J. Meteor. Res.  2014, Vol. 28 Issue (4): 592-606   PDF    
http://dx.doi.org/10.1007/s13351-014-3072-0
The Chinese Meteorological Society
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Article Information

ZHAO Bin, ZHANG Bo. 2014.
Diagnostic Study of Global Energy Cycle of the GRAPES Global Model in the Mixed Space-Time Domain
J. Meteor. Res., 28(4): 592-606
http://dx.doi.org/10.1007/s13351-014-3072-0

Article History

Received October 16, 2013;
in final form June 17, 2014
Diagnostic Study of Global Energy Cycle of the GRAPES Global Model in the Mixed Space-Time Domain
ZHAO Bin, ZHANG Bo     
National Meteorological Center, Beijing 100081
ABSTRACT:Some important diagnostic characteristics for a model's physical background are reflected in the model's energy transport, conversion, and cycle. Diagnosing the atmospheric energy cycle is a suitable way towards understanding and improving numerical models. In this study, formulations of the "Mixed Space-Time Domain" energy cycle are calculated and the roles of stationary and transient waves within the atmospheric energy cycle of the Global-Regional Assimilation and Prediction System (GRAPES) model are diagnosed and compared with the NCEP analysis data for July 2011. Contributions of the zonal-mean components of the energy cycle are investigated to explain the performance of numerical models.
The results show that the GRAPES model has the capability to reproduce the main features of the global energy cycle as compared with the NCEP analysis. Zonal available potential energy (AZ) is converted into stationary eddy available potential energy (ASE) and transient eddy available potential energy (ATE), and ASE and ATE have similar values. The nonlinear conversion between the two eddy energy terms is directed from the stationary to the transient. AZ becomes larger with increased forecast lead time, reflecting an enhancement of the meridional temperature gradient, which strengthens the zonal baroclinic processes and makes the conversion from AZ to eddy potential energy larger, especially for CAT (conversion from AZ to ATE). The zonal kinetic energy (KZ) has a similar value to the sum of the stationary and transient eddy kinetic energy. Barotropic conversions are directed from eddy to zonal kinetic energy. The zonal conversion from AZ to KZ in GRAPES is around 1.5 times larger than in the NCEP analysis. The contributions of zonal energy cycle components show that transient eddy kinetic energy (KTE) is associated with the Southern Hemisphere subtropical jet and the conversion from KZ to KTE reduces in the upper tropopause near 30±S. The nonlinear barotropic conversion between stationary and transient kinetic energy terms (CKTE) is reduced predominantly by the weaker KTE.
KeywordsMixed Space-Time Domain energy cycle     energy reservoir     energy conversion     stationary wave     transient wave     GRAPES model    
1. Introduction

Atmospheric systems such as cyclones and anticyclones are measured in terms of their kinetic energy(KE)(Storch et al., 2012), and those systems that areintensifying or weakening are often defined as gainingor losing KE(Luo,1994). Therefore,knowledge regarding the sources and sinks of KE in this context isvery important(Li and Zhu, 1995; Gao et al., 2006).

The total energy of the whole atmosphere will remain constant under adiabatic motion and the onlysource and sink of KE should be the available potential energy(APE). The APE can be considered as thedifference between the total potential energy and minimum potential energy, and we can state that APEshould vanish when the system's distribution becomesuniversally horizontal and stable. However,the general motion of the atmosphere is not adiabatic; thepresence of friction should alter KE directly, and conversion between APE and KE should be considered asthe generation and dissipation energy within the wholelife cycle of the atmospheric motions.

Lorenz(1955)developed a life cycle for energyconversions and defined a series of formulations to represent such conversions from APE to KE. He subdivided APE and KE into mean and eddy forms. Theeddy form is the deviation from the mean form and themean form can convert into the eddy form by eddytransport of sensible heat from low to high latitudes.In his energy cycle process,the general circulation canbe characterized as a conversion of zonal APE,whichis generated by low-latitude heating and high-latitudecooling,to eddy APE,then to eddy kinetic energy and to zonal mean KE. The conversion between the twoforms of energy involves horizontal and vertical transport of momentum and sensible heat. The dissipation and generation terms within the life cycle can barelybe estimated directly, and they are only a few balanceterms in the budget equations.

This life cycle can be used to distinguish differentcontributions from different synoptic-scale and generalcirculation processes. It should give an intuitive judgment for ev aluating the sources of different model performances. With regard to the Hadley cell,this largescale system involves a conversion from mean APE tomean KE(Dickinson,1969; Wu,1987), and for thebarotropic atmosphere,the rate of transport betweenthe eddy and mean KE is given by the product of theeddy transport if the momentum and gradient of meanangular rotation are both taken in the north-south direction. Concerning the baroclinic atmosphere(Stone,1978),by the eddy transport of sensible heat from lowto high latitudes,the mean APE converts into eddyAPE and the eddy conversion from APE to KE isgiven by vertical motion and temperature within thelatitudinal circle. Thus,it is a result of warm air rising and cold air sinking(Stein,1986; Huang and Vincent, 1998). In terms of the real atmosphere,the entire energy life cycle should display a complete conversionfrom APE to KE.

Oort(1964,1983)used the classical Lorenz energy cycle concept to estimate the reservoirs of APE and KE,together with related sources and sinks forthe Northern Hemisphere. Steinheimer et al.(2008)estimated the conversion of Lorenz theory both in gridscale processes and subgridscale processes obtainedfrom parameterization schemes. Their results showedthat the subgridscale processes contributed signifi-cantly to the Lorenz energy cycle and the total dissipation terms of the subgridscale were more intensethan what all earlier gridscale estimates had indicated.

Lorenz formulas can be introduced in the spacedomain, and we can further acquire the energy valuein the mixed space and time domain,the so-called\Mixed Space-Time Domain" energy cycle. The eddyenergy is subdivided into stationary and transientwaves. The stationary form is the time mean and a result of diabatic and orographic forcing. The transientform is the departure from the time mean and a resultof baroclinic instability of zonal mean flow(Simmons and Hoskins, 1978,1980).

Ulbrich and Speth(1991)exp and ed the Lorenzclassical process to give a series of detailed formulations for the "Mixed Space-Time Domain" energy cycle(Arpe et al., 1986), and examined the role of stationary and transient waves within the atmosphericenergy cycle with the ECMWF data for winter and summer. Their results showed that all terms of theenergy cycle related to stationary waves reveal a predominance of the planetary scale while the transientwaves are governed by synoptic-scale waves.

In the present study,an approach based onthe \Mixed Space-Time Domain" energy cycle isadopted. The formulations of the energy cycle arecalculated, and the role of stationary and transientwaves within the atmospheric energy cycle from theGlobal-Regional Assimilation and Prediction System(GRAPES)is firstly diagnosed and compared withNCEP Final Operational Global Analysis(FNL)datafor July 2011. Three main kinds of considerable processes(planetary scale,barotropic conversion, and baroclinic conversion)are examined separately in order to investigate in detail the characteristics and features of energy cycle and its component contribution.The zonal-mean components of the energy cycle areinvestigated to diagnose the performance of numerical integrations. The forecast results at different leadtimes are used to explain the reason for deterioratingforecast performance.2. Method

By following Ulbrich and Speth(1991)'s energycycle framework(illustrated in Fig. 1),all the energy reservoirs and conversions are calculated in thisstudy with Ulbrich and Speth's detailed formulations.Zonal available potential energy(AZ) and zonal kinetic energy(KZ)are zonal APE and KE. Stationaryeddy available potential energy(ASE) and transienteddy available potential energy(A TE)are stationary and transient eddy APE, and the stationary and transient eddy KE is named KSE and KTE,respectively .Besides energy reservoirs,some terms of the energycycle,such as CZ(conversion from AZ to KZ),CAS(conversion from AZ to ASE),CA T(conversion fromAZ to A TE),CES(conversion from ASE to KSE),CET(conversion from A TE to KTE),CKS(conversion from KZ to KSE),CKT(conversion from KZ toKTE), and the nonlinear conversions between stationary and transient terms(CA TE and CKTE)all playimportant roles in the global energy cycle process and can be regarded as an important benchmark to estimate the basic model performance.3. Data

The GRAPES model daily forecast data for July2011 with four different lead times of 24,72,120, and 168 h are used. The model resolution is selected as 0.5° and it is initialized with global 1200 UTC analyses of the NCEP FNL data. Archived GRAPES modeldata consist of geopotential height,temperature,specific humidity,zonal and meridional wind, and verticalwind for 29 pressure levels(1000,962.5,925,887.5,850,800,750,700,650,600,550,500,450,400,350,300,275,250,225,200,175,150,125,100,70,50,30,20, and 10 hPa). NCEP FNL data are selectedas the analysis data for comparison and are interpolated from 1.0° to 0.5° grid, and vertically from 26 to 29 pressure levels. NCEP global forecast(not analysis)data are also selected for the same time period and the same horizontal and vertical resolutions forcomparison.

Fig. 1. Diagram of the global atmospheric energy cyclein the Mixed Space-Time Domain. Arrows indicate orientation of conversions corresponding to the definitions ofparameters(from Ulbrich and Speth, 1991). Note: G denotes generation of potential energy; D denotes dissipationof kinetic energy .
4. Results4.1 The glob al energy cycle for July 2011

As a preliminary work for the energy cycle analysis,it is necessary to ev aluate the performance of theGRAPES model and provide an intuitive impressionof the quality of the FNL data,which serve as thecomparative observ ation. In the classical treatmentof statistical verification for different model forecasts,root-mean-square-error(RMSE)is a predominant index used as a measure of model forecast performance.T emperature and wind velocity are the main variablesinvolved in the calculation of energy cycle and conversion terms. Figure 2 depicts the global averagedRMSE for temperature and wind velocity against theFNL analysis data and NCEP BUFR(Binary Universal Form of the Representation of meteorological data)sounding data. The latter dataset is chosen as the observ ation,which is only distributed between 850 and 50 hPa. Figure 2a shows that the maxima of temperature RMSE are mostly concentrated within 200hPa, and with increasing lead time,RMSE grows from1.59 K(24 h)to 3.80 K(168 h). Meanwhile,in Fig. 2c,the maxima of wind velocity RMSE are locatedwithin 250 hPa, and with increasing lead time,RMSErises from 6.14 m s-1(24 h)to 16.16 m s-1(168 h).The RMSEs of GRAPES model outputs relative to theFNL data in Fig. 2b and 2d present a similar patternto that in Figs. 2a and 2c. T emperature RMSE atdifferent lead times in Fig. 2c is consistently smaller than that in Fig. 2a(e.g.,at 200 hPa,1.09 K for24 h and 3.53 K for 168 h). Moreover,wind velocityRMSE is smaller in Fig. 2d than in Fig. 2b at 120-h lead time and increases to 17.00 m s-1(168 h)at250 hPa. This is possibly due to the GRAPES modelbeing initiated with the FNL data. With respect toupper levels(above 50 hPa),where there are no comparative observ ations,large temperature and wind velocity RMSE maxima are observed to intensify withlead time. This will lead to strengthening potentialenergy and KE.

Fig. 2. Global averaged RMSE for GRAPES produced(a,b)temperature(K)against(a,c)NCEP BUFR observation and (b,d)FNL analysis in July with different leadtimes.

Following Ulbrich and Speth's work(1991),wehave calculated the globally averaged energy cycle ofthe GRAPES model with different lead times and theresults are shown in Fig. 3. It is confirmed that theGRAPES model has the capability to reproduce themain features of the global energy cycle as comparedwith NCEP analysis data. AZ is converted into ASE and A TE; the stationary waves cannot be neglectedcompared with the transient ones, and ASE and A TEhave about the same value. The nonlinear conversionbetween the two eddy available potential energy terms,i.e.,CA TE,plays an important role in the global energy cycle and is directed from the stationary to the transient reservoir of APE. It can be deduced that thedamping of stationary temperature by horizontal transient fluxes of sensible heat is an important process inthe global general circulation.

Fig. 3. The global atmospheric energy cycle of GRAPES in July 2011. Various energy components(in boxes)are inJ m-2,while conversions between the components are in W m-2 . Numbers at the top indicate values based on NCEPFNL data, and 24,72,120, and 168 h are the different lead times from 1 to 7 days. The dotted frame refers to theplanetary-scale(Hadley cell)process,the dashed frame refers to the barotropic process, and the dot-dashed frame refersto the baroclinic process.

With increased forecast lead time,AZ becomeslarger,which reflects the meridional temperaturegradient between high and low latitudes becomingsteeper. This enhances zonal baroclinic processes,which increases the meridional heat flux and enhancesthe conversion from AZ to eddy potential energy,especially the conversion of the transient term,CA T. Thestationary conversion of APE,i.e.,CAS,is just 1/6 ofthe magnitude of the transient conversion of CA T.The zonal KE(i.e.,KZ)has a similar value to thesum of stationary and transient eddy KE(KSE and KTE), and the transient term is three times largerthan the stationary term,while there is almost noglobal net conversion between the two eddy KE terms.Barotropic stationary and transient conversions(CKS and CKT)are directed from eddy KE to zonal KE.The zonal planetary-scale conversion CZ(from AZ toKZ)is about 1.5 times larger in GRAPES than in theNCEP analysis.4.2 Planetary-scale proc esses

The globally averaged energy values are presentedin Fig. 3,which gives us an intuitive impression of howthe global energy cycle works. It is also a useful diagnosis tool to analyze the source of the bias betweendifferent model forecasts. However,globally averagedvalues can barely depict the contributions and interrelations of special energy terms. More needs to bedone to reveal detailed features. We further separatethe framework of the energy cycle into three majorprocesses: planetary-scale,barotropic, and baroclinicatmospheric processes.

With regard to planetary-scale processes,largescale systems such as the Hadley cell provide a conversion from zonal APE(AZ)to zonal KE(KZ). The AZ and KZ increase with the increasing lead time. Figure 4 shows the zonal mean temperature distribution ofNCEP FNL analysis and the bias of the GRAPES forecast relative to FNL data at different lead times. Asexpected,the maximum overestimation is located atlow levels near the equator and at high levels near thepoles, and the overestimation becomes stronger withincreasing lead time. This indicates that the strongwarm bias in the low latitudes increases the meridional temperature gradient,which leads to strongerAZ. Concerning the CZ term,which represents theconversion between AZ and KZ,this reflects the zonalfeatures of the vertical wind and temperature. Whenwarm air rises and cold air sinks,CZ > 0 and showsHadley cell features. In contrast,when CZ < 0,itshows the features of the F errel cell. In Fig. 3,itpresents positive values of CZ,so it reflects a Hadleycell feature in planetary-scale processes.

Fig. 4.(a)Zonal averaged temperature distribution ofFNL and (b)-(e)biases of GRAPES relative to FNL withdifferent lead times(1-7 days,i.e.,D+1 to D+7).
4.3 Barotropic conversion

In this section,the barotropic conversion and KEare diagnosed. As discussed in Section 4.1,zonal KE(KZ)is the sum of the stationary and transient eddyKE,while KSE is about 1/3 of KTE and there is almost no net global conversion between the two eddyterms. The zonal distribution of KTE(Fig. 5)showsthat the maxima in the Southern Hemisphere are displaced northward at the location of the zonal mean jet(50° S) and the maxima in the Northern Hemisphere are displaced southward in the opposite latitudes.With increasing lead time,the strong western flow decreases in the upper troposphere(near 300 hPa) and stratosphere(near the top of the model),which leadsto a decreasing of the global averaged energy value.

Fig. 5. Transient eddy kinetic energy(KTE)in July(Jm-2 Pa-1).(a)FNL data, and (b)24-,(c)72-,(d)120-, and (e)168-h GRAPES forecast

The stationary eddy KE(KSE)displays a verydifferent pattern to the transient one(Fig. 6). Thecomparatively weak maxima are presented at the locations of 30° S,15° N, and 45° N,separately, and are associated with the zonal mean jets in both hemispheres.Another maximum appears in high latitudes of theSouthern Hemisphere,which is related to the polarjet. With increasing leading time,the four weakermaxima decrease significantly . A b and of high energyvalues presents in the Southern Hemisphere over 100hPa due to the presence of a large zonal wind jet atthe upper 30-hPa level,which causes a strengtheningof KSE.

Fig. 6. As in Fig. 5,but for the stationary eddy kineticenergy(KSE)in July(J m-2 Pa-1).

As mentioned before,the nonlinear conversion between KSE and KTE is directed from KSE to KTE, and it is di±cult to determine the symbol of the globalaveraged value because it is approximately zero. However,the zonal mean distribution of transient eddymomentum against or along the direction of the stationary eddy momentum gradient can be explained.The zonal mean distribution of the nonlinear conversion CKTE shows a pair of strong maxima in Fig. 7.Comparing the location with respect to the zonal mean contribution of KSE and KTE,we find that the maximum of the nonlinear conversion is displaced near thelocation of the maximum KTE and minimum KSE.This means that the strong nonlinear conversion canbe considered as a physical mechanism forcing the atmosphere to a more uniform state. Figure 7 showsthat as the lead time increases,the maximum nonlinear conversion value becomes weaker,which indicatesa weakening of the local contribution.

Fig. 7. Distributions of the conversion term CKTE(fromKTE to KSE; 10-6 W m-2 Pa-1)in July .(a)FNL data, and (b)24-,(c)72-,(d)120-, and (e)168-h GRAPES forecast.

CKTE is a very important nonlinear conversionterm and its positive or negative value indicates thedirection of transfer between transient waves and stationary waves. Moreover,the strength of KSE canbe used as a basis to determine the jet intensitychanges. When CKTE is positive,heat transport istransferred from transient waves to stationary waves,which strengths KSE. Conversely,if CKTE is negative,heat transport is directed into transient waves,resulting in a weakening of KSE. The result obtainedby Ulbrich and Speth(1991)showed that a strengthening of KSE corresponded to local jet maxima whilea weakening prevailed over the jet entrance regions.

Figure 7 shows the conversion term CKTE fromFNL analysis and GRAPES forecast,while the CKTEin the Southern Hemisphere is depicted in Fig. 8.It is seen that in the FNL analysis,positive values are mainly found downstream of the jet maximaover Southwest Pacific,while negative values are distributed in the jet entrance regions over Southeast Atlantic where wind velocity is relatively weak. The distribution of positive and negative local values and jetregions verifies Ulbrich's conclusion. Compared withthe FNL analysis,the strength of the local jet in theGRAPES forecast becomes gradually weaker with increased lead time,while the corresponding CKTE decreases significantly,together leading to the dissipation of KSE. Until 7 days,the positive values over thelocal jet maxima show a clear decreasing trend,whilethe corresponding jet is significantly weaker than inthe FNL analysis. It can be concluded that CKTE canbe used to determine stationary wave changes, and actas an indicator of the jet intensity features.

Fig. 8. Wind velocity(m s-1)at 250 hPa in July 2011 in the Southern Hemisphere. Shaded areas depict the localcontributions to CKTE greater than 50×10-6 W m-2 Pa-1(dark) and lower than -50×10-6 W m-2 Pa-1(light).(a)FNL data, and (b)24-,(c)72-,(d)120-, and (e)168-h GRAPES forecast.
4.4 Baroclinic conversion

For the baroclinic conversion process,the globalaveraged values reported in Fig. 3 indicate how thisprocess is working. With increased lead time,the conversion from zonal APE to stationary eddy APE remains constant. As a result of the meridional temperature gradient increasing,meridional transport ofsensible heat enhances,which causes an increase inthe conversion CA T,transferring energy from zonal totransient eddy APE.

In order to compare details of the process associated with baroclinic conversion,the zonal contributions of ASE and A TE are plotted in Fig. 9. LargerASE values appear in both the Southern and Northern Hemispheres. In the Northern Hemisphere,thelargest ASE is found below 850 hPa between 20° and 60° N, and the second largest ASE is seen between 400 and 200 hPa around 30° N. However,in the SouthernHemisphere,the largest ASE occurs between 850 and 700 hPa and further south of 60° S,with the maximum value greater than 30 J m-2 Pa-1 . In contrastto ASE,the zonal mean distribution of A TE has a similar structure to KTE(Fig. 5). The maximum value oftransient eddy potential energy A TE is only about halfthat of ASE. With increased lead time,the maximumvalue of ASE increases and A TE decreases slightly .

Fig. 9.(a1-e1)Stationary eddy available potential energy(ASE) and (a2-e2)transient eddy available energy(A TE)(Jm-2 Pa-1)in July .(a1-a2)FNL data, and (b1-b2)24-,(c1-c2)72-,(d1-d2)120-, and (e1-e2)168-h forecast.

In terms of the zonal mean distribution of ASE,Fig. 10 shows that the maxima of ASE are associated with the linear conversion term CAS. The zonalcontribution of stationary conversion is negative over200-400 hPa at 30° N,corresponding to similar conversion rates of ASE maximizing at a similar location.The same coincidence can be seen in high latitudesof the Southern Hemisphere. The zonal mean contribution to the conversion from zonal to transient eddyAPE,i.e.,CA T,is determined by the meridional temperature gradient. Comparing CA T(Fig. 10)withA TE(Fig. 9)reveals that a coincidence in the maximum energy value with conversion terms is apparent. The conversion value increases over low levels inthe Southern Hemisphere with increasing lead time.

Fig. 10. As in Fig. 9,but for the conversion terms CAS(a1-e1) and CAT(a2-e2)(10-6 W m-2 Pa-1)in July .

This is determined by the decreasing of vertical stability and ,simultaneously,the decreasing of transientsensible heat transport. The coincidence in the distribution of CAS is found to be very similar to thatobserved for the transient term with respect to midtropospheric values. This indicates that the baroclinic process associated with the stationary wave is comparable to that associated with the transient wave.The nonlinear conversion CA TE is directed fromASE to A TE. Local zonal mean values of this nonlinear conversion are depicted in Fig. 11. The maximumcontribution to the global averaged energy is located at lower levels over Antarctica,where the maximumvalue of ASE presents. It is considered that this kindof energy conversion does not originate from the zonalreservoir of AZ,but from the stationary eddy APE'snonlinear interactions. The maximum ASE above thetroposphere at 30° N is not associated with the strongnonlinear conversions. The negative values of CA TEis seen to intensify over Antarctica with increased lead time. The nonlinear conversion is thought asthe horizontal heat transport by transient waves(Lau,1982) and a negative value means that the heat transport is directly from warm to cold regions.

Fig. 11. As in Fig. 7,but for CATE(A TE to ASE; 10-6 W m-2 Pa-1)in July .

As the maximum zonal mean CA TE appears at700 hPa in the Southern Hemisphere,we choose toanalyze the nonlinear conversion CA TE at 700-hPa inthe Southern Hemisphere(Fig. 12). With regard tothe FNL analysis,some negative and positive valuesof CA TE are located around Antarctica,coincidingwith regions of relatively warm and cold air. We superimpose temperature on CA TE, and see that thedistribution coincides with the horizontal heat transport by the transient waves. When heat is transportedagainst the local temperature gradient by transientwaves,meaning that heat transport is directed intothe warm region,the CA TE value is positive. In contrast,a negative value indicates that the heat transport is directed into the cold region. Compared withFNL data,the GRAPES forecast data show a largertemperature gradient and increasing negative values.

Fig. 12. Temperature(K)at 700 hPa in July 2011 in the Southern Hemisphere. Shaded areas depict local contributionsto CATE greater than 50×10-6 W m-2 Pa-1(dark) and lower than -50×10-6 W m-2 Pa-1(light).(a)FNL data, and (b)24-,(c)72-,(d)120-, and (e)168-h forecast.
4.5 Comparison with NCEP_GFS

According to the aforementioned analysis of theatmospheric energy cycle,the main characteristics ofthe energy cycle is now used to aid in traditional verification of model performance. Real forecast datawith the same resolution as that of FNL data fromthe NCEP Global Forecast Systems(NCEP_GFS)areused to compare the features of the energy cycle withthe GRAPES model. The same 31 days of analysis arecarried out and monthly averages are considered.

Firstly,the anomaly correlation coe±cient(ACC)is calculated for geopotential height at 500 hPa.We use wavelet analysis and our verification procedure include a separation of the waves with differentzonal wave numbers. The long waves of the planetary scale(zonal wavenumbers 0-3),synoptic scalewaves(zonal wavenumbers 4-9), and small-scale waves(zonal wavenumbers 10-20)are distinguished separately . We assume that fast moving waves are synopticor small scale, and slowly moving ones are predominantly planetary scale(Kung,1988).

In Fig. 13,the separation into the differentwavenumber groups is shown in order to compare theperformance of NCEP forecast and GRAPES forecast.With respect to NCEP forecast results,the ACC ofGRAPES falls behind with different lead times. Thebias at 168 h is approximately 0.03 and all verification indices are significant at the 95% confidence level.The planetary-scale contribution is roughly similar tothe aggregate performance. However,the synopticscale and shorter scale represent some differences: forthe synoptic scale(wavenumbers 4-9),the confidenceinterv al becomes larger at 168 h,meaning that thest and ard deviation of ACC bias also becomes larger.Therefore,the bias can barely satisfy the 95% confi-dence level. For the shorter scale(wavenumbers 10-20),the bias of model performance becomes more statistically insignificant after 48 h. We conclude that significant bias is reflected on the large and meso scales, and is roughly equal on the smaller scale.

Fig. 13. Monthly mean of 500-hPa geopotential height ACC for GRAPES and NCEP_GFS with different lead timesof 1-7 days.(a)Total statistical score,(b)planetary scale(wavenumbers 0-3),(c)synoptic scale(wavenumbers 4-9), and (d)short scale(wavenumbers 10-20). Note: "w. r. t." means "with regard to."

Figure 14 shows the energy values for the globalintegrals of NCEP_GFS with different lead times. Incontrast to the GRAPES model,it is generally accepted that most energy values calculated by baroclinic and barotropic processes are roughly similar in July . The primary difference lies in the conversionof zonal APE to zonal KE,which is a result of theplanetary-scale processes. AZ of NCEP_GFS is largerthan in GRAPES,which means that NCEP_GFS hasa steeper meridional temperature gradient between thehigh and low latitudes. The conversion term CZ ofNCEP_GFS is smaller than in GRAPES,which ismainly due to the simulated weak vertical wind. Dueto the hydrostatic assumption,NCEP_GFS simulatesweaker vertical air motion than GRAPES,leading tothe nonlinear conversion CZ becoming smaller. Allof these features will seriously affect the Hadley cellsimulation. KZ of GRAPES is larger than that ofNCEP_GFS,mainly because of the zonal mean windamplitude being too large. It should be noted at thispoint that the difference in model performance between GRAPES and NCEP_GFS is mainly reflectedin the large-scale process, and such a conclusion is consistent with the results obtained via traditional verifi-cation in Fig. 13. F urthermore,detailed characteristics should be investigated and compared with a fullanalysis of unique energy cycle processes.

Fig. 14. The global atmospheric energy cycle in the Mixed Space-Time Domain for NCEP_GFS in July 2011. Variousenergy components(in boxes)are in J m-2,while conversions between the components are in W m-2 . Numbers at thetop indicate values based on NCEP FNL data, and 24,72,120, and 168 h are the different lead times from 1 to 7 days.The dashed box indicates the large difference of NCEP_GFS with the GRAPES model.
5. Summary

An investigation on the atmospheric energy cyclewas carried out by using GRAPES forecast data,witha focus on the role of model performance at differentlead times. Three main atmospheric-scale processeswere diagnosed separately and the characteristics ofstationary and transient eddy energy terms and theirconversions were calculated and presented. The results show that:

(1)The GRAPES model has the capability to reproduce the main characteristics of the global energycycle as compared with NCEP FNL analysis data.

(2)ASE and A TE have approximately the samevalues and the nonlinear conversion is directed fromthe stationary to the transient.

(3)Barotropic conversions(CKS and CKT)aredirected from eddy kinetic energy to zonal kinetic energy, and the kinetic energy of stationary eddy is about1/3 of that of the transient eddy .

(4)With increasing forecast lead time,AZ becomes larger and the zonal conversion CZ(from AZto KZ)in GRAPES is around 1.5 times larger than inthe NCEP analysis.

(5)In contrast with traditional verification,theenergy cycle diagnosis can help to derive statisticalscores and identify the source of model differences.

This study on the diagnosis of the energy cycleis at a preliminary stage in terms of operational application. There are some areas of work that need tobe improved and some problems that should be noted.For example,only short-term integrations of forecastdata were collected for analysis in order to acquirestable performances of energy values. Low-resolution and long-term integrations should be run for "seasonalforecasts." Moreover,we have recognized that diagnosis of the energy cycle can be achieved with a similarconclusion to traditional verification methods,but howto combine traditional verification methods with thisenergy cycle diagnosis for model ev aluation remains tobe examined. These problems should be discussed infuture investigations.

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