comparative energetics of the observed and simulated global circulation during the special observing...

Quart. J . R . Met. SOC. (1986), 112, pp. 593-611 551.5O6.24:551.513.1

Comparative energetics of the observed and simulated global circulation during the special observing periods of FGGE

By E. C . KUNG Department of Atmospheric Science, University of Missouri-Columbia, Columbia, Missouri 65211

and

W. E. BAKER Laboratory for Atmospheres, NASAIGoddard Space Flight Center, Greenbelt, Murylund 20771

(Kcceivcd 5 March 1YX.5; rcviscd 10 Dcccmher 1YXS)

SUMMARY Energetics of the observed and simulated global circulation are evaluated in the zonal spectral domain for

the special observing periods of FGGE. The study utilizes GLA analyses of FGGE observational data and parallel simulation experiments. There are noticeable differences in energy transformations between the observation and simulation during SOP-I. These include the baroclinic conversion C(n) by the zonal mean motion and short-wave disturbances, and the nonlinear wave-wave interaction L ( n ) at the long and short waves. The energy transformations of the short-wave disturbances are much more intense in the simulated circulation than in the observation. However, good agreement is noted in the conversion and dissipation of kinetic energy in the large- and cyclone-wave range n = 1-10, Spectral distributions of global energy transformations at thc long- and cyclone-wave range indicate that the SOP-2 simulation agrees more closely with the observed fields than the SOP-I simulation. Other pertinent points of energetics diagnosis are also included in the discussion.

1. INTRODUCTION

Evaluation of the simulated atmosphere with reference to the observed atmosphere is an important area of investigation with the First GARP (Global Atmosphere Research Program) Global Experiment (FGGE). The energetics diagnosis of the global circulation is a pertinent concern in this regard since it yields basic information concerning the internal working mechanisms of the atmosphere. The general circulation models (GCMs) have demonstrated their capability in simulating the mean climatic state and in producing reasonably accurate short- to medium-range forecasts (e.g. Bengtsson 1985; Halem er al. 1982). However, the ability of GCMs to simulate the correct energetics is yet to be thoroughly investigated.

Because the four-dimensional assimilation of a large volume of meteorological observations provides the level IIIb data sets for the global grid, a global energetics diagnosis is feasible for the FGGE period. However, as pointed out by Kung and Tanaka (1983) and Lorenc and Swinbank (1984), the models and techniques involved in data assimilation may influence the data sets produced and hence the energy variables computed. Despite differences exhibited by various versions of FGGE data sets we may expect, as evidenced in comparative analyses by Lorenc and Swinbank (1984) and Rosen and Salstein (1980), a reasonable agreement among those data sets in representing the observed circulation of the atmosphere, and that the energetics differences among the assimilated data sets could be less than those between the assimilated observations and simulations. Thus in this comparative energetics diagnosis of the observed and simulated atmospheres an identical model is employed in the data assimilation and parallel simulation experiments to minimize the influence caused by different models. The global observational data in this study are produced by the Goddard Laboratory for Atmos- pheres (GLA) utilizing a fourth-order nine-level general circulation model (see Kalnay er af. 1983). Simulation of the global circulation is performed with the same model.

The global energetics diagnosis reported in this paper is based on the standard methods of spectral energetics and grid-point variables for defined durations of the first

593

594 E. C. KUNG and W. E. RAKER

and second special observing periods (SOP-1 and SOP-2) of FGGE. The energy flow and energy balance in the zonal wavenumber domain are examined for the observed and simulated circulation. Spectral characteristics of the global transformations and meridional variations of energy components are then presented. Gross kinetic energy budgets are also considered. The major focus of attention in this paper is the difference in the energetics of the observed and simulated atmospheres, but additionally we discuss the energetics characteristics of the GLA analyses of the FGGE observational data in reference to the Geophysical Fluid Dynamics Laboratory (GFDL) version of the data.

2. OBSERVED AND SIMULATED DATA SETS

The GLA analyses of the FGGE observational data were examined for two periods, 5 January-5 March and 9 May-7 July 1979. The objective analysis scheme utilized in data assimilation is described in detail in Baker (1983). In summary, eastward and northward wind components, geopotential height, and relative humidity are analysed on mandatory pressure surfaces with the first guess provided by the model 6 h forecast. Surface pressure and temperature are reduced to sea level and analysed there. The analysis at each level is performed with a successive correction method (Cressman 1959) modified to account for differences in the data density and statistical estimates of the error structure of the observations. The simulation experiments were conducted with the GLA GCM for two periods during SOP-1 and SOP-2, 15 December 1978 to 4 February 1979 and 1 June to 30 July 1979. The initial conditions for 0000 GMT 15 December 1978 were provided by the European Centre for Medium Range Weather Forecasts (ECMWF) FGGE IIIb analyses (see Bengtsson et af. 1982). Those for the OOOOGMT 1 June 1979 case were generated with the GLA analysis/forecast system described above.

The forecast model utilized in this study is the fourth-order global atmospheric model described by Kalnay-Rivas et al. (1977) and Kalnay-Rivas and Hoitsma (1979), and more recently by Kalnay et al. (1983). There are nine vertical layers equally spaced in sigma with a uniform non-staggered horizontal grid (4" latitude by 5" longitude). It is based on an energy-conserving scheme in which all horizontal differences are computed with fourth-order accuracy. A sixteenth-order Shapiro (1970) filter is applied every two hours on the sea level pressure, potential temperature and wind fields. In this scheme wavelengths longer than four grid lengths are resolved accurately without damping. Wavelengths shorter than four grid lengths, which would otherwise be grossly mis- represented by the finite differences, are filtered out while they are still infinitesimal. Even though there is no explicit balancing of the wind and mass fields in the assimilation cycle, the use of the Euler backward differencing scheme during the model integration damps most of the gravity waves.

The basic data from the observed and simulated atmosphere for this study include twice daily global values of geopotential height, temperature, humidity, wind and vertical velocity at 1000, 850, 700, 500, 400, 300, 250, 200, 150, 100, 70 and SO mb at 0000 and 1 2 0 0 ~ ~ ~ . In this paper references are made to the GFDL level IIIb version of the observed atmosphere (see Miyakoda et af. 1982); energetics variables computed in studies by Kung and Tanaka (1983, 1984) are processed and utilized for this purpose.

3. SCHEME OF ENERGETICS ANALYSIS

The equations of kinetic energy and available potential energy in the zonal wavenumber domain may be written, after Saltzman (1957, 1970), as

ENERGETICS OF THE GLOBAL CIRCULATION 595

aK(n)/at = - ~ ( n ) + L(n) + C(n) - D(n) (n = 1 , 2 , 3 , . . . ) (2)

(3)

(4)

N

dP(O)/at = - C ~ ( n ) - C(O) + G(O) n = l

aP(n)/at = R(n) + S(n) - C(n) + G(n) (n = 1 , 2 , 3 , . . . ). Equations (1)-(4) state the balance requirement over the total mass of the atmosphere. The variables used are as defined by Saltzman (1970), and are listed in the appendix.

If the kinetic energy equation is averaged zonally with respect to longitude, it may be written as

ak/dt = -V.Z - awk/ap - FQ - D

k = $(u2 + u').

-V*V@ = -- - a q / a p - GiT

( 5 )

(6)

(7)

where

The production term -V.V@ may be considered as a summation of three process terms

and the conversion term -EZ as a summation of conversion by mean meridional circulation and conversion by large-scale eddy convection

- (1)& = - w"d' - W'&' .

The basic energetics analysis scheme with the FGGE level 111 data sets as described by Kung and Tanaka (1983,1984) is utilized for computation of the spectral components and grid-point values of energy variables. The dissipation terms of kinetic energy and generation terms of available potential energy in Eqs. (1)-(5) are obtained as residual terms to balance the respective equations after evaluating other terms with the data. The maximum wavenumber computed for energy variables is N = 36. However, it is confirmed that shorter waves beyond N = 30 do not contribute to spectral sums. In evaluating the conversion of the zonal mean component C(0), the relationship

-- - - (8)

N

V-VG dm - C(n) n = l

(9)

is utilized instead of direct computation by -22, As discussed by Kung and Tanaka (1983), this removes the direct dependence of C(0) on W. Thus, the energy balance analysis may minimize the effect of the zonal mean field 0 whose magnitude in various FGGE data sets seems to be overly influenced by the respective data assimilation schemes.

Computation is performed at the twice daily synoptic times on the individual isobaric surfaces. The energy variables are presented for the mass of the atmosphere between the defined pressure levels. Time averages are taken for various periods in SOP-1 and SOP-2.

4. ENERGY FLOW AND GLOBAL BALANCE

In an extensive compatibility study of two sets of analyses by the ECMWF and the Meteorological Office (UKMO), Lorenc and Swinbank (1984) compare them with

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various FGGE data sets available, including those of the GLA. Despite some noticeable differences among data sets in the zonal mean fields of circulation, there is good qualitative (and often good quantitative) agreement, and we may regard each of them as a fair description of the observed general circulation. As the assimilated data sets are prone to biases by models and analysis techniques, the energetics computation is expected to be influenced by these error components. However, as demonstrated by Lorenc and Swin- bank with ECMWF and UKMO data sets and by Rosen and Salstein (1980) with the conventional upper air observations at network stations and NMC global Hough analysis, there is still reasonable agreement among energy variables of various data sets. It is apparent that, as evidenced by the energetics comparisons between the GLA analyses and simulations and between the GLA and GFDL analyses in this study, these differences among analysis data sets should be much less than the differences between the analysis of observations and a parallel simulation experiment. To focus our attention on the differences between the observation and simulation, the identical GLA GCM is employed to produce the analysis data and to perform the parallel simulation experiment.

Energy flows of the observed and simulated global circulations are compared in Fig. 1 for the period 5-24 January 1979, and in Fig. 2 for the period 21 June-10 July 1979. They represent, respectively, the 20-day periods in SOP-1 and SOP-2 beginning from the 21st day after the initialization of the model (see section 2). During these periods the simulation is well beyond the period of the initial adjustment. Figures 3 and 4 compare the energy flow diagrams for the GLA and GFDL analyses of the global observation for the entire 60-day periods of SOP-1 and SOP-2. Energy flows in these four figures are presented for wavenumber ranges n = 0, 1-5, 6-10 and 11-36 to describe the energy balance in the zonal mean components and the long-, cyclone- and short-wave ranges for the eddy components.

The FGGE SOP-1 was dominated by a sequence of blocking episodes. During the 20-day period of energetics analysis 5-24 January, the development and decaying of a Pacific blocking was followed by the development and maturing of an Atlantic blocking. For the same period the simulation shows the development and decay of a weak blocking over Siberia to be followed by another weak blocking over Alaska. As illustrated in the 10-day-mean 500 mb patterns during 5-14 January in Fig. 5 , the simulation evolved into a considerably different pattern from that of the observation 20 days after the initialization. As illustrated in the lower half of Fig. 5 , the SOP-2 simulation also evolved into a pattern different from the observation. However, such a difference is more significant for SOP-1 than for SOP-2 because of pronounced blockings in the winter. Thus the observed energetics of two 20-day periods may respectively represent the typical energetics processes during SOP-1 and SOP-2, whereas the simulation energetics of these two periods may represent the energetics of the simulated winter and summer atmospheres which have drifted into different circulation patterns from the observations.

The level of kinetic energy and available potential energy is comparable between the observed and simulated atmospheres for both winter and summer periods in all wavenumber ranges except for n = 0 and 11-36 (Figs.1 and 2). The K(0) in the simulations is significantly larger than that in the observation, which is a commonly noted feature of GCM simulations (e.g. Baker et al. 1977; Gilchrist et al. 1973; Manabe et al. 1970; Stone et al. 1977). As illustrated in Figs. 6 and 8, the larger values of K(0) in the simulations are mostly from the latitudes of the westerly jet, and are more significant in the winter hemisphere than in the summer hemisphere. The larger P(0) values in the simulation experiments also may be noted in Figs. 1 and 2. However, as shown in Figs. 7 and 9, the differences between the observed and simulated values of P(0) are not as pronounced as those for K(0) at any one latitude.

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5 Jan - 14 Jan 79

Observation Simulation

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0

Observation Simulation

Figure 5. 10-day-nican 500 mb pattern o l ttic obw-ved and simulated circulation during the periods 5 January to 24 January 1079 and 21 June to 10 July 1079. Contour lines lire at 5 0 m intervals.

The differences in the energy level at n = 0 for the observation and simulation are related to the transformation rates of the zonal-mean components. During the SOP-1 simulation (Fig. 1) . the large value for K(0) is due to larger transfer of eddy kinetic energy to thc zonal component, whereas that during SOP-2 is due to larger conversion, C(0). It is noted here that C(0) varies greatly between observation and simulation both in SOP-1 and SOP-2. Although C(0) is obtained indirectly with Eq. (9), to suppress the erroneous variations, it still reflects the general pattern of the zonal-mean field of vertical motion 55 (see Kung and Tanaka 1983, 1984). The latitude-height cross-sections of 73 in

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602 E. C. KUNG and W. E. BAKER

mb 50

100

200

300

1100

500

700

850

1000

mb 50

100

200

300

1100

500

700

850

1000

5 Jan -24 Jan 79 Observation

N 60 30 0 30 60 S

Simulation

N 60 30 0 30 60 s

Figure 10. Latitude-height distribution of observed and simulated W during the period 5 January to 24 January 1979 in units of 10"ph s I.

Figs. 10 and 11 indicate considerable difference between observed and simulated data. The meridional circulation in the observed atmosphere is more intense than that in the simulated atmosphere at all latitudes, with particularly strong vertical motion in tropical and polar latitudes. Although the conversion of the zonal mean component C(0) is not a decisive term in the global energy balance, its measurement suffers an uncertainty in the evaluation of W. Similar uncertainty in C(0) and W was pointed out by Kung and Tanaka (1983) in comparing the ECMWF and GFDL versions of FGGE level IIIb data


rnb 50

100

200

300

400

500

700

850

1000

21 Jun -10 ju179

Observation rnb 50

100

200

300

1100

500

700

850

1000 N 60 30 0 30 60 5

Simulation I r

N 60 30 0 30 60 5

Figure 11. As Fig. 10, but for the period 21 June to I0 July 1979

sets. Figures 3 and 4 further indicate that a considerable discrepancy exists between C(0) values of the GLA and GFDL analysis data. This is also consistent with the discrepancies between latitude-height cross-sections of W in Figs. 10 and 11 for the GLA analysis and those in Tanaka and Kung (1983) for the GFDL analysis. The W analysis appears to be the most uncertain of the basic fields of motion in all versions of the global analysis of observations, making the conversion C(0) the most affected transformation variable.

The levels of eddy kinetic energy are generally comparable between the observation


and simulation except for K(1-5) in SOP-1. The obviously less kinetic energy in n = 1-5 is due to a large loss of kinetic energy through the wave-wave interaction in this range, L(1-5), and this may be considered in reference to the weak winter blocking in the simulation in contrast to the pronounced blocking in the observation. An interesting thing to note here is that there is more baroclinic conversion C(n) in all wave ranges of the simulation to provide a larger kinetic energy source than the observation. We also note in Figs. 1 and 2 that both SOP-1 and SOP-2 simulations show significantly larger negative values of L(n) in both long- and cyclone-wave ranges, whereas the simulated L(l1-36) shows much larger positive values than the observation. It is clear then that the larger energy converted in the simulation cascades down to the short-wave range through the nonlinear wave-wave interaction. This strong energy input in the short waves through the direct conversion C(11-36) and wave-wave interaction L(11-36) supports the often observed intense energetics of short waves in GCM integrations (e.g. Baker and Brin 1985). In this study, L(ll-36), C(l1-36) and dissipation D(11-36) in the simulation are two to four times higher than in the observation, although K(11-36) shows only f to 4 higher kinetic energy levels in simulations than in observations.

Generation of available potential energy, G(O), is significantly higher in simulations than in observations, for both SOP-1 and SOP-2. Eddy generation C(n) in the SOP-1 observation is higher than the simulation in all wave ranges, but in thc SOP-2 experiment G(n) in the cyclone- and short-wave ranges becomes larger than in the observation. Transfer of P(0) to P(n) through the R(n) process is significantly more active in simulations than in observations in all wave ranges. The transfer of available potential energy through the wave-wave interaction, S(n ) , shows that the simulation loses a larger amount of P(n) in the long-wave range, which appears as a significant gain at the short waves. Thc gains at the short waves through S(11-36) and R(l1-36) in turn are converted into kinetic energy through C(l1-36), and this contributes as a factor in producing the over-intense short-wave energy processes.

If we measure the intensity of the general circulation by G(n), C(n) or D(n) for n = 0-36, the values in Figs. 1 and 2 yield the intensities shown in Table l(a). Likewise from Figs. 3 and 4, the intensities of the general circulation for the entire periods of SOP-1 and SOP-2 as determined by the assimilated data by the GLA and GFDL arc as shown in Table l(b).

Both observational data sets indicate that there is a significant difference in the intensities of SOP-1 and SOP-2. This is consistent with the finding in Kung and Tanaka

TABLE ](a). INTENSITY OF THE GENERAL CIRCIJLA7ION FROM Fios.1 A N D 2

Period Observation Simulation (1979) (W m-') (w m-2)

5-24 Jan. 3.7 21 June-I0 July 1.9

3.9 3.9

TABLE l(b). INI'ENSII'Y OF THE GENERAL CIRCULATION FROM FIGS. 3 AND 4

GLA observation GFDL observation Period (W m-') (W m-*)

SOP-I 3.1 4.6 SOP-2 2.5 3.5


(1983, 1984) that the difference in the seasonal variation between the northern and southern hemispheres leads to a seasonal contrast in the globally integrated energy budgets. The northern hemisphere contributes most to this seasonal contrast, and the SOP-1 cnergy processes are more active than those in SOP-2. However, the global energetics listed first indicate a similar level of intensity for the SOP-1 and SOP-2 simulations. Comparing the energy flow in the two simulations (Figs. 1 and 2) we note two points. First, the largest difference between the SOP-1 and SOP-2 simulations is found in transformations to support the zonal kinetic energy K(0) . Transformations are generally higher in the SOP-1 experiment, but the zonal conversion C(0) is significantly higher in the SOP-2 experiment than in SOP-1. Second, the SOP-1 and SOP-2 simulation difference in energy transformations in general appears to be less than the difference between the SOP-1 and SOP-2 observations, and in many instances less than the difference in the observed and simulated data for the same period. The transformations exhibit noticeable differences between the observations and simulations, except that they agree best for the kinetic energy conversion C(n) and dissipation D ( n ) in the large and cyclone waves.

Energy flow patterns for GLA and GFDL observations, as shown in Figs. 3 and 4, indicate general qualitative agreement in the long- and cyclone-wave range. The GFDL analysis shows more intense short-wave energetics in the n = 11-36 range than the GLA analysis. As has been mentioned, there is a noticeable discrepancy in zonal conversion, C(0). The GFDL version shows a distinguishably larger C(0), which contributes significantly to the higher intensity of the general circulation than in the GLA version. Despite these differences, however, both observational data sets show a consistent pattern of seasonal variation between SOP-1 and SOP-2 with an intensified energetics process during SOP-1 in all eddy ranges.

5. SPECTRAL DISTRIBUTION OF TRANSFORMATION VARIABLES

Spectral distributions of three transformation variables in the observation and simulation are compared for the cyclone- and short-wave range in Figs. 12 and 13 as a function of wavenumber from n = 1 to 15. Shown are the global means of transfer of the zonal-mean available potential energy to eddy available potential energy R(n) , transfer of the eddy kinetic energy to zonal-mean kinetic energy M ( n ) , and conversion of the available potential energy to kinetic energy C(n) . Figure 12 is for 5-24 January 1979 and Fig. 13 for 21 June-10 July 1979.

As shown in Fig. 12, the SOP-1 simulation has considerably higher R(n) for n = 2-6. In the same wave range, M ( n ) and C(n) are also generally higher in the simulation experiments than in observed data. The largest discrepancy between observed and simulated data is noted for n = 2 and 6. In view of the important roles played by these waves during SOP-1, this is an important discrepancy. For the SOP-2 simulation, as shown in Fig. 13, the differences in the observed and simulated transformations tend to spread over all wave ranges. It is difficult to identify specific wavenumbers at which the differences in the transformations are concentrated. Thus, the SOP-2 simulation shows more agreement with the observations than that for SOP-1.

Kinetic energy and available potential energy in the observed and simulated circulations result from the respective transformation processes during the two periods and show characteristic meridional variations as presented in Figs. 6, 7, 8 and 9. In the distribution of kinetic energy, the most distinct contrast between the observation and simulation occurs for K(0) . The simulated jet core in terms of a maximum K(0) in SOP-1 i c not only much stronger than in the observation, but also shifts approximately 10"


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ENERGETICS OF 'THE GLOBAL CIRCULATION 607

north in both hemispheres. In SOP-2, K(0) in the northern hemisphere becomes very small, but the simulated K(0) is still much larger than the observed K(0) . The K(0) in the southern hemisphere dominates in SOP-2. While the simulated K(0) indicates a single jet core at 3 0 3 , the observed K(0) has a double maxima at 30" and 60"s. On the eddy component side, the level of simulated kinetic energy at ultralong waves n = 1 and 2 in the northern hemisphere is significantly lower than that in the observation in SOP-1. This is consistent with the discussion in the preceding section that a large amount of energy in the long-wave range cascades down to the short-wave range, and this is related to the wcakcr winter blocking of the simulation than the observation. As for the meridional distribution oi P(n) , agreement between the observations and simulations is better than for K ( n ) . Some notable differences are seen for the higher observed values of P at n = 0 in the antarctic and at n = 1 and 2 in the mid to high latitudes of the northern hcmisphere during the SOP-1 simulation period.

6. GROSS KINETIC ENERGY BUDGET

The global kinetic energy balance and eddy conversion for the observed and simulated atmosphere are presented for the two simulation periods separately in Tables 2 and 3. If Eq. ( 5 ) is integrated with respect to latitude for the global average, the transport term V . V k will vanish. If we ignore the time change d x / d t , the kinetic energy balance may be considered in terms of --, -dwk/ap and D. Vertical distributions of energy production -V.V@ and dissipation D for the observations and simulations are compatible in general with the double maxima in the lower - boundary and the upper troposphere. Vertical distributions of the eddy conversion - w'a' for both observed and simulated data are also reasonably close, with a mid tropospheric maximum in the 700-500 mb layer. As discussed carlier, the intensity of the general circulation in the simulation experiment of SOP-2 is about the same as for SOP-1. As seen in Tables 2 and 3, the simulation energy budgets for SOP-1 and SOP-2 actually do not exhibit a noticeable difference, even though there are very significant differences between the SOP-1 and SOP-2 simulations (see Figs. 12 and 13) in the spectral distribution of energy variables.

Tables 4 and 5 compare the kinetic energy budgets of GLA and GFDL observations for the whole of SOP-1 and SOP-2. There is qualitative agreement of the pattern of vertical distributions of production and dissipation between the two analyses. However, above the mid troposphere the GFDL version shows significantly larger values for -V.V@ and D , and at the jet stream level the transformation rates of the GFDL version are nearly twice that of the GLA version. Because of this, the values of production and dissipation in the lower troposphere are less than those in the upper troposphere in the GFDL version, whereas they are approximately balanced in the GLA version. On the other hand, the eddy conversion -da' appears to take place throughout most of the troposphere in both - versions. Above the tropopause level, the GLA analyses exhibit negative values of - d a y ) , which indicates a lack of a kinetic energy source and return of kinetic energy to the reservoir of available potential energy. In the GFDL version during SOP-1 it is noteworthy that there is positive conversion well above the tropopause level.

-

7. CONCLUDING REMARKS

The mean patterns of the global circulation and their spatial and temporal variations have been simulated by GCMs with considerable success, which offers encouragement for extended range forecasting. To further the capability of the GCMs through modelling


TABLE 2. KINETIC ENERGY BUDGET OF THE OBSERVAlION AND SIMULATION DURING 5'JANUARY TO 24 JANUARY 1979 IN UNITS OF w - -

Pressure -v,vql - a Z / a p D - w"' layer (mb) Obs. Sim. Obs. Sim. Obs. Sim. Obs. Sim.

100-50 150-100 200-150 250-200 300-250 400-300 500-400 700-500 8.50-700 SFC-850

400-50 700-400 SFC-700

Total

0.16 11.07 0.32 0.09 0.42 0.11 0.38 0.18 0.28 0.26 0.33 0 4 6 0.10 0.26

0.30 0.49 1.40 1.76

1.89 1.17 0.13 0.53 1.70 2.25 3.72 3.95

0.03 0.27

-0.02 -0.04 -0.04

0.03 -0.01

0.02 0-07 0.06

-0.03 -0.05

-0.06 0.13

-0.08 -0.01

0.03 0.09 0.12 0.05

--0.ll -0.25 -0.03

0.06 0.03 0.01

-0.07 0.03 0.04 0.00

0.14 0.10 -0.06 0.00 0.28 0.18 -0.05 -0.01 0.38 0.23 -0.04 0.03 0.41 0.23 -0.01 0.11 0.27 0.15 0.07 0.21 0.35 0.21 0.43 0.64 0.17 0.23 0.62 0.70 0.09 0.33 1.17 1.26 0.27 0.52 0.71 0.72 1.35 1.77 0.29 0.36 1.83 1.10 0.34 0.98 0.26 0 4 6 1.79 1.86 1.62 2.29 1.00 1.08 3.71 3.95 3.13 3.92

TABLE 3. KINETIC ENERGY BUDGE1 Of. THE OBSERVATION AND SlMLlLATlON DURING 21 JUNE TO 10 JULY 1979 IN u N m OF w m-*

- ~

Pressure -v.vqJ -d;;;i;ldp D --w'ff '

layer (mh) Ohs. Sim. Obs. Sim. Ohs. Sim. Ohs. Sim.

100-50 150-100 200- 150 2.50-200 300-250 400-300 500-400 700-500 850-700 SFC-850

400-50 700-400 SFC-700

Total

0.01 0.11 -0.03 0.19 -0.01 0.21

0.08 0.22 0.13 0.23 0.17 0.35

-0.01 0.22 --O.ll 0.29

0.24 0.44 1.49 1.64

0.35 1.30 -0.12 0.51

1.73 2-08 1.96 3.90

0.01 0.03 0.04 0.03

-0.01 -0.03

0.00 0.00

-0.01 -0.05

0.07 0.00

-0.06 0.01

0.00 -0.01 -. 0 4 2

0.02 -0.05 -0.09

0.01 0.07 04.5 0.02

-0.15 0.08 0.07 0.00

0.02 0.11 0-00 0.18 0.03 0.19 0.11 0.20 0.12 0.18 0.14 0.26

-0.01 0.23 -0.11 0.36

0-23 0.49 1.44 1.66 0.42 1.12

-0-12 0.59 1.67 2.15 1.97 3.86

-0.01 -0.02 -0.03 -041

0.06 0.34 0.44 0.7 1 0.43 0.21

0.33 1.15 0.64 2.12

-0.01 -0.01

044 0.08 0.14 0.48 0.56 0.97 0.61 0.31

0.72 1.53 0.92 3.17

of physical processes and the application of models for forecasting, it is desirable to clarify energetics characteristics of the simulated atmosphere in reference to the observed atmosphere for the same periods. This investigation has attempted to provide such an assessment of the simulated global circulation in terms of spectral energetics. The study is based on the GLA version of the FGGE observed data and parallel simulation experiments. In view of the compatibility of GCMs today, the results obtained in this study may indicate what we might expect from GCM simulations and what we should look for in their future development.

From comparison of the spectral energetics of the observed and simulated global circulation we find the following:

1. Contrary to observations, the simulated atmosphere does not show a clear


TABLE 4. KINETIC ENERGY BUDGET FROM GLA AND GFDL OBSERVED DATA DURING SOP-I ( 5 JANUARY TO 5 MARCH 1979) IN UNITS OF W m-*

Pressure layer (mb)

100-SO 1 SO- 100 200-150 250-200 300-250 400-300 500-400 700-SO0 8.50-700 SFC-850

400-50 700-400 SFC-700 Total

-v.vf$ GLA GFDL

0.17 0.21 0.33 0.30 0.39 0.60 0.32 0.67 0.20 0.47 0.21 0.53 0.02 0.21

-0.09 0.06 0.22 0.28 1.36 1.28

1.63 2.78

1.58 1.56 3.14 4.61

-047 0.27

- a w k l a p GLA GFDL

-0.02 0.00 -0.05 -0.07 -0.06 -0.11

0.01 -0.08 -0.01 -0.00

0.04 0.04 0.07 0.12 0.07 0.14 0.00 0.02

-0.03 -0.03

-0.09 -0.22 0.14 0.26

-0.03 -0.01 0.01 0.04

D -

- w'a,'

GLA GFDL

0.15 0.22 0.28 0.23 0.33 0.49 0.33 0.59 0.19 0.46 0.25 0.57 0.09 0.34

-0.02 0.20 0.22 0.29 1.33 1.25

1.54 2.56 0.07 0.54 1.55 1.54 3.15 4.64

GLA GFDL

-0.04 0.14 -0.04 0.18 -0.04 0.16 -0.01 0.12

0.06 0.20 0.40 0.61 0.58 0.65 1.09 1.00 0.67 0.51 0.29 0.19

0.34 1.41 1.67 1.65 0.96 0.70 2.96 3.76

TABLE 5 . KINETIC ENERGY BUDGET FROM GLAS AND GFDL OBSERVED DATA DURING SOP-2 (9 MAY TO 7 JUL.Y 1979) IN UNITS OF Wm-'

- - Pressure -v.vg, -awklap D -tu'n'

layer (mb) GLA GFDL GLA GFDL GLA GFDL GLA GFDL

100-50 150-100 200-150 250-200 300-250 400-300 500-400 700-500 850-700 SFC-850

400-50 700-400 SFC-700

Total

0.08 0.14 0.13 0.17 0.18 0.28 0.21 0.40 0.20 0.31 0.23 0.27 0.01 0.09 0.12 0.09 0.22 0.32 1.40 1.49

1.03 1.57 0.11 0.18 1.62 1.81 2.54 3.55

0.00 0.02 0.04 0.05 0.00

-0.02 -0.01 -0.02 -0.02 -0.03

0.09 -043 -0.05

0.01

-0.02 0.08 0.11 0.00 -0.01

-0.04 0.22 0.24 -0.04 0.06 -0.02 0.26 0.37 -0.02 0.07

0.02 0.20 0.32 0.07 0.14 0.08 0.21 0.36 0.39 0.40

0.5 1 0.41 0.08 0.00 0.16 0.05 -0.14 0.13 0.83 0.72

0.20 0.31 0.49 0.53 0.23 0.22

0.00 1.12 1.55 0.39 0.65 I .34 1.13 0.13 -0.14 0.29 0.72 0.75 -0.04 1.57 1.77

0.09 2.55 3.62 2.45 2.52

-0.02 0.15 0.15 -0.02 -mi

-0.01 -0.03 1.37 1.46

distinction in the intensity of the general circulation between SOP-1 and SOP-2. The transformations in SOP-2 show the same high level of intensity as in SOP-1.

2. The largest differences between the observation and simulation in the energy budget are seen in the transformation for the zonal mean component in both SOP-1 and SOP-2, reflecting large discrepancies in the zonal mean field of vertical motion between the observed and simulated data sets.

3 . In the long- and cyclone-wave range a significant loss of kinetic energy through the wave-wave interaction in the simulation is related to the low kinetic energy in this range and weak simulated blockings during the winter.

4. The energy processes in the short-wave range of the simulation are very intense because of the direct baroclinic conversion and the gain of kinetic energy through the wave-wave interaction.

5. Spectral distributions of the global transformations R(n) between the zonal-mean

610 E. C. KUNG and W. E. RAKER

and eddy available potential energy, M ( n ) between the zonal-mean and eddy kinetic energy, and C(n) between the available potential energy and kinetic encrgy, all show that the SOP-2 simulation is more compatiblc with observations than the SOP-1 simulation.

6. The simulated maximum of K ( 0 ) is larger than the observed maximum, and there is alqo a noticeable shift in the latitudinal position of the jet core. The observed and simulated components of the available potential energy agree better in both their magnitude and latitudinal distribution.

ACKNOWIMXMENTS

The authors arc indebted to H. Tanaka for assistance in the computational analysis and to D. Edelmann, J . Ptacndtncr. J. Woollen and Y. Brin tor their help with the GLA simulation experiments and thc analysis/forecast system. Thcy arc grateful t o anonymous referees who provided valuable comments. L. K. Gibson, R. R. Rccs, S. B. Suits and G. Vickers are acknowledged for their technical ;issistancc. This rcscarch was performed at ECK Research Consulting, Inc. under NASA Contract NASS-28 I 16.

APPFNDIX

Symbols. definitions ~ i t d uanubles Pressure, time Eastward, northward. wind component Horizontal wind vector Mass of the atmosphere Specific volume Vertical y velocity ( d p l d t ) Geopotential Horizontal del operator along an isobaric surface Zonal average of a n arbitrary function q Departure of q , Lj, from zonal, global, average Zonal wavcnurnbcr, maximum zonal wavenumber Kinetic energy, K at wavenumber n Available potential energy, P at wavenumber IZ Transfer of K(n) to K ( 0 ) where tz # 0 Transfer of eddy kinetic energy from all other wavenumbers to K ( n ) Conversion from P to K . conversion of P(n) to K ( n ) Transfer of P(0) to P(n) where n # 0 Transfer of eddy available potential energy from all other wavenumbers to P(n) Dissipation of K ( n ) , generation of P(n) Local time change of kinetic energy

-G.Vk, - d o k / d p -V.C@ -Y.V@, -a o@/dp Horizontal, vertical, flux convergence of potential energy

- _ - w ' d , - d'd

Horizontal, vertical, flux convergence of kinetic energy Production of kinctic energy by cross-isobaric motion

Baroclinic conversion from P to K Conversion by eddy convection, by mean meridional circulation


Baker, W. E

Rakcr, W. E. and Brin. Y.

Raker, W. E. , Kung, E. C. and

Bengtsson. L.

Bcngtsson, I.. , Kananiitsu, M.,

Cressman, G. P.

Gilchrist, A., Corby, G. A. and

1 lalcm, M., Kalnay-Kivas. E., Baker,

Kalnay, E., Halgovind, R., Chao,

Somerville, R . C. J .

Killberg. P. and Uppala, S

Ncwson, R. L.

W. E. and Atlas, R.

W . , Edclmmn, D., Pfaendtner, J . , Takacs, I d . and Takano. K .

Kalnay-Riv;is, E. and Hoitsma, D.

Kalnay-Rivas, E.. Bayliss, A. and

Kung, E. <‘. and Tanaha, 11. Storch, J .

Lorenc. A. C . and Swinbank, R.

Manabe. S . , Smagorinsky, J , , Holloway, J . L., Jr. and Stone, H. M .

Sirutis, J . Miyakoda, K . , Sheldon, J . and

Rosen, K. D. and Salstein, D. A

Saltzman, B

Shapiro, K. Stone, P. H.. Chow, S. and

Ouirk, W. F.

1983

1985

1977

19x5

19x2

1059

1973

1Y82

19x3

1979

1977

1983

1984

1984

1970

1982

1980

1957

1970

1970 1977

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Spectral characteristics and meridional variations of energy transformations during thc first and second observation periods of FGGE. ibid., 41, 1836-1849

On the accuracy of general circulation statistics calculated from FGGE data-a comparison of results from two sets of analyses. Quart. J . R. Met. Soc., 110, 915-942

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Four-dimensional analysis experiment during the GATE period. Part 11. J . Afmos. Sci., 39, 486-506

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Equations governing the energetics of the larger scales of atmospheric turbulence i n the domain of wavenumber. J . Meteor., 14, 513-523

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climate simulated by the GISS general circulation model. Mon. Wea. Reu., 105, 170-194

comparative energetics of the observed and simulated global circulation during the special observing...

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