The annual variation in the global heat balance of the Earth

VOL. 83, NO. C4 JOURNAL OF GEOPHYSICAL RESEARCH The Annual Variation in the Global APRIL 20, 1978 Heat Balance of the Earth J. S. E).).IS • AND T. H. VONDER HAAR ColoradoState University,Fort Collins, Colorado80523 S. LEVlTUS AND A. H. OORT Geophysical Fluid DynamicsLaboratory/NOAA, Princeton,New Jersey08540 An annualvariationwith a rangeof 31 W m-• is found in the global net radiationbalanceof the earth. The net radiation flux valuesmeasuredfrom satellitesand the changesin total heat contentcomputed from independentsetsof atmosphericand oceanicdata show annual variationswhich are consistentwith eachother in both phaseand magnitude.The net energygain and lossby the planet within a year is storedand releasedwithin the systemprimarily by the oceans. INTRODUCTION A planetary albedo; C,•, Co specificheat at constantvolume for atmosphereand The analysesof independentsetsof satelliteradiation flux, ocean; oceanic temperature, and atmospherictemperatureand hug acceleration due to gravity; midity data presentedin this paper give, for the first time, I incoming solar flux; estimatesof the annuallyvaryingheat balanceof the earth.As L, latent heat of evaporation; far asthe authorsknow,an annualvariationin the globalheat q specifichumidity of air; balancehas not been reportedin the literature.However,an R long-waveflux to space; annual variation in the global net radiationbalancewas sugt time; gestedby Simpson[1929]. VonderHaar and Suomi[1971]and T temperature; Raschke[ 1973]indicatedthe possibilityof an annualvariation z height; in the radiation balance from limited sets of early satellite p density. data. The annualvariationin the radiationbalancereportedin this paperhasbeendeterminedfrom a 29-monthcompositeof A height of 20 km was chosenas the 'top' of the atmosphere satellite data. -and a depth of 275 m as the lower limit of integrationfor the For global energybalance the net radiation flux acrossthe oceansbecauseof the almost negligiblecontributionsbeyond upperatmosphericboundarymustat all timesequalthe rate of these limits. changein total heat content of the combinedatmosphereBASIC DATA ocean-cryosphere-land system.Energy available due to geoData setsused in this study will be briefly described.Net thermalheatingis extremelysmallin comparisonwith the flux of solarradiation [Sellers,1965]and hasbeenneglectedin this radiative flux valueswere computedfrom a 29-month set of study.Thus the energybalancefor the atmosphere-earth sys- satellite data. Some of the important characteristicsof this data setare shownin Table 1. The compositedradiationvalues tem can be written as follows: include data from wide-anglefield of view sensorson board FrA = SA +So + SL + SL (1) Experimental, Essa 7, Itos 1, and NOAA 1 satellites and medium field of view scanningsensorson board Nimbus2 and in which 3 satellites.Ellis and VonderHaar [1976] have discussedthe spatial and temporal distributionof the data and uncertainties in the measurements. In a later part of this paperwe will show lobe that the total uncertaintyin the compositedglobal mean valis the netglobalflux of radiationat the top of the atmosphere, uesis probably lessthan 10 Wm-". Atmospheric temperature and humidity data between the surface and 20-km height were taken from 5 years (May p(CAT + gZ + L,q) dA dz (3) 1968-April 1973) of daily rawinsondemeasurementsat 850 meteorologicalstations over the globe. Figure 1 showsthe is the rate of storagein the atmosphere, distribution of these stations and illustrates the relative lack of =f [(1 - - (2) 6q fo20km fg observingstationsin the southernhemisphere.As a result,less confidence canbe placedin the southernhemisphere contribution to our results.The method of analysisof this data set is is the rate of storagein the oceans,S• is the rate of storagein the sameas the one usedby Oort and Rasmusson[1971]. The land (neglectedin thisstudy),S• is the rate of storagein snow uncertaintyin the rate of atmosphericstorageis lessthan I W and ice, and m-•' for the northernhemispherebut somewhatlargerfor the southernhemispherebecauseof data void regions. Oceanictemperatureanalyseswere basedon historicaldata •Now at Lawrence Livermore Laboratory, Livermore, California filesfrom the National Oceanographic Data Center,Washing94550. ton, D.C., containingapproximately400,000 hydrographic Copyright¸ 1978by the AmericanGeophysical Union. soundings,740,000mechanicalbathythermograph soundings, OCoT dA dz Paper number 7C0932. 0148-0227/78/047C-0932503.00 (4) 1958 Et.tas ET AL.: Gt.O}•A[.HEATTRANSFER 1959 TABLE 1. ChronologicalList of Earth-Orbiting SatellitesFrom Which PresentRadiation MeasurementsWere Taken Year Sample 1964 January February March April May June July August September October November December Annual 1965 1966 1967 1968 EX (1030) EX (1035) EX (1040) EX EX EX EX EX EX N2 (1130) N2 (1130) N2 (1130) (0830) (0855) (0915) (0940) (1005) (1030) 6 3 3 0 1969 1970 E7 (1430) E7 (1430) E7 (1430) N3 (1130) N3 (1130) N3 (1130) N3 (1130) N3 (1130) N3 (1130) E7 (1430) E7 (1430) E7 (1430) N3 (1130) 3 9 1971 I1 (1500) I1 (1500) II (1500) NOI (1500) 4 I Size 3 2 2 2 4 3 3 2 1 3 2 2 29 Theapproximate localtimeat which ea• satellite crossed theequator during daylight hours isgiven in parentheses. EX stands for experimental'N2, Nimbus 2; N3, Nimbus 3' E7, Essa 7; II, Itos 1' and NOI, NOAA 1. and 100,000 expendablebathythermographsoundings.The data were averagedby month for each 1ø latitude-longitude squareat 11 standardlevelsbetweenthe surfaceand 250 m. An objectiveanalysisschemeof the iterative difference-correction type [Cressman,1959] was applied at each standard level to produce a global analysis.A depth of 275 m was taken as the maximum significantdepth for the penetrationof the annual temperaturewave. Figure 2 showsthe distributionof seasurface temperature observationsfor the month of March. The attempt to describelarge-scalepermanent or semipermanent features of the oceanic temperature distribution. The use of observationsthat may have been taken during anomalous situationswill be reflectedin the analysis.Uncertainty in the rate of oceanic storage is about 10 W m-2, but owing to samplingdeficiencies, particularlyin the southernhemisphere, even this error estimate must be considered tentative. A com- plete descriptionof the oceanographicdata, their representativeness,and the analysismethodsused can be found in the biastowardMoreobservations in thenorthern hemispherework of Let•itusand Oort [1977]. coastalregionsis true of all other months as well. Becauseof The ratesof heat storagein the atmosphereand oceanwere this bias the oceanicestimatesfrom the southernhemisphere computedas follows.Monthly meansof the heatcontentwere must be considered less reliable than the estimates from the evaluated at all grid points for each month. Rate of heat northernhemisphere. Examinationof the distributionof ob- storagefor any particular month was then computedas the servationsas a functionof depth for all monthsindicatesthat differencein heat contentbetweenthe followingand previous down to 250 m the distributions are similar to the surface distribution, although the number of observationsdoes decrease.The use of historical data and the general lack of observations must be considered in evaluation of the oceanic rate of storageestimates:Essentially,a samplingproblem is involved. With the exceptionof areas around oceanweather ship stationswhere relatively long-term serialdata exist, most of our data are scatteredin time. Our ocean analysisis an months. The rate of storagein snowand icewascomputedfrom the changein areal coverageof snow and ice reportedby Kukla and Kukla [1974] for the period August 1968-July1969, an averagewater equivalentdepth of 50 cm for the snow and ice beingassumed. The resultingvaluesarequitesmall,aboutone half the atmosphericvalues,and correspondingly, their uncertainty contributeslittle to the uncertaintyin the total rate of 90øN 60 ø 30 ø 0o 30 ø 60 ø 90øS 1E Fig. 1. Distribution of radiosondestations. ELLIS ET AL.' GLOBAL HEAT TRANSFER 1960 90ON 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 •_90ON ß :; :.. :... 60 ø ............ 30 ø •i.•i;:: •::.i'i• if•:•;•;:•::.::::;,.•!..,.....•i;•:....,;•i•g..'f•tf•;:.;.•L .. :;11iii!:...i!;11•i .......":"':""::::. ..... ßiii) ":.::i .......... ß :;i."{':•:::•ii' ..•. ':".•i ..... :'• :::'•" ':::'•:':'•: •:'.•i' . 30ø :!i!•!.• ::•i:. ?.:i:..'!'?""' .. • .•... •.•:'•. .. ' •:."::• ,.:r'i i:. ß.: I•[.L....; ...:..: ... ß . .:.::....: :ß ... .. .... ::i ........ '..... : '. .::;!::... ':::i: ...... " ::::: 30 ø '::iiii%:: ..:.":.:..•:i:• .... ." ßßß :...... ':i::•i:!:55•=ii! '..... :.... : ... i::::::...' ?i.•:iiiiiiii;ii!11:11:' " '; ::' .. 60 ø :.. ::::::::::::::::::::::: :L.L.:a..: ...... 30 ø .... " . .. ß . .:. :.:1: ':" " ' :'!i::':•! :. : '" •:•..•::I•.•.' 90 øS 90øS 0ø 30øE 60ø 90ø 120ø 150øE 180 150øW 120ø 90 ø 60ø 30øW 0ø Fig. 2. Distributionof seasurfacetemperatureobservations for the monthof March. A smalldot indicatesa 1ø square containing lessthan 10 observations,and a large dot indicates 10 or more observations. storage. More detailed information on the methodsused in determininguncertaintyin the ratesof storagecan be found in the work of Oor! and VonderHaar [1976]. RADIATION BALANCE COMPONENTS The mean values of the radiation terms on the left-hand side of (1), which are basedon the 29-month set of satellitedata, are tabulated by month in Table 2. Shown are the global averagesof reflectedand long-waveflux to spaceat the top of the atmosphere.In addition,the computedglobalaverages of incoming solar flux and net radiation at the top of the atmosphereare given aswell asthe albedoof the earth-atmosphereocean system.The incoming solar flux is computedfrom the known characteristicsof earth-sungeometryand an assumed solar constantof 1360 W m -2 [Drummondet al., 1968]. The meanglobal valuesof planetaryalbedo,long-wave,and net radiation flux are also showngraphicallyin Figure 3. The values for the 29 individual near-zerovalues),six are Essa7 values.As a part of the Essa7 data reduction method, global radiative equilibrium (FrA = O) was assumedto exist on a time scale of several days. This assumptionwas a necessaryconstraint for determiningthe planetary albedo. It is apparentfrom the distributionof values in Figure 3 that global radiative equilibrium does not generally exist even at the longer monthly time scale. The scatterof the valuesabout the compositednet radiation profile should be a measureof the uncertainty.The plotted valuessuggesta valueof about 10 W m-2 for the uncertainty. •..v' x ß 31 O 29 • I A (1 - A)I January February 350.7 347.6 0.308 0.309 242.7 240.2 March 342.5 0.299 240.1 April May 336.8 332.0 0.304 0.314 234.4 227.8 June 329.1 0.311 226.7 July 328.8 0.296 231.5 August September 331.1 335.7 0.290 0.287 235.1 239.4 October November December Annual 341.6 347.1 350.5 339.5 0.298 0.313 0.318 0.304 239.8 238.5 239.0 236.3 R FrA 231.1 11.8 230.0 227.8 246.8 245.0 245.4 236.5 235 2 231 1 235 8 232 6 230 7 235 7 10.1 12.1 -12.4 -17.1 -18.6 -5.0 -0.3 8.4 4.1 5.8 8.5 0.6 All values(exceptA) are in units of watts per squaremeter. ., + x NIMBUS 6 WIDE ANGI.[ .1• I by a solid curve. Of the seven zero net radiation values (or Radiation Componentsof the Global Heat Balance .x •:..I • x months of our data set are in- dicatedby crosses,while the mean annual variation is shown TABLE 2. + APR BAY JUN J I I I I I x x x I AIJ6 SEP OCT • I I [ DEC I (b) x 240 • 23O ß 220 • x x x x x [ I 1 - x x_ 29,-MONTHSET 4- NIMBUS6 WIDEANGLE /l I I I [ I ol.t • ,\• x /, JAN FEB 14&q• I I I II x x +••/ x -I , , , , , , ,/ MAY JUN JUL AU• SEP OCT NOV OEC Fig. 3. Components of theglobalradiation balance of theearth. Shown are (a) the planetaryalbedo, (b) long-waveflux to space,and (c) net radiative flux. ELLIS ET AL.: GLOBAL HEAT TRANSFER TABLE 3. StorageComponents of the Global Heat Balance S0 SA Sl • So"• SA "• Sl -6.4 1.6 0.9 0.7 -0.1 0.3 -5.6 2.6 March 18.8 0.7 0.6 20.1 April May -5.2 -25.5 1.6 2.2 0.9 0.9 -2.7 -22.4 January February June -9.5 2.6 1.2 July August September -!.7 -6.0 5.5 0.6 -2.1 -3.1 0.6 -0.1 -0.4 -0.5 -8.2 2.0 5.7 9.4 13.4 0.0 -2.8 - 1.4 0.0 0.0 -0.9 - 2.0 - 1.1 0.0 2.0 6.0 12.3 0.0 October November December Annual -5,7 1961 sunin Januaryandfarthestfromthesunin July.Thiscreates an annual 11.2 W m-• amplitudevariation in the solar flux receivedby the planetearth.Thisvariationis a purelyexternal drivingmechanism,sinceit dependsonly on earth-sungeometry. When a value of 30.4% (Table 2) for annual me.an global albedois used,the annual11.2W m-• amplitudevariationof incomingsolarflux translates into an approximate 7.8 W m-• variation in absorbedsolar flux at the top of the atmosphere. This value is of interest, since it gives an estimate of the variation in absorbedsolar flux apparently due solely to a changein earth-sundistance. The globalalbedovariesconsiderably from the annualmean of 30.4%.This seasonalvariabilitymay be nearlydescribedby a linear combination of an annual and semiannual wave. The All values are in units of watts per square meter. *Estimated from Kukla and Kukla [1974]. minima, 29.9 in March and 28.7 in September,occurat a time when the sun is most directlyover the earth'sequatorialzone, whichapartfr6m a narrowbandof cloudiness associated with It is clear that there is an approximate15 W m-• amplitude theintertropical convergence zonehasa loweralbedothanthe wavein the seasonalnet radiation profile detectableabovethe extratropics. Maxima occurwhenthe snow-and ice-covered scatter of values. polar regionsare receivingthe greatestamountof incoming As an independentcheck,monthly averagedvaluesof the componentsof radiation balance from the wide-angleEarth Radiation Budget (ERB) experimenton board the Nimbus 6 satellite are also plotted in Figure 3 for the months of July solarflux, nearthe solstices. An annualwaveand other anom- 1975-June long-wave emission to spacebecause of thelargesurfacetemperaturecontrasts betweenlandandoceansandtheasymmet- 1976. These data are not included in the com- positedmean profile. They are preliminarydata which incorporate correctionsto the calibration transfer function and earth view factor as discussedby Smith et al. [1977]. The ERB albedo valuesare generallylarger than the compositedmean values,but the phaseand amplitude of the profilesare quite similar.The ERB long-way6valuesare an averageof daytime and nighttime data, and they compare favorably with the 'composited profile. During themonths ofAprilandMaysome differences are noted which could be a manifestation of inter- annual variability ot diurnal time-sampling bias [Ellis and VonderHaar, 1976]. HEAT STORAGE COMPONENTS The terrestrialcomponentsof the heat balancein the righthand side of (1), which are measuredin situ, are presentedin Table 3. Shownare the globalratesof storageof energyin the oceans,in the atmosphere,and in the snowand ice cover for each calendar aliesmaybe associated with the advanceandretreatof seaice and snowcover and with seasonalvariability in cloud cover. It is reasonablealsoto expectan annualcyclein the earth's ric land-sea distribution between the northern and southern hemispheres. Atmospheric data showan annualcyclein the globalaveragenear-surface temperature withan amplitudeof 2øC [VanLoon,1972] Maximumand minimumvaluesare foundin JulyandJanuary, respectively. Thistemperature variationmay be interpretedasan amplitudevariationof 7 W m-•' in the long-waveflux emissionto spaceif typicalatmosphericemissions areconsidered andall temporalvariations in theintervening atmosphere areignored[Ellis,1977].Thiseffect in the long-waveflux combineswith the effect in the absorbedflux to givea 15 W m-• amplitudevariationin the annual net radiation balanceprofile. The variation found in this suggested accountingof a causeand effectrelationshipis in closeagreementwith the variation observedin the com- posi'ted profilefromsatellitedata. month. GLOBAL HEAT BALANCE To computethe typicalrate of oceanstorageper unit ocean area, the value of So in Table 3 should be divided by 0.71, whichis the proportionof oceanto land. The storageof energy in the atmosphereand cryosphereis foundto be muchsmaller than and approximately90ø out of phase with the ocean storageand the radiation flux. The rate of storagein land is negligible,as was shownby Gabires[1950]. i i !i ! GLOBAL HEAT BALANCE A graph of the global componentsis shownin Figure4. It shows that the rate of ocean storage is in close agreement with the net radiation flux exceptfor the monthsof January and February. (This disagreement may be due in large part to possibleerrorsin southernhemisphere oceandata.) The annual variation in the earth's net radiation balance may largelybe accountedfor by consideringthe effectswhich the presentday earth-sungeometryand the asymmetricaldistribution of continents between the northern and southern • //',. •t ,' / / '•' - -10 -15 , , NET, .DIATION FLUX -20 -25 I I I I I A M J J A S hemispheres have on the net radiationbalance.The orbit of Fig. 4. Principal components of theglobalheatbalance of theearth the earth about the sun is such that the earth is closest to the (in wattsper squaremeter). ELLIS ET AL.: GLOBAL HEAT TRANSFER 1962 Examination of the storagecomponentsof the global heat balanceshowsthat the world oceansplay the dominantrole in balance. The resultsof this study should be testedwith more accurate and more extensive data as these data sets become the earth'sresponse to the annualvariationin incomingsolar available. Of particular interestare possibleinterannualvariaflux. This result is expectedbecauseof the exceptionally tions from the averageconditionsreported in this paper. high heatcapacityof water and the largeportionof the planeAcknowledgments. Researchperformedat Colorado StateUnivertary surfacecoveredby oceans.The rate of heat storagein the sity waspartially supportedby the National Aeronauticsand Space ocean is of nearly the same amplitude and in phasewith the Administration grant NGR06-002-102. net radiationflux. The globaloceancanmaintainequilibrium REFERENCES by an averagechange in its heat content betweentimes of maximum storageand maximum releaseof lessthan IøC over a 50-m-thick layer. Cressman,G. P., An operationalobjectiveanalysisscheme,Mort. The atmosphericcomponentof the global heat balanceis Drummond, A. J., J. R. Hickey, W. J. Scholes,and E.G. Love, New seento be out of phasewith the net radiationflux.This is a result of the global land-seadistribution. The maximum and minimum of the atmosphericcomponentoccurduring northern hemispheresummerand winter, respectively.The extremes of heating and cooling of the atmosphereover the northern hemispherecontinentsdominate the annual cycle. Weather Ret)., 87, 367-374, 1959. value for the solar constant, Nature, 218, 259-262, 1968. Ellis, J. S., Cloudiness,the planetary radiation budget,and climate, Ph.D. dissertation,Dep. of Atmos. Sci., Colo. State Univ., Fort Collins, 1977. Ellis, J. S., and T. H. Vonder Haar, Zonal averageearth radiation budgetmeasurements fromsatellites for climatestudies, Atmos.Sci. Pap. 240, 50 pp., Colo. StateUniv., Fort Collins, 1976. Althoughtherateof s•orage in iceandsnowis relatively Gabites,J. F., Seasonalvariationsin the atmosphericheatbalance,D. small,their presenceor absencemay influencethe globalheat balance because of their effect on the earth's albedo. There is no doubt that each of the data sets used in this Sc. thesis,272 pp., Mass. Inst. Technol., Cambridge,1950. Kukla, G. H., and H. J. Kukla, Increased surface albedo in the northernhemisphere,Science,183, 709-714, 1974. Levitus, S., and A. H. Oort, Global analysisof oceanographicdata, Bull. Amer. Meteorol. Soc., 58, 1977. study contains inaccuracies.One must also considerthat the observationalperiods during which the data in each set were taken are different. However, the fact that the satellite radiation budget and the atmosphere-ocean heat storagedata sets are independentof each other yet give resultswhich nearly satisfyboth sidesof ( 1) suggests that the annualcycleof global heat balancepresentedin this paper is real. Furthermore,the Oort, A. H., and E. M. Rasmusson, Atmosphericcirculationstatistics, NOAA Projl Pap. 5, 323 pp., U.S. GovernmentPrinting Office, Washington, D.C., 1971. Oort, A. H., and T. H. Vonder Haar, On the observedannualcyclein the oceanatmosphere heatbalanceoverthe northernhemisphere, J. Phys.Oceanogr.,6, 781-800, 1976. Raschke, E., Satellitesmeasurethe radiation budget of the earth (in independent data setsare not likely to begrosslyin error.The Sellers,W. D., PhysicalClimatology,272 pp., Universityof Chicago finer details in the annual variation must be considered tenta- tive until improved data are collectedand assimilatedinto a compositeprofile. SUMMARY German), Umschau,73, 464-466, 1973. Press,Chicago, Ill., 1965. Simpson,G. C., The distributionof terrestrialradiation,Mem. Roy. Meteorol. Soc., III(23), 53-78, 1929. Smith,W. L., J. Hickey,H. B. Howell,H. Jacobwitz,D. T. Hilleary, and A. J. Drummond, Nimbus-6 earth radiation budgetexperiment, Appl. Opt., 16, 306-318, 1977. Van Loon, H., Temperaturein the southernhemisphere,in Meteorologyof the SouthernHemisphere,American MeteorologySociety, The observationsdiscussedin this paper may be summarized as follows. There is a significantannual variation in the Boston, Mass., 1972. two major componentsof the global heat balance:net radiaVonder Haar, T. H., and V. E. Suomi, Measurementsof the earth's tion flux and rate of ocean storage.No causeand effect relaradiation budget from satellitesduring a five-yearperiod, I, Extionship is established•however, the effectsof the earth-sun tendedtime andspacemeans,J. Atmos.Sci.,28(3), 305-314, 1971. geometry, land-seadistribution, and pole to equator albedo differencein the global net radiation balanceare discussed. The combinedeffectsare in agreementwith the observedan(Received December 16, 1976; nual variation. The world oceansapparentlystoreand release revisedSeptember8, 1977; acceptedSeptember15, 1977.) heat in phase with the annual variation in the net radiation