Effect of Irrigation

Withdrawals on Stage of 

Lake Washington, Mississippi

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1460-1

Prepared in cooperation with 

the Mississippi Board of 

Heater Commissioners

Effect of Irrigation 

Withdrawals on Stage of 

Lake Washington, Mississippi

By G. EARL HARBECK, JR., HAROLD G. GOLDEN, and EDWARD J. HARVEY 

CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1460-1

Prepared in cooperation with 

the Mississippi Board of 

Water Commissioners

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1961
UNITED STATES DEPARTMENT OF THE INTERIOR 

STEWART L. UDALL, Secretary

GEOLOGICAL SURVEY 

Thomas B. Nolan, Director

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

Washington 25, D.C. - Price 20 cents (paper cover)
CONTENTS

	Page 

Abstract___ _ ____________________________________________________ 359

Introduction.___ __________-___________-_------__--_-----_--_---_-- 359

Acknowledgements _______-______________-_--_-_____--____-__----_- 360

Description of the area.____________________--_-__-_--------_-----_- 360

Climatology-_._-_______________________--_-__-__-_----__-_----- 362

Ground-water conditions_________^____-__--__-___-_--_---_-----_-_- 362

Instrumentation_ _ __________________-__-_-_-_____---__--__------- 366

Theory and analysis_________________________---_____----_-___----- 367

Hydraulic considerations.__________________________________________ 373

Seepage as indicated by water-table elevations________________________ 374

Conclusions_ ____________________________________________________ 388

References cited___________________________________________________ 388

ILLUSTRATIONS

FIGURE 33. Map of Lake Washington, Miss., and vicinity showing location of instruments._________________________________ 361

34. Variation in monthly rainfall at Greenville, Miss._________ 363

35. Relation between fall in stage of Lake Washington and product u (e 0 ea) for spring and fall periods__-_------------ 370

36. Seasonal variation in seepage losses and gains, Lake Washington, Miss__________________________________ 372

37. Section A A', water-table elevations in Lake Washington 

vicinity during October and December 1956 and April 

1957_--___-______________________________---_ 375

38. Section B B', water-table elevations in Lake Washington 

vicinity during October and December 1956 and April 

1957___--_-_______.________________________ 376

39. Elevation of water surface in alluvium on November 11-23,

1954__ ________________________________--_-- 377

40. Elevation of water surface in alluvium in April 1955.______ 378

41. Elevation of water surface in alluvium in June 1955__ _____ 379

42. Elevation of water surface in alluvium on January 20, 1956 _ 380

43. Elevation of water surface in alluvium on October 4-9, 1956_ 381

44. Elevation of water surface in alluvium on December 27, 28,

1956______.________________________________ 382

45. Elevation of water surface in alluvium on April 18, 1957_ 383

46. Elevation of water surface in alluvium in March 1958__-__- 384

47. Elevation of water surface in alluvium on September 9, 1958_ 385

48. Rise in water levels from November 1954 to March 1958- __ 386

49. Water-surface elevations of Lake Washington and Mississippi River near Kentucky Bend, year ending September 

30, 1957_--__-_________________________-__----__--- 387

in
IV CONTENTS

TABLES

Page 

TABLE 1. Maximum and minimum water-surface elevations of Lake

Washington, Miss., for the water years 1955-58___________ 362

2. Hydrologic and meteorologic data at Lake Washington for

selected periods in the 1957 water year_________________ 371
CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

EFFECT OF IRRIGATION WITHDRAWALS ON STAGE OF 

LAKE WASHINGTON, MISSISSIPPI

By G. EARL HARBECK, JR., HAROLD G. GOLDEN, and 

EDWARD J. HARVEY

ABSTRACT

The increase in the amount of water pumped from Lake Washington, Miss., 

for supplemental irrigation caused concern among residents of the area over the 

possible effect of the irrigation withdrawals on the stage of the lake, which is used 

for recreation. Records of the stage of Lake Washington, ground-water levels 

in the area, and meteorological data were used to determine the seasonal variation 

in the amount of seepage into and out of the lake. In spring, the nearby 

Mississippi River is high, and the net seepage into Lake Washington is much 

greater than the out seepage during fall, when the river is low.

Irrigation withdrawals in 1957 were small compared with both rainfall on the 

lake and seepage into the lake. If the rate of irrigation withdrawals ever became 

large enough to lower the lake level by more than a few inches, those withdrawals 

would be partly balanced by an increase in the amount of seepage into the lake 

when the ground-water level in the area is high. Thus an increase in the amount 

of water withdrawn would not result in lowering the lake level by an equivalent 

amount.

INTRODUCTION

This report describes an investigation of the effects of irrigation 

withdrawals on the level of Lake Washington, Washington 

County, Miss. The increase in the amount of water pumped from 

the lake during the drought period 1951-56 caused concern among 

residents of the area over the possible effects of the withdrawals 

on the level of the lake, which is an important recreation center. 

This concern led local people to request a study of the problem. 

The Mississippi Geological Survey, W. C. Morse, director, assisted 

in an earlier preliminary investigation in late 1954. The present 

study was conducted between October 1956 and September 1958 

in cooperation with the Mississippi Board of Water Commissioners, 

Sam A. Thompson, chairman. The results of the observations 

and the conclusions derived from analyses of the data are the basis 

of this report. The report was prepared in the Water Resources 

Division of the U.S. Geological Survey, L. B. Leopold, chief hydraulic engineer.

359
360 CONTRIBUTION'S TO THE HYDROLOGY OF THE, UNITED STATES

The lake-level, meteorological, and streamflow data were obtained 

by personnel of the Surface Water Branch, Jackson, Miss., under 

the administrative supervision of I. E. Anderson, district engineer, 

succeeded by W. H. Robinson, and under the technical supervision 

of G. Earl Harbeck, Jr., research engineer, General Hydrology Branch. 

The data on ground-water conditions in the Lake Washington area 

were obtained by personnel of the Ground Water Branch, Jackson, 

Miss., under the administrative supervision of J. W. Lang, district 

geologist.

The summer and fall of 1954 were extremely dry throughout 

Mississippi. Many streams receded to new minimum flows of record. 

The water surface of Lake Washington was lower than it had been 

for several years, according to local residents who were concerned 

that the low level of the lake was the result of withdrawal of water 

for supplemental irrigation of cotton, corn, soybeans, and pasture, 

rather than from the drought. Withdrawals for irrigation during the 

1954 growing season probably totaled less than 1,000 acre-feet. 

They were estimated to total about 600 acre-feet in 1957, a year of 

more seasonal rainfall.

Lake Washington is a popular resort and fishing site. Consequently, 

the low water level of the lake caused concern among recreational 

interests, who assumed that the irrigation withdrawals were largely 

to blame. In 1954, supplemental irrigation was a comparatively 

new practice in the area. Landowners anticipated that irrigation 

withdrawals from Lake Washington might expand within a few 

years to perhaps 10 to 20 times the amount used in 1954.

ACKNOWLEDGEMENTS

Many persons living in the vicinity of Lake Washington contributed 

to this study. W. F. McKamy, Jr., served as rain-gage observer, 

and made observations of maximum-minimum water temperatures 

prior to the installation of the recording thermograph. W. H. Caffey, 

Roy Shanks, and Wayne Reed served as rain-gage observers. The 

Highland Club permitted the installation of a water-stage recorder 

on its pier. Rife Wade permitted the installation of meteorological 

equipment on his private pier. The irrigators making withdrawals 

from Lake Washington maintained logs of their operations. The 

cooperation and assistance of these people were evidence of the keen 

local interest in the problem, and were greatly appreciated.

DESCRIPTION OF THE AREA

Lake Washington is an oxbow lake in the "Delta" area of northwestern Mississippi about 25 miles south of Greenville. The crescentshaped lake (fig. 33) whose surface area is about 3,300 acres, occupies
EFFECT OF WITHDRAWALS ON STAGE, LAKE WASHINGTON, MISS. 361

D 

Rain gage

EXPLANATION

o Observation well Levee

A 50 <X> Meteorological equipment Depth of well, in feet Water-stage recorder

A A'

Line of sections for

water-table elevations

0

! I . I I I__________

2 MILES 

J

FKJTJEE 33. Map of Lake Washington, Miss., and vicinity showing location of instruments.

1 or possibly 2 old meanders of the Mississippi Kiver and is about 1% 

miles from Kentucky Bend on the north and 5% miles from Carolina 

Landing on the south. The lake is about 8 miles long, lying generally 

north-south, and % to % mile wide. The shoreline, except for the 

north and south ends, is composed of high banks with a few drainage 

ditches sloping into the lake. The north and south ends of the lake 

are low marshy areas that are inundated during winter and spring. 

The elevation at the lowest point of the lake bottom is estimated to 

be about 75 feet above mean sea level. The drainage area trib-
362 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

utary to the lake is small compared to the area of the lake surface. 

A low-head dam, with the spillway crest at an elevation of 96.9 feet, 

is located at the lake outlet to Washington Bayou. Maximum and 

minimum water-surface elevations during the 1955-58 water years 

are given in table 1.

TABLE 1. Maximum and minimum water-surface elevations of Lake Washington, 

Miss., for the water years 1955-58.

Water year

1955__. -_______.-_.._.

1956. _________________

1957 ___ _ _ _ __ ____

1958---_-_--_--______

Maximum elevation (in feet 

above mean 

sea level)

99. 19

98. 68

98.96

102. 72

Date

Mar. 24

Mar. 17

Mar. 6

May 11

Minimum elevation (in feet 

above mean 

sea level)

i 95. 10

95.42

95. 26

97. 17

Date

Oct. 24-27

Nov. 2, 3 

Sept. 30

Oct. 20

Oct. 14

1 May have been less prior to recorder installation Oct. 20,1954.

CLIMATOLOGY

The climate at Lake Washington is humid. The mean January 

temperature is 46°F, the mean July temperature is 82 °F, and the 

mean annual rainfall is 51.9 inches at Greenville, Miss., according to 

U.S. Weather Bureau records. The maximum temperature recorded 

during 1902-41 is 110°F, the minimum, 5°F. A comparison of 

monthly observed rainfall during 1951-57 with the mean monthly 

rainfall at Greenville (fig. 34, based on U.S. Weather Bureau records), 

indicates that rainfall in 1951, 1953, and 1957 was about normal or 

above, but rainfall in 1952, 1954, 1955, and 1956 was below normal. 

Greenville is located near the Mississippi River about 20 miles north 

of Lake Washington. There is little or no difference in the climate at 

Greenville and at Lake Washington.

GROUND-WATER CONDITIONS

Oxbow lakes such as Lake Washington are abandoned meander 

loops of the Mississippi River. Older lakes are filled with fine-grained 

material such as clay, silt, and fine sand. Where the material is relatively impervious it forms a seal or barrier to water movement and is 

referred to as a clay plug. Younger lakes are partly filled. On the 

inside of the meander loops are the point-bar deposits. In these, sand 

occurs commonly at or near the ground surface and extends down to 

the top of the Tertiary bedrock. The upper part of the sand is more 

or less silty. The sand occurs at shallow depth as indicated by the 

depths of driven wells, which range from 19 to 38 feet. The location 

and depth of wells in the vicinity of Lake Washington are shown on
Mean monthly rainfall

FMAN FMAN FMANFMAN

FIOTIEE 34. Variation in monthly rainfal
364 CONTRIBUTION'S TO THE HYDROLOGY OF THE, UNITED STATES'

figure 33. On the outside of the meander loop are the backswamp 

deposits consisting of clay and silt with some sand. Although there 

are some shallow wells in this area, the wells tend to be deeper (19 to 

71 feet) than in the inside of the meander loops.

The clay plug underlying Lake Washington and other oxbow lakes 

is the abandoned filled-in channel of the river; it is crescent shaped, 

conforming to the lake bottom, and the fine-grained sediments may 

reach depths of 60 to 80 feet below the land surface. Cross sections 

of other oxbow lakes in the alluvial plain show that the clay plug 

generally has steep sides and underlies the lakes along their entire 

lengths. Fine-grained materials consisting of clay, silt, and lenses of 

sand probably underlie both Lake Jackson (fig. 33) and Lake Washington. Wells located on the bank and along the extension of Lake 

Jackson, and at the lower end of Lake Washington, were driven to 

depths of 71 to 100 feet, probably because they could not be completed 

at shallower depths for lack of sand. A short distance from the edge 

of Lake Washington shallow wells are also present, indicating that 

the belt of impermeable deposits does not extend landward far beyond 

the shores of the lake.

During the nongrowing season and periods of favorable rainfall the 

area of point-bar deposits will allow recharge to the water table. The 

backswamp area will allow recharge also, but to a lesser extent than 

that in the point-bar area. Kecharge will be the least in the clayplug area as the clay extends deeper, and the clay-plug area is narrow 

in contrast to the backswamp area.

The water-level contour maps, figures 39-47, are based on elevations established in the summer of 1955 by instrumental leveling to 

67 driven wells and 1 irrigation well in the vicinity of Lake Washington. Well depths and water levels were measured in November 1954, 

and water levels in many of the wells have been measured on many 

occasions since then.

Water-table conditions should exist in the point-bar area and 

artesian or semiartesian conditions probably occur in the backswamp 

area. Water under water-table conditions will stand at the height 

at which it is first tapped in a water-bearing stratum. Water under 

artesian conditions rises in a well to some height above the top of the 

water-bearing stratum. Semiartesian conditions exist where watertable and artesian conditions are known to exist at different times of 

the year in the same place. This has been observed in other parts of 

the delta where continuous records are obtained of water levels in 

abandoned irrigation wells.

The water in the ground-water reservoir comes from several sources; 

rainfall on the land and lake surface in the general area of Lake Washington, seepage from the Mississippi River, and probably upward
EFFECT OF WITHDRAWALS ON STAGE,, LAKE WASHINGTON, MISS. 365

movement of water from the underlying artesian aquifers in the Tertiary formations. The source of water in the area of Lake Washington 

is largely rainfall, although a part of the water available must be 

derived from the river, because the annual rise of the river prevents 

loss of water to the river, and a small amount probably infiltrates to 

the ground-water reservoir.

A large amount of water is in storage in the shallow sand and gravel 

deposits that extend to depths of 100 feet or more. Although more 

water is stored in clay and silt per equivalent volume of material 

(because of higher porosity) than in sand and gravel, this water is not 

readily available because of the much lower permeability of the finegrained material. In sand and gravel the ground water is readily 

available. Pumping tests of wells so far made in the delta have 

yielded storage coefficients ranging from values characteristic of watertable conditions (0.1) to values characteristic of artesian conditions 

(0.005). The coefficient of storage of an aquifer is defined as the 

volume of water it releases from or takes into storage per unit surface 

area of the aquifer per unit change in the component of head normal 

to that surface. It is expressed as the decimal fraction of a cubic foot 

of water discharged from each vertical column of the aquifer having a 

base 1 foot square as the water level falls 1 foot. For water-table 

conditions the storage coefficient is practically equal to the specific 

yield of the material drained or filled; for artesian conditions it is equal 

to the water obtained from storage by the compression of a column of 

water-bearing material whose height equals the thickness of the waterbearing material and whose base is 1 foot square, plus a small amount 

derived by expansion of the water itself as the pressure head declines.

Ground water in the alluvium is in continuous movement from 

places where the elevation of the water table is high to places where 

it is lower. The point-bar deposits west of Lake Washington constitute a recharge area. Ground water drains in all directions from this 

area where the water table is high. Although Lake Jackson lies within 

the recharge area, it is doubtful that in a short tune much water sinks 

to the water table through the lake bottom, as it is underlain by the 

plug of relatively impervious silt and clay. Over a long period of 

time, however, the amount of water added to the water table would be 

great.

Much of the rainfall available for recharge probably soaks into the 

sandy area surrounding the lake after soil moisture depleted during the 

growing season has been replenished during the nongrowing season, 

and begins its movement to the lake, river, or tributary streams. 

Late in the year when the lake is low, water seeps into the lake from 

its flanks and discharges through the ground northward and southward to the river. In spring the reverse is true (figs. 37-48). Water
366 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

movement is perpendicular to the contour lines on the water-table 

maps.

The volume of water per unit cross-sectional area that seeps into or 

out of the lake is proportional to the product of the permeability and 

the hydraulic gradient. This is in accord with Darcy's law, expressed 

in the form Q=PIA, in which Q is the quantity of water discharged in 

gallons per day, P is the permeability in gallons per day per square 

foot, / is the hydraulic gradient measured in a direction perpendicular 

to the contour lines of the water table on piezometric maps, and A 

is the cross-sectional area, in square feet, through which the water 

percolates.

The permeability of the alluvial deposits under the land surface 

surrounding Lake Washington is much higher than the permeability 

of the deposits beneath the lake itself if the lake is mostly underlain 

by a clay plug. Since Lake Washington is not entirely filled with 

mud, as Lake Jackson is, there probably is a fringe of moderately permeable material surrounding the lake reaching from the shoreline 

out into the lake to some unknown depth. Water may move more 

freely through this material than it can through much of the bottom farther from shore. Test holes would show the relationships. 

However, a gravel-washing plant located several years ago on the 

west shore of Lake Washington is evidence of the presence along that 

reach of shoreline of permeable deposits through which ground water 

might move freely in either direction.

According to Darcy's law the quantity of water seeping into or 

out of the lake is directly proportional to the hydraulic gradient. If 

the hydraulic gradient doubles owing to lowering of the lake level, 

the seepage should likewise double. However, the validity of Darcy's law may be questionable when applied to deposits such as this 

where the entire section is not completely saturated. The possible 

variability in permeability of the sides and bottom of the lake precludes the possibility of using Darcy's law with any assurance of accuracy in computing the amount of water draining into or out of the 

reservoir, without a certain amount of test drilling and extensive 

permeability tests.

INSTRUMENTATION

A continuous record of the level of Lake Washington has been obtained since October 20, 1954, except for periods when the recorder 

clock was stopped. Several water-stage recorders were operated in 

a wooden shelter over a 30-inch corrugated steel-pipe well attached 

to the south side of the Highland Club pier (fig. 33). The stillingwell intakes were eight %-inch diameter holes in the pipe wall. All 

gage-height record is referred to mean sea level, datum of 1929. A 

weekly recorder with a 10:12 gage-height ratio (10 inches on the
EFFECT OF WITHDRAWALS ON STAGE, LAKE WASHINGTON, MISS. 367

chart equals 1 foot of water) was in use October 8 to December 24,, 

1956, and May 20 to August 19, 1957. A continuous recorder with 

a 4:12 gage-height ratio and a 4.8-inches-per-day time scale was inuse December 24, 1956, to May 20, 1957.

The temperature of the lake water at the surface was measured 

with a maximum-minimum thermometer located near the recorder 

site. The temperature record was not complete because wave action 

moved the slugs in the thermometer and the entire thermometer 

several times. A recording thermometer was installed at Wade's 

pier on June 17, 1957, to assure a more accurate measurement of the 

average lake-surface temperature.

All the meteorological equipment was located at Wade's pier (fig. 

33). Wind speed was measured by two anemometers (airways type, 

3-cup) located 100.5 feet and 103.0 feet above mean sea level (2.5 

feet and 5.0 feet above the water surface on April 30, 1957). An 

operations recorder was used to record the wind-speed data. The 

electrical circuit for the upper anemometer frequently failed to operate, and this record was discarded.

Temperatures and humidities were measured with a weekly recording hygrothermograph. The humidity was checked once weekly, 

when the hygrothermograph chart was changed, with a sling 

psychrometer.

Four nonrecording standard U.S. Weather Bureau rain gages were 

located near the lake (fig. 33). The observers measured rainfall 

amounts once each day.

Surface outflow from Lake Washington was measured weekly by 

current meter at a low-water control downstream from the low-head 

dam. These discharge measurements defined a rating curve relating discharge to lake stage. Daily discharges were taken from the 

rating curve, using daily mean gage heights obtained from the recorder charts.

Withdrawals from Lake Washington were measured by current 

meter where possible. Estimates of rate of withdrawals were made 

using the rated capacity of pumps and other methods. Irrigators 

kept logs of their time of operation so that the volume of withdrawals 

could be computed.

THEORY AND ANALYSIS

The basic technique used in measuring the net seepage into and out 

of Lake Washington was first developed by Langbein and others 

(1951, p. 13-15). After allowance has been made for surface inflow 

and outflow, the change in reservoir stage consists of two components, 

evaporation and seepage. In the mass-transfer theory of evaporation, 

the exchange of water vapor between a water surface and the atmos-
368 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

phere is calculated from measurements of certain factors affecting the 

removal of water vapor from a lake by processes of turbulent diffusion 

and transport. Many equations have been suggested for this purpose. 

A; discussion of the differences between the different equations is 

beyond the scope of this report but has been given elsewhere (Marciano 

and Harbeck, 1954, p. 46-70; Harbeck and others, 1958, p. 29-35). 

All the mass-transfer equations can be expressed in a form similar to 

the following:

E=Nu(e0 -ea) (1) 

in which

E= evaporation

i£=wind speed, in miles per hour

£0=saturation vapor pressure corresponding to the temperature of 

the water surface, in millibars

ea=vapor pressure of the air, in millibars

The equations differ primarily in the mathematical expressions used to 

compute the value of the coefficient N. In the Langbein technique the 

the value of Nis of no consequence; it is merely assumed that evaporation is proportional to the product u (e0 e^).

In the complete absence of wind, evaporation occurs only by 

molecular diffusion, an extremely slow process. Using an equation developed by Yamamoto (1950, p. 354) itcan be shown that evaporation in 

still air is very small, even if vertical convection currents exist. Evaporation is also very small when the vapor-pressure difference, (e 0 ea) 

is almost zero, for then the layer of air over the lake is saturated with 

water vapor. For the present study, it is assumed that evaporation is 

zero as a result of either u or (e 0 ea) being zero, as stated in equation 1.

The application of the foregoing theory to the measurement of 

seepage is straightforward. For several selected periods, the change 

in stage in the lake, the wind speed, the water-surface temperature, 

and the humidity of the air were measured. The change in stage for 

each period (AH) was plotted against the product u (e 0 ea)' The 

intercept on the AH axis represents the net seepage loss or gain, for at 

this point evaporation is zero.

The length of period to be used was determined primarily by the 

accuracy with which changes in lake stage could be measured. Preliminary studies at Lake Washington were made using a stage-gage 

reading directly to 0.0001 foot. Stage observations were made at 

5-minute intervals during a 6-hour period on October 5, 1956. The 

results indicated that wind-induced seiches in the lake were 

sufficiently large to obscure the changes in stage caused by evaporation 

and seepage, at least for periods as short as a few hours. The record 

obtained with a continuous water-stage recorder did not permit 

measuring changes in stage as precisely as did the above-mentioned
EFFECT OF WITHDRAWALS ON STAGE, LAKE WASHINGTON, MISS. 369

direct-reading gage; therefore, it was necessary to increase the length of 

the time interval to obtain a change in stage of comparable accuracy. 

Moreover, as there was only one recording gage, it was necessary to select 

periods so that the beginning and end of each period fell at times when 

the lake was calm, to avoid errors resulting from the water surface not 

being level or from surges in the stilling well. The data were divided 

into two groups, one consisting of periods in October, November, and 

December 1956, when the Mississippi River was at alow stage, and the 

other of periods in May and June 1957, when the river was at a high 

stage.

The periods selected in each group were of different lengths, ranging from, 24 to 153 hours (table 2). Rainy periods were excluded 

because surface inflow to the lake was not measured, and because 

average rainfall on the lake surface could not be determined with 

sufficient accuracy from the few rainfall records available. Changes in 

stage were taken from the water-stage-recorder chart and adjusted, 

if necessary, for outflow from the lake. For each of the priods, average air temperature and relative humidity were taken from the hygrothermograph record; average water-surface temperature was computed 

from the readings of the floating maximum-niinimum. thermometer, 

and average wind speed was obtained from the anemometer record. 

The anemometers were rigidly mounted at the end of a pier, therefore 

the height of an anemometer above the water surface varied with the 

lake stage. During the periods in the fall of 1956, the lower anemometer was 4.8 feet above the water surface and in the spring of 1957, it 

was 2.9 feet above the water surface. Assuming a logarithmic variation of wind speed with height and using a surface roughness parameter 

estimated from vertical velocity profiles obtained at other lakes, the 

recorded wind speeds during spring were increased by 5 percent to 

make them comparable with those recorded during the previous fall. 

An error in this adjustment would only change the slope of the regression slightly.

In this analysis the slope of the line is unimportant; the intercept 

provides the desired answer. From these data the product u (e0 ea) 

was computed for each period and the results plotted against AH, 

the change in stage (fig. 35).

A similar analysis was made for selected periods in July and August 

1957, but the correlation was poor, probably because the seepage rate 

was changing rapidly at that time.

In a preliminary statistical analysis, the October-December data 

and the May-June data were considered to be completely independent. 

A regresssion coefficient was computed for each set of data; there 

was no significant difference between the two regression coefficients, 

and an average of the two was therefore used for both groups. The
370 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

0,03

-0.01

50 60 70

u , in miles per hour 

PRODUCT u(e0 -ej e , j n millibars

FIGURE 35. Relation between fall in stage of Lake Washington and the product u (e, e<,) for spring and

fall periods.

intercepts were, of course, not the same. That there was no statistically significant difference between the regression coefficients is 

in accord with the results of other studies of mass-transfer theory. 

Only at lakes much larger than Lake Washington is the seasonal 

effect of changes in atmospheric stability noticeable. Such an effect 

would cause significantly different regression coefficients for the two 

groups of data.

The average intercept of 0.0024 foot per day during October, 

November, and December 1956, indicates that the stage would 

have fallen that amount each day if there had been no evaporation. 

In other words, there was an average net seepage loss from the lake 

of 0.0024 foot per day. During May and June 1957, there was an 

average net seepage gain of 0.0061 foot per day. At these rates 

there would be a net loss of 430 acre-feet during a 60-day period 

in fall and a net gain of 890 acre-feet during a 44-day period in spring, 

assuming an approximate surface area of 3,000 acres in fall and 3,300 

acres in spring.

The seepage losses and gains for the two periods represent the 

average loss or gain during those periods, not necessarily the peak 

rates. Little is known concerning seepage rates between the two 

periods; there is probably a gradual seasonal change from inseepage 

to outseepage. An idealized sinusoidal seasonal variation is shown 

in figure 36. Planimetering the areas above and below the horizontal 

line of zero seepage shows that, during October 1956 to January 

1957, net seepage out of Lake Washington totaled about 650 acre-feet 

and that, during February to September 1957, seepage into the lake
TABLE 2. Hydrologic and meteorologic data at Lake Washington for 

Period

From To

Length 

of 

period 

(hours)

Observed 

fall in 

stage 

(feet)

Correction 

for surface 

outflow 

(feet)

Adjusted 

fall in stage 

(feet per 

day)

Average 

water-surface temperature

A

a

p

)ct. 11 (7:00 p.m.) _ .

3ct. 13 (5:00 p.m.).....

3ct. 15 (12:00 p.m.)....

)ct. 17 (12:00 p.m.). ...

)ct. 22 (12:00 p.m.)....

)ct. 23 (12:00 p.m.)....

3ct. 27 (10:00 p.m.)....

3ct. 31 (9:00 p.m.).....

sTov. 3 (12:00 p.m.) ....

NOV. 7 (12:00 p.m.)....

3ec. 3 (12:00 p.m.)....

Oct. 13 (5:00p.m.)..._.

Oct. 14(5:00p.m.) .

Oct. 17 (12:00 p.m.) 

Oct. 20 (6:00 a.m.).....

Oct. 23 (12:00 p.m.)....

Oct. 25 (4:00 a.m.).. ...

Oct. 28 (10:00 p.m.)....

Nov. 1 (9:00 p.m.) .....

Nov. 5 (6:00 a.m.).. ...

Nov. 11 (10:00 p.m.),..

Dec. 10 (9:00 a.m.)....

46

24

48

54

24

28

24

24

30

94

153

0.0235

.0085

.021

.018

.006

.008

.0075

.0075

.007

.064

.014

0

0

0

0

0

0

0

0

0

0

0

0.0123

.0085

.0105

.0080

.0060

.0069

.0075

.0075

.0056

, 0163

.0022

22.5

22.3

23.2

22.8

22.2

22.0

22.0

20.3

20.8

15.7

13.2

1957 

May 13 

May 14 

May 15 

May 17 

May 29 

May 30 

June 5 (: 

June 6 (1 

June 14 

June 25

12:00 p.m.)... 

12:00 p.m.)... 

12:00 p.m.) ... 

12:00 m.).....

7:00 a.m.).... 

7:00 a.m.)..__ 

2:00 p.m.). ... 

2:00 p.m.) .... 

9:00 p.m.). ... 

6:30 a.m.).___

May 14 (12:00 p.m.) ... 

May 15 (12:00 p.m.) ... 

May 17 (12:00 m.).....

May 18 (12:00 m.) ..... 

May 30 (7:00 a.m.) .... 

May 31 (7:00 p.m.).... 

June 6 (12:00 p.m.) .... 

June 7 (12:00 p.m.) .... 

June 16 (9:00 p.m.) .... 

June 26 (6:30 a.m.)....

24 

24 

36 

24 

24 

36 

24 

24 

48 

24

0.030 

.020 

.048 

.027 

.021 

.027 

.015 

.015 

.045 

.017

0.028 

.026 

.036 

.021 

.010 

.013 

.017 

.016 

.019 

.016

0.0020 

-.0060 

.0080 

.0060 

.0110 

.0093 

-.0020 

-.0010 

.0130 

.0010

25.6 

27.0 

27.8 

28.6 

29.2 

29.4 

27.2 

28.0 

29.0 

28.9
372 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

totaled about 3,100 acre-feet. These estimates are subject to error, 

but they indicate that seepage into the lake was much greater than 

seepage out of the lake. Moreover, seepage into the lake was probably much greater than the amount of water pumped for irrigation 

during the summer of 1957. During July 18 to August 19, pumping 

records and estimates of nonrecorded pumping indicate that about 

425 acre-feet of water was used for irrigation. Presumably, irrigation began in July and continued until the rains began in September. 

The total volume of water used during the summer probably did 

not exceed 600 acre-feet, which is equivalent to a depth of abojit 

2 inches over the lake surface area.

Net seepage into Lake Washington during the year that ended 

September 30, 1957, was about 2,500 acre-feet. The discharge of 

the Mississippi River at Vicksburg was in the normal range during

Net seepage gained, 

3100 acre-feet

Net seepage lost, 

650 acre-feet

OCT. NOV DEC FEB MAR APR MAY JUNE JULY AUG SEPT

1956 1957

FIGUEE 36. Estimated seasonal variation in seepage losses and gains at Lake Washington, Miss. Net 

seepage lost from October to January and gained from February to September. Hatched areas represent 

loss of 430 acre-feet during period of meteorological observation, October 11 to December W, 1956, and gain 

of 890 acre-feet during period of observation, May 13 to June 26,1957.

that same period, and the seepage amount was reasonably representative of normal conditions.

During the 1957 water year, surface outflow from Lake Washington was about 3,500 acre-feet, which agrees with the outflow 

that might be expected. Average annual rainfall at Greenville is 

51.9 inches. If this amount is applicable to Lake Washington, 

rainfall on the lake surface is about 14,000 acre-feet. According 

to U.S. Weather Bureau records, gross evaporation from Lake Washington is about 44 inches, or 12,000 acre-feet. The difference of 

about 2,000 acre-feet would become surface outflow. Adding the 

net seepage of 2,500 acre-feet calculated for 1957, the total surface 

outflow (neglecting surface inflow) would be 4,500 acre-feet. Thus, 

the outflow from Lake Washington as measured in 1957 (3,500 acrefeet) and as estimated from clirnatological data (4,500 acre-feet) 

agree reasonably well, and in normal years the outflow from the
EFFECT OF WITHDRAWALS ON STAGE', LAKE WASHINGTON, MISS. 373

lake should be about 4,000 acre-feet. The- period of maximum 

outflow from the lake is several months earlier than the period of 

irrigation demand. Raising the outlet structure only 4 inches 

would provide an additional 1,000 acre-feet of storage, which is 

much more than the volume of water withdrawn for irrigation in 

the summer of 1957.

HYDRAULIC CONSIDERATIONS

During July and August 1957, the volume of water withdrawn for 

irrigation was about half as great as the surface outflow from the lake. 

Because the period of maximum lake level does not coincide with 

the period of maximum irrigation demand, raising the level of the 

dam that controls the outflow would provide additional storage for 

irrigation use. Irrigation withdrawals have not yet greatly lowered 

the lake level. Withdrawals in 1957 were equivalent to a depth of 

only about 2 inches over the lake-surface area. Moreover, about 

two-thirds of the water pumped during 1957 was pumped prior to 

mid-August, when outflow ceased. " ;

Although the lake was spilling much, of. the time when water was 

being pumped for irrigation, it cannot be assumed that the irrigators 

were merely using water that would otherwise hava" been .wasted. 

This argument would be valid if Lake Washington/spilled.at all times. 

But if the lake ceases to spill in summer,, the date at which it ceases 

to spill would be la.ter if no water had. been withdrawn previously 

for irrigation. However, if 500 acre-feet (equivalent to a depth of 

1.8 inches over the 3,300-acre lake) were withdrawn in a month,-the 

month-end stage would not necessarily have been 1,8 inches higher 

if there had been no pumping. The outflow from the lake depends 

only on the lake stage, and the volume of flow over the. broad-crested 

weir is proportional to the hydraulic head raised to some power 

greater than unity. . -

During May 1957, no water was withdrawn for irrigation;,. The 

lake stage fell 0.6 foot during the month, and total outflow was. about 

2,700 acre-feet. Using the close approximation of a simple exponential rating curve and assuming that the natural fall of 0,6 foot per 

month and the irrigation withdrawals both occurred at a uniform 

rate, a mathematical analysis was made to determine the effect of 

the withdrawal on the lake stage. A withdrawal of 500 acre-feet 

is equivalent to 1.8 inches over the lake surface. But pumping reduced the hydraulic head on the discharge weir, and therefore decreased the outflow from the lake. The net effect was that the lake 

level would have been lowered only an additional 0.4 inch if 500 acrefeet had been withdrawn for irrigation.
374 CONTRIBUTION® TO THE HYDROLOGY OF THE UNITED STATES

SEEPAGE AS INDICATED BY WATER-TABLE ELEVATIONS

Observations of water levels in wells in the Lake Washington area 

were made at irregular intervals during November 1954 to September 

1958. A map showing water-table contours was prepared for each 

set of measurements (figs. 39-47). To investigate the possible relation between the stage of the nearby Mississippi River and seepage 

to and from Lake Washington, two sections were selected, A-A' and 

B-B' (fig. 33). From the topographic map and the maps of watertable contours, sections were constructed to show the gradient of the 

water table in October 1956, December 1956, and April 1967. In 

October 1956 Lake Jackson was nearly dry, and there was a gentle 

gradient from that area toward both Lake Washington and the Mississippi River (fig. 37). Section B-B' indicates that the water-table 

gradient was away from Lake Washington and in the direction of 

Kentucky Bend to the northwest (fig. 38).

The December 1956 sections (figs. 37 and 38) show that gradients 

were similar to those in October, but were not as steep in the direction of the Mississippi River. Lake Washington was still losing 

water by seepage in December, which is in agreement with the estimated seasonal variation in seepage illustrated in figure 36.

During April 1957 the river was at a higher elevation than Lake 

Washington, indicating net seepage into Lake Washington (figs. 37 

and 38). Section B-B' shows that there may have been also some 

seepage out of the lake toward the southeast. The net seepage, however, was into the lake, which is corroborated by figure 36.

Figure 39 shows the general relation between the level of Lake Washington and the stage of the Mississippi River. During late summer, 

fall, and early winter, the river elevation was below the lake elevation. 

During most of February to July, the reverse was true. The seasonal 

variation in the relation between these two water levels is in reasonable agreement with the sinusoidal variation postulated in figure 36.

Changes in water-level elevations in 27 wells in the vicinity of Lake 

Washington and the previously computed figures of seepage losses 

and gains may be used to approximate the storage coefficient of the 

alluvium in the area. During August 2 to October 8, 1956, the decline hi water levels in the 27 wells ranged from 0.17 to 3.66 feet, 

averaging 0.023 foot per day. The seepage analysis indicated that 

during October, November, and December 1956, the net seepage loss 

was 0.0024 foot per day. If the seepage loss during this period is 

associated with the decline in water levels during the antecedent 

months of August to October, the computed storage coefficient is 0.10..

During December 28, 1956, to April 18, 1957, the rise in water 

levels in the 27 wells ranged from 1.30 to 12.48 feet, averaging 0.033 

foot per day. The computed net seepage into Lake Washington dur-
90

70

Average water-surface elevation 

Dec. 27, 28, 1956. Average / 

elevation of Mississippi River 

for preceding 30 days: 81 ft

Average water-surface elevation 

Oct. 4-9, 1956. Average 

elevation of Mississippi River 

for preceding 30 days: 80 ft

0 1 

DATUM IS MEAN SEA LE

FIGURE 37. Section A-A' showing water-table elevations in the Lake Washington vicin
RIVER MISSISSIPPI to I 

Bend) (Kentucky 

Levee

9Z8
Contour interval 2 feet; datum 

is mean sea level

FIGTJEE 39. Water-level contour map of Lake Washington area showing the elevation 
378 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES
 Water-level contour

Contour interval 2 feet; datmn

is mean sea level

FIQUBK 41. Water-level contour map of Lake Washington area showing the elevation 
Water-level contour

Contour interval 2 feet; datum

is mean sea level

FIGTOE 42. Water-level contour map of Lake Washington area showing the elevation 
_ 92 

Water-level contour

Contour interval H feet; datum 

is mean sea level

FIGTJKE 43. Water-level contour map of Lake'Washington area showing the elevation of 
EXPLANATION

 92 

Water-level contour

Contour interval Hfeet; datum

is mean sea level

o 

Observation well

 

Irrigation well

FIGURE 44. Water-level contour map of Lake Washington area showing the elevation of t
Water-level contour 

Contour interval 2 feet 

is mean sea leve

FJGUBE 45. Water-level contour map of Lake Washington area showing the elevation of 
Water-level contour

Contour interval 2 feet; datum 

is mean, sea

FIGTTKE 46. Water-level contour map of Lake Washington area showing the elevation o
- 94 

Water-level contour 

Contour interval 2 feet; datum

FIGURE 47. Water-level contour map of Lake Washington area showing the elevation o
EXPLANATION

o 

4

Rise in water level, in feet

o 

Observation well

 

Irrigation well

FIGURE 48. Kise in water levels from November 
FEET IN LEVEL, SEA MEAN ABOVE ELEVATION 

o o u> 

01 o tn 

NO 'aovxs asvi 'NOXDNIHSVA*. '-SSIH 2,88 
388 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

ing May and June 1957, was 0.0061 foot per day. If spring inseepage 

results from the winter rise in ground-water levels, the computed 

storage coefficient is 0.18.

The above values of storage coefficient, 0.10 and 0.18, are only approximate, and are given only to show that in general, water-table 

conditions prevail in the Lake Washington area. The aquifer is heterogeneous, however and the coefficient varies widely throughout the 

area. A more dependable value of the average for the alluvial deposits 

would aid in determining the probable increase in seepage caused by 

steepened hydraulic gradient in the lake area as a result of increased 

irrigation withdrawals.

CONCLUSIONS

The basic question is the possible effect of increased irrigation withdrawals on the level of Lake Washington. Normal annual precipitation in this area is 52 inches, which over a surface area of 3,300 acres 

is about 14,000 acre-feet. Evaporation from Lake Washington is 

somewhat less than the rainfall, so that in normal years, the lake 

would spill even if it received no surface inflow. Irrigation withdrawals in 1957 were small in comparison with both rainfall on the 

lake and discharge of ground water into the lake. If irrigation withdrawals ever became large enough to lower the lake level appreciably, 

the hydraulic gradient toward the lake would be steeper, thus increasing the seepage into the lake during periods when the Mississippi 

River stage is high or when the water table is high. Also, the relation 

between lake stage and outflow is such that if the volume of water 

pumped for irrigation were increased by a specific amount, the lake 

will not be lowered by an equivalent amount.

REFERENCES CITED

Harbeck, G. E., Jr., Kohler, M. A., Koberg, G. E., and others, 1958, Water-loss 

investigations Lake Mead studies: U.S. Geol. Survey Prof. Paper 298,100 p.

Langbein, W. B., Hams, C. H., and Culler, R. C., 1951, Hydrology of stockwater reservoirs in Arizona: U.S. Geol. Survey Circ. 110, 18 p.

Marciano, J. J.7 and Harbeck, G. E., Jr., 1954, Mass-transfer studies in Waterloss investigations Lake Hefner studies, technical report: U.S. Geol. Survey 

Prof. Paper 269, 158 p.

Yamamoto, G., 1950, Investigations of evaporation from pans: Am. Geophys. 

Union Trans., v. 31, no. 3.

o