Spectral Energetics of the General Circulation and Time Spectra of Transient Waves during the FGGE Year

Ernest C. Kung Department of Atmospheric Science, University of Missouri—Columbia, Columbia, Missouri

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Abstract

The spectral energetics of the general circulation are presented for the entire FGGE year based on the GFDL analyses of FGGE observations. The global energy balance and those of the Northern and Southern hemispheres show a reasonable agreement. However, examining the energy flow in the wavenumber domain reveals a marked contrast between the two hemispheres in both energy and energy transformations. The annual variations of energy variables are large, and there are also pronounced differences of seasonal characteristics between the hemispheres.

With the one-year time series of energy variables, time spectra of transient waves are examined at 500 and 100 mb in order to evaluate their contribution to the time-averaged kinetic energy and baroclinic conversion. Characteristic distributions of power spectra for kinetic energy and available potential energy are described for the Northern and Southern hemispheres. In cyclone-scale disturbance almost the entire baroclinc conversion is supported by transient waves. There are pronounced contrasts between the Northern and Southern hemispheres in the conversion cospectra at various zonal wavenumbers.

Abstract

The spectral energetics of the general circulation are presented for the entire FGGE year based on the GFDL analyses of FGGE observations. The global energy balance and those of the Northern and Southern hemispheres show a reasonable agreement. However, examining the energy flow in the wavenumber domain reveals a marked contrast between the two hemispheres in both energy and energy transformations. The annual variations of energy variables are large, and there are also pronounced differences of seasonal characteristics between the hemispheres.

With the one-year time series of energy variables, time spectra of transient waves are examined at 500 and 100 mb in order to evaluate their contribution to the time-averaged kinetic energy and baroclinic conversion. Characteristic distributions of power spectra for kinetic energy and available potential energy are described for the Northern and Southern hemispheres. In cyclone-scale disturbance almost the entire baroclinc conversion is supported by transient waves. There are pronounced contrasts between the Northern and Southern hemispheres in the conversion cospectra at various zonal wavenumbers.

VOLUME 1 JOURNAL OF CLIMATE JANUARY 1988Spectral Energetics of the General Circulation and Time Spectra of Transient Waves during the FGGE Year* ERNEST C. KUNGDepartment of Atmospheric Science, University of Missouri--Columbia, Columbia, Missouri(Manuscript received 18 March 1987, in final form 7 August 1987)ABSTRACT The spectral energetics of the general circulation are presented for the entire FGGE year based on the GFDLanalyses of FGGE observations. The global energy balance and those of the Northern and Southern hemispheresshow a reasonable agreement. However, examining the energy flow in the wavenumber domain reveals a markedcontrast between the two hemispheres in both energy and energy transformations. The annual variations ofenergy variables are large, and there are also pronounced differences of seasonal characteristics between the twohemispheres. With the one-year time series of energy variables, time spectra of transient waves are examined at 500 and100 mb in order to evaluate their contribution to the time-averaged kinetic energy and baroclinic conversion.Characteristic distributions of power spectra for kinetic energy and available potential energy are described forthe Northern and Southern hemispheres. In cyclone-scale disturbances almost the entire baroclinic conversionis supported by transient waves. There are pronounced contrasts between the Northern and Southern hemispheresin the conversion cospectra at various zonal wavenumbers. 1. IntroductionThe availability of global gridded data from the First~GARP (Global Atmospheric Research Program)Global Experiment (FGGE) presents an opportunityfor a comprehensive energefics diagnosis of the generalcirculation. The global circulation models and techniques employed in data assimilation may influencethe dataset produced. Yet energetics comparisons ofthe assimilated data and parallel simulations indicatethat the former clearly represent the observed fields ofthe general circulation rather than the model atmosphere (e.g., Kung and Baker, 1986a,b). Further, despitedifferences exhibited by various versions of FGGE datasets, we may expect a reasonable agreement amongthem in representing the observed circulation of theatmosphere (see Chen and Lee, 1985; Lorenc andSwinbank, 1984; Rosen and Salstein, 1980). A number of spectral energetics studies with the FGGE data are available. Kung and Tanaka (1983, 1984) described the gross spectral characteristics of the global energetics, including the energy flow in the wavenumber domain, for the special observing periods * Missouri Agricultural Experiment Station Contribution No.10287. Corresponding author address: Prof. Ernest C. Kung, Dept. of Atmospheric Science, University of Missouri--Columbia, 701 HittStreet, Columbia, Missouri 65211.c 1988 American Meteorological Society(SOP-1 and SOP-2). The winter and summer spectralenergetics of the Northern and Southern hemisphereswere examined by Chen and Lee (1985) with varioussets of level IIIb data. Lambert (1986) studied thenonlinear exchanges of eddy kinetic energy in theSouthern Hemisphere for January and July. In an attempt to examine the simulation capability of globalcirculation models, Kung and Baker (1986a,b) conducted comparative encrgetics studies for the observedand simulated global circulation of SOP-1 and SOP2, and for the Northern Hemisphere circulation duringwinter blocking episodes. Further, to describe energyproperties of Rossby and gravity modes and associatedtransformations, a three-dimensional normal modeenergetics scheme was developed and applied to observations and to simulations by Tanaka et al. (1986). Most of the FGGE energetics studies, however, havebeen performed with data from limited time periods.One exception is the study by Arpe et al. (1986) whichincluded the European Centre for Medium RangeWeather Forecasts (ECMWF) FGGE level IIIb analyses for the entire FGGE year. Nevertheless, this energetics analysis was presented in the zonal mean-eddypartitioning format without a breakdown into wavenumber components. It is then very desirable to examine the energetics characteristics of the global circulation through the entire FGGE year in light of theearlier FGGE studies. The FGGE year covers a oneyear period from I December 1978 to 30 November1979. Although the dataset for a one-year period doesnot allow the study of interannual variations, a gross6 JOURNAL OF CLIMATE VOLUME 1budget and time series analysis for the entire FGGEyear will provide baseline information for future diagnoses of the general circulation. In this study theannual mean global energy balance and the contrastbetween the Northern and Southern hemispheres arepresented in the wavenumber domain using the Geophysical Fluid Dynamics Laboratory (GFDL) FGGElevel IIIb analyses. Time variations of the energeticsvariables are then examined in terms of monthly variations and power spectral analysis of the time seriesduring the FGGE year.We use the GFDL version of the FGGE dataset because only the ECMWF and GFDL analyses are available through the entire FGGE year. Currently bothdatasets are in the process of being reanalyzed byECMWF and GFDL. The GFDL analyses were chosenover the ECMWF analyses because the multivariateoptimum interpolation scheme used in the ECMWFanalyses suppressed the divergent field 0fthe wind, and,in turn, the vertical motion field generated by the kinematic method (see Chen and Lee, 1985). Comparative spectral energetics analyses by Chen and Lee(1985) and Kung and Tanaka (1983) both indicate thatthe ECMWF analyses exhibit the lowest energy levelsand weakest energy transformations among the FGGEdatasets. Kung and Tanaka further show that the tageostrophic kinetic energy production of the ECMWF v manalyses is very weak in the upper troposphere. It is ~important, however, to point out that the GFDL anal- vyses also seem to possess some major problems. Comprehensive comparative statistics by Rosen et al. (1985) ureveal an excessively strong Hadley circulation in the vGFDL analyses (also see Kung and Tanaka, 1983). Thismakes direct computations of energy variables with Bthe zonal mean vertical motion field difficult. Rosen flet al. also point out that continuous data insertion used q~by GFDL tends to excite excessive gravity noise. Ac- qAcording to Miyakoda et al. (1982) the GFDL global qroptimum interpolation in the final stdge of the forecast/ nanalysis cycle may cause a dynamic imbalance in the N K(n)dataset. The intercomparisons of various datasets, P(n)however, are readily available in the literature, and the M(n)results presented with the GFDL analyses will be useful L(n)in understanding the energetics characteristics of thegeneral circulation. C(n) a(n)The energy equations in the one-dimensional zonal S(n)wavenumber domain, as used in this study, were originally proposed by Saltzman (1957, 1970), and they D(n)have proven their usefulness in the energetics descrip- C,(n) Kidtion of the general circulation. The scheme, however, Kemay not always allow a simple interpretation of ener- P~getics budgets (e.g., McIntyre, 1980; Plumb, 1983). For Pethe study of specific systems or mechanisms in the gen- M(KE, K,~) C(P~:, KE)eral circulation, it is often desirable to supplement the R(P~, P~)zonal spectral energetics with a local energy budget or D(K-)with an additional energetics scheme such as a three- c(p~)dimensional normal mode scheme (Tanaka et al., -v.v~01986). However, the spectral energetics in the zonalwavenumber domain offers the most convenient energetics description of the general circulation, to whichother specific schemes can be easily related.2. Energy equations and scheme of analysis Since the details of the analysis scheme are availablein our preceding reports (Kung and Baker, 1986a;Kung and Tanaka, 1983, 1984), only an abbreviateddescription of the energy equations and their evaluationare provided here. Table 1 lists symbols, definitions,and variables used in this paper. The equations of kinetic energy and available potential energy in the zonal wavenumber domain maybe written, after Saltzman (1957, 1970), as NOK(O) = ~ M(n) + C(O) - D(O) (1) Ot n=l OK(n) _ M(n) + L(n) + C(n) - D(n), n -~ 0 (2) OtTABLE 1. Symbols, definitions, and variables.timehorizontal wind vectormass of the atmospheregeopotentialhorizontal del operator along an isobaric surfacecomplex-valued coefficient of u-component of windcomplex-valued coefficient of v-component of windcomplex-valued coefficient of temperaturecomplex-valued coefficient of vertical velocityannual mean component of an arbitrary function qannual cycle of qtransient component of qzonal wavenumbermaximum zonal wavenumberkinetic energy at wavenumber navailable potential energy at wavenumber ntransfer of K(n) to K(0) where n -~ 0transfer of eddy kinetic energy from all other wavenumbers to K(n) where n ~: 0conversion of P(n) to K(n)transfer of P(0) to P(n) where n -~ 0transfer of eddy available potential energy from all other wavenumbers to P(n) where n ~= 0dissipation of K(n)generation of K(n)zonal mean kinetic energyzonal eddy kinetic energyzonal mean available potential energyzonal eddy available potential energyconversion from K~ toconversion from P. toconversion of P~a to P~dissipation of K~generation of PEproduction of kinetic energy by cross-isobaric motionJANUARY 1988 ERNEST C. KUNG 7 NOP(O) = _ E R(n) - C(O) + G(O) Ot n=lOP(n.__~) = R(n) + S(n) - C(n) + G(n), n ~ O. Ot The equations of eddy kinetic energy and availablepotential energy may be obtained by summing (2) and(4) from n = 1 to the maximum wavenumber N:OK~r _ M(K~r, KM) + C(P~r, K~r) - D(K-)OtoP~- R(PM, PE) - c(PE, K~) + G(P~). Equations (1)-(6) state the balance requirement overthe total mass of the atmosphere. When the equationsare applied over the Northern and Southern hemispheres, an equatorial wall is assumed at the boundaryof both hemispheres to avoid computing the crossequatorial flux of potential energy. Our computationwith the GFDL and other datasets indicates that thetotal cross-equatorial flux of kinetic energy is 0.020.03 W m-2 in winter and summer. However, the potential energy fluxes by eddies and zonal mean motionacross the equator are, respectively, on the order of 0.1W m-2 and 1-2 W m-2. The direction of flux is fromthe summer to winter hemisphere, which parallels themovement of the summer hemisphere Hadley cell intothe winter hemisphere. However, the magnitude of potential energy flux, particularly that of the zonal meancomponent, is erroneously large in view of the globalenergy balance (see Fig. 1). The spuriously large transport is apparently caused by large values of potentialenergy in the higher levels of the atmosphere, whichgrossly amplifies the errors involved in observation anddata assimilation. The placement of an equatorial wallis thus necessary, although it leaves out the questionof the real cross-equatorial transport. Comparison ofthe gross energy budgets of the Northern and Southernhemispheres with the global budget, as shown in Fig.1, seems to indicate that an equatorial wall is acceptablein computing the hemispheric budgets. As pointed out by Chen and Lee (1985), Kung and Baker (1986a), and Kung and Tanaka (1983), uncer tainty in the magnitude of the zonal mean vertical mo tion in various FGGE datasets seems to overly influ ence the computed values of the zonal mean conversion C(0). According to Chen and Lee, the computed value of C(0) during SOP-1 ranges from -0.66 W m-2 for the ECMWF analyses to 2.23 W m-2 for the GFDL analyses, with 0.01 W m-2 for the Goddard Laboratory for Atmospheres (GLA) analyses. Apparently, the GFDL analyses overestimate C(0) for the very strong Hadley cells (see Rosen et al., 1985). Thus, to minimize the effect of errors in the zonal mean vertical motion, the relationship G (0)(3) 3.3 i p(o)(4) / 47.7 R(PM,PE) &(5) 2'01 I(6) 5.5 / 1.1 G (PE) 1.3C (0)JC(PE,KE)IGlobal D (0) ~,1.6K (0) [7.4 tM (KE,KM) 0.315.9 2.8 D (KE) 3.2(3.4) P(O) 45.0 (50.4) 2.0 t (2.0) t5.5 (4.5) 1.3 (0.9) 1.4 (1.7)1.2 K(O) [(1.4) (9.0) t0.2 (0.3) 3.0 (2.5) Northern Hemisphere (Southern Hemisphere) FIG. 1. Global and hemispheric mean energy balances during theFGGE year. Energy is in units of 10~ J m-2 and transformation inW m-2. fm N C(O) = - V. Vckdm - Z C(n) (7)is used to remove the direct dependence of C(0) on thezonal mean field of vertical motion. It has been shownthat the computation of-V. %0 with a dataset withouta geostrophic constraint, such as the GFDL analyses,yields reasonable values of ageostrophic production ofkinetic energy (e.g., Holopainen and Eerola, 1979;Kung, 1977; Kung and Tanaka, 1983). This is not thecase in a dataset with a geostrophic constraint such asthe ECMWF analyses (see Kung and Tanaka, 1983).8 JOURNAL OF CLIMATE VOLUME I To avoid the problem of -V. V- computations asso ciated with the lower boundary, the surface value of -V. V- is obtained from the surface wind vector and the V4~ value at 1000 mb, setting the lower boundary of vertical integration at surface pressure. The eddy variables in (5) and (6) are obtained as spectral sums over wavenumbers n = 1-30, and the dissipation terms of kinetic energy and generation terms of available potential energy in (1)-(6) are ob tained as residual terms to balance the respective equa tions. For the wavenumber interactions L(n) and S(n), however, no specific attempt is made to adjust the computational results to achieve a balance among wavenumbers. The energy variables are presented for the mass of the atmosphere from the surface to 50 mb unless stated otherwise. The feasibility of examining large-scale turbulence in frequency-wavenumber space is presented by Kao (1968) in his comprehensive formulation of the prob lem. In this study, a power spectral analysis of the time series is applied to the transient components of energy variables in the Northern and Southern hemispheres. The complex-valued coefficient U(t) of the u-compo nent of wind for a zonal wavenumber n is partitioned into U(t) = U~u + UA(t) + Ur(t) (8)where UMis the annual mean, UA the annual cycle, andUr the transient component. After subtracting UM fromU(t), the first harmonic of the one-year time series istaken as the annual variation U~ (0, and the residualin (8) is considered to be the transient component Ur(t)without the annual variation. The power spectra ofUr(t) are then computed at 500 and 100 mb for eachwavenumber as aperiodic functions of frequency. The- complex-valued coefficient V(t) of the v-component ofwind is processed in the same way, and the sum of thepower spectra of Ur(t) and Vr(t) at wavenumber ngives the spectra of kinetic energy K(n) of the transientwaves. The spectra of available potential energy P(n)of transient waves are given by the power spectra ofthe transient component of the complex-valued coefficient Br(t) of temperature with global mean staticstability parameters obtained from the annual meantemperature at 500 and 100 mb. In the case ofn = 0,the zonal average of the deviation of temperature fromthe hemispherical mean is used in lieu of Br(t). In asimilar manner, the baroclinic conversion C(n) oftransient waves is examined using cospectra of transientcomponents of complex-valued coefficients Br(t) oftemperature and fir(t) of vertical velocity. All thecomplex-valued coefficients used in the time series areaveraged for each hemisphere. The original level IIIb GFDL analyses on a 1.87- X 1.87- latitude-longitude grid from I December 1978 to 30 November 1979 were interpolated to a 4- x 5- grid from 90-S to 90-N and from 0- to 355-E as de scribed by Kung and Tanaka (1983). The data includetwice-daily values at 0000 and 1200 UTC for geopotential height, temperature, horizontal wind, and vertical velocity at 1000, 850, 700, 500, 400, 300, 250,200, 150, 100 and 50 mb. All energy variables arecomputed at each of the twice-daily analysis times.However, the computed values are averaged for eachday to eliminate diurnal variations from the time series.3. Global spectral energy balance and hemispheric contrasts The gross energy balance of the general circulationduring the FGGE year is summarized in Fig. 1 in Lorenz' (1955) box diagrams for the global mean and forthe Northern and Southern hemispheres. The globalmean energy balance for the entire FGGE year is veryclose to the average of SOP-1 and SOP-2 obtained byKung and Tanaka (1983) with the same dataset. Thereis an overall agreement on the direction of the energyflow with the previous observational estimates of theenergy cycle (e.g., Oort and Peixoto, 1983; Newell etal., 1970; Saltzman, 1970; Wiin-Nielsen, 1968). However, there are considerable numerical variations between the present FGGE estimate and previous estimates. Most of the discrepancies may be attributableto the fact that the data coverage of the earlier estimateswas mainly restricted to the middle latitudes of iheNorthern Hemisphere. According to the global energybalance in Fig. 1, the intensity of the general circulationas measured by G(0) + G(P~r), C(0) + C(PE, KE), orD(O) + D(K~r) is 4.4 W m-e, or 1.3% of one-fourth ofthe solar constant. As discussed in section 2, the estimate of the zonalmean conversion C(0) is uncertain in various analyses.Thus caution must be exercised in adopting a computed value in order to balance the global or hemispheric budget. Rosen et at. (1985) computed this termindependently for the Northern Hemisphere duringJanuary and June 1979 with the GFDL and traditionalstation-based analyses, using the monthly mean fieldsof the zonal mean u- and v-components of wind. Theirwinter and summer values of 1.72 and 0.06 W m-2yield an average of 0.89 W m-2 with the GFDLdata,and an average of 0.54 W m-2 with the station-baseddata of 0.76 and 0.31 W m-2. Considering that estimates by Rosen et al. are based on the monthly meanfields of the circulation, their estimates of C(0) comparefavorably with our estimate of C(0) -- 1.2 W m-2 forthe Northern Hemisphere (Fig. 1). Likewise, the estimates of R(P~a, P~r) and M(K~r, K~u) by Rosen et al.also 'agree favorably with ours. Chen and Lee's (1985) energy budgets for the FGGEwinter in the Northern Hemisphere show negative values for C(0) with the ECMWF analyses. This corresponds with Kung and Tanaka's (1983) estimate withthe same dataset, reflecting the problems with theHadley cells in the early version of the ECMWF analJANUARY 1988 ERNEST C. KUNG 9yses. Chen and Lee's estimate of M(KE, K~r) with theGFDL analyses shows small negative values. The discrepancy of their estimate with ours and that of Rosenet al. (1985) cannot be resolved at present. The grossenergy balance obtained by Arpe et al. (1986) from theECMWF FGGE and operational analyses andECMWF forecasts is basically similar to Kung andTanaka's (1983) computed with the ECMWF analyses.The value of C(0) is negative. The change of sign isalso noted for G(PE) between the initialized analysesand 12 h forecasts, and between the hemispheres. The energy flow in the box diagrams of Fig. I showsa similar basic pattern for both the Northern andSouthern hemispheres as the global mean. The largestenergy flow proceeds from P(0) via Pe to Ke, and someKE is further transformed to K(0). Dissipation takesplace in both KE and K(0). There is a direct generationof P~, and the direct conversion between P(0) and K(0)is also appreciable. It is apparent, however, that bothfor kinetic energy and available potential energy thezonal mean components in the Southern Hemisphereare much larger than those in the Northern Hemisphere, and the eddy components in the former aresmaller than those in the latter. The totals of zonalmean and eddy components are significantly larger inthe Southern Hemisphere than in the Northern Hemisphere both for kinetic and available potential energy.These contrasts 'obviously reflect the stronger differential heating and more uniform topography of theSouthern Hemisphere, which has a predominant watersurface. However, the differences between hemispheresin energy transformations are not clear in the box diagrams, since the large differences in the wavenumberdomain, as will be discussed later, disappear whensummed up over all wavenumbers. - Figure 2 illustrates the annual mean energy flow for each wavenumber for n = 0-15. In the annual mean budget the contribution from n = 15-30 is negligible and is therefore omitted. Although the ultralong and large cyclone-scale waves contribute to the eddy gen eration G(n), conversion C(n), and dissipation D(n) more significantly than the short synoptic waves, the contribution of the latter is by no means negligible. For the nonlinear wave-wave interactions S(n) and L(n) and wave-mean interaction M(n), the contribu tion of short waves beyond n = 7 is small. It should be emphasized, however, that an energy flow pattern for a single observation time or that associated with a spe cific synoptic development may deviate markedly from the annual mean pattern. For example, Kung and Baker (1986b) illustrated that the wave-wave interac tion of kinetic energy L(6-10) during a period of blocking development in the Northern Hemisphere becomes several times larger than the annual mean value to support the amplification of the ultralong waves. Examination of the daily time series against the annual mean pattern reveals that S(n), L(n) and M(n) from ultralong to short cyclone-scale waves are all acGCn) R(n) P(n) S~n) C(n) LCn) K(n) M(n) D(n)330 477 ? 7r~~51.55~12 ~, 10~ 2~7 8 19 ~ n:2 ~ n:~~'8 7 86 5-'~ 27 ? 23 _113~ 4 27 7 28 18_6~ 3 65 2 2? 4 15~ ? 14~6~ I 3 6_ ~ -' 2 I 10 9 4 I ,_ 2 5~ 1 1 4 I ~ 1 6~ 3 0 ~ 1 3 0 ,,, P 1 3 ~ 1 MG. 2. Global energy flow diagram in the wavenumber domainduring the FGGE year. Energy is in units of 10n J m-2 and transformation in 10-2 W m-2.tive for individual observation times, although the dailysignificance of medium and short cyclone-scale wavesis cancelled out in a long time mean. For G(n), R(n),C(n) or D(n), the dally spectral distribution patternsover all wave ranges are well preserved in the annualmean pattern. This may indicate that the wave-waveand wave-mean nonlinear interactions of kinetic energy, L(n) and M(n), and wave-wave nonlinear interaction of available potential energy S(n) are moreclosely associated with the manifestations of synopticdisturbances, whereas other transformation processesare more closely associated with the maintenance ofthe basic patterns of the general circulation. The annual mean spectral distributions of P(n) andK(n) are compared between the Northern and Southernhemispheres in Fig. 3. The large P(0) and K(0) in theSouthern Hemisphere (Fig. 1) apparently come at theexpense of P(n) and K(n) of ultralong waves n = 1-3.The large land-sea contrast of the middle latitudes ofthe Northern Hemisphere leads to the dominance ofultralong waves in that portion of the atmosphere. Thel0 JOURNAL OF CLIMATE VOLUMEo- - -0 8. Hemlm~m15, 0FIG, 3. Spectral distributions of P(n) and K(n) in the Northern andSouthern hemispheres during the FGGE year.eddy kinetic energy transformations of n = 1-10 forthe Southern Hemisphere. Although his presentationcovers only January and July of 1979, a qualitativeagreement of his spectral distribution with ours andChen and Lee's may be recognized:4. Annual variations Kung and Tanaka (1983, 1984) and Chert and Lee(1985) noted pronounced differences in energy levelsand transformations in the Northern Hemisphere between SOP-I and SOP-2. The differences, however,were much less in the Southern Hemisphere. This leadsto a large seasonal contrast of the globally integratedenergy budget which comes mostly from the Northern.Hemisphere. With the analysis data of the entire FGGE year, theannual hemispheric variations of K(0) and P(0) areshown in Figs. 6 and 7, and those of K(n) and P(n) inFig. 8 for n = 1-4 over which the seasonal differencesarc most evident. Both the Northern and Southernhemispheres possess the highest level of energy in theirrespective winters and the lowest in the summer. The 0.:30 0.25 0~0? E 0.15- O.lO o.o5 0.oocontrast of the Northern and Southern hemispheres isparticularly strong at n: 2.As indicated in Figs. 4 and 5, the dominance of ultralong waves in the Northern Hemisphere over thosein the Southern Hemisphere is supported bY a largetransfer of zonal available potential energy into n = 23, and subsequently large conversion of available po- o.~otential energy to kinetic energy C(2-3). In the Southern o.z~Hemisphere, the generation of available potential energy G(I) and corresponding conversion C(1) are large, o.~obut P(1) and K(1) are respectively depleted by wave- '~ o.,~wave interactions S(1) and L(I) to shorter wavenum- -hers. In the Southern Hemisphere, the mean-wave o.~transfer of available potential energy R(n) is most active 0.o~at n = 4-6, with corresponding large baroclinic conversion C(4-6). However, both P(n) and K(n) are de- -~oopleted by the wave-wave interactions S(n) and L(n)and also by wave-mean interaction M(n) at this range.Consistently more active baroclinic conversion C(n) is ~[noted in the Northern Hemisphere in all waves beyond o~ tn = 6. ?~ o. o[Chcn and Lee (1985) presented spectral distributions -of energy and transformations for the FG~E winter -o..and summer separately for the Northern and Southernhemispheres. Their computed spectra with various -~FGGE datasets are qualitatively in agreement with ourannual mean spectra. Lambert (198.6) computed the, , R(n) S(n) nFIG. 4. As in Fig. 3 except for G(n), R(n) and S(n).JANUARY 1988 ERNEST C. KUNG 11O.4OO.350.300.250.200.150.10O.05; ~ .o.. o- --o $. ~,,,, ~,p.', 'o,,, -(eo0.10o.o5O.05 FIG. 5. As in Fig. 3 except for C(n), L(n) and M(n).spring transition into summer seems more rapid thanthe fall buildup into winter. The hemispheric differences in K(0) and P(0) are largest in the Northern summer (Southern winter) because of the very high Southern Hemisphere energy level and very low NorthernHemisphere energy. However, for K(n) and P(n) of n= 1-3, the hemispheric differences are more pronounced in the Northern winter (Southern summer)because of the amplified ultralong waves of the Northern Hemisphere in the winter. This is an obvious resultof the Northern Hemisphere winter heating field inassociation with the topography and land-sea distribution. If the energy components are integrated overthe globe and all wavenumbers, we may expect a globalseasonal variation as presented by Arpe et al. (1986). Annual variations of the baroclinic conversion C(n)in the Northern and Southern hemispheres are contrasted in Fig. 9 for n = 1-7. It is interesting to notethat in the Northern Hemisphere C(I) has a primarymaximum in August and a secondary maximum,which is much smaller, in January, although all otherNorthern Hemisphere conversions C(n) have the maxima in the winter and the minima in the summer. Thelarge Northern Hemisphere conversion by n = 1 in thesummer is associated with the summer monsoon system in the subtropical latitudes, as indicated by Kungand Tanaka's (1984) SOP-2 latitudinal distributionof C(I). During the northern winter, the strong conversionby n = 2 dominates along with those by n = 3-4 insupport of the amplified ultralong waves. Because ofthe dominance of C(2) in the northern winter, C(2)also shows the largest hemispheric difference amongall waves in all seasons. From April to October, thehemispheric difference in C(2) is very limited. For n= 3-6, however, the stronger C(n) in the SouthernHemisphere becomes noticeable during the Northernsummer (Southern winter) with the maximum hemispheric difference at n = 5. From n = 7 and beyond,the hemispheric difference becomes less distinctive andalmost indistinguishable in the short-wave range. This study is based on one-year data during theFGGE and thus the problem of interannual variationsis beyond the scope of the present investigation. Arpeet al. (1986) used various ECMWF data from 1979 to1985 to compute energetics in zonal mean and eddypartitioning. The standard deviations of interannualvariations in energy levels are only 1-2% of the multiannual averages. Transformations, with the exceptionof C(0) and G(P~r), also show interannual variations ofless than 10%, and mainly within 5%. If this is an indication of the interannual variation of energetics inthe general circulation, the energetics characteristicspresented in this study should not be subject to largeinterannual variations.5. Time spectra of transient waves After subtracting the annual mean and annual variation from the one-year time series, as illustrated withU(t) in (8), the residual time series may be treated asdescribing transient waves. The residual daily time series of the one-year period allows us to compute stablepower spectra for periods of 2-128 days. Figures 10and 11 show the time spectra of K(n) and P(n) of transient waves for n = 0, 1, 2 and 5 at 500 and 100 mbfrom 4-128 day periods. Because the annual variation,the largest component of the time variation (see Figs.6 and 7), has been filtered out from the original timeseries, the power spectra obtained are appropriate toexamine the transient character of the zonal waves.The variance associated with periods between 128 daysand I year is confirmed in computations to be negligible. The time spectra of K(0), K(I), and K(2) indicate agradual increase of energy from the shortest period to30-60 days and then a sudden drop of energy densitybeyond that. Both the Northern and Southern hemispheres show a similar trend, but for K(0) the energypeak is reached earlier in the Northern Hemisphere.At 100 mb the sharp increase of energy density for12 JOURNAL OF CLIMATE -OLUMEIE13.512.0 -10.5 7.56.04.5 3.0 1.5'--Dec'Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov78 79 12.0 10.5 A A A N. Hemisphere ~ t, Itdk a II ^ S'Hemisphm'e~ - ?.5 8.0 4.5 3.0 ~ Dec Jan Feb Mar ,A~or May Jun Jul Aug Sep Oct Nov 78 79FIG. 6. ~it7 time variations of K(0) and K~ in the No~he~ and Southe~ hemispheres during the F~E year.E8072645648403224Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov78 7912.010.59.07.55.o4.5Dec Jan Feb78Mar Apr May Jun Jul Aug Sep OcJ NovFIG. 7. As in Fig. 6 except for P(0) and PE.JANUARY 1988 ERNEST C. KUNG 13K(1)E0.?0.6O.S0.40.30.20.11'01 .... ~.~.~~...~4 P(3) I I I I I I I I I I I I1'01, , ,,o.,oo', , '~...~., .. ' '~'~'"~' ' '~-, ~ , , ~ ..<...~, ,K(3) 0.6 t 0.51.O .~..~,~...,6._..d~o- o - '-'~.~,~._ ~ _ ~_ o. o .d~-,.~,~--~ K(4) ....... T ; , , , ~ 0.4 ~ ,,~t .O ~ ~ ~ ~.~ ~1.0 0.12'0~i .1.0 m~r~~ .~ ...M '' "' P(2) 0.0 0.6 '' m '' I I m I I'~'~1 ..T._~..~ o.~ ~.~ ~.$ ~.~ P~4) o.~1 'OIi i "'~'~r~'~"-'''l i i i I i ~ ~4-..l ~ i oec ,lan r~a Mat a0e Ma~ Jun ~ut ~ S~ Oct I~n 1978 1979FIG. 8. Monthly time variations of K(n) and P(n) for n = I-4 inthe Northern and Southern hemispheres during the FGGE year.K(0) is observed on the longer side of the period, afeature consistent with the steady zonal flow in thelower stratosphere. For waves shorter than ultralongwaves, as exemplified by the large cyclone-scale waveK(5), the peaks of energy shift to shorter periods. Unlikeultralong waves, the cyclone-scale waves show a noticeable difference in the spectra between the Northernand Southern hemispheres. The K(5) in the NorthernHemisphere has a maximum around 20 days, and inthe Southern Hemisphere around 12 and 5 days. Thetime spectra of P(n) in Fig. 11 closely resemble thoseof K(n) in Fig. 10, indicating a close alignment of thethermal field and the wind field in transient motionsof the atmosphere. The baroclinic conversion C(n) transforms availablepotential energy P(n) into kinetic energy K(n) and isthe critical linkage in the energy flow that maintainsthe general circulation against frictional dissipation.For the zonal mean conversion C(0), the percentileratio CM:CA :Cr is 77:21:2 in the Northern Hemisphereand 82:15:3 in the Southern Hemisphere. We see thatfor the zonal mean motion, the baroclinic conversionis mostly from the standing cells, with the remainingcontribution largely from the annual migration of thecells. For eddy disturbances, as shown in Fig. 12, the19790.$0.302FIG. 9. As ,in Fig. 8 except for C(n) for n = 1-7.C1)C13)C(4)C(6)C-7)14 JOURNAL OF CLIMATE . VOLUME I500 mb 100 mb106 [ ...... S. Hemisphere 106! I I I I' I I I I I - 64 32 16 10 8 6 4 Period (Day)106 10~ i"'"..~ - "'"' '.... ".' ...~ ~ K(1)105 , 105 .-.lO4 I I I I I ! I 64 32 16 10 8 6 4 Period (Day),=1o5 I 64 32 16 10 8 6 4 Period (Day) 104/1"' ~ , I I i I I 64 32 16 10 8 6 4 Period (Day)104 I I I I I I I64 32 16 10 8 6 4 Period (Day)106 I I I I I I 64 32 16 10 8 6 4 Period (Day)106 t K(5) I I I I I I I 6432 16 10 8 6 4 Period (Day)F~. 10. Time spectra of the transient component of K(n) for n = 0-5 at 500 and 100 mb in the Northern and Southern hemispheres.JANUARY 1988 ERNEST C. KUNG 15 500 mb 100 mb106 L N. Hemisphere 106 I ..~.^ ...... S..Hemisphere I I I I I i I i .... ". ..... . - 6432 16 10 8 6 4 64 32 16 10 8 6 Period (Day) Period (Day)10610s104106, 105.lo4106~.= 105E- 106 ~.= 105 I I I I I I I 64 32 16 10 8 6 4 Period (Day). 106- ""."- '"..../~ ~ ~ E I I I I I I I64 32 16 10 ' 8 6 4 Period (Day)106 I I I I I I I64 32 16 10 8 6 4 Period (Day)104104 '". .. P(1)64 32 16 10 8 6 4 Period (Day)6432 16 10 8 6 4 Period (Day)P(5)64 32 16 10 8 6 4 Period (D~y)FIO. 11. As in Fig. 10 except for P(n).transient component Of conversion Cr is more significant than Cst and Ca, components associated withannual mean fields and annual variations of temperature and vertical velocity at respective wavenumbers.The ultralong waves ofn = 1, 2, and 3 in the NorthernHemisphere and n = 1 in the Southern Hemisphere16 JOURNAL OF CLIMATE VOLUME 1CM FIG. 12; Spectral distributions of the baroclinic conversion associated with the annual mean motion C3t, annual variation CA, andtransient waves Cr in the Northern and Southern hemispheres duringthe FGGE year.still receive a notable contribution from CM and CA.However, beyond these ultralong waves, essentially allthe baroclinic conversion in the cyclone-scale disturbances is associated with transient waves. The spectraldistributions of Cr show a clear maximum at n = 6 inthe Northern Hemisphere and at n = 5 in the SouthernHemisphere. It is noted that on large cyclone scales thetransient waves are more energetically active in theSouthern Hemisphere than in the Northern Hemisphere, but they become slightly less active in theshorter wave range. The difference in the hemisphericspectral distribution of baroclinic conversion C(n) asshown in Fig. 5 should reflect the hemispheric differences in the activity of standing and. transient waves. Since transient waves dominate the.energy conversion which takes place in the large-scale atmosphericdisturbances, the baroclinic conversion by transientwaves is examined with the cospectra of Br(t) and ~2r(t)for n = 0-7 at 500 and 100 mb, respectively, in Figs.13 and 14. Hemispheric differences of the cospectraare very distinctive in the midtroposphere, as shownin Fig. 13. In each hemisphere, there are also consistentbut very large variations of cospectral distributionamong wavenumbers. For the zonal mean wave n = 0and ultralong waves n = 1 and 2, in which CT is eithernegligibly small or only of limited importance, theconversion peaks are observed at longer periods of ap proximately 40-80 days. From n = 3 on, the cospectral peaks shift to the short periods. In the Northern Hemi sphere at n = 6 where Cr is at the maximum, two conversion peaks are at periods of 10-20 days and 5 7 days. In the Southern Hemisphere at n = 5 where Cr is at the maximum, we observe two distinctive con version peaks around 5-day and 12-day periods. It may be noted that the transient waves, which are mainly responsible for the eddy conversion of the general cir culation, show characteristic but complex patterns of cospectral distributions over the frequency domain for different waves. There is a general trend that the shorter the wavelength, the shorter the corresponding period of the maximum conversion. However, due to the co existence of various waves at each wavenumber at dif ferent latitudes, any general statement concerning the cospectral distribution would be impossible. 'Comparing Fig. 13 with Fig. 10 as representative of the tropospheric situation, it is seen that the cospectra of baroclinic conversions are not as smoothly distrib uted over the period as those of the energy level. The discrepancy between the cospectra and power spectra may be related to the activities of nonlinear wave-wave and wave-mean interactions of kinetic energy. For ex ample, Kung and Baker (1986a, b) identified the im portance of nonlinear transfers for winter Northern Hemisphere blocking in the maintenance of kinetic energy at n = I and 2. This may be identified in part in Fig. 13 as the sharp drop of cospectra at these wave numbers at approximately 10-20 days. Figure 14 shows that transient waves of cyclone scaleare not energetically active at the 100 mb level. In theNorthern Hemisphere, significant negative conversion(destruction of kinetic energy) is indicated in the slowmoving ultralong waves and large cyclone-scale waves.These are consistent with the prevailing view that nosource of energy for eddy motions appears to be presentin situ in the lower stratosphere (e.g., Newell et al.,1970; Oort, 1964). It is noted here, however, that thezonal mean motion and n = 1 of the Northern Hemisphere and n = 1 ahd 2 of the Southern Hemisphere. show a significant positive conversion at the low-frequency side. In fact, there is a similarity between the100 and 500 mb patterns of the cospectral distributionof n = 1 and 2 in the Southern Hemisphere. It may beseen that the slow-moving tropospheric ultralong wavesof the Southern Hemisphere extend into the lowerstratosphere.6. Concluding remarks A basic energetics description in the zonal wavenumber domain is offered with the GFDL FGGE analysis data for the entire FGGE year. The global energybalance and those of the Northern and Southern hemispheres show a reasonable agreement in the patternand magnitude of energy transformations, although thezonal mean field of the circulation is much stronger inJANUARY 1988 ERNEST C. KUNG 17~ 1?E-13500 mb 3~ N. Hemisphere...... S. Hemisphere 2 n=O I I I I I I I -1[4 32 16 10 8 6 4 Period (Day)3 n=l ~ 2 O64 32 16 10 8 6 ,4Period (Day) I I I I I I .I64 32 16' 10 8 6 4 Period (Day): : n=5 -Period (Day)~G. 13. Cospectral distributions of transient components of C(n) for n = 0-7 in the Northern and Southern hemispheres at 500 mb.Period (Day) n=3 " 1 E O~>4 32 16 10 8 6 4~ 1'7,E n=7 I I ! I I I I64 32' 16 10 8 6 4 Period (Day)64 32 16 10 8 6 4 64 32 16 10 8 6 4 Period (Day) Period (Day)3 3 0 0 i18 JOURNAL OF CLIMATE VOLUME I 100 mb ~ N. Hemisphere 2 ...... S. Hemisphere 2i !..~.~,~; :O ~i "."' \/__ n=4 ' ~ ~. ,/'"X ~o.' 'oo' '~.~ ..?.. ~ ~,~_,.~o 0 : '.-' _.; A .. ..... - - '-x..:---~.~- 0 - -,, . --. %j ..... ' ~ -.*- 'oO* - -2 : J ~ I I I I -2 ~ ~ i i ~ ~ I ~ 64 32 16 10 8 6 4 64 32 16 10 8 6 4 Period (Day) Period (Day) 6 . 6 4 :I 4,," ,~ ~~ 2 : n:l 'E,, - .~ o ' "'"~-'~- -- ",.'~:' t-,-'~'. ..' Z'. -.~..~. -2 [ I I I I I I ! -2 I I ! I I I I I 64 32 16 4 64 32 16 410 8 6Period (Day)-2Period (Day) I I I I I I I64 32 16 10 8 6 4 Period (Day)10 8 6Period (Day) 2'= O?E-2 I4 I I I I I I I64 32 16 10 8 6 4 Period (Day)n=7 I I I , I I I ,, I64 32 16 10 8 6 4 Period (Day)FIG. 14. As in Fig. 13 except at 100 rob.the Southern Hemisphere than in the Northern Hemisphere. However, examination of the energy flow inthe wavenumber domain reveals a marked contrastbetween the two hemispheres in the spectral distribution of energy and energy transformations. The differences are most pronounced for ultralong waves andlarge cyclone-scale waves, but the differences in theshort-wave range are also noticeable. The annual variJANUARY 1988 ERNEST C~ KUNG 19 ations of energy and energy transformations are large, and there are also pronounced differences in the sea sonal variations between the Northern and Southern hemispheres. Although these differences are masked when the energy variables are integrated globally, they are important if energetics analyses are to be performed with reference to specific synoptic systems or model forecasts. With the one-year time series of energy variables, time spectra of transient waves are examined with ref erence to kinetic energy, available potential energy and baroclinic conversion of individual wavenumbers for periods of 2-128 days. The time spectra are presented separately at 500 and 100 mb. The peak energy inten sity of ultralong waves is observed around 30-60 days. The peak density shifts to shorter periods for cyclone scale waves, with different spectral distributions for the Northern and Southern hemispheres. On the cyclone scale almost the entire baroclinic conversion is supported by transient waves, whereas an appreciable conversion in the ultralong waves is as sociated with the annual mean motion and annual variations. For the ultralong waves the baroclinic con version by transient disturbances peaks around 40-80 days, then the peak shifts to shorter periods for cyclone scale waves. Throughout all wave ranges there is a pro nounced contrast in the conversion cospectra between the Northern and Southern hemispheres. In each- hemisphere a different cospectral distribution exists for each wavenumber, and the coexistence of various waves at the same wavenumber is indicated by the complex patterns of cospectral distributions. The im portance of nonlinear interactions at different wave numbers for different periods can be inferred through a comparison of kinetic energy spectra and conversion cospectra. A three-dimensional normal mode energetics anal ysis was performed with the same database to describe the energy flow in the wavenumber-vertical mode do main and energy conversions between the barotropic and baroclinic components. The results will be reported in a separate paper. Acknowledgments. The author is indebted to H. Tanaka for his assistance in the computational analysis, and to V. F. Peters and G. Vickers for their technical assistance. He is also grateful to Dr. R. D. Rosen and anonymous reviewers who provided thorough, con structive reviews in the revision of the original manu script. This research was jointly supported by the National Oceanic and Atmospheric Administration and the Na tional Science Foundation under NOAA Grant NA86AA-D-AC114 and NSF Grant ATM-8410487. REFERENCES Arpe, K., C. Brankovic, E. Oriol and P. Speth, 1986: Variability in time and space of energetics from a long series of atmospheric data produced by ECMWF. Beitr. Phys. 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Salstein, 1980: A comparison between cir culation statistics computed from conventional data and NMC Hough analyses. Mon. Wea. Rev., 108, 1226-1247. --, J. P. Peixoto, A. H. Oort and N.-C. Lau, 1985: Circulation statistics derived from level IIIb and station-based analyses during FGGE. Mon. Wea. Rev., 113, 65-88.Saltzman, B., 1957: Equations governing the energetics of the larger scales of atmospheric turbulence in the domain of wavenumber. J. Meteor., 14, 513-523. ,1970: Large-scale atmospheric energetics in the wavenumber domain. Rev. Geophys. Space Phys., 8, 289-302.Tanaka, H., E. C. Kung and W. E. Baker, 1986: Energetics analysis of the observed and simulated general circulation using three dimensional normal mode expansion. Tellus, 38A, 412-428.Wiin-Nielsen, A., 1968: On the intensity of the general circulation of the atmosphere. Rev. Geophys., 6, 559-579.

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