Vertical leakage and vertically averaged vertical ... - Wiley Online Library

WATER RESOURCES RESEARCH, VOL. 34, NO. 2, PAGES 159-167, FEBRUARY

1998

Vertical leakage and vertically averaged vertical conductance for karst

lakes in Florida

L. H. Motz

Water ResourcesResearchCenter,Departmentof Civil Engineering,Universityof Florida, Gainesville

Abstract. In the karst lake districtin peninsularFlorida in the southeasternUnited States,as many as 70% of the lakeslack surfaceoutlets,and groundwateroutflowis an importantpart of the water budgetsof theselakes.For 11 karst lakesin the Central Lake District,verticalleakagefrom the lakesto the upperFloridanaquiferaverages0.12 to

4.27rnyr-•. Thevertically averaged vertical conductance Kv/b, a coefficient that representsthe averageof the verticalconductances of the hydrogeologic unitsbetweenthe bottomof a lake and the top of the upperFloridanaquifer,wasdeterminedto rangefrom

0.0394to 1.00yr-• fortheselakes.Forsixof thelakes,various hydraulic parameters previouslycalculatedby other investigators are shownto be equivalentto the Kv/b values calculatedin this study.If Kv/b is determinedfor a lake, then verticalleakagecan be estimatedfor other conditionsof lake stageand hydraulichead in the upper Floridan aquifer,usingKv/b for the lake and Darcy'sequationwritten for verticalflow. The methodologydescribedin this paper for quantifyingKv/b, whichrequiresonly limited data (i.e.,verticalleakage,lake stage,andhydraulicheadin the upperFloridanaquifer),could be usedto investigatethe apparentassociation betweenrelativelylargeKv/b valuesand lake levelinstabilities at somelakesin the CentralLake Districtandsimilarhydrogeologic settings.This methodologyfor calculatingverticalleakageis applicableto the Central Lake Districtin Florida and to other similarlake and groundwatersystems. 1.

Introduction

In water budgetcalculations for lakes,groundwateroutflow canbe a significant componentof thewaterbudget.In seepage lakes,fromwhichlossesoccurbyseepageinto the groundwater [Wetzel,1983],groundwater outflowcanbe quitelarge.Evenin drainagelakes,from whichlossesalsooccurby surfacewater flow from an outlet, the groundwateroutflowcomponentcan be relativelylarge[Deevey,1988],andsomedrainagelakeslose nearlyas muchwater via groundwateroutflowas they do via surfacewater outflow[Annableet al., 1996]. In thispaper,verticalleakageto the upper Floridan aquifer is investigatedfor 11 karstlakesin the Central Lake District in peninsularFlorida. Values for the verticallyaveragedvertical conductanceKv/b are calculatedfor these lakes. This coefficientrepresentsthe averageof the verticalconductances of the

hydrogeologic unitsbetweenthe bottomof a lake andthe top of the upper Floridan aquifer.Also, varioushydraulicparameters previouslycalculatedby other investigatorsfor six of these lakes are comparedwith the Kv/b valuescalculatedin this study.

2.

Hydrogeology

formationsthat underliesFlorida and partsof adjacentstates [Miller, 1986]. Over much of Florida, a low-permeabilitysequenceof rockscalledthe upperconfiningunit of the Floridan aquifersystemseparatesthe Floridan aquifersystemfrom the surficialaquifer.Also, in mostof Florida, lesspermeablecarbonateunitsof subregional extentseparatethe Floridanaquifer systeminto two aquifers,calledthe upper and lower Floridan aquifers. There are approximately7800 lakesin Florida, and most of these are circular-shapedsolution lakes called dolines that occurin surfacedepressions or sinkholes[Palmer,1984;Thornbury,1969].A large numberof theselakesoccurin the central highlandregionof Florida [Hutchinson, 1975],whichis called the Central Lake District physiographicregion by Brooks [1981].This regionis a sandhill karstwith solutionbasinsthat trendsnorth-southalong the longitudinalaxis of peninsular Florida(seeFigure1). In the CentralLakeDistrict,asmanyas 70% of the lakes lack surfaceoutlets [Palmer,1984], and groundwateroutflowvia seepage,or vertical leakage,is an importantpart of the water budgetsof theselakes.Lake levels and groundwaterlevelsin the surficialaquifer generallyare higherthanthe hydraulicheadsin the upperFloridanaquifer, and this regionis a major rechargearea for the underlying upper Floridan aquifer [Stringfield,1966; Stringfieldand Le Grand, 1966;Brooks,1981].

The mean annual rainfall rangesfrom 1.22 to 1.52 m in nearlyall of Florida,and annuallake evaporationrangesfrom about 1.17to 1.32 m [Jordan,1984].The groundwatersystem 3. Water BudgetEquationWith Vertical Leakage that underliesFloridagenerallyconsists of two water-bearing A water budgetfor a lake consistsof accountingfor the units,a surficialaquiferandthe Floridanaquifersystem,which is a regionally extensivesystemof limestone and dolomite principalinflowsand outflowsfor the lake and the resulting changein storagethat occursif inflows and outflowsare not Copyright1998by the AmericanGeophysicalUnion. balanced[Hutchinson, 1975].For manylakesin Florida,deep seepageto the upperFloridanaquiferis an importantpart of Paper number 97WR03134. 0043-1397/98/97WR-03134509.00 the water budget.For these lakes the principalinflowsare 159

160

MOTZ:

VERTICAL

LEAKAGE

I

AND CONDUCTANCE

I

IN FLORIDA

KARST LAKES

ing upper Floridanaquifer (see Figure 2). The water budget for suchlakes can be describedby

30øN

dS/dt = P + Is + R + Ig- E - Os- Og- L

Lake

AI•TAA•L F

(1)

wheredS/dt is the changein lake storagewith respectto time, P is precipitation,Is is surfacewater inflow,R is directrunoff

(i.e.,overland flow),Ig is surficial-aquifer inflow,E is evaporation,Osissurface wateroutflow; Ogis surficial-aquifer outflow; and L is vertical leakage from the lake to the upper Floridan aquifer. Lakesin the karstlake districtof Florida gainwaterfrom the adjoiningsurficialaquifer and lose water to the underlying upperFloridanaquiferby verticalleakagethroughthe confining unit that separatesthe surficialaquifer from the upper Floridan aquifer [Lichtleret al., 1976]. Vertical leakage of

29øN

0.30-0.50m yr-• is considered typical[Deev•y,1988].Studies

• Lake O•taGra•Lake\ • LakeJohio• •

•

•

Lake•

at Lake Lucerne in central Florida indicate that the lakes can

serveas focal pointsfor groundwaterdischargefrom the surficialaquiferandalsoasfocalpointsfor rechargeto the upper Floridanaquifer[Leeet al., 1991]. The lossof water from the bottom of a lake to the underlying upperFloridanaquifer,or verticalleakage(seeFigure3), can be describedin termsof Darcy'sequationwritten for vertical flow, or Kv

Lucern• ©Lake

28øN

L = •- Ah

Roy

where Kv is the verticallyaveragedhydraulicconductivityof the unitsbetweenthe bottomof a lake andthe top of the upper Floridanaquifer,b is the thickness of the hydrogeologic units betweenthe bottom of a lake and the top of the underlying upperFloridanaquifer;Kv/b is the verticallyaveragedvertical

Central take District

(basedon Brooks,1981)

conductance of the units between the bottom of a lake and the

Lake

0

I

15

I

upper Floridanaquifer,and Ah is the differencebetweenthe water surfaceelevation(or stage)of a lake and the hydraulic

30 km

I

Scale

L•

Placid

27ON

I

82ow

(2)

I

81øW

head in the upper Floridanaquifer.As is indicatedby (2), leakagewould not necessarily be constantfor a givenlake, sinceAh can change,and it couldbe quite differentevenfor adjacentlakesif the Kv/b valuesthat characterizethe subsurface units beneath the lakes are different and/or if values of Ah

Figure 1. Locationsof selectedlakes in the Central Lake Districtphysiographic regionof Florida.

are different.

The Kv/b value for a lake includesthe influenceof all the unitsbetweenthe bottom of the lake and the top of the upper

Floridan aquifer.For example,if lake sediments,a surficial precipitationin theformof rainfall,surfacewaterinflow,direct aquifer,anda confining unit arepresent(seeFigure3), Kv/b is runoff (i.e., overlandflow), and groundwater inflowfrom the surficialaquifer,and the principaloutflowsare evaporation, surfacewater outflow,groundwateroutflowto the surficial = (3) aquifer,and deepseepage, or verticalleakageto the underly-

Kv(bLbsA b')-1

whereKvL/bL= verticalconductance of thelakesediments;

08

Figure 2. Waterbudgetcomponents for karstlake.

Figure3. Verticalleakagecomponent.for karstlake.

MOTZ:

VERTICAL

LEAKAGE

AND

CONDUCTANCE

IN FLORIDA

gvsA/bsA = verticalconductance of the surficial aquifer,and K'/b' = vertical conductance,or leakance,of the confining unit. If the leakanceof the confiningunit is significantlyless than the other conductances in the denominatorof (3), then Kv/b • K' /b ' .

4.1.

LAKES

81ø15' W

81•0'W

I....

I

I

AVON •.

ß

PARK I

•xplanation: :i::•.•SEBRING ••©.•'Location Cross Section_ Boring &of Well Location Lake \ SCALœ

Conductance

Selected

Lakes

in the Central

161

81ø•0' W

4. Vertical Leakage and Vertically Averaged Vertical

KARST

0

Lake

5

10km

District

Vertical leakageto the upperFloridanaquiferwascompiled for 11 lakes (Brooklyn,Barco, Kerr, Grace, Orienta, Johio, Sherwood,Lucerne, Roy, Jackson,and Placid) that extend from north to southin the Central Lake District in peninsular Florida(seeFigure 1). Theselakeswere selectedbecausethey are all in the same physiographicregion and thus would be expectedto be in similar hydrogeologicsettings.Also, these l•kes were selectedbecauseadequatepublisheddata for lake stageand hydraulichead in the upper Floridan aquifer were found to be availableto allow valuesfor Kv/b to be calculated

PLACID

LAKE

27"lYN

Placid

for each lake.

4.2.

Generalized HydrogeologicSetting

The generalizedhydrogeologicsettingfor the lakes in the Central Lake District can be representedby a crosssection alongthe HighlandsRidge in the southernpart of the district in which the surficialaquifer,confiningunit, and upper Floridan aquifer are spatiallyhomogeneous units (see Figure 4). Heterogeneitiesin the subsurfaceunitsbetweenthe bottom of the lake andthe upperFloridanaquifermayexist,however.At Lake Barco, for example,geophysicalinvestigationsindicate that subsidence features and a karstified limestone

surface are

Explanation:

I Boring& Well Location

A

-..

.

•

ß..,.., • .

';::::: :i

..•

A'

,....1 ...:

presentbeneath the lake [Sackset al., 1992], which may inso creasethe potentialfor hydraulicconnectionbetweenthe lake I I I [ I 1 I I I I I I I andthe upperFloridanaquifer[Leeetal., 1991](seeFigure5). I I I I I I I I I I I I ! I I I - I I I I I I I I I I I ! I I I I I I I I I I I I I ! ! In suchcases,Kv/b calculatedfor the subsurfaceunitsbeneath zg __ I I I I I I ' ' ' ' ' ' ' 3 __ a lake would be larger than the vertically averagedvertical I ,,,,,, I • I I I I I I I I I I I I I • I I I conductanceof the subsurfaceunits adjacentto the lake. If I I I I I I I I I • i i i [ i i i i i i i I I i i i i ! heterogeneitiesexistin the lake sedimentsand subsurfaceunits I I I I I I I I I I I I I [ I I I [ I I I I [ I I I I 1 I I I I I ,I I I I I i I ! beneaththe lake itself,it is assumedthat theseheterogeneities • I ; i • :1 i i I; I I I I I i i i i I I [ I I I I I I I • • are spatiallyaveragedin the horizontalplane beneaththe lake o 5 lO 15 km I I I I when calculatinga singlevalue that representsKv/b of the Vertical Scaleis Greatly Exaggerated. subsurfaceunits beneaththe lake. This usuallyis a necessary assumption,becausespatiallyvaried data for the subsurface Figure 4. Generalizedhydrogeologic sectionalongthe Highunits are not available at most lakes. landsRidge in southcentralFlorida (modifiedfrom Hammett [19811). 4.3. Values for L and Kdb The valuesof vertical leakagefor the 11 lakes range from

0.12to 4.27m yr-• (seeTable1). ThevaluesforKv/b,which were calculatedusingthe vertical leakagevalues,the differencesbetween lake stage and hydraulichead in the upper Floridan aquifer,and equation(2), rangefrom 0.0394to 1.00

periodwas about 259 ha, and thus the verticalleakagefrom

MarchthroughOctober1960averaged 4.27m yr-•. Fromthe leakagevalueof 4.27m yr-• anda headdifference of about yr-•. Forfourof thelakes(Barco,Johio,Sherwood, andPlac- 8.7 m (basedon Clarket al. [1963]),Kv/b is 0.491yr-•. id), Kv/b valueswere calculatedusing data for monthly or At Lake Barco,whichis in north centralFlorida, a groundmorefrequentintervals,but for the other sevenlakes(Brook- waterflowmodel[McDonaldandHarbaugh,1988]wasusedby lyn, Kerr, Grace, Orienta, Lucerne,Roy, and Jackson),only Lee [1996] to calculateleakagefrom the lake to the upper one Kv/b value couldbe calculatedbecauseonly one leakage Floridan aquiferfor monthlyintervalsfrom May 1989 to Devalue was available for each of these lakes.

cember1990.Thesevaluesrangefrom4600m3 for September

At Lake Brooklyn,whichis in north centralFlorida, leakage 1990to 6710m3 for January 1990andtotal112,800 m3 for the from the lake to the upper Floridan aquifer averaged3.03 x 20-monthperiod. On the basisof stageversustime and stage 104 m3 d- • duringan8-monthperiodfromMarchto October versuslake surfacearea curvesfor Lake Barco [Sackset al., in 1960 when the lake was full and surface water outflow was 1992],thisleakagerangesfrom 0.045m for September1990to occurring[Clarket al., 1963].The lake surfacearea duringthis 0.0628m for January1990andaverages 0.631m yr-• for the

162

MOTZ:

VERTICAL

AND

CONDUCTANCE

!

Explanation:

IN FLORIDA

KARST

LAKES

lake that served as a control. The vertical leakage averaged

82ø00'30"W

82o01,02,,W

ß

LEAKAGE

1.83myr- • forGraceLakeand0.366myr- • forLakeOrienta. At Grace Lake during January-May 1971, the lake level was approximately6.10 m abovethe hydraulichead in the upper Floridan aquifer in the vicinity of the lake [Andersonand Hughes,1975]. Basedon this head differenceand the vertical

•'Location ofCross SectionA Boring & Well Locatio

leakageof 1.83m yr-•, Kv/b is 0.300yr-•. At LakeOrienta duringJanuary-May 1971,basedon the lake stage,the hydraulic head at the nearby control well, and an estimated1.52-m differencein hydraulichead betweenthe controlwell and the lake (basedonAndersonandHughes[1975]),the averagehead differencebetween the lake and the upper Floridan aquifer wasapproximately3.29 m duringJanuary-May 1971,andKv/b

29o40,30',N

is 0.111yr-•. At lakes Johio and Sherwood, which are in central Florida,

•' ' '2•)0Meters 29o40'11,,N

A !

A 5O

I•lLake Sediments

/

4O

net seepagewasdeterminedfrom water budgetcalculationsby Lichtleret al. [1976] for Lake Johio for 49 time periodsfrom April 13, 1967,throughOctober2, 1968,and for the northern part of Lake Sherwoodfor 23 time periodsfrom January16, 1967,throughDecember31, 1967.Then for eachlake, leakage was calculatedfrom an equation derived based on the net seepageresults.At Lake Johio,leakagefrom the lake to the

upperFloridanaquiferrangedfrom 0.00878m d-• during August21-31,1967,to 0.0106m d-• duringMay 1-11, 1968. Leakagetotaled 4.90 m for 516 days,and the averageleakage

was3.46myr-•. Usingtheleakage valuesandheaddifferences ;,.?..:?,,..:...':.,...:..

z•

•

.

the49timeperiods. ForLakeJohio,Kv/baverages 0.241yr-• witha standard deviation of 0.00835yr-• (seeFigure7).

20 i.:..'.:..'.:..',:..',:..'.:.2:..'.:..'.:..'.

..:iii!ii•!i:.

: ..'.:..'.:..-.:..'.:..-.:... :.

!;?.::..':z-•':.:: c:•,:.'..: ......:..•...:..:..:. :...'.'. :..:.':

• •o

For Lake Sherwoodthe leakagevaluefor March 1-15, 1967, basedon Table 2 of Lichtleret al. [1976,Table 2] is 0.00052m

d-•, andit appears to be toolowby a factorof 10 owingto a typographicalerror. If thisvalue is rejectedas an outlier, leakage from the lake to the upper Floridan aquiferrangedfrom

Sea

0.003m d-• duringAugust16-31, 1967,to 0.00827m d-•

Level

•l-UpperFloridah•')i'..?'.'::.?.."•,•" I '• '• '• '1 10

from Lichtleret al. [1976],valuesfor Kv/b were calculatedfor

ß• .

u'

.'.

• •"r":"',•('-'•.

•.

•. •.

•. •.

Vertical Scaleis Greatly Exaggerated.

during May 1-15, 1967. Leakage totaled 1.84 m for 335 days

andaveraged 2.00myr-•. Usingtheseleakage valuesandhead differences fromLichtleret al. [1976],valuesfor Kv b- • were calculatedfor 22 insteadof 23 time periods.For Lake Sher-

wood,Kv/b averages 1.00yr-• with a standarddeviationof Figure 5. Generalized hydrogeologicsectionat Lake Barco 0.0959 yr -• (see Figure 8). in northcentralFlorida (modifiedfromLee [1996]andSackset

At Lake Lucerne, which also is in central Florida, leakage from the lake to the upper Floridan aquiferwas calculatedby Lee and Swancar[1997] by meansof a flow net analysisand then revisedupwardon the basisof an analysisof the error in period from May 1989 to December1990.Using the leakage the waterbudgetequation.For October1985throughSeptemvalues and head differencesbased on Lee [1996], values of ber 1986the adjustedleakageis 0.445m yr-•. Usingthe valueof 0.445m yr- • andan average headdifference Kv/b were calculatedfor Lake Barcofor eachmonthfrom May leakage 1989 to December 1990. The averageof thesevaluesis 0.386 of 2.33 m betweenthe water level in the lake and the potenyr- • witha standard deviation of 0.0369yr-• (seeFigure6). tiometric surfaceof the upper Floridan aquifer from Lee and At Lake Kerr, whichalsois in north centralFlorida, monthly Swancar [1997]andLeeet al. [1991],Kv/b = 0.191 yr-• for changesin the stageof the lake were calculatedby Hughes Lake Lucerne. At Lake Roy, whichis in the Winter Haven chainof lakesin [1974]for 1962-1969usinga water budgetequationsimilarto (1). Verticalleakagefrom the lake to the upperFloridanaqui- central Florida, an experimentwas conductedby closinga fer was assumedto be approximatelyconstantat a rate of canal that connected the lake with other lakes in the chain 1981].As a resultof isolatingLake 0.03m month-•, or 0.366m yr-•. Fromthe leakagevalueof [SinclairandReichenbaugh, 0.366m yr-• andan estimated headdifference betweenthe Roy from the chain of lakes, the lake declined at a rate of lake and the upper Floridan aquifer of 1.22 m during 1962- 0.0122m d-• duringa 30-dayperiodin 1978,andthe rateof downwardleakagefrom the lake to the underlyingupperFlori1969[Hughes, 1974],Kv/bis 0.300yr-•.

al. [1992]).

At Grace Lake and Lake Orienta, which are in east central

danaquiferwasestimated tobe0.00914m d-•, or 3.34myr-•.

valueof 3.34m yr-• andan average head Florida, vertical leakage was estimated by Anderson and Usingtheleakage Hughes[1975]for January-May,1971on the basisof changes differenceof about 4.9 m for the 30-dayperiod from Sinclair [1981],Kv/b = 0.684 yr-• for LakeRoy. in lake levelsand comparisonwith the stagein another,nearby andReichenbaugh

MOTZ:

VERTICAL

LEAKAGE

0

AND

('q

,,•

('q

CONDUCTANCE

0

IN FLORIDA

KARST

0

0

0

'::1-

0

o

o

0

•

LAKES

163

164

MOTZ:

VERTICAL

LEAKAGE

AND

CONDUCTANCE

IN FLORIDA

KARST

LAKES

Lake Sherwood

Lake Barco 0.5

1.2

0.4

Mean= 1.00yr'l•

s.d. = 0.0959 yr"

0.3 0.8

0.2 0.1

0.4

May 1989- December 1990 0.0

Figure 6. Kv/b for Lake Barco.

January 16, 1967- December 31, 1967

Figure 8. Kv/b for Lake Sherwood.

Leakagefrom Lake Jackson,in southcentral Florida, was calculatedby Hammett [1981]for two 33-monthperiods.From October 1954 to June 1957 the vertical leakagefrom the lake

logicstructurechangesbeneaththe lake. In actuality,valuesof

to theupperFloridanaquiferwas0.33m,or0.12myr-•, based Kv/b calculatedfor different time periods may be different on solvingfor leakageas a residualin the water budgetequation. From October 1970 to June 1973 the verticalleakagewas

0.996m, or 0.362m yr-•, basedon assuming that the head differencebetweenthe lake level and potentiometricsurfaceof the upper Floridan aquifer had increasedfrom about 3.0 rn to about9.1 m andthat Darcy'sequation(similarto (2)) couldbe usedto calculatedownwardleakagefrom the lake to the upper

Floridanaquifer.Usingthevaluefor leakageof 0.12m yr-• and the head difference

of about 3.0 m for 1954 to 1957 from

Hammett[1981],Kv/b = 0.0394 yr-• for LakeJackson. At Lake Placid,whichis approximately30 km southof Lake Jackson,monthlyvaluesof verticalleakagefrom the lake to the upper Floridan aquifer were calculatedby Kohoutand Meyer [1959] as a residualin the water budgetequation.For the 19month period from January1955 to July 1956,leakageranged from 0.0058m for July1955to 0.11m for June1956andaveraged

0.68myr-•. ValuesofKv/bforLakePlacidwerecalculated for

becauseverticalleakage,whichis usedin (2) to calculateKv/b, is calculatedas a residualin the water budgetequation(equation (1)). Errorsin measurements or calculationsin the other terms in the water budget equation generallywill affect the accuracyof valuescalculatedfor verticalleakageand then for Kv/b. Errors in determining the head difference between a lake and the upper Floridan aquifer alsowill affect the accuracyof Kv/b valuescalculatedfrom (2). At the four lakes (Barco, Johio, Sherwood,and Placid) whereKv/b valuescould be calculatedfor more than one time period, sometemporalvariation in Kv/b did occur,but generally it is quite small (see Figures6-9). At Lake Barco the calculatedvaluesof Kv/b are greatestfrom December1989 to April 1990 and in December 1990. These months approximatelycoincidewith the periodsfrom November1989to February 1990 and from November to December 1990, in which the calculatedevaporationwas substantiallyless than in the other months,and the periodsfrom December 1989 to March

each month from January 1955 through July 1956 using the monthly values for leakage and lake stagefrom Kohout and 1990 and December 1990, in which the calculated vertical Meyer[1959]and a constantvalueof 18.3m abovesealevelfor leakagewasgreaterthan in other months[Lee, 1996,Table 2]. the head in the upper Floridan aquifer,whichwas estimated Vertical leakage at Lake Barco was calculatedbased on a fromBishop [1956].Theaverage of thesevalues is0.0704yr-• groundwatermodel studyin whichthe transientrechargerate applied to the modeled lake surfacewas the differencebewitha standard deviation of 0.0396yr-• (seeFigure9). tween the monthly rainfall and lake evaporationrates [Lee, 1996]. The possibleerror in the evaporationrates (i.e., the 5. Temporal Variation in Kv/b standarddeviationaroundthe true value)is about7.3% [Sacks Conceptually,the Kv/b value calculatedfor a lake from (2) et al., 1994].If the lake evaporationreportedby Lee [1996]for shouldbe constantwith respectto time unlessthe hydrogeo- November 1989 to February 1990 and from Novemberto December1990 is too low, then the lake leakagecalculatedfrom LakeJohio

0.3I' Mean= 0.241yr'1.

I_r•'d-'•90'00835 yr"

Lake Placid 0.16

0.12 n=19

0.2

0.08

0.0

.

April 13, 1967 - October 2, 1968

Figure 7. Kv/b for Lake Johio.

January 1955 - July 1956

Figure 9. Kv/b for Lake Placid.

MOTZ:

VERTICAL

LEAKAGE

AND

CONDUCTANCE

the groundwatermodelwould be too high for thesemonths, and the resultingvaluesof Kv/b alsowould be too high. The standarddeviationfor the Kv/b valuesfor Lake Barcois 9.6% of the mean value (Table 1), which is consistentwith the amountof error they maybe presentin the evaporationrates. At Lake Johio,calculatedvaluesof Kv/b are greatestin May andJunein both 1967and 1968and smallestin Septemberand October in both 1967 and 1968. in the water budgetcalculationsperformedby Lichtleret al. [1976],lake evaporation was calculatedusinga constantpan coefficientof 0.85 insteadof usingmonthlycoefficientsthat normallywould be greaterin

IN FLORIDA

KARST

sectional area of the materials

LAKES

between

165

the bottom

of the lake

and the top of the upper Floridan aquifer divided by the thicknessof the same materials. Dividing B by the crosssectionalarea of verticalflowyieldsKv/b. For Lake Johio,B =

0.00741 had-•, andthelakesurface areaaveraged about11.2 ha.ThusB/11.2 ha = 0.241yr-•, whichis the samevalueas Kv/b determined for Lake Johio. For Lake Sherwood,B =

0.0720 ha d-•, andthe lake surfaceareaaveragedabout27 ha. ThusB/27 ha = 0.973yr-•, whichis nearlyequalto the Kv/bvalue(1.00yr-•) determined for LakeSherwood. For Lake Lucerne, a "spatiallyaveragedvalue of vertical

the warm summer months and smaller in the cooler winter

hydraulic conductivity in the sublakearea [Kvsub = 0.027m byLeeandSwancar [1997,p. 45]onthe months.As a result,lake evaporationprobablywasunderesti- d-•]" wasdetermined mated in the summer months relative to the other months and

overestimatedin the other months.Also as a result, the vertical

basisof water budgetcalculationsfor a 3-weekperiod in which the volume of vertical leakagewas dividedby the area of the

leakagereportedby Lichtleret al. [1976]and the Kv/b values bottomof the lake.To obtainKv/b,theirvaluefor Kvsub was calculatedin the presentstudyfrom (2) probablyare overes- first divided by the "elevationdifference [dZ] between the timated in the summer months and underestimated in the lake bottom and the screenedintervalof well 1PN-155 [in the other months. upperFloridanaquifer]"[Leeand Swancar,1997,p. 45], which Constantpancoefficients alsowereusedin the waterbudget is 39.0m. Then,thevalueof Kv•/dZ wasmultiplied by0.56, calculations for Lake Sherwood[Lichtleret al., 1976]andLake whichis the ratio of the projectedarea of the lake bottom and Placid [Kohoutand Meyer, 1959], and this may accountfor the area of the lake surfacefor Lake Lucerne. The resulting someof the variabilityin the Kv/b valuesfor theselakes.At valueof 0.56Kv•/dZ alsowasmultiplied by 1.39,whichrepLake Placid,unaccounted-forsurficialaquifer inflow and out- resentsthe revisionmade by Lee and Swancar[1997] in the leakagefrom 0.32to 0.445m yr-• basedon their flow and pumpagefrom the lake alsomaybe sourcesof error estimated in thewaterbudgetcalculations [KohoutandMeyer,1959].The analysisof the error in thewaterbudgetequationafter the flow hadbeenmade.Theresulting value(0.197yr-•) is assumption madein the presentinvestigation that the headin netanalysis the sameastheKv/bvalue(0.191yr-•) deterthe upper Floridan aquiferwas constant(becauseno other approximately data couldbe found) may haveresultedin errorsin the Ah mined for Lake Lucerneusing(2). At LakeRoy a valueof 0.0856m d-• for the "composite valuesusedin (2) to calculateKv/b and also may have contributedto the variabilityin theKv/b valuescalculatedfor Lake vertical hydraulicconductivity"of the material between the Placid. bottomof Lake Roy and the top of the upper Floridan aquifer dividedby the thicknessof 45.7 m for the surficialaquifer and confiningunit [Sinclairand Reichenbaugh, 1981] is equivalent

6.

Equivalent Parameters

For sixof the lakes(Barco,Johio,Sherwood,Lucerne,Roy, and Jackson),varioushydraulicparametersthat characterize verticalleakagehavebeenreportedpreviouslyby investigators of these lakes. These previousresultsare equivalentto the Kv/bvaluesobtainedin the presentinvestigation (seeTable 1). For Lake Barcoan equivalentKv/b valuewascalculatedfor the lake sediments,surficialaquifer, and confiningunit beneath the lake usingthe hydraulicpropertiesand confining unit verticalleakancesin the groundwatermodel [Lee, 1996, alsopersonalcommunication, January14, 1997]and equation (3). The resultingvaluevariesspatiallyin the horizontalplane

to Kv/b. At Lake Jacksonthe "downward leakage rate" of

0.015m d-• (0.05feetd-•) dividedbythe 122-mthickness of materials overlying the upper Floridan aquifer [Haminert, 1981] is equivalentto Kv/b. It has the same value if it is consideredthat the "downwardleakagerate" (whichactuallyis the verticalhydraulicconductivity)apparentlywasroundedup

from0.01317m d-• (0.0432feet/d-•). 7.

Discussion

The averageleakagevalues compiled in this investigation,

ranging from0.12to 4.27m yr-• (Table1), areapproximately

beneaththe lake approximately from 0.220to 0.649yr-•, 10 to •300% of the order of magnitudeof the averagerainfall whichbrackets theKv/bvalue(0.386yr-•) determined using and lake evaporationin Florida. Thus thesevaluesare signif(2). Also for Lake Barco,basedon the resultsof traveltime icant partsof the water budgetsfor all 11 lakes,and they vary calculationsfor chemicalconcentrationsin water recharging spatiallyfrom lake to lake. The leakagevaluescalculatedby

include values of 0.901myr-• for the upper Floridan aquifer [Katz et al., 1995],K'/b' values Dee•ey[1988]for 1954-1986 0.366m yr-• for LakeKerr,0.316m yr-• for were inferred for two sites immediately adjacent to Lake LakeBrooklyn, and0.404m yr-• for LakePlacid.The values Barco.At thesetwo sitesthe K'/b' valuesare approximately LakeJackson, 0.290and0.621yr-•, whichalsobrackets theKv/b valuede- compiledin this investigationfor Lakes Kerr, Jackson,and Placid (Table 1) generally are in agreementwith Dee•ey's terminedin the presentstudy. For LakesJohioand Sherwood,an equationfor calculating [1988]values.Dee•ey's[1988]value for Lake Brooklynreprenet seepage,or the net exchangeof water betweena lake and sentsa long-termaverage,whereasthe value calculatedin this basedon Clarket al. [1963],is for a shortertime the surficialand upper Floridan aquifers,was developedby investigation, owing Lichtleret al. [1976]with coefficients A and B that represent periodduringwhichthe lake levelhad risensignificantly lumpedparametersfor propertiesof the surficialaquiferand to a resumptionof surfacewater inflowfrom upstream,with a large head differencebetweenthe lake and the materialsbetweenthe lake bottomand the top of the upper correspondingly Floridanaquifer,respectively. The coefficientB represents the the underlyingupper Floridan aquifer,which would have reproduct of the vertical hydraulic conductivity and cross- sultedin greaterleakage(basedon (2)). Overall, the leakage

166

MOTZ:

VERTICAL

LEAKAGE

AND

CONDUCTANCE

IN FLORIDA

KARST

LAKES

valuescompiledin this investigationare somewhatlarger than

Floridan aquifer), providesa meansof investigating whether

the0.30-0.50m yr-• thatDeevey[1988]considered typicalfor

this relation

Florida lakes.In general,Deevey's[1988]valuesmay underestimate leakage rates becausethey were calculatedonly for monthswhen evaporationexceededprecipitation[Staufferand Canfield,1992]. Deevey[1988]assertedthat leakageis drivenby a hydrostatic head that includesthe lake depth plus many meters of saturated groundwaterconduitsand that lake levelfluctuationscan changethisheadby a few percentat most.The useof Darcy's equation (equation (2)) to calculatevertical leakageclearly showsthat the headdifferencebetweenthe lake and the upper Floridan aquifer is the drivingforce for vertical leakage.The head differenceis certainlymore sensitiveto changesin lake stagethan somemeasureof the lake depthplusthe thickness of the groundwatersystem.Thus fluctuationsin lake stage couldaffectthe headdifferenceand the resultingverticalleakage by significantamounts,even leading in some casesto upwardflowfrom the upperFloridanaquiferinto a lake if the headdifferencewere reversed.The possibilityof thiscondition has been reported for at least two lakes in the Central Lake District.In September1966and August1967the potentiometric surfaceof the upper Floridan aquiferwasbrieflyabovethe

other similarhydrogeologic settingsby comparingK•/b values

lake level at Lake Herrick, which is near Lakes Johio and

Sherwoodin central Florida [Lichtleret al., 1976]. Also, the potentiometricsurfacemaybrieflyriseabovethe water levelin

exists at lakes in the Central Lake District

and in

to lake level instabilities.

Calculatingvertical leakage using the head difference betweena lake and an underlyingaquiferand the K•/b value that characterizesthe conductivityof the subsubsurface units beneaththe lake, as representedby (2), is not limited to lakesin the Central Lake District of Florida. Instead,this conceptis equallyapplicableto other similarlake and groundwatersystems,i.e., systemsin whicha lake in a surficialaquiferoverlies a deeper,confinedaquifer and verticalleakagefrom the lake to the deeper aquifer is a significantcomponentof the water budgetof the lake.

8.

Summary and Conclusions Vertical leakagefrom lakes to the upper Floridan aquifer

averages 0.12-4.27m yr-• for 11 karstlakesin the Central Lake District in peninsularFlorida. Values for K•/b, the coefficient that representsthe averageof the vertical conductancesof the hydrogeologic unitsbetweenthe bottom of a lake and the top of the upper Floridan aquifer,rangefrom 0.0394

to 1.00yr-• for theselakes.Varioushydraulic parameters

previouslycalculatedby other investigatorsfor sixof the lakes are equivalentto the K,/b valuescalculatedas part of this Cranes Roost sink, which is near Lake Orienta in east central study.This paper demonstratesthat vertical leakageis a sigFlorida. This may occurat the end of a dry period when the nificantcomponentof the water budgetfor these11 karstlakes potentiometricsurfacerises faster than the lake level in re- and that it variesspatiallyfrom lake to lake. Also, it demonsponseto rainfall, therebycausingwater to moveupwardfrom stratesthat a singleKv/b value can be calculatedto characterthe upper Floridan aquiferinto CranesRoost [Anderson and ize the vertical conductivitybeneathan individuallake if adeHughes,1975]. quate data are available. Then vertical leakage could be Therangeofvalues forKv/bfrom0.0394to 1.00yr- • (Table estimatedfor otherconditionsof lake stageandhydraulichead 1) extendsovermore than an order of magnitude.This seem- in the upper Floridan aquifer,usingthe value of K,/b for the inglywide rangenevertheless is consistentwith similarbroad lake and Darcy's equationwritten for vertical flow (equation rangesthat are reportedfor leakancevaluesfor confiningunits (2)). Also, the methodologydescribedin this paper couldbe [e.g.,Johnstonand Bush, 1988],which typicallyare the most used to investigatethe apparent relation betweenK,/b and significantpart of the verticalconductance equation(equation lake level instabilities at some lakes in the Central Lake Dis(3)). If Kv/b is determinedfor a lake, then vertical leakage trict and other similarhydrogeologic settings.Calculatingvercould be estimated for other conditionsof lake stage and tical leakageusing(2) is not limited to lakes in the Central hydraulichead in the upper Floridan aquifer, usingK•/b for Lake District; instead,this conceptis equally applicableto the lake and Darcy'sequationwritten for verticalflow (equa- other similar lake and groundwatersystems. tion (2)). Thesechangesin the headdifferencemaybe due to phenomenasuchas naturallyoccurringseasonalor long-term Acknowledgments. Financial support for this investigationwas fluctuationsin lake levelsand/or headsin the upper Floridan aquifer: Lowered heads in the upper Floridan aquifer also providedin part by the U.S. GeologicalSurveyStateWater Research InstituteProgramand the St. JohnsRiver Water ManagementDistrict, could be due to increasedpumpingfrom the upper Floridan Palatka,Florida.The informationin thispaperrepresentsthe opinions aquifer.As was demonstratedby Hammett [1981],the impact and conclusions of the author and doesnot necessarily representthe that changesin verticalleakagecan haveon the other compo- officialpositionof the U.S. GeologicalSurveyor the St. JohnsRiver nentsin the water budget,suchaslake storageand stage,could Water ManagementDistrict. Also, appreciationis expressedto T. M. Lee for discussions concerningthe hydrologyand modelingof Lakes be investigated using(1). Also,if K,/b is determinedfor a lake, Barco and Lucerne. water managementschemessuchas pumpingfrom the upper Floridan aquifer to augment lake levels [e.g., Stewartand Hughes,1974] or, conversely,pumping from a lake for water References supplycouldbe evaluatedusing(1) and (2). At somelakes a relativelylarge magnitudeof K,/b may be Anderson,W., and G. H. Hughes,Hydrologyof three sinkholebasins in southwestern SeminoleCounty,Florida,Rep.Invest.Fla. Bur. of associatedwith significantfluctuationsin the lake stage,parGeol., 81, 35 pp., 1975. ticularlywith declinesduringdroughtperiods.This association Annable, M.D., L. H. Motz, D. S. Knapp, G. D. Sousa,and W. D. BeddowII, Investigationof lake and surficialaquifer interactionin apparentlyoccurs,for example,at Lake Brooklyn[Motzet al., the Upper Etonia CreekBasin,contract93W296,242 pp., St. Johns 1992], a very unstablelake with a relativelylarge K•/b value River Water Manage. Distr., Palatka, Fla., 1996. (Table 1). The methodologydescribedin thispaper for quan- Bishop, E. W., Geology and ground-waterresourcesof Highlands tifying Kv/b at lakes,which requiresonly limited data (i.e., County,Florida, Fla. Geol. Surv.Rep.Invest.,15, 115 pp., 1956. Divisionsof Florida, 11 pp., vertical leakage,lake stage,and hydraulichead in the upper Brooks,H. K., Guideto thePhysiographic

MOTZ:

VERTICAL

LEAKAGE

AND

CONDUCTANCE

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LAKES

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