Seasonal Variation of the Global Water Balance Based on Aerological ...

JOURNAL OF GEOPHYSICAL

RESEARCH, VOL. 89, NO. D7, PAGES 11,717-11,730, DECEMBER 20, 1984

Seasonal Variation

of the Global

Water

Balance

Based on Aerological Data FRANK

BRYAN

GeophysicalFluid DynamicsProgram, Princeton University,New Jersey ABRAHAM OORT

GeophysicalFluid DynamicsLaboratory/NOAA, PrincetonUniversity,New Jersey The distribution of evaporation minus precipitation over the globe and its seasonalvariations are estimatedfrom global atmosphericcirculation statisticsfor the period May 1963 to April 1973. Meridional profiles of evaporation minus precipitation over the Atlantic, Pacific, and Indian oceans,over all oceanscombined,and over all continentscombined,as well as the total evaporationminus precipitation over each oceanicand continentalregion, are shown.The Pacific Ocean is found to have an excessof

precipitationand the Atlantican excessof evaporationthroughoutthe year. Over the Indian Ocean, precipitationexceedsevaporation during December-February,while evaporation exceedsprecipitation during the rest of the year and in the annual mean. The resultsare generally in qualitative agreement with previousestimatesof the annual mean world water balancebasedon surfaceobservations.There are large quantitative discrepancies,however, particularly in the subtropics.A comparison with the analysisof 2 months of data from the FGGE period suggeststhat the primary sourceof error in our resultsis associatedwith spatialsamplingdeficiencies in the generalcirculationstatistics.It appearsthat in many regionsthe current operational rawinsondenetwork is inadequateto give reliable quantitative estimatesof differentiatedquantitiessuchas are requiredin computingthe atmosphericwater balance.

1.

nental runoff seemsto occur in small ungaugedrivers or as

INTRODUCTION

The regionaldistributionsof evaporation,precipitation,and runoff are of great interestto both climatologistand oceanographers. Accurate estimatesof evaporation and precipitation over the ocean will be required for the successof most studies of ocean-atmosphere interactionsplannedfor this decade(e.g., the "Cage" [Dobson et al., 1982], and "TOGA" (Tropical Ocean-Global Atmosphere)[National ResearchCouncil,1983] experiments).Another important factor is that the salinity distribution in the ocean is forced by the input and removal of freshwaterat the surface.Unfortunately,the surfacewater balanceis extremelydifficultto monitor. Heretofore, estimatesof the world water balance have generally relied on direct surfacemeasurementsfor precipitation, on empirical formulae for evaporation,and on stream gauges in the major rivers for runoff. Various remote sensingtechniques for estimating these parametershave been proposed (e.g.,the GOES PrecipitationIndex lArkin, 1983]) but, as yet, have not been implementedoperationallyfor sufficientlylong periods to obtain climate means. Furthermore, these techniquesare often only valid in certainclimaticzonesand hence do not provide global coverage. Existing precipitation measurementsare very spotty. In fact, over the oceansit is necessaryto use empiricallyderived correlationsbetweenprecipitation frequencyand amount or to extrapolatefrom adjacent coastal or island stations. Reed [1980] has shown that the topographicinfluenceof even the lowest islandscan cause significant errors in the extrapolated precipitation values. Evaporation estimatesusing empiricallyderived bulk formulae, especiallywhen applied to climatological data, are also subjectto large errors.Finally, although river gaugesprovide reliable "natural rain gauges,"up to 35% of the total contiCopyright 1984 by the AmericanGeophysicalUnion. Paper number 4D 1192. 0148-0227/84/004D- 1192505.00

diffuserunoff [Baurngartnerand Reichel, 1975]. Due to the obviousincompatibility among the terms of the surfacewater balance,previousestimateshave required rather

subjectiveadjustmentsin the individual terms in order to obtain local and global balances[Baurnqartnerand Reichel, 1975; Baum•tartner,1981]. Baumgartner provides a comprehensive account of the problems and the resulting uncertainties in estimating the world water balance from surface observations.In light of these difficultiesit is desirable to obtainan independentestimateof the world waterbalance. The aerological method, which utilizes the conservation equationfor atmosphericwater substanceto obtain the surfacewater balanceas a residual,providessuchan independent estimate.In contrastto the traditional method the aero!ogical method is basedon first principlesand does not require empiricallyderivedconstantsor formulae.In addition the aerologicalmethod lendsitself to studiesof the temporal varia-

bility of atmosphericbalances,suchas the seasonalvariation of the world water balance.The errors incurred by neglecting terms in the balance equation can generally be quantified throughscaleanalysis.Successful useof the methoddoesrequire that the accumulatederrorsof the individualtermsin the balanceequationbe small comparedto the residualwe are seeking.Significanterrorsin the estimatesof the surfacewater balancethen will be due solely to inadequateor inconsistent data. As discussedbelow, the data usedin this study may not

be adequateto providereliableestimatesof the surfacewater balancein someregions. In this studywe apply the aerologicalmethodto the global atmosphericcirculationstatisticsfor the period May 1963 to April 1973 that were compiledby Oort [1983]. While this method has beenapplied to the water balanceof specificcontinental[e.g.,Rasmusson, 1968,for North America]and maritime [e.g., Peixoto et al., 1982, for the MediterraneanSea] regions,this is, to our knowledge,the first attempt to so obtain an estimateof the world water balance,treating oceans

11,717

11,718

BRYANANDOORT:GLOBALWATERBALANCE

and land separately.Maps of the global distribution of water vapor flux divergence(approximately equal to evaporation minus precipitation, see section 2) have previously been presentedby Peixoto ['1972] and Peixoto and Oor• [1983], but they did not explicitlyconsiderregional budgetsor land-ocean contrast.Rosenand•Omolayo[1981], on the other hand, consideredthe transfer of water vapor acrosscontinental boundaries for the northern hemisphere,but they did not compute the associatedflux divergences.Our resultswill be presented as annual and seasonalmean meridional profilesof evaporation minus precipitation (E- P) for each ocean, all oceans combined, all continents combined, and as tabulations of total

E - P for each oceanicand continental region. In order to provide a preliminary estimateof the effectsof data deficiencieson theseresultswe have repeatedsomeof the calculationsfor the months of January and July 1979 using the First GARP Global Experiment (FGGE) level 3b data set produced at the Geophysical Fluid Dynamics Laboratory (GFDL). This set of analysesis based on a somewhat better observational network than ours, so that differences between

the water balanceobtainedfrom our generalcirculationstatistics and the FGGE data may given an estimateof the spatial and temporal samplingerrors in our results.The resultssuggestthat there are large uncertaintiesin someof our regional water budget estimates,resultingprimarily from spatial sampling deficiencies in the generalcirculationstatistics. Despite the uncertaintiesin our results,they can provide valuable

information

on the world

water balance and on the

reliability of the aerologicalmethod when applied to regional budgets.The resultsare undoubtedlyqualitativelycorrectand provide the only estimate of the seasonal variation of the water balancein someregions.In contrastto previousstudies of the world water balance, the homogeneousnature of our data set and the objective,and relatively simple, analysisprocedure enable us to maintain internal consistencywith no needfor subjectiveadjustments. In section2 an outline is given of the aerologicalmethod and its applicationto regionalwater balancestudies.In section 3 the data and analysisproceduresare described.In section 4 our world water balance estimatesare presentedand comparedwith those of previousauthors.In section5, some

possiblesourcesof errorsin our resultsare presented, and in section6 the resultsare summarizedand objectivesfor future work are suggested. 2.

TIIE AEROLOGICAL METHOD

The balancerequirementsfor atmosphericwater vapor and the basisof the aerologicalmethodhave beenthoroughlydiscussedby Peixoto[1973]. We will brieflyreviewsomeof the relevant aspectshere. The balanceequationfor atmosphericwater substanceis •

c•t

+ V. Q - E ....

•t

V. Q• - P

(1)

In this equationthe quantities w

=•oPSq dp

(2)

sdp

(3)

--

and

Q =

qv --

are the verticallyintegratedwater vaporcontentand the verti-

cally integratedhorizontalflux vectorof water vapor,respectively. W• and Qc are the corresponding quantities for condensed-phase atmosphericwater. Finally, E is the evaporation from the surface,P is the precipitation falling on the surface,¾ is the horizontal divergenceoperator, Psis the sur-

face pressure,q is the specifichumidity,v is the horizontal velocityvector of the air, and g is the gravitationalacceleration.

As discussed by Peixoto ['1973], the condensed-phase water contentWcis typicallytwo ordersof magnitudesmallerthan the water vapor content W; its time tendencyis similarly small. The divergenceof the condensed-phase flux can be of the same order of magnitudeas the divergenceof the water vapor flux, but only in regionsof persistentcloud formation or cloud destruction.This may be the case over coastalupwellingregions,for example.However,by averagingin space and time, the contributions of the condensed-phaseterms shouldbe much reducedand can thereforebe neglectedin the presentstudy.Thus we may write (1) after averagingin time and integratingover spacein the form

(c•-•-/+ (V. Q)= (E-P)

(4)

The spatial integral is given by

(())=

( )a2 cos•pd). &p I

(5)

1

and the time averageby an overbar

1t•f,2( (--)--t2-at, )dt

(6)

where2 is longitudeand 4>latitude.The regionaldistributions of evaporationminus precipitationare evaluatedby computing the termson the left sideof (4). This equationcan be rewritten after applyingGauss'theoremto the secondterm in the form

•

+ Q.ndl=(E-P)

(7)

where F is the boundary of the region, n is the outward unit normal vector, and dl is the element of length along the boundary. We will use the form (4) in this study. Previous studiesof regionalwater balanceshave tendedto usethe form (7) of the balanceequation.We will briefly discussthe relative meritsof theseapproachesin section5. 3.

DATA AND ANALYSIS

The data usedin this study are from objectivelyanalyzed,

griddedmonthlygeneralcirculationstatisticsfor the period May 1963to April 1973.This data setwascompiledat GFDL usingonceand,for somestations,twicedaily rawinsonde reportsfrom the globalstationnetworkdepictedin Figurelb. In addition,ship and surfaceobservationshave beenusedto supplement the rawinsondedata at the lowestlevel,as shown in Figure la. We will not describethe detailsof the objective analysisprocedure.However,we must point out two aspects of it which will have an important bearingon our results.The first is that the proceduretreats each level independently,so that the greatlyenhancedobservationalnetworkat the lowest level doesnot affectthe analysesaloft. Second,the procedure usesa zonal averageof the station data as the initial guess field. The interpolationprocedure,using a relaxation technique, adjuststhe initial-guessfield by adding the station

BRYANAND OORT' GLOBALWATER BALANCE

11,719

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•

7

7

6

6

7

8 •

3

5

6

1

7

5

7

60N

30N

AAAAAAAA

EQ

30S

1

60S

180

120W

60W

0

60E

120E

180

120W

60W

0

60E

120E

180

90N

60N

30N

EQ

30S

60S

90S 180

Fig. 1. (a) Distribution of surfacedata used in the mean January analysesand number of years of observations available,rangingfrom 1 to 10 (- A). Data over land are from rawinsondestations(1000 mbar), and data over oceanare from 2ø x 2ø averagedsurfaceship reports(only plottedfor every 5ø of longitude).(b) Distributionof rawinsondedata usedin the meanJanuaryanalysesof all levelsabovethe earth'ssurfaceand the numberof yearsof observations available, rangingfrom 1 to 10 (= A). The total numberof stationsover the globefor Januarywas 1093.

anomalies.After severaliterations a gridded final field is produced which still contains some zonally symmetric features due to the choice of the initial guess.The data set and the

analysisprocedurees have beendescribedextensivelyby Oort [1983]. Peixoto and Oort [1983] have given a thorough dis-

cussionof the subsetof these data, which describesthe atmo-

sphericbranchof the hydrologiccycle. The monthly means,variances,and covariancesof the specifichumidity and horizontalcomponentsof the velocitywere available at the 1000, 950, 900, 850, 700, 500, 400, and 300

11,720

BRYANAND OORT' GLOBALWATER BALANCE

90N

60

30

0

30

60

90S 180W

120

60

0

60

120

180E

90N

•'

. ::::i.",•:•ii!iii!iii::'

60 i!::•i+ ..........

.:•::•::':::

' '

.......

3O

o 30

•o

180W

::............................................................ •::::::iiiiiiiiiiiiiii:: .:•

120

60

0

60

120

180E

120

60

0

60

120

180E

90N

60

30

0

30

60

90S 180W

Fig. 2. (a) Thedivergence of thevertically integrated horizontalwatervaportransport(in units10-6 kg m-: s-x) for annualmeanconditions. Negativevalues(indicatingnet precipitation) are stippled.The contourintervalis 25 x 10-6 kg m-2 s-• (to obtainvaluesin cm yr-2, multiplyvalueson mapby 3.16).(b)As in Figure2a,exceptfor December-February (DJF) conditions.(c) As in Figure 2a, exceptfor June-August(JJA)conditions.

mbar levelsat grid points spacedapart 2.5ø in latitude and 5ø in longitude. It should be noted that 950 and 900 mbar are nonstandardreporting levelsand that there is a reductionin the amount of data available for these analyses(see Tables 2 and 3 of Oort [1983] for a precisemeasure).From thesevalues the vertical integrals(2) and (3) were evaluated for each of the 120 months as describedin the appendix. The annual and seasonalmeans of these fields are presentedin Peixoto and Oort [1983] and will not be reproducedhere. The divergence of the vertically integrated water vapor flux was computed usinga finite differenceoperator which retainscertain integral propertiesof the differentialoperator as describedin the apo pendix. Composite seasonaland annual means were then formed.

It is difficult to determine the uncertaintiesin the regional

water budgetsarising from samplingdeficiencies.In order to provide a preliminary estimateof the reliability of our results we have repeated some of the analysesfor the months of January and July 1979 using the FGGE level 3b data set producedat GFDL. During FGGE, the rawinsondenetwork was improved in someregionsand also augmentedby several ground- and satellite-based observingsystems.The final analyzed fields were produced by a four-dimensionalcontinuous data assimilationsystem[Stern and Ploshay, 1983]. Thus besidesthe differencesin the raw data, the analysisschemeused during FGGE differs in some important aspectsfrom that used for the 1963-1973 general circulation statistics.For example,model forecastsof the variousfieldswereusedas a first guessin the objectiveanalysisrather than zonal meansof the observations.For comparisonpurposesthe FGGE analyses

BRYANAND OORT' GLOBALWATER BALANCE

9øNI' ' 60

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11,721

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::•• .... ::•:• ••!•:•:•:•:,:: ....: i!J ß "•iliHi!i !i ii•iill ::::::::::::::::::::: :i:!:i:i:i:i:i:i:i:} ................... •:•:::•:•:•• •..... •:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•: ................... [•3

30 -

ii•!:::::'

::: 180

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:...................:::

150W

120

90

60

::: 'Anta'rctic• : 30

0

30

60

::

90

120

150E

180

Fig. 3. Areatemplateusedin the regionalintegrations. Offshoreislandsare includedin the regionwith the samedensity stippling(e.g.,New Guinea with Australia).

questionof the extentof theseproblemsis beyondthe scopeof the current study and is addressedelsewhere[Rosen et al., 1984].The FGGE data are usedhere only as a way of obtaining a first impressionof how samplingdeficiencies in the general circulation statisticsmay affect regional budget calcula-

wereinterpolatedto the samegrid as was usedin the analysis of the 10-yeargeneralcirculationstatistics. While the F66E data are not subject to sampling deficienciesas seriousas in the 10-yeargeneralcirculationstatistics, the FGGE analysesare subjectto other shortcomings whichprecludeconsideringthem as beingmore reliablethan our generalcirculation statisticsat this time. First, they are basedon a singleyear of data and may not be representative of climatic means.More importantly, the biasesof the atmosphericgeneralcirculationmodelusedin the data assimilation systemwill affect the resultsin (as yet) unknown ways. The '

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ANNUAL (103 m3 s-')

lOO

tions. 4.

RESULTS

DivergenceFields

In most casesthe divergenceterm dominatesover the storage term on the left side of (4). Therefore one can get an

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Fig. 4. (a) Meridionalprofilesof annualmeanevaporation minusprecipitation evaluatedover5øzonalbandsfor each oceanandexpressed asa volumeflux(10a ma s-•). Note that thedatapointsrepresent integrals overthe 5øbandsandare plottedat the centerof eachband. The connectinglines are only to aid viewingand shouldnot be usedto obtain intermediate values. (b)Asin Figure4a,exceptexpressed asan areanormalized flux(m yr-•).

11,722

BRYANAND OORT: GLOBALWATER BALANCE

ated with

TABLE 1. RegionalAreasby 5ø Latitude Bands

Area, 109 m2 Latitude Band

Pacific

Atlantic

Indian

Oceans

Continents

85øN-90øN 80øN-85øN 75øN-80øN 70øN-75øN 65øN-70øN 60øN-65øN 55øN-60øN 50øN-55øN 45øN-50øN 40øN-45øN 35øN-40øN 30øN-35øN 25øN-30øN 20øN-25øN 15øN-20øN 10øN-15øN 5øN-10øN 0ø-5øN

0 0 0 0 33 555 2,305 3,337 4,070 4,782 5,571 6,249 6,912 7,842 8,832 9,942 10,784 10,635

1,030 2,390 3,506 3,310 1,294 1,437 2,072 2,210 2,447 2,903 3,368 3,777 4,586 4,631 4,190 3,764 3,136 3,776

0 0 0 0 0 0 0 0 0 0 0 0 140 715 1770 2787 2983 3160

1,030 2,390 3,506 3,310 1,327 1,992 4,377 5,546 6,517 7,684 8,939 10,026 11,638 13,188 14,792 16,493 16,903 17,570

0 510 1,302 3,370 7,175 8,266 7,559 7,978 8,492 8,694 8,686 8,710 8,068 7,337 6,395 5,195 5,123 4,624

0ø-90øN

81,849

53,827

11,555

147,229

107,483

5øS-0ø 10øS-5øS 15øS-10øS 20øS-15øS 25øS-20øS 30øS-25øS 35øS-30øS 40øS-35øS 45øS40øS 50øS-45øS 55øS-40øS 60øS-55øS 65øS-60øS 70øS-65øS 75øS-70øS 80øS-75øS 85øS-80øS 90øS-85øS

9,787 9,254 9,038 8,314 7,769 7,390 7,026 6,791 6,315 5,678 5,259 4,763 4,132 3,260 1,981 500 0 0

3,314 3,059 3,012 3,015 3,276 3,558 3,640 3,913 3,922 3,752 3,381 2,984 2,564 2,014 1,000 260 0 0

3,699 4,969 5,273 4,708 4,418 4,446 5,064 5,871 5,687 5,211 4,696 4,145 3,562 1,314 26 0 0 0

16,800 17,282 17,324 16,038 15,463 15,393 15,729 16,574 15,924 14,641 13,336 11,892 10,258 6,587 3,007 760 0 0

5,395 4,743 4,365 5,150 5,061 4,312 3,007 1,051 455 367 188 44 0 1,914 3,674 4,048 2,900 1,030

97,257

46,663

63,089

207,009

47,703

90øS-0ø

To obtainE - P valuesin termsof m s-•, dividevaluesin figures or tablesby the appropriatearea shownhere.

impressionof the spatial distribution of evaporation minus precipitationfrom the maps of water vapor flux divergenceas shownin Figures2a, 2b, and 2c for the annual mean,northern winter, and summer seasons,respectively.Note that the fields in Figure 2 have beensmoothedfor displaypurposes,usinga median smoother [Rabiner et al., 1975-1,and that the actual divergencefields used in the subsequentcalculationscontain considerablymore spatial detail. Regions of divergencehave an excessof evaporation over precipitation,regionsof convergence an excessof precipitation over evaporation. The intertropical convergencezone (ITCZ) and its seasonalmigration are evidentnear the equator,but it does not form a continuouszonal belt of net precipitation. Centers of particularly strong net precipitation are located over the Amazon region of South America, over central Africa, over the western Pacific-Indonesianregion, and over the central Indian Ocean. Net evaporation takes place over much of the subtropicsin both hemispheresbut is most intensein the winter hemisphere.Severalcentersof strong net evaporation are located over the oceansbetween 10ø and 25ø latitude in both hemispheres.Net precipitationpredominates over most of the mid- and high-latituderegions.This is associ-

transient

baroclinic

disturbances

rather

than with

convectivecirculations which are mainly responsiblefor the precipitationin lower latitudes. The intensity of the net precipitationin mid and high latitudesis much lower than that in the equatorial region. Regional Profiles of E-

P

In order to quantify the regional differencein E- P we have applied(4) to the verticallyintegratedvapor flux divergenceand vapor contentfieldsfor eachof the 120 monthsand then formed compositeseasonaland annual means.The regional templateusedin the calculationsis shownin Figure 3. The integrals (5) were evaluated for zonal bands 5ø and 10ø latitude wide, with the longitudinallimits of integrationgiven by the boundariesof eachregionshownin Figure 3. The results for annual-mean conditions over each ocean,

evaluatedfor 5ø zonal bands,are shownin Figure 4. In Figure

4a, evaporationminusprecipitationis expressed as a volume flux, while in Figure 4b the same results are presentedas area-normalizedfluxes.All subsequentresultswill be presented in terms of volume fluxes. The areas in 5 ø latitude bands for

each ocean, all oceans combined, and all continents combined

are givenin Table 1 so that any of our resultsmay be converted to area-normalizedfluxes. The equatorial region of net precipitationis centerednorth of the equator in the Atlantic and Pacific oceans but is broader

and extends further south in

the Indian Ocean. As a rule the prominent featuresin the Indian Ocean are displacedto the south of their counterparts in the other two oceans.As can be seenby comparingFigures 4a and 4b, many of the differencesbetweenthe profilesfor the various

oceans can be related

to the differences in the size of

the oceans.Whereas the equatorial Pacific receivesthe largest volume of water of the three oceans, the area normalized flux is smallestfor this ocean. In the subtropicsof the southern hemispherethe volume of net evaporation over the Pacific Ocean

is less than

that

over either

the Atlantic

or Indian

oceans,despiteits greaterwidth at theselatitudes.The meridional extent of the region of net evaporationis also lessin the Pacific than that in the other two oceans,so that, overall, the South Pacific Ocean seemsto be a relatively weak sourceof water vapor for the atmospherein the annual mean.Although the southern hemisphereoceans are poorly sampled by the rawinsondenetwork, the relative magnitudesof E- P for the threebasinsagreequalitativelywith thoseobtainedby Baurngartner and Reichel[1975]. The seasonalcycle of E - P over each oceanis depictedin Figure 5(a-d). From Figures 5a and 5c it is apparent that the net evaporation in the subtropicstends to be strongerin the winter hemisphere.This is probably due to the increased strengthof the easterlytradesin winter. The relativeweakness of the annual mean net evaporationover the SouthPacificcan be attributedto the virtual absenceof a regionof net evaporation during December-February and the continued weak evaporationduring March-May. During the rest of the year, the net evaporation is comparableto that in the other two oceans.In equatorial latitudes the ITCZ migratesover 5ø of latitude toward the summerpole and is strongestwhile at its northernmostpositionduring June-Augustin all threeoceans. The net precipitation in the extratropicsdoes not follow a simple seasonalcycle. In the Atlantic and Pacific oceansthe net mid-latitude precipitation reachesmaximum valuesduring June-Augustsimultaneouslyin both hemispheres. The seasonalcycleof E - P over the three oceanscombined is shownin Figure 6. Most of the featuresfollow the pattern of

BRYANAND OORT: GLOBALWATER BALANCE

400

I

I

[

,•

300 DJF

11,723

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ß

i

a

, Pacific

--o- -o- Atlantic

(103 m3 s-1)

---+--+

Indian

200

100

"ø"ø',,, / +

o©

-

- -0•

-0--0- --•'-•

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-200

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-200

-300

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90S

60

30

0

30

60

90N

Fig. 5. Meridional profilesof evaporationminus precipitationfor each ocean for the four seasonsevaluatedover 5ø zonal bands.SeealsolegendFigure4a.

the Pacific Ocean due to the dominance of its contribution in

the area integrals.Again, the strengtheningof net evaporation in the subtropicsof the winter hemisphereand the northsouthmigration of the ITCZ are clearin this figure.In Table 2 the valuesof E- P are presentedfor 10ø-latitude-widebands over the world ocean with, in parentheses,a measureof the interannual variability of this quantity. The measuregiven is the 95% confidenceinterval for normally distributedvariates,

In Figure 7a we have plotted the annual mean E- P over the three oceanscombined,along with the corresponding valuesfrom Baumgartnerand Reichel [1975]. The most striking differencebetweenthe two curvesis the reducedpoleward extent of the subtropicalevaporationzonesin the presentcalculation. In other terms the region of excessprecipitationin the middle latitudes of each hemisphereextendsfurther equatorward in our data, particularly in the northern hemisphere.

which is defined as twice the standard error of the mean, i.e.,

The net effect of these differences is to make the total E-

2a/x/•,where N = 10isthenumber ofyears (orseasons) and

over the ocean much lessin the presentcase(comparehemispheric and global estimatesin the last two columns of Table 2).

a is the standarddeviation.This quantity containssomebias due to changesin the station network itself, sincenot all stations reportedfor the entire 10-yearperiod.

In Figure 7b the analogousprofilesof E-

P

P for all land

11,724

BRYANAND OORT: GLOBALWATERBALANCE

i

I

700

600

ß •

ALL OCEANS (103 m3 s-•)

+--+

--o-

, DJF o MAM JJA

-o--

SON

500

400

300

200 100

-Too -200

*

/: '

\

/'

-300 -400 -500 90S

6 60

30

0

30

60

90N

Fig. 6. Meridional profiles of evaporation minusprecipitation for all oceans combined for thefourseasons evaluated over5øzonalbands.SeealsolegendFigure4a.

areascombinedare plotted.Again,the greatestdiscrepancyevaporationfor every season.The South Atlantic and the Atbetweenthis study and that of Baurngartner and Reichel lanticOceanas a wholeshowan excessof evaporationover [1975] occursin the subtropics. We find that evaporation precipitationthroughoutthe year. In the Indian Ocean we exceeds precipitionoverland in the subtropics of both hemi- finda netevaporation duringmostof theyear,exceptduring spheresfor annual-meanconditions,whereasthe previous December-February. Thispatternof evaporation minusprestudyshowedprecipitationgreaterthan evaporationat all cipitationis consistent with the observed highersalinityfor latitudesover land. The differences are greaterthan can be the Atlantic than for the PacificOcean.However,a definitive explained by interannual variabilityasshownby thevaluesin assessment of thesaltbalance of theoceanrequires knowledge parenthesesin Table 2 and describedabove. of both the river input of freshwater and the salinitytransportsin theoceans, whicharebeyondthescopeof thisstudy. The World Water Balance The issueraisedpreviously in the discussion of Figure7b, To gain anotherperspective on the world water balancewe concerningan unexpectedand perhapsunrealisticexcessof have also integrated our E- P values over each continent evaporation overland,is alsobroughtout clearlyin Table 3. and oceanseparately.However,as we will showin this section For every continentexceptNorth Americawe find an excess

thisfurtherstratification of thedataleadsto additional prob- of evaporationover precipitationduringat leastone season. lems. In fact the further breakdown in the east-westdirection For Africa,Australia,and the combinedEurasiancontinent, putsa heavyburdenon thedataqualityandtheregionaldata evaporation exceedsprecipitation in the annual mean. For distribution. Moreover,theintegrationwith respect to latitude Australia, in fact,thisis thecasein everyseason. The strength tendsto lump togetherpositiveand negativecontributions of the hydrologiccycleas measuredby global continental fromdifferentclimaticzones,leadingto a muchgreateruncer- runoffis an orderof magnitude lessthan that obtainedby tainty in the final numbers.Therefore we caution the reader in

Baurngartner and Reichel[1975].

usingourresults in Table3, sincetheyareof a distinctly lower The last row in Table 3 gives,for eachseason, the global qualitythanthosepresented in Table2 andin all figures. excess of evaporationoverprecipitation, i.e.,the globalrate of Thedistribution of evaporation minusprecipitation among increaseof atmospheric watervapor.It showsthat the atmothe various continentsand oceansis shown in Table 3 for each sphericwater vapor increasesgraduallyduring northern season and the annual mean. We have also entered the results winter,spring,and summerand then drops'sharplyduring of Baurngartner and Reichel[1975] for comparison. One northern autumn. shouldnotethatourdefinitionof theregions maydiffersome5. DISCUSSION whatfromtheirs.In particular thevaluesof E - P forEurope an Asiashouldbe combined for intercomparison. The largenet evaporationover subtropicalregionsof the Considering the balanceof watervaporoverthe oceanson continents impliedby aerological datawasfirstpointedoutby a hemisphericor global scale,we find that in the North and

Starr and Peixoto [1958]. They spectulatedthat the surface

SouthPacificoceans andin theNorthAtlanticOceanevapo- waterbalancein theseregionsmightbe maintainedby a conration exceedsprecipitationin winter and spring,while the vergence of subterranean water.What is evenmorestrikingin oppositeis true during summerand autumn.However,the PacificOceanasa wholeshowsan excess of precipitation over

our results,and perhapsmore difficultto explainwith their hypothesis,is the net evaporationover entire continentsfor

BRYANAND OORT: GLOBALWATER BALANCE

11,725

TABLE 2. The Meridional Distribution of Evaporation Minus Precipitation Over All Ocean Regions Combined for Seasonal- and Annual-Mean Conditions in Units of 103 m 3 s-l

This Study ' Latitude

80øN-90øN 70øN-80øN 60øN-70øN

DJF

MAM

BR,

JJA

SON

- 18(3) -47(5) - 31(8)

Year

- 13(2) -23(4) - 30(7)

- 10(2) - 19(4) - 19(6)

- 19(4) -28(10) -42(9)

60øN-90øN

-65(10)

-48(11)

-89(13)

50øN-60øN 40øN-50øN 30øN-40øN

- 132(24) -44(28) -34(28)

-75(14) - 118(14) - 124(27)

-93(15) - 150(28) -311(42)

- 115(14) -87(14) 18(23)

- 103(11) - 100(10) - 113(20)

-202 - 149 306

30øN-60øN

-210(36)

-317(11)

-555(49)

- 184(38)

-316(22)

-45

20øN-30øN 10øN-20øN 0ø-10øN

444(42) 1110(66) -224(101)

356(37) 997(73) -601(70)

278(45) 269(100) -865(84)

420(47) 14(89) -798(85)

373(11) 596(54) -621(57)

673 303 -684

348(70)

291

0ø-30øN 0ø-90øN

1330(115) 1054(113)

752(126)

-317(151)

387(116)

-961(154)

-424(95) 683(52) 385(52)

166(86) 1334(62) 584(65)

-96(7)

363(153) -644(137)

-75(5)

- 1 - 12 -45 -59

-42(59)

187

- 138(65) 717(43) 306(57)

172 625 700

885(54)

1497

10øS-0ø 20øS-10øS 30øS-20øS

-466(156) 48(95) - 18(98)

30øS-0ø

-436(167)

40øS-30øS 50øS-40øS 60øS-50øS

109(85) -97(64) -364(57)

85(31) -286(27) -359(38)

60øS-30øS

-352(110)

-560(68)

-552(95)

-156(73)

-405(51)

-220

70øS-60øS 80øS-70øS 90øS-80øS

- 177(35) 0(7) 0

- 179(38) - 16(7) 0(0)

-248(33) -32(5) 0(0)

-250(22) -32(3) 0(0)

-213(20) -20(4) 0(0)

- 175 -30 0

90øS-60øS

- 177(39)

- 195(44)

-280(36)

-282(21)

-233(22)

-205

90øS-0ø 90øS-90øN

-965(117) 89(119)

- 112(104) 275(89)

643(96)

2083(116) 76(76) -240(43) -388(56)

1251(102) 290(83)

174(83) 806(74) 273(101)

- 15(1) -29(4) - 30(3)

Year

1253(102) 192(77) -42(34) -306(43)

814(102) 170(91)

115(40) - 166(18) -353(31)

248(46) 206(54)

373 -233 -360

1071 1258

The valuesin parenthesesare measuresof the interannual variability of E - P, i.e., twice the standard error of the mean (seetext). The resultsof Baumgartnerand Reichel[1975] for annual-meanconditions are given in the last column. annual mean conditions. In this section we will consider sevresultshow reliable regional integrals will be. The problems eral possiblesourcesof error in our results. associatedwith spatial sampling cannot be consideredseparOne possiblesourceof systematicerror in the observations ately from the data analysis proceduresused. Thus in datais related to the differences in radiosondes used in various sparseregions the choice of the first-guessfield will have a partsof the globe.Teweles[1970] has discussed the tendency profound impact on the final analyzed fields. On the other for radiosondes manufacturedin the United Statesto report hand, where the station coverageis densethe final fields will spuriouslylow relativehumidities,particularlythoselaunched be nearly the same, irrespectiveof what analysis schemeis

duringdaytime.The problemarosefrom changesin the design used. of the radiosonde package and the composition of the In order to obtain an independent estimate of the spatial hygristorelementmade in the early 1960'sand was not recti- sampling errors in our results we have also computed the fied until after 1970. The data of some of our radiosonde divergenceof the vertically integratedhorizontal water vapor stationsare thus affectedfor nearly the entire period under flux for January and July 1979 using the FGGE level 3b data study.However,the errorsshouldnot be large over the conti- set producedat GFDL. Sincethe observationalnetwork used nental United States,since00 and 12 GMT launchingsare in compiling the FGGE data set was enhancedcompared to madewhenthe sunis low in the sky,and the designproblems that used in the 1963-1973 general circulation statistics,the are minimized.

differencesbetween the two data setswill give some measure

A potentially more seriousproblem in our results arises from spatial and temporal samplingerrors. Basedon testsof the rawinsondenetwork using the output of a generalcirculation model, Oort [1978] found that the general circulation statisticscompiledfrom the operationalnetworkgavea rather poor representationof the mean meridional transports of water vapor south of 20øS.We might expectthe water vapor flux divergenceto be similarly unreliable for these latitudes and other data sparseregions.Oort [1978] consideredonly zonal mean quantities,and it is difficult to determinefrom his

of the spatialsamplingerrorsin the generalcirculationstatistics.However,thiscomparison cancertainlynot be considered as a definitive test, since differences will also arise from interannual variability and from differences in the analysis

schemes.The valuesof the zonally integrateddivergenceover each of the three oceansfor January and July 1979 are shown in Figures 8a and 8b. Sincethe water vapor storagemakes a relativelysmall contribution to E - P, thesemay be compared with the curvesin Figures 5a and 5c. The agreementin position and relative amplitude of most of the major featuresis

11,726

BRYANAND OORT: GLOBALWATER BALANCE

400

ALLOCEANSYEAR (10 3m3s-t) /ø" / \,

300

lOO

__

,

\\

o---o---oBaumgartner

- thisstudy

CI_

\\•\\& Reichel

//ø/ / '••

200

o

,,;/ •

-lOO -

/ •

/

-200

-300

-400

I

-500

I

I

•

,•

I

L

•

I

I

30

9os

60

ß

ALLLAND YEAR

......

90N

ß this study

Boum9ortner & Reichel

50

_

',, /

-50

1/--o.. /

'xy/

-... \

/

_

/

-150 90S

60

30

0

30

60

90N

Fig. 7. (a) Meridionalprofilesof the annualmeanevaporationminusprecipitationevaluatedover 5ø zonal bandsfor all oceanscombinedfrom this studyand from Baurngartner and Reichel[1975]. (b) As in Figure 7a, exceptfor all land areas combined.

very good. However, the absolute magnitude of the peak valuesof E- P in the FGGE resultsis much larger than in the results from the 1963-1973

circulation

statistics. As a fur-

ther comparison the regional integrals of the divergence averagedfor January and July 1979 are shown in the last column of Table 3. These entries should be close to the annual

mean E- P values for the year 1979. The resultsfrom the FGGE data set shownet precipitationfor all land areasand a much greatertotal continentalrunoff than obtainedfrom our 1963-1973statistics.In fact there is good correspondence with Baurngartnerand Reichel's[1975] estimates. The large systematicdifferencesin the regional E- P valuesobtainedfrom the two data setssuggestthat our results are subjectto significantsamplingerrors. Poor data coverage combinedwith the choiceof initial-guessfieldsfor the objective analysisschemecould lead to overly zonally symmetric fieldsof horizontal water vapor transport.This in turn would causethe absolutemagnitudeof E - P to decreaseover both land and ocean regions. Another problem related to spatial samplinginvolvesthe

resolutionof regional boundaries.The nature of our data set requiresus to approximatethe coastlinesby the edgesof 2.5ø latitude by 5.0ø longitudeboxes.Since there tends to be a large gradientin E - P near coastlines,the useof coarseresolution boundarieswill systematicallyreduce the contrast of the regionallyintegratedE- P betweenadjacentregions.In order to obtain a crude estimate of the sensitivityof our resultsto this effectwe have recomputedthe regionallyintegrated divergenceafter shifting the regional template one grid interval (5ø longitude)to the east or west usingthe July 1979 divergencefield. The resultsare shown in Table 4. They suggestthat poorly resolvedboundariesmay make a significant contribution to the error in the estimated regional E- P. It doesnot appearto be as large or as systematicas that due to spatialsamplingproblemshowever.Furthermore,this should only be consideredan error in the sensethat the accountingis done inaccurately,whereassamplingerrors are a more fundamental problem with the data itself. It may be possibleto reducethis type of error by usingthe line integralmethod(7), dependingon the lengthsof the boundary segmentsused in

BRYANANDOORT:GLOBALWATERBALANCE TABLE

3.

11,727

The Evaporation Minus Precipitation Integrated Over Various Continental and Oceanic

Regions for SeasonalandAnnual-MeanConditions in Unitsof 103 m3 s-1 FGGE

Region

109 me

Africa Antarctica Asia Australia Europe N. America S. America

DJF

MAM

30,000 178(38) 17(61) 13,600 16(21) - 13(14) 40,000 101(37) -53(33) 8,700 144(24) 136(21) 17,200 -24(22) 72(27) 27,500 -119(33) -83(28) 18,300 -357(35) -284(60)

Continents 155,200 N. Pacific S. Pacific N. Atlantic S. Atlantic Indian

1979, (January + July/2) Year

This Study

Area,

-62(115) -208(88)

81,800 701(83) 97,300 -811(86) 53,800 363(46) 46,700 204(39) 74,600 - 370(70)

181(82) -428(62) 165(76) 257(45) 99(64)

89(119)

JJA

BR,

SON

Year

-69(57) - 102(66) 6(30) - 108 -33(10) -45(8) - 19(9) -63 -249(69) 6(54) -49(31) -387 78(18) 102(19) 115(14) -76 158(24) 44(26) 62(15) -90 -156(9) -174(24) -133(12) -185 17(41) -137(55) -190(31) -350

-255(85)

-305(81)

-974(97) -354(60) 257(62) 98(45) -85(63) -138(81) 487(51) 385(48) 605(45) 179(44) 290(83)

-448 120 370 424 668

354,200

206(54)

1260

1161

N.H. S.H.

254,700 1219(137) 98(106) -1645(122) -981(127) -328(40) 254,700 -1192(135) -31(109) 1680(119) 846(129) 327(40)

-586 586

-601 601

Globe

509,400

0

0

67(14)

35(8)

170(91)

-1161

-530 27 563 593 618

Oceans

27(14)

275(89)

-207(51) -1260 -112(29) -220(25) 76(47) 333(28) 129(41)

-31 -40 -350 -49 - 18 -210 -466

- 135(17)

- 1(7)

The areas for each region are given in column 2. The values in parenthesesare measuresof the interannual variability of E- P, i.e., twice the standard error of the mean (see text). The results of Baumgartnerand Reichel(1975) for annual-meanconditionsare given in the secondto last column. In the last columnthe averageof the regionallyintegrateddivergencefor Januaryand July 1979is given.

the calculation. Rosenand Omolayo [1981] computed the' found a large diurnal variability in the water vapor transport ocean-to-land water vapor transports in the northern hemi- fieldsover North America during summer. From the comparisonof the resultsobtained from the two sphereusing boundary segments556 km in length. We have carried out the line integralsabout North America (assuming data sets it appears that the source of the largest possible no transportbetweenNorth and South Americaalong the errorsin our resultsis spatialsampling.In particular the curIsthmus of Panama) and Greenland using their Figures 1-4. rent operationalrawinsondenetwork is inadequateto give Their net fluxesof - 117, - 108, - 157, -80, and - 115 x 103 reliableestimatesof differentiatedquantities(suchas the water m3 s-• for the winter,spring,summer,and autumnseasons, vapor flux divergence)in data-sparseregions.Holopainenand and the annual mean, respectively,compare favorably with Oort [1981] reacheda similar conclusionin their attempt to estimate the curl of the surface wind stress over the ocean our valuesof the area integrateddivergencesof -114, -106, from the atmosphericvorticity balance.It must be kept in - 169, - !41, and - 132 x 103m3 s- • for the sameregion. As another source of error in our results we have considered

temporal sampling biases.For example, near a coast we may expecta large diurnal variation in the water vapor transport associatedwith land-seabreezes.This diurnal cycle would not be properly sampledin our statisticswith only one or two samplesper day. Furthermore, the phase of the diurnal cycle at 00 or 12 GMT will be different at different longitudes.It is unclear how the use of a mixture of stations,some reporting once, some reporting twice daily, will affect the results.The FGGE

data are available

at 4-hour

intervals.

We have com-

pared the regionally integrated divergencesobtained by averagingover all six of the available times for each day, averagingthe 00 and 12 GMT times only, or using only a singletime. The resultsfor July 1979 are shown in Table 5. Except for the African and Australian continents,the error incurred from using only the 00 and 12 GMT samplesis less than 10%. The errors incurred in using only the 00 GMT samplesare also small. It does not appear that a temporal samplingbias makesa significantcontributionto errorsin our results.However, a word of caution is necessary,sincethere are indicationsthat the extrapolation proceduresused in the FGGE data assimilation system somewhat suppressedthe diurnal cycle near the earth's surface.Furthermore, these results seem to contradict those of Rasmusson[1966], who

mind that the traditional

method based on surface observa-

tionssuffersnot only from similarsamplingproblemsbut also from seriousuncertaintiesin the various empirical relations that must be used. It is apparent from our analysisof the FGGE data that certain improvementsin the observational network and in the analysisprocedurecan improvethe world water balance resultsobtained using the aerologicalmethod. However, before carrying out extensivebudget studieswith the FGGE level 3b analyses,we feel they should be more thoroughlyexaminedfor biasesin the analysissystemand other problems. 6.

SUMMARY

We have estimatedthe regionaldistributionsof evaporation minusprecipitationover the globeon the basisof aerological data for the period May 1963 to April 1973. The resultswere presentedas meridional profiles of E- P for each ocean,all oceans combined, all continents combined, and for seasonal and annual mean conditions. Estimates of the total evapora-

tion minus precipitation for each continent and ocean were also given.This study extendsthe existingwork on the globalscalewater balance in two ways. To our knowledge,it is the first time that aerologicaldata have been usedto estimatethe world water balance,treating land and oceanareasseparately.

11,728

BRYANAND OORT: GLOBALWATERBALANCE 400

January 1979

300

/'•

/A

/

-

/x,

/%/

_

o

•--o.

_•/_•'

\

O---O----O ATLANTIC_

/,?.,.,.\ /i \

200 100

- - PACIFIC a_

\

.....

-

', L,"/x,

/\

",b"// ,h;

•

-

"% 'X,.

,,_

;,._-o-.-.---•......

-•

-

_

-100

-_

-200

60

90S

30

0

30

60

400 T July1979

90N

b•

3OO 2OO

-

./..o__o_q,

-

0

-100

-200 -300

-400

-500

90S

60

30

0

30

60

90N

Fig. 8. Meridionalprofilesof thedivergence of theverticallyintegrated watervaporflux(103m3 s-•) over5ø zonal bandsfor eachoceanfor (a) January1979and (b) July 1979,computedfrom the GFDL four-dimensional assimilationof the F6GE

data.

Furthermore,it appearsto be the first estimateof the seasonal cycle of the region-by-regionwater balance over the entire globe. The regionalresultsobtainedin this study,usingthe general circulation statistics for 1963-1973, are different from those

obtainedin previousstudiesof the world water balance,using surfaceobservations.We find that the excessof evaporation TABLE 4. Water Vapor Flux DivergenceIntegratedOver Various Continental and OceanicRegionsfor July 1979 Computed by Shiftingthe RegionalTemplate 5ø West,by usingthe Correct Position,and by Shiftingthe Template 5ø East Shifted 5 ø West Africa Antarctica Asia Australia

Europe North America South America Continents Pacific Atlantic Indian Oceans

238 - 40 - 1198 107

132 - 231 - 133 - 1125 -625 642 1108 1125

Unshifted 11 - 42 - 585 46

125 - 241 - 244 -927 - 784 626 1085 927

Shifted 5 ø East - 8 - 46 - 723 143

191 - 170 - 398 - 1010 - 549 565 994 1010

over precipitationover the oceansis much lessthan the estimate of Baumgartnerand Reichel [1975]. Also, we find large continental regionsin the subtropicswhere evaporationexceedsprecipitationin the annual mean. The net effectis that the strengthof the global hydrologiccycle in our results(as measuredby total runoff from the continents)is much reduced from that in previousstudies. In order to estimate to what degree spatial and temporal sampling errors affect our results we have repeatedsome of the calculations,usingF66E level 3b data for Januaryand July 1979. These data were compiled from observationswith better spatial coverage and were analyzed using a fourdimensional, continuous data assimilation system. The resuiting regional water balancesare much closer to those obtained in studies based on surface observations

than to our

resultsfor 1963-1973. It appearsthat spatial samplingproblems, combined with our choice of zonal mean first-guess fieldsin the objectiveanalysisof the 1963-1973 statistics,have led to a systematicunderestimateof the magnitude of the water vapor flux divergence. Coarse resolution regional boundariesmay also contribute to the disparity betweenour results and those of previous authors. Temporal sampling biasesdo not seemto causelarge errorsin the regionalwater balances.We should add that the comparisonbetweenthe results obtained from the FGGE

and the 1963-1973

data sets

can only be consideredas a preliminary error estimate.An extensiveobservingsystemsimulationstudy,similarto that of

BRYAN AND OORT: GLOBAL WATER BALANCE

11,729

TABLE 5. Monthly Mean, Water Vapor Flux DivergenceIntegratedOver Various Continentaland OceanicRegionsDuring July 1979for Six SynopticTimes,the Daily Average,and the Mean of 00 and 12 GMT

24-Hour

00Z

Africa Antarctica Asia Australia Europe North America South America Continent

28 -42 - 555 56 104 - 287 -387 - 1079

04Z

08Z

12Z

115 -37 -483 80 119 - 289 -356

151 -39 -486 54 135 - 244 -216

32 -47 -682 47 154 - 203 -68

Mean

of

16Z

20Z

Mean

00 and 12Z

- 128 -45 -684 20

- 123 -41 -620 20

144 - 200 - 151

97 - 222 -293

11 -42 - 585 46 125 - 241 -244

30 -45 -620 52 129 - 245 -225

-851

-646

-767

- 1044

- 1181

-927

-923

Pacific Atlantic Indian

-703 717 1066

-801 712 940

-886 565 967

-860 488 1139

-738 593 1188

-713 686 1209

-784 626 1085

-782 602 1103

Oceans

1079

851

646

767

1044

1181

927

923

Oort [1978] would be very useful in helping to better determine the effect of sampling deficienciesand analysis procedureson the generalcirculationstatisticsand the systematic differencesbetweenthe regional water budgetsobtained using traditional methodsand the aerologicalmethod.Issuesof particular importance for studiesof the global hydrologic cycle that were not addressedin the Oort [1978] study include the effect of the diurnal cycle, the importance of extra surface data, and the reliability of regional as well as zonal mean quantities. In spiteof the many difficultiesmentionedabove we believe that the aerologicalmethod is inherently superiorto the traditional method of obtaining surfacebalances,since it is based on soundphysicalprinciplesand doesnot require any ad hoc assumptions.However, we have shown that it does place a rather severedemand on data quality and spatial data coverage. There is an increasinginterest in obtaining basin-scale oceanicheat balances[Dobsonet al., 1982]. With the advent of satelliteand other observingsystemsto augmentthe rawinsondenetwork, and with future improvementsof the analysis systemsto processthe raw data, the prospectsfor monitoring the ocean balancesand the world water balance by using the aerologicalmethod are much better than by using the traditional method. This study providesa preliminary assessment of the accuracywhich can currentlybe achievedwith the aerological method and a referencewith which to comparefuture results obtained by new analysis proceduresand new data

Evaluationof Horizontal Divergence

The divergenceof the vertically integratedhorizontal water vapor flux is givenby

V. Q = •

For a generic variable X its vertical integral is approximated by

(A2)

whereQXandQ* arethezonalandmeridionalcomponents of

fo2'•;;V.Qa2cosckdckd (A3) Due to the paucityof data in the polar regions,we will find it desirableto treat the polar capsseparately.We may separate the integral(A3) into three regions:the north polar cap, definedas the area polewardof latitude(PN;the southpolar cap, definedas the area polewardof (Ps;and the regionbetween and (Ps.On applyingGauss'theorem,(A3) can be written as

fo2'•fq,•NV.Qa2cosckdc $

where

Qs = Qs= -

Evaluation of Vertical Integrals

(Q* cos•p)

Q, respectively.An important property of the divergencefor this work is that its integral over the globevanishes

sets.

APPENDIX

+

a cos(pk c•$t •-•

Q•'(•s)acos•psdJ. •0 2•t

(A5)

Q•'(qbs)a cos(Psd,[

(A6)

are the fluxesinto the north and south polar caps acrossthe latitudes (Pn and (Ps,respectively.In practice we place the polar cap boundariesat 80ø latitudein both hemispheres. The divergenceoutsidethe polar cap regionsis computedusinga finite differenceoperator and is similar to the box method which satisfiesthe integral constraint (A4) [Bryan, 1966]. Under the polar capsthe divergenceis assumedto be uniform.

t'Sx dP • •g 1(Xk6• '•=k=, +X•+ ,6•+ ,)(P• - Pk+ ,) (A1) wherethe 6• are tagsindicatingwhethera data point is above or belowgroundand whosevaluesare givenby

Acknowledgments.The authors would like to thank J. Sarmiento, K. Bryan, S. Manabe, D. Hahn, and the anonymousreviewersfor their criticalcommentson this manuscript;M. Rosenstein for help in data reduction;and P. Tunison, W. Ellis, C. Raphael,and J. Connor for preparingthe figures.J. Callan carefullyand cheerfullytyped several revisionsof the manuscript.F. Bryan is supportedby ARL/ NOAA grant NA83RAC00052.

6•, ={• P•, >annual-mean surface pressure P• < annual-meansurfacepressure

The pressurelevelsat which data are available are p• = 1000 mbar, P2 = 950 mbar..... P8 = 300 mbar.

11,730

BRYANAND OORT: GLOBALWATERBALANCE REFERENCES

Arkin, P. A., A diagnosticprecipitationindex from infrared satellite imagery, Trop. Ocean-Atmos.Newslett.,17, 5-7, 1983. Baumgartner,A., Water balance,in Land SurfaceProcessesin General CirculationModels,editedby P.S. Eagleson,World Meteorological Organization, Geneva, 1981. Baumgartner,A., and E. Reichel, The World Water Balance,p. 27, Elsevier, New York, 1975.

Bryan, K., A schemefor numericalintegrationof the equationsof motion on an irregulargrid freeof nonlinearinstability,Mon. Weather Rev., 94, 39-40, 1966.

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