 

120 

5.60 

.22 

.95 

10 

:50 

18.5 

.96 

6.00 

0 

.30 

0 

0 

.29 

3.01 

.lO 

0 

.23 

28.0 

2.60 

2.65 

4.3 

.3 

.l 

.l 

.7 

9.9 

::: 

.6 

.3 

5.4 

4.9 

6.0 

15.7 

1.9 

2.5 

3.0 

4.2 

1; 

7.2 

1;:; 

.3 

.3 

0 

.l 

.2 

:i 

.2 

:: 

3.7 

.1 

.2 

.6 

26.4 

2.4 

3.3 

53 
SUPPLEMENT C--Continued 

OBS STAN DA INDEX COR3Q20 COM3Q20 

321* 

322 

is34 * 

325 

326* 

327 

328 

329* 

330* 

331 03570650 

332 03570800 

333 03570810 

334* 03570840 

335 03570855 

336 03570870 

337 03571320 

338 03571700 

339 03571775 

340* 03571825 

341 03571827 4.42 75 0 

342 03572030 .42 50 0 

343" 03572090 78.2 50 .58 

344 03577966 25.7 50 0 

345 03577985 22.4 49 0 

346" 03578030 21.6 48 .21 

347 03578190 18.4 125 0 

348* 03578500 41.3 80 3.20 

349* 03578504 50.5 92 4.00 

350 03579620 12.3 140 .29 

351* 03579700 41.2 

352 03580000 20.2 

353 03580200 10.3 

354" 03580500 77.1 

355* 03580700 24.6 

356 03581000 23.1 

357 03582532 26.1 

358 03582646 22.5 

359 03583319 52.0 

360* 03583330 28.9 

03567590 12.1 80 0.50 

03567940 3.00 120 .lO 

03568630 63.9 65 3.20 

03568670 70.7 65 4.60 

03569016 1.16 65 0 

03569193 6.37 65 .15 

03569245 22.6 32 0 

03570480 20.6 32 0 

03570560 12.1 100 1.40 

03570602 106 93 5.10 

154 93 

15.4 32 

66.1 33 

1% 3656 

17.9 35 

6.14 32 

12.9 51 

16.9 50 

117 52 

140 

50 

50 

9": 

50 

35 

40 

41 

105 

0.9 

.5 

5:: 

.l 

.3 

0 

0 

1::; 

9.50 16.2 

0 0 

0 .l 

.20 .3 

0 0 

0 .l 

0 0 

0 .3 

0 .4 

2.85 2.8 

.3 

0 

1.7 

.5 

.4 

3:: 

3.1 

5.1 

2.7 

8.40 

12 

:55 

4.50 

4.40 

1.90 

0 

0" 

2.55 

9.3 

.4 

.2 

;:6" 

:: 

:25 

3.8 

54 
SUPPLEMENT C--Continued 

OBS STAN DA INDEX COR3Q20 CObl3QZO 

361* 03583400 86.6 

362* 03583480 22.9 

363* 03584050 8.10 

364 03584300 35.7 

365 03585200 13.5 

366 03587270 23.5 

367 03587300 38.8 

368" 03588200 18.6 

369* 03588260 53.6 

370* 03588340 31.5 

371" 03588515 8.58 140 .90 

372* 03588600 46.6 140 10.0 

375" 03593585 21.7 130 6.60 

378* 03594140 84.4 95 6.50 

379 03594163 15.5 51 0 

380 03594200 19.0 77 0 

386* 03594484 251 150 55.0 

388 03594900 3.29 140 .15 

389 03594920 7.12 140 .17 

390 03595000 55.2 135 4.00 

391* 03595100 13.0 140 2.26 2.9 

392 03595200 19.2 135 .75 4.0 

393* 03595500 40.4 120 4.60 6.9 

394 03595300 8.64 140 .56 1.9 

395 03596090 22.8 140 1.00 5.1 

396 03596100 28.1 140 2.80 6.3 

397* 03596130 30.6 140 11.0 6.9 

398 03596200 3.32 140 0 .7 

399 03596543 .45 77 1.20 0 

400 03596550 5.92 56 2.36 .2 

401* 03596700 16.8 50 .20 .4 

402 03596900 12.1 45 0 .2 

403* 03597200 80.1 51 1.60 1.8 

404* 03597220 85.5 50 1.70 1.8 

405 03597535 5.97 34 0 0 

406 03597600 36.4 35 0 .1 

407* 03597787 17.2 52 .68 .4 

408 03597800 18.3 51 .90 .4 

409* 03597900 49.6 34 .lO .l 

410 03598100 30.7 35 0 .1 

70 

50 

zi 

140 

140 

140 

140 

140 

140 

6.70 

.50 

l lO 

0 

0 

2.85 

2.90 

4.40 

6.00 

10.5 

4.8 

.5 

.2 

3:: 

5.3 

4"*; 

12:1 

7.1 

1.9 

10.5 

4.2 

9.2 

1:; 

64.9 

.7 

1.6 

11.7 

55 
SUPPLEMENT C--Continued 

OBS STAN DA INDEX COK3Q20 COM3Q20 

411 03598150 9.32 32 

412 03598180 40 32 

413 03598190 31.5 33 

414 03598250 71.9 32 

415 03598298 23.7 32 

416 03599100 48.7 33 

417* 03599250 916 62 

418 03599300 28.9 32 

419 03599403 41.6 32 

420* 03599418 1028 60 

421 03599420 9.24 32 

422 03599421 6.21 32 

423* 03599450 74.0 35 

424* 03600256 32.8 38 

425 03600280 15.1 41 

426 03600410 6.39 35 

427* 03601080 14.8 95 

428* 03601100 48.3 74 

429 03601250 36.7 34 

430* 03601500 112 54 

431* 03601550 45.2 72 4.40 

432* 03601700 99.8 115 23.0 

433 03601855 25.5 140 0 

434* 03601900 154 130 44.0 

435* 03601980 5.69 95 .56 

436* 03602110 9.0 95 1.15 

437* 03602192 21.2 140 5.00 

438* 03602200 6.21 80 .50 

439* 03602229 6.31 110 .56 

440* 03602232 13.7 120 1.05 

441* 03602245 19.8 140 5.80 

442 03602316 12.6 140 0 

443* 03602590 22.9 140 6.40 

444* 03602630 7.64 140 2.10 

445* 03602660 30.8 140 4.15 

446* 03602700 51.2 140 8.10 

447* 03603479 26.9 125 4.90 

448* 03603500 75.1 130 19.0 

449* 03603540 21.4 140 6.30 

450* 03603560 12.1 140 3.30 

0 

0 

; 

0 

0 

23.5 

0 

0 

30.0 

0 

0 

.20 

.55 

i 

1.15 

3.50 

.29 

2.30 

0 

0 

0 

.l 

0 

.l 

38.2 

: 

39.2 

0 

0 

.2 

l 2 

.l 

0 

1.6 

3.0 

.1 

3.1 

2.7 

15.8 

5.7 

30.7 

.6 

1 .o 

4.7 

.5 

2:; 

4.4 

2.8 

5.1 

1.7 

1::; 

4.9 

14.9 

4.8 

2.7 

56 
SUPPLEMENT C--Continued 

OBS STAN DA INDEX COK3Q20 COM3Q20 

451* 03603580 101 

452* 03603586 10.1 

453* 03603590 15.3 

454* 03603600 126 

455* 03603690 19.3 

456* 03603710 6.57 

457 03603713 4.67 

458* 03603716 20.1 

459* 03603730 24.6 

460* 03603770 56.6 

461 03603780 6.85 

462* 03603850 22.8 

463* 03603860 12.3 

464* 03603900 56.4 

465 03604012 16.2 

466 03604020 14.3 

467 03604030 1.68 

458* 03604050 516 

469 03604120 21.0 

470* 03604150 15.2 

471* 03604200 45.1 

472* 03604240 83.6 

473* 03604620 31.3 

474 03604900 2.22 

475 03605200 10.8 

476 03605500 20.1 

477 03605525 27.4 

478 03605580 6.22 

479* 03605953 24.8 

430* 03605968 54.5 

481 03607585 .78 

482 03607590 .73 

433 03607598 .46 

484 03607300 2.14 

435 03608310 2.04 

486 03608020 4.15 

487 03608022 .59 

488 03608030 1.79 

489 03608035 2.23 

490 03608040 1.29 

491 03608043 1.53 

492 03608046 1.00 

140 

140 

140 

140 

140 

130 

140 

135 

135 

95 

105 

140 

140 

115 

130 

130 

140 

120 

55 

105 

115 

14906 

120 

120 

120 

120 

120 

120 

120 

120 

120 

120 

120 

120 

120 

120 

120 

120 

120 

120 

120 

16.00 

1.36 

2.60 

25.0 

5.00 

2.00 

0 

3.00 

4.10 

11.5 

22.9 

2.2 

2::; 

4.3 

1.3 

1.0 

4.2 

5.2 

6.1 

0 

2.40 

1.58 

7.90 

0 

0" 

105 

2.00 

2.30 

.9 

5.1 

2.7 

8.9 

3.2 

2.8 

.4 

90.0 

.6 

2.0 

10.0 7.1 

18.1 9.3 

7.30 7.0 

0 .4 

0 1.8 

.58 3.4 

1.10 4.6 

0 1 .o 

2.00 4.2 

6.00 9.3 

0 

0 

i 

0 

0 

0 

0 

0 

0 

0 

0 

.l 

.l 

1 

14 

.3 

.7 

.l 

.3 

.4 

.2 

.3 

.2 

57 
0000000000 0000000000 0000000000 0000000000 

6 

ooooooomoo Nln000N0000 001Dh00maJ00 h000000000 

mmmOmO~hwO oommo-cumc0m ocow~wQocoaJ”m 00b-~hCOLOhOLD 

.C . aOrnbll)LOWV)hhcu cocomcnoooooo -N*ewOlOlOahh cumo---cornbe 

%S 

oo.-~-~-cF---c ?,--,NNNNNN NNNNNNNNNN ~~mmmmmmmm 

bebbetd-=f*bb ecrbbbbbbbb bbctbb*bQbb bbbU~~-tbbb 

=: 

mmmmmmmmmm mmmmmmmmmm mmmmmmmmmm mmmmmmmmmm 

0000000000 0000000000 0000000000 0000000000 

58 
wm-mnrtm~mo~ mo 2 m wow?- w 

. . . . . . . . . . . . . . . . . . 

~wo(u-lnm~lnmw o~F?wcuwm~mw 

. . . . m Q1.--Vl7Wh wV)--b-wh(Um- (; o ok.... . . . . . . . . . . 

w- - h.- -mm OIN ?-w-?-Y 

s 

? c m m 

ohulooommoo 01WbOUlWV)hWOJ ooooo%toooo NCUCUbOmoooN 00w0wm00N~ NtnmlnwwmOh7 ~00wwwo00N 

-cc-- 7-77 F- rnWLDrnCOhOh--0 

- - 7 77 

cv(Y-o-0 mm rumom - 

. . . . . . meOk% NbNI-0 Lw 

. . . . . . 

Trmw WV) - 

w~ww~Nwu7wo m7-mhmwmwm 

*~-wOw-mV)Cd . . . . . . . . . . . . . . . 

Nm-~-mw-~~ 

“o”“g.--~--~g 

I--b- WC-JCOCUN(U~V)hCli 

I-m,-,- c cu ^z---“-N”N 7 - ” 

OhOOOOOOOO oomomoooor? oooooov)ooo 00~000-000 ooowoooNow oooNmoo.-00 

woo*hmO-(Ub blnmlnmmwwww hmmOCUmwO~N hO*womm-wc.-J mhwwO*(U--N 00w0cu0(\1-00 

wwwm--*wLDw v)omwwoum~N 

mmmm”mm”mm **-r*cfb-cr*-=r* mr.-JmLnwwwwww wwww6hhwmmm 

wwwwwwwwww 

moww-Nb~mw 

rfbbbUbWcr-=tb WOhhhWWWWWW 

mmmmmmmmmm 0000000000 mmmmmm~mmm 

e-u-=tb-u-=fueu 

mwa,mmmmmmmc, 

-rbbbr+ebbbb 

0000000000 0000000000 mmmmmmmmmm 0000000000 

59 
t-+?hCO~UlWD(UCOPI+- *NWO5U3o)OcU’W mO”mhN hbrn COmwhOdNmOm 

. . . . . . . ..I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

0NV)t-BNt-O “ZZ 

mmN.-hObmCU* egcu ,mgm WIN In -(\I 

” N 7 

0 

wuJhctmOCOCDOh 0wm00mwOh00 0 WCOCUN CUhO co~om~wwomm 

. . . . . . . . . . . . . . . . . . . . 4.“; . . . . .,’ . . . . . . . . . 

I-NWbNW “ZZ ~wN”~2wm~~ 

V)WNui hu?-cd r-h m 

cu 

we-bwcu?-m N UlQ3UbhNN*Q3mO NwmuYN-O-CUw wON(Uwa3m-mhO 

d4ri’o;n;c; 

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

“EiF m(u--wwm3cuoIT “E’ m,gm ww m 0 

t-3 7 c 

60 
N co “WWWOh 

. . . . . . . 

ujr;mcobe*‘btn O~Wl--3Q)b”bNW Num.- 

‘~~~““‘“” 

. . . . . . . . . . . . . . . . . . 

~r-r-d&* -r-. 

syoo e 

. . 

w-wzl%w--mh 

?*-u) 

h m c N -cu 

m-m&d 

h 

0 h NO”,,- Nwohw~mo~ 

mm03 

. . . . . 

-0-roG0;-wh 

~m100h~--0001 m-o 

. . . . . . . 

cc- 

;;&ome -7 

NW-0 0 

. . . . . . . . . . . . . 

C? 

e - 

h m-w2:“--“h - ““S - 

’ ‘c-k&&+ 

oov)ov)oooo 

r-u-l--bhNNNN Ou-JOOLoOCQOh0 

Nw~mmmQwww 

ON00mmm000 Ow00h000mO 

-?cc---,-- 7 -7 N~cocnCOwwLncovi tn’m~mtnowh~ -7 - 7 

wocoowoooo 

r’)0600bQ3NW 000w00000m ooo~oomooo 0000000000 

No-v)moo.-- mooNv)wNNmb 

~hh-~l.nY)ww Nmu-l-NN~*~w 0co0~00~000 lnmwpa3ow*ow- ooooowooouJ 

wmwwwwwwww h000.-~-alaJol mcoNom,mmornN 

*mwwwwwww wwwwwwwwww WDhhhhhhhhh OO.-Nmmmcr’bw 

~*~uJulmu)mm oJa3aJcocoCOcocomm 

~mmmmmmc9m 

LDmwmtnmmtn*uY mv)wwuJmmv)mm u-lmlnmlnmv)uJwm 

000000000 

mmmmmmmmmc*, 

0000000000 

mmm,mmm,mmmm 

0000000000 

mmmmmmmmom 

0000000000 

61 
62 
e 

h WO 0 

ONN rov)Ql-o- ~OmOv)OmW 0 N: NrncoW~-r 02 0 08W8 w 

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 

“5;“““~e.l~ “~~c3’2~ g=;z 

2 - Nwmr2zmz 

N 

lnootnuiooooo 00m000~mm0 oouioowooo oooowomoooo~ 

OIw~Nm-m-eOO 

s-s--I-NNNN 

ooooolnoooo 

wowoomwooo 

000000000 oooooomooooo 

?u000N0w0000 

Oc--mw*NmON 

0000000000 V)OONOO~OOO 

NmmhOmmrnOm 

ooooooowo 

V)hOwmo-m~ ebmhOO~NbWhU7 

bbc+b~LnWWhh 

0000000000 

~b~~Wv)Lov)WrN hhQ)wwmQImm mmmmoooooo~ui 

NNNNNNNNNN NNNNNNNNN NNcuNmmmmmmmm 

wwwwwwwwww 

mmmmmmmmmm 

0000000000 

hhhhhhhhhh 

000000000 

hhhhhhhhh 

00000000000I 

hhhhhhhhhhhm 

0000000000 0000000000 000000000 000000000000 

**c+ **CC****** **+**u**+ ***CC+***** 

-NmUmWhwmO 

ooooooooo- 

-Nmbww~wmo -NmWfmW-wm o-wmb~whwmoc 

7--------N NNNNNNNNN mmmmmmmmmma* 

NNNNNNNNNN NNNNNNNNNN NNNNNNNNN NNNNNNNNNNNN 

63 

*U.S. GOVERNMENT PRINTING OFFICE 1988-631-262/40003