Mar 16, 2001 - following expression [e.g., Kimball, 1981 ], es = 0.61078 exp (17'269T/(237'3 ..... Physics, 2nd ed., Edward Arnold, London, 1990. Morton, F. I. ...
JOURNAL OF GEOPHYSICALRESEARCH,VOL. 106,NO. D5, PAGES4695-4701,MARCH 16,2001
Dynamicsof evaporationfrom salinewater bodies I. M. Oroud• Department of Geography, Collegeof Arts,KingSaudUniversity, Riyadh,SaudiArabia
AbstractThesensitivity of evaporation fromsalinesolutions resulting froma variationin their salinity/activity coefficients ([•)is investigated. Thecalculations arebasedona theoretically derived parameter (7= or / Off), whichaccounts forthetemperature change following a departure in thesalinity/activity coefficient. Results revealthat7 isa function of salinetemperature. thelevel of theactivitycoefficient, andthetransfer coefficients forwatervaporandsensible heat.Fora
transfer coefficient of15Wm ' kPa 4 7ranges from•-6 K fora saline temperature of 5øCand activitycoefficient of 0.95to • - 27 K fora salinetemperature of 40oC andactivitycoefficient of 0.4.Thepresent formulation provides a robust method thatcanbeusedto identifylowerandupper theoretical limitsforthevariations of salinetemperatures, andalsoto derivethedepmmres ofthe activitycoefficient andevaporation ratesfor salinesolutions fromroutinemeteorological observations only.Calculations withthePenman equation revealthattheaerodynamic termisthe mostsensitive parameter influencing evaporation fromsalinesolutions followinga departure in theirsalinity/activity coefficients, with a contribution rang/rigfrom • 50%- 65% of totalannual evaporation departure. A!temtions to netradiationfollowinga variationin [• accounts for a contribution of about25% of totalannualchangein evaporation.
1. Introduction
Adequateevaluationof evaporation from salinewaterbodies is importantfor geophysical andoperational purposes. Salineand hypersaline lakes typicallydevelopin endorheic basinssituated in dry climateswhereevaporation is largerthanthewatersupply [M•beck, 1995]. The chemicalcomposition,areal extentand depth of these lakes are primarily establishedby a balance betweenwaterinflowandevaporation. Tem•nal freshwater lakes have beenusedextensively to reconstruct paleoclimates basedon their depth and arealextent[e.g.,Kutzbach,1983;Street-Perrot and Roberts, 1983; Tetzlaff and Adams, 1983; Burgis and Troughton, 1987; Adams and Tetzlaff, 1989; M•beck, 1995; Hostetler, 1995]. In theseinvestigations, evaporation ratesfrom the surface of the studied lakes were assumed either constant or a
function of air temperature[e.g., Kutzbach,1983]. Likewise, paleoclimatescan be investigatedusing terminal saline lakes basedon their level fluctuations[e.g.,KleinandFlohn, 1987]. Whereasevaporationfrom freshwaterbodies is established by meteorologicalforcingsalone,its counterpart fromsalinelakesis controlledby two factors,namely,meteorological parameters and salinity/density levels.Whenthelevelof a salinelakechanges, its salinitychanges accordingly andassuchthetransport of heatand water vapor acrossthe surface-atmosphere boundaryis altered. The feedbackbetween salinitychangesandthe varioussurfaceatmosphere processes,suchassurfacetemperature, heatstorage, and sensible and latentheatfluxes,is neitherlinear nor constant
throughoutthe year. Unlike its counterpart from freshwater, evapore2ionfrom saline lakes is a dynamicprocesswhich is sensitiveto level/salinitychanges, anditsresponse is dependent on prevailingmeteorological forcings.Thus it is important to
realize thatevaporationratesfrom salinewaterbodiescannotbe assumedconstantwhenwaterlevel changesoccur. On the operationalside, evaporationfrom saline and
hypersaline lakesis importantfor evaluatingverticalmixing (neededto establishnutrientdistribution for aquaticlife, energy production),mineralextraction,andprojections of futurelevels of saline water bodies when subjectedto intensivehuman intervention. For instance, the level of the Dead Sea hasbeen
decliningsince 1960 due to upstream projectsandcommercial activities
at
its southern comer. The level of the Dead Sea
droppedfrom 394 m belowsealevel in 1960to about413 m in 1999, and its level will continuethlling as long as itswater
balanceis negative. A I•w attempts havebeenmadeto projectthe futurelevelsof theDeadSea[e.g.,Anan'andShasha,1989,1990; Klein, 1990 ] but evaporationestimatesfromtheDead Seawere tbrmulated in a rudimentary way. Furthermore, evaporation is an important element which controlsthe extractionof mineral
reservespresentin mesosaline andhypersaline waterbodies.For instance,the Dead Sea is estimatedto haveapproximately 43 bill/on tons or'mineral substances. Thusadequate evaluation of the sensitivityof evaporationresultingfrom a variationin the activity coefficient serves ninny theoreticaland operational purposes.
Data presentedby Turk [! 970],Folchitto[1991],andOroud [ 1994] suggest thatevaporation fromsalinesolutions decreases as salinityincreases, andthereductionbecomes morepronounced as
the specific•avity of thesolution exceeds 1.2.Folchitto[1991] presentedtwo empiricalequationsthat relateevaporation from saline solutions to that from freshwater Ibr clin•atic conditions
prevailing in southernItaly. More recently,Stanhill [1994] presemedan empirical expressionin which he related the fromtheDeadSeatbllo•dngchanges in •Now at the Departmentof Physical Geography,Mu'tah responseof evaporation its salinity. The qualitativenatureof theseexpressions andtheir University,KeralqJordan. site-specificit3.' precludegeneral conclusions frombeingdrown, Copyright 2001bytheAmerican Geophysical Union. and as such the results are limited to the particular geographic Papernumber2000JD900061. regionswhere theseexpressions weredeveloped. Thusthereis a 0148-0227/01/2000JD900061 $09.00 4695
4696
OROUD: EVAPORATION DYNAMICS
need for a quantitativelinkage betweenevaporationresponse respond accordingly. Fromenergy balance considerations, when of a salinesolution changes, a numberof nonfrom salinesolutions/sabkhas andchanges m thesaliniW/activity the salinity/density coefficients.The objectiveof th/sstudyis to providea general, linear interactionsoccur which influencethepartitioningof net of thesalinesolution.The analyticlir• betweenthe responseof evaporation fromsaline radiationand as suchthetemperature influencing solutionsandvariationsof the activitycoefficients.Resultsof tiffs latter leads to a numberof coupledinteractions investigationare useful for paleoclimatic reconstruction, energy evaporation, including vaporpressure gradient across thesurfaceboundary, the slopeof saturation vaporpressure, balancestudies,mineralex-traction, andfutureprojections of the atmosphere thesediment-lake bottom, level of saline lakes whensubjected to intensiveantl•opogenic back radiation,heat exchangeacross intervention and/or sudden climatic changes (e.g., a rapid andatmospheric buoyancy [e.g.,Oroud,1997,1998!.Some of temperature increasesimilar to the hypothesizedincrease these interactions need a three-dimensional tbrmulation to resultingfroma buildupof greenhouse gases). capture theiractualimpactsonevaporation.
Assumingthat a change in salinity hasa negligible impacton the ambientenvironment(novariationin heatandmasstransfer coefficients, ambientvaporpressure and air temperature), the
2. Theoretical Background
totalchangein evaporation following a departure in [• of a saline
The manualevaporation froma freshwater bodyexperiencing solutionmay be derivedusingthe followingexpression (see thermal equilibrium(no heat storage/release) dependson the equation(1)), prevailingmeteorological forcings,whereasthat from a saline dE aE aE a/x aT aE URn solution is determined by two factors, the prevailing + + •-, (4) meteorological forcingsand thelevelof theactivitycoefficient. dp ap aT ap aT ap The activity coefficientis definedas the ratio of watervapor evaporation change resulting from pressure overa salinesolution compared to thatovera freshwater wherethefrrsttermrepresents that theothertermsareconstant; the planewith the sametemperature [e.g.,CalderandNeal,1984; a variationin •3assuming termrepresents evaporation change duetothevariation in Salhotra et aI., 1985].Tiffscoefficient is unityfor freshwater and second the slope of the saturation vapor pressure curve resulting from a always less than that for salinesolutions(0 < 13< 1). The
dependence of 13onT is quiteweak,andassuch13isregarded as a functionof salinity/specific gravityonly[e.g.,CalderandNeaI,
temperature changeof the salinesolution; andthe thirdterm
accountsfor the changein evaporation due to a changein net radiation as a fimction of temperature changeinducedby a 1984; Salhotra et al., 1985]. Evaporationfrom salinewater variation in [•. It is assumed in the above formulation thatthe bodiesmay be evaluatedusingthe Penmanformulation [e.g.,
depmmre of 13doesnotinfluence airtemperature ortheheatand masstransport coefficients. This is true forsmallsahnewater bodies,but may introduce a smallerrorwhenthearealextentof the affected waterbodyis relativelylarge.It is alsoassumed that a changein 13hasa negligible impactonsurthce emissivity and whereE is evaporation rate(Wm'2), [•istheactivity coefficientsolarradiationabsorption bythesalinesolution (i.e.,thecolorof
Monteithand Unsworth,1990;Oroud,1995, 1997],
E=
+
P%* -
of the saline solution,zXis the slopeof saturation vaporpressure thewatersurfacedoesnot changeappreciably).
(kPaK'i),• is thepsychrometric constant (kPa K4),f(u) isthe
Equation(4) canbe expandedfurther to obtain theseparate
windfunction (Wm'2 kPa'•),e• ande•' arethecorresponding contribution of theenergy,aerodynamic, andnetradiation terms, expressions for ambient andsaturation vapor pressures (kPa)at Term 1
airtemperature, respectively. Theavailable energy (Wm '2)is definedby,
+v/)2 '
Rn=S(1c•)+aLz> - •crT 4-C,• h 8Ti &
(2)
Term 2
whereS is solar radiation (Wm'ø),o;istheoverall albedo ofthe water body, Lz>is longwaveradiationcomingfrom the Term atmosphere (W m'2),• is surface emissivity, c•is theStefan-
Boltzmarm constant (5.667x 10'8 W m'2 K'4),T is surface temperature (K), C• isthevolumetric heatcapacity ofthewater Term body (J.m-3K4),hisdepth ofthewater column (m),and8Ti/bt is
•f (u)(•ea*+ Aea) aEl•= ap (pzx + '
(6)
aE
(9)
3
4
the integrated averagetemperature change with• thewater columnwith respectto time.
Symbolically, theactivity coefficient (13) maybeexpressed in Term
5
thefollowing form[Salhotra etal., 1985,1987],
fl(s,r) =es(s'r) ef(T)
=
(3)
flA (_4ecrr 3) aT +
ß
wherethe subscripts E and A standfor the energyand aerodynamic terms, respectively. Theslopeofdeltawithrespect whereesis saturation vaporpressure of the salinesolution at to surfacetemperature, (a/X/aT), ½,is derivedfrom Teten's
temperature T and salinity s,andef issaturation vapor pressure
withrespect to a freshwater plane withatemperature similar to that of the saline solution.
If [5changes byasmall value, sayfrom 13o to[50- 8[•,then the temperature andevaporation ratefrom thesaline water body will
•brmulation[Teten's, 1930],
c3A =(4098) •'es- 4098(2T +474.6)
c3T
(237.3 + T)4
(10)
OROUD' EVAPORATION DYNAMICS 0.2
4697
es•is the saturation vapor pressure atthesaline temperature, and theothertermsareaspresented earlier.
0.18
Assumingsimilarity,thetransfercoefficients Ibr sensible and
0.16
latentheatfluxesmaybeexpressed inthefollowing tbrm[e.g.,
0.14
Brutsaert,1982;MahrtandEk, 1984;Arya,1988;Matthias, 1990;OttonietaI., 1992;Oroud,1998],
KH /X• •uk2-• =•q•h
0.12
(13)
kn(z)2 zo
KE= 11:!7 •uk 2
0.08
½rln(__z )2 zo
where pisairdensity (kgm'3), C•isthespecific heat ofmoist air, takenas 1010J kg4 K4, u is windspeed (m s4),• is the 0.02
4
12
20
28
36
Temperature (•) Figure 1. The slopeof A (q•)withrespectto temperature. Notethe y axisshouldbe dividedby 10.
psychrometricconstant,k is the yonKarmanconstant (0.4),z is the measurement height(m), Zois roughness length(m), andq•is the departure from atmosphericneutrality. For a longer integrationtime, (e.g., a dayor longer)theatmospheric surface layermaybe assumed neutral(q•= 1) [e.g.,Brutsaert,1982]. Assumingthat the variousenvironmental parameters donot changefollowing a changein 13(cq= ct2;e•=a2;Kin=Kin;K,•= Xœ2;Ta•=Ta2; ½a• = ea2),thensubtracting 12a fromI2b leadsto the followingexpression,
ec•(r• 4 -T24)+ K• (r•-T2)+ K•(•e• - •2½,2) = 0.
whereT is temperature ofthesalinesolution ( øC), ande, is the saturation vaporpressure attemperature T (kPa)calculated bythe followingexpression [e.g.,Kimball,1981],
(15)
Assumingfurtherthatthechangein T asa resultof changing 13 by a small mount is relativelysmall (T >> 6T), •ve may es = 0.61078 exp (17'269T/(237'3 +/'))' (11) approx/matebackradiati6nand sensibleandlatentheatfluxes with very little lossof accuracy. Neglectinghiker-order terms, The dependence of q• ontemperature followsanexponemial the radiation term may be approximatedby the following form,with a valuerangingfrom • 0.004kPaK-2at 5 øC to expression,
0.018k_PaK'2 at 40oC (Figure1). Thestrong temperature dependence of this term is expectedto affectthe water-
OT
•cr(T14 -T24)•4eo-T3(T1 - r2),•4,•crT3 •--•-8,8 ' (16)
atmosphere complex interactions, thereby influencing the Sensible andlatentheatfluxesmaybe expressed similarly, evaporation ratesduringthe courseof the year. The variations of evaporation ratespresented in equations (7)•T (9) (terms 3, 4, and 5) follo•v closelythe rateof temperature (17) changewith respectto 13(•T/315),¾.The functionalform of this parameteris derivedin section3.
•T: 10øCL ,,---*-T=40øC /
3. Derivation of¾
Under thermalequilibrium,that is, changein heatstorageis negligible, and assumingsimilarityin turbulenttransfers,the energy balanceequationfor a saline solutionwhoseactivity coefficient is [3• may be written m the tUllowingIbrrn (e.g., Oroud,1995],
,•-......•...• ....
.,-,...•
S(1-0Cl) +gILD- $1txrl 4-KHi(T1- ral) - K,•(•es• - e•) = 0.
(12a)
When [• changes to [3:,theenergy balance is expressed in a
,
,
similar form, ,,,
S(1-(x:) +e,_Lz) - a?.crT24 -KIn(T2- Ta2) - Kœ2(•2es•_ - ea2)=0.
(12b) 0.4
0.5
0.6
0.7
0.8
0.9
1
where S istheaveragedaily/monthly solarradiationreaching the
surlhce (W m'2),ctiistheoverall albedo ofthewater body,T•is variationof y ( 5'7/ aT ) followinga the temperatureof the salinesolution(K), T• is the ambient Figure 2. The percentage temperature, Kmisthetransfer coefficient forsensible heat(wm2 unit changein K, asa lhnctionof salinetemperature andactivity
K'•), Kmisthetransfer coefficient forwatervapor (Wm'2kPa4),
coefficient.
4698
OROUD: EVAPORATION DYN•CS
4. ObservedVersus Theoretically-Derived¾Values
KEC•lest - •2es2) • (KEesi +tikE•-•-•)•fi, (18)
The theoreticallyderived ¾ valuesarecompared to observed resultscompiled bySaIhotraetal. [1985]andOroud[1994].The observedvalues(%) were reproducedfrom the compileddata
where the slopeof saturation vaporpressure with respectto temperature(0e/0T) can be evaluatedusing the Teten's usingthe followingtbrm, formulation (seeequation (11)),
Oe
4098%]
c3T
(237.3 +rl )2
--=A=
2'o=
(19)
-L+l) (?i - ?i+l )
(23)
where Ti, 13i,Ti+•and13i+• represent thetemperatures andactivity
From energybalance considerations, a risein temperature of a coefficientsof parti andi+1, respectively (seeTables3 and4 of salinesolution,as a resultof a drop in [3,increases bothback Salhotra er al. [1985]). The data were collectedat intervals radiation and sensible heat on the one hand and decreases rangingfrom3 daysto severalweeks.Thetheoretically derived¾ evaporation on the other,andunderthermalequilibrium (steady valuesare obtainedusing equation (21). In thistbrmulation the state)thetwo opposite contributions wouldbe equal.Thus transfercoefficienttbr watervapor(seeequation21) is assumed to be 15 W m'2 kPa4. This value is consistentwith values
4ecrT30T
8T
presented by Morton[1983,pp24-26)andOroud[1995].Figure
Oe8T
•--fi S•+KH.•.•-8•• (KEesi+tikE•- •- )8]5' (20) 3a presentsa scatterplotof the theoreticallyderived ¾values
Dividing both sidesby 813,insertingA for the slopeof saturation vapor pressureandrearranging,we obtainthe followinganalytic equationfor the slopeof temperature withrespectto
=
OT
=
-KEesl
jr 0fl (4•o-T13 +½,KE +fi•vZkK E)
a -5
(21)
-10
where•tK•=KH,13avis theaverage valueofl3•and132, andAisthe
•'
slope ofsaturation vapor pressure ofthesaline solution atT•.The • -15
average of Ti andT2should beused toevaluate e•and Amore • precisely, buttheuseofeither temperature does notintroduce any
•
appreciable eflbct ontheobtained results, particularly when the O -20
variation in 13is relativelysmal. When the variationin [3 is relativelylarge,theaveragetemperature to obtaine, andA should
beused, however.
-25
An importantquestionis thesensitivity of ¾to uncertainty in the transfercoefficient.This is significantfor the procedure
developed in thispaper considering thefactthat¾depends stronglyonthewindfunction.Thesensitivity of ¾withrespectto uncertaintyin the transfer coefficientcan be evaluatedby differentiating 7 (see equation(21)) withrespecttothetranslkr
-25
-20
-15
-10
b
-5
- 4sort 3es
OKE (4scrT 3+ g/K•+ ]5'zXKE) 2
-5
Calculated
coefficient,
07.=
-30-30
(22)
-10
Theabove relation shows thatthevariation in ¾ following a • departure in the transfercoefficient is a complexfunctionof
-• -15
surface temperature, thetransfer coefficient itself, andthelevelof
•
the activitycoefficient. Figure2 shows theabsolute percentage $ variationin ¾ (85'/7)as a functionof surfacetemperature and activity coefficient.The transfercoefficientwhichis usedto
O -20
produce this figureis assumed to be 15W m2 kPa•. The percentage errorintroduced due to a unitvaration inK• ranges from lessthan 1.7% at a salinetemperature of 10 o C andan activitycoefficientof 0.4 to a little morethan 1%ata saline temperature of 40 o C and-a[3 value-of0.40. Therelative variation becomeseven smaller as K•. increases. Theseresults
-25 -30
-30
-25
-20
- 15
- 10
-5
Calculated
showthat T is insensitive to smallvariations in K•, andassuch,
of theoretically calculated ¾valuesversus small errors in the wind function havenegligibleimpacton7. Figure3. A scatterplot Thislendsfiu•er support to the diagnostic capabilities ofthis those derived from(a) Salhotraet aI. [1985] and(b) the average parameterin evaluating evaporation andotherparameters of monthlyand annualvaluesas compiledby Oroud[1994Jand saline solutions.
Sa!hotraet al. [1985].
OROUD: EVAPORATION
DYNAMICS
4699
10
againsttheobserved % valuescalculated withequation (23). The
-' KE=10W/(m^2.kPa) I
correlation coefficient between thetwosetsis0.36(R2 • 0.13).
--
The apparentlypoor correlationisrelatedto thelargescatterin
KE = 16 W/(m^2.kPa)
the observedresults.The theoreticallyderivedvaluesfall in the
range [7-15K,whereas some oftheobserved values exceed 160Kl(notshown inthediagram). These ex•eme values, which can be labeledin stochastic termsasoutliers,wereproduced by Salhotra et aI. [1985] and severelydegradedthe correlation
•
6
coefficient between the two sets. Such extreme values are a result
of severalsourcesof errors,includingerrorsin the observed ra/nthll over the sunkenpans,molecularheatconduction across thesunkenpans-adjacent soilmedium[seeOroud,1998],thermal expansion[seeSteinhorn,1991] and humanand/orinsmunent errorsin the observation of waterleveland/ortemperature. Figure 3b displaysa scatterplot of the computed¾ values against those calculatedwith the average monthly 13and
temperature valuesderivedfrom Oroud[1994]andtheaverage
o
annualvaluesderivedfromSalhotraet at. [1985].The correlation 0.4 0.5 0.6 0.7 0.8 0.9 1 coefficientbetweenthe computed andtheobserved values(%) is 0.79. The agreementbetween the two sets is improved substantially. This. tendency is related to the thct that changes of annualevaporation observationaland otherrandomerrorstendto averageoutasthe Figure5. The percentage following a 1% variation in the activity. coefficient. observational periodis increased[e.g.,FritschenandGay, 1979]. Generally, an errorin.calculatingrainlhllor watertemperature of any sunkenpan would contributesignificantly to a singlecase, but the error contributions smooth out as the data values are appreciabledifferencein the calculated results.Figure4 shows groupedtogether. the theoreticallyderivedg[3,calculatedwith equation(24), versus The present procedure is also extendedto evaluatethe the observedvalues(g]3c = 13i-[3i+1) compiled by SaIhotraet aI. variation of [3 for the ei•t sunkenpansbasedonly on the [1985]. The correlation coefficiembetweenthe two setsis
temperature data of the sunken pansascompiled bySalhorraet approximately 0.96(R2 • 0.92).Thiscorrelation coefficient isa al. [1985]. The variation in the activitycoefficient(g]3)is considerable improvementover thatpresented in Figure3. This calculatedusing the followingexpression (compareequation trend is linked to the thct that water temperature, which is (2•)), employedin equation 24, is aneasilymeasured element, whereas the [3 valuescompiledby Salhottz• etaI. [1985]weresubjectto numeroussourcesof errors,includingerrorsresultingfrom
•fi= (Ti-Ti+l)( 4øecrT3 +JfpI +fiavAfi'E) (24) (Kses)
where A and es are calculated attheaveragetemperatures of Ti and Ti+l.Thetransfercoefficient forwatervaporis assumed to be
15 W m'2 'kPa -1 assuggested above; increasing thevalueofthe transfercoefficient to 18 W m'2kPa 4 didnotleadto any
providesimprovedresultsthansomefieldmeasurement methods which are arduous,more expensive, and subject to potentially large errors (see alsoSteinhorn[1991] andSaIhotraet al. [1991]).
0.2
0.15 ß
•
•
rainfall(advectionanddilution),evaporation quantity,lateralheat conduction,thermalexpansion,and otherobservationaVhuman errors.For instance, whenprecipitation occursovera sunkenpan, it tendsto disruptthethermodynamic characteristics of thesaline solutionwithin the pan because thetemperature of rainwateris usuallylower thanthatwithina salineparkandalsoraintendsto dilute the salinesolution.Thus,evaluating ]3usingequation (24)
ß
o.1 5. Sensitivityof Evaporation to Variation in 13
o.o5
The present procedureis extendedto studyevaporation dynamics at different ]3values. Calder' and NeaI [1984] calculatedthat annualevaporationfrom the DeadSeain 1984 was 95 mm lessthan its counterpart prior to 1960 (during historical time). They also estimatedthe average annual temperature of themixedlayer(theupper40 m) of theDeadSea
o
•4
to be 0.5oC higher thanitscorresponding value prior to1960. •.2 •.2
•.15
•,!
•.05
0
Calcul•
0.05
0.1
0.15
0.2
The use of equation (21), usingthesameinputvalues presented by CalderandNeal,wouldshowthatduringthesame period the
mixed layertemperature was approximately 0.55oChigher than its counterpart priorto 1960.Thepresent formulation shows also
from the Dead Sea for thatperiodwas Figure.4. Derivedand observed variations in theactivity that evaporation suppressed byabout 90nunyr4. coefficient([3).
4700
OROUD: EVAPORATION DYNAMICS
250
.....
='
200
a_
150
Term1
•
Term2
ß
Term 3
•'
Term 4
•
Term 5
conditionsencountered nearthe Dead Sea.For a changeof 1% in 13,thepercentage variationin evaporation rangesfrom • 1% at [5 of 0.95 to • 8% at [• of 0.40. Additionally,evaporation depar•e increases as windspeed increases. In absoluteterms, a 1% departurein [5leadsto a depart•e in annualevaporation by about
35and21mmyr4 at[3of 0.40and0.95,respectively. loo
.
o
I
-100
1
,
2
3
4
5
6
7
8
9
10
11
12
Month 250
•__•,•_ Term 1 - Term 2 Term 3 Term 4
2OO
,Term 5
150
The contributionsof the various evaporation terms(terms1 through5) were evaluatedunderthree [3values,namely,0.95, 0.70 , and0.45,respectively. Theseactivitycoefficientvaluesare operationallyimportantbecause thefirstvaluerepresents a Dead Sea with the proposedcanal connecting this 'dnuinishing water body to the open seas,the secondvaluerepresents the current Dead Sea, and the third value representsapproximatelythe chemicalcompositionat which potashis recovered.Figure 6 showsthe annual coursefor eachof the five terms,andFigure7 displaysthe annual contribution of eachterm.It is quiteevident that term2 is themostimportantone,with a contribution ranging from about 53% at [5of 0.95 to 65% at [5of 0.45. Thisis dueto the aridity of the site where thistestis conducted. The second most importantterm affectingevaporationis the changeto net radiation,with anannualcontribution of approximately 25%. The contributionsof terms 3 and 4 are relatively small, andthey usually negateeach other.at [5 closeto unity, but at small[5
100 25
0
2O
-5O
15
-1GO
2
3
4
5
6
7
8
9
10
11
12
Month 25O
I • Term 1 I•Term 2
200
I '- Term3
150-
L .• Term5
I .• Term 4
3
c,,,,i lOO
Terms 25
•: 5o
b 2O
!5
-5O
-100
1
2
3
4
5
6
7
8
9
10 11 12
Month
Figure 6.
The annual courseof thefive termsin thePenman
equation(see text) at (a) [3= 0.95,(b) 13= 0.7,and(c) 13= 0.45, with atmosphericforcings si_n'fi!ar to thoseencountered nearthe southern corner of the Dead Sea. -5
1
2
3
Terms
4
5
Given the above congruent values,thepresentformulation is extendedto evaluatethedynamicsof evaporation underdifferent Figure 7. Total contributionof the five evaporation terms [5. Figure 5 showsthepercentage changes of annualevaporation followinga 1% variationin [5at activitycoefficients of (a) 0.95 (o"E/E ) following a variationin [5 under the meteorological and(b) 0.45,respectively (seetext).
OROUD' EVAPORATION
( • 0.45) the annualcontribution of term3 approaches zero.The
DYN•CS
4701
Folchitto,$., Seawateras salt and water sourcefor solarponds,Sol.,
Energy, 46, 343-352, 1991. abovefiguresshowthat evaporation variation exhibits a strong Instrumentation, 216pp., annual trendin all terms,with net radiationbeingthe most Fritschen,L. J.,andL. W. Gay,Environmental Springer-Verlag,New York, 1979.
noticeable,particularlyfor very hypersalinesolutions.This Hostcrier,S. W., Hydrologicalandthermalresponses of lakesto climate: distincttrend in term5 is linkedto thestrongannualvariationin Descriptionandmodeling,in PhysicsandChemistry ofLakes,2nded., editedby A. Letman,D. M. imboden, and.R. Gat,pp.63-82,Springer surfacetemperature which stronglyinfluencestheslopeofthe Verlag, New York,.1995. saturation vaporpressurecurve (A) andqt.It appears, therefore, B. A•, A rapidlyconvergent algorithm fornon-linear humidity that evaporationfrom saline solutionis quite non-linearwith Kimball, and thermal radiationterms. Trans.A•4_E, 24, 1476-1477, 1981. complexfeedback mechanisms influencing it, including thelevel Klein, C., and H. Flohn, Contributionsto the knowledge of the of solarradiation,the transfercoefficients forwatervaporand fluctuationsof the Dead Sea, Theor.Appl. Climatol.,38, 151-156, 1987. sensible heat,,andthelevelof theactivitycoefficient/salinity. Klein,.M., Dead Sealevelchanges (comment),Isr. J. EarthSci.,39, 4950, 1990.
6. Conclusion
The presentformulation provides a robustmethodto studythe dynamics of saline water bodies (temperature,activity coefficients,and water loss),regardlessof size, usingroutine meteorological observations without measuring evaporation per se. The only required parameter is watertemperature, aneasily detenvJned parameter using routine meteorological measurementsor thermalimagery..The ramificationsof this fi.ndingare quite operationalfor evaluatingevaporationfrom operating hypersaline solutions similarto thoseneartheDeadSea and also for the design andconstruction of salinelagoonsused for harvestingminerals. Calculations
with
the Penman formulation
reveal that the
Kutzbach,J. E., Monsoonrains of the late Pleistocene and early Holocene:Patterns,intensityandpossiblecauses,in k•riationsin the Global PP•terBudget,editedby A. Street-Perrot,M. Beran,andR. Ratcliffe,pp. 371-389•D. Dordrecht,Norwell, Mass,1983. Mahrt, L., andM. El
