ADVANC]<~S IN ATMOSPHERIC SCIENCF.:S, VOL. 20, NO. 1,2003, PP. 17- 27

Systematic Errors of Zonal-Mean Flow in Dynamical

Monthly Prediction and Its Improvement

CHEN Bomin*i,2 (ll*fi3 l'C) , ,JI Liren1 (rc.:1r...A.), YANG Peicai\ (f~J:i1' ;1-), and ZHANG Daomin1 (*J!tR)

1 I,ASC, InstitulR. of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029

2 Shanghai Typhoon Institute, Shanghai 200030

(Received April I, 2002; revised September 20, 2002)

ABSTRACT

An analysis of a large number of cases of 500 hPa height monthly prediction shows that systematic errors exist in the zonal mean components which account for a large portion of the total forecast errors, and such errors are commonly seen in other prediction models. To overcome the difficulties of the numerical model, the authors attempt a "hybrid" approach to improving the dynamical extended-range (monthly) prediction. The monthly pentad-mean nonlinear dynamical regional prediction model of the zonal-mean gf'opotential height (wave number 0) based on a large amount of data is conBtituted by employing the reconstruction of phase-space theory and the spatio-temporal ~eries predictive method. The dynamical prerliction of the numerical model is then combined with that of the nonlinear model, Le., the pentad­mean "onal-mean height produced by the nonlinear model is tran~formed to its counterpart in the numerical model by nudging during the time integration. The foreca;;t experiment remIts show that the above hybrid approach not only reduces the systematic error in zonal mean height by the numerical model, but also makes an improvement in the non-axisymmetric components due to the wave-How interaction.

Key words: dynamical extended-range prediction, zonal-mean component, nonlinear regional predictioll, nudging

17

1, Introduction

In recent years, dynamical prediction of the monthly mean has been gradually paid more and Inore attention because of its increasing requirements and the concern over the problems related to short-term climate prcdiction from society and the scientific com­munity. As Miyakoda (1993) mentioned, monthly pre­diction should be the chief goal of exploration in t.he field of climate prediction.

fail to positively contribute to the monthly-average pattern.

Some achievements have been made in extendcd­range (or monthly) predictability and prediction tech­niques in the la.st twenty years. However, limited by a myriad of difficulties, monthly forecast skill remains relativcly low, all the while below the useful level the monthly anomaly-correlation coefficient (ACC) of 500 hPa height forecast is not less than 0.5. f\lrthcr im­provement!; in the skill of monthly prediction have been limited /linee the t990s. A prominent featurc in prediction is that the skill after the second 10-day period is low, and therefore thc estimation of the monthly-avcrage is made only by the forecast of the first lO-day period because thooe after the 10th day

.E-mail: chenbm@263.net

011 a(;(;ount of zonal-mean flow as well as the extra­long wave (as wave 0- 3 in the spectral model) being the main contributor!; to the monthly-average pattern, attention should be paid to these to cnhance the fore­cast skill (Chou, 1986; Wang, 1996). In fact, the above l:OlIlponents have been, in recent years, found to be a significant source of forecast error of the nu­merical models, although they have longer predictable tirne.~ theoretically. In particular, the zonal-mean com­ponent (the 7.onal wave 0) account\! for a large por­tion of the total monthly IlIeall errors which exists in common in different numerical models (Saha, 1992; Baumhefncr,1996; Zhang, et aL, 1997; Gong, 1999; Chen, 2000; Li, 2000). While the majority of these works are empirical, they indicate the importance of the zonal-mean for forecasts.

Owing to the complex nonlinear feature of the at­mospheric system, and ill order to make the best use of a large number of historical data, we will try the nonlinear dynamical regional prediction method (the

IS ADVANCES IN ATM08PHEIUC SCIENCES VOL.2U

nonlinear spatitrtemporal series prediction method) along with phase-space Teconlitrllction theory (Packarcl et 11.1.. 1980; Taken , 1981; Essex et aI., 1987; Kep­penn~ and Nicolis, 1989; Abarbanel. 1993; Yang et a!.. 2000; Chen, 2(00) to predict the dynamica\ly­siguifkant zonal component. At first, the systematic. forecast error of the IIurnericaJ model related to the zonal mean error could be eliminated by means of the Iloulinear Illethod . Then the nonlinear forecast of the :lOOnal mean and the prediction of the numer­ical model will be combined to eorreet the counter­part in t.he numerical model (a process generally called nUdging"). We hope that the wave components (non­axi:;.ymmetric components) will be altered in virtue of a wave-flow nonlinear interaction , thus improving the monthly mean pattern produced by the numerical model as a whole. III summary, the spatio-temporal se­ries analytic ano predictive method hlls the following advantages: (a.) it is of a dynamical nature, i.e., the predictive equation thus established still approaches the original dynamical system, (b) the nonlinear char­acteri~tics of the system are preserved, i.e., the feed­back of the physics in the system is implicitly incll1de.d to an extent, and (c) the best use of historical data can be realized, which has proven to be important and effective in prediction of short-range climate (Yang, 1996; Gong and Chou, 1999; Cao et aI., 20(0)-

In this paper, the numerical predictioIl rnodellll,ed is the global spectral model based on the ECMWF model and devdoped further by the Institute of Atmospheric Physics/Chinese Academy of Sciences (lA P /CAS) (hereafter T42L9) in which rather sophis­ticated physical processes are included (Zhang et al., 1995). The data lIsed consist of the NCBP/NCAR re­analysis data of the pentad-mean goopotential height from 1960 to 1996.

The paper is organized as follows. After the intro­duction, section 2 introduces 1\ brief analytic result of the zonal-mean flow in T42L9 model. The nonliuear regional prediction model of the pentad zonal-me<U1 heLght. is built up in sectiou 3, and the correction to T12L9 with the above nonlinear method after and dur­ing int(!gration is made in section 4. The last section provides the conclusion and discussion.

2. The monthly mean forecast errors of the nu­merical model

Figure 1 indicates the 500 hPa forecast error dis­tribution of the monthly-mean height and its zonal component by the T42L9 moclel (average of ,16 caseQ from 1995 - 1996, with ECMWF data as initial value and verification fields). We call sec that the height over the' mid latitudes of the Northern and Southern Hemispheres !l;iven by the T42L9 model is consider­ably nn'lerforecasted, with the lIIaximwn error of - 90

JON

EO

JOS

60S

a) H(T42M)-H(OBV)

b) H(T42M)-H(OBV) OVe(ogeo olong lotitude

60N

JON

£Q

J05

605

-81) 20 "<J

Fig. 1. Systematic errors of liDO hPa height (a) and its ><cnal component (b) foreCWlted by T42L9 trlodel (the averages of 36 cases from 1995 -1996, with the initial field of ~:CMWF data)

gpm. Clearly, such systematic forecast errors of height are, by and large, caused by those of the zonal com­ponent. Our analyses show further that at 500 hPa, the spectral coefficient related to the zonal height contributes the lIIost to the total forecast error of the monthly mean patteru, acculllulating up to a1>ollt 40.1%.

It should be mentioned that the forecast system­atic error of the T42L9 model does not disappear sub­stantially with different initial data used (see section 3) , and moreover its analogue has been found in sorue other numerical prediction models (Baumhcfner, 1996; Chen, 2000i Gong, 1999; Li, 2000; Zhang et aI. , 1997) . That is to say, such syst.cmatic error seems common.

The zonal error of the T42L9 model tends to smooth down the meridional gradient of the height, causing a reduction of the averaged geostrophic C:Uf­

rent over the mid latiturtes of both hemispheres. with magnitudes of 10 m 5- 1 and -20 III ~ - 1 at 500 hPa respectively over the two regions, and mrrespond­ingly with the meridional grooient variability of ±2 x 10 - 5 S - 1, which is enough to conSiderably impac:t the

NO.1 ()HI:;N KOMIN, .11 LIREN. YANG PEreAI , AND 7.HANG DAOMIN 19

evaluation of synoptic-scale systems and dynamical processes and characteristics.

3. The nonlinear regional forecast of pentad­mean zonal height

3.1 The nonlinear regional forer.ast of pentad­mean zonal height

[n pha~e-spac.c reconstruction theory, a nonlinear dynamical system may be represented by means of the temporal series of one of its variables. When Lhe spa­tial dimension m and the time-delay parameter Tare reasouably introduced , the related time-delay ordinate is properly built up and consequently the embedding space if; reconstructed, the attractor of the original dynamical system lllay be reestahlished, on condition thi1.t t.he rt"lation m > d is satisfied (the parameter Tn

is generally called the embedding dimension and d the attractor dimension of the system). An important ap­plica.tion of the above reconstruction theory is to con­stitute a nonlinear predictivc model. However, since the lengLh of the climatic observed series is limited and doC's not usually meet the theoretical requirement, it is hardly ahl(' to provide a good description for the state sel of the ::.ystem (mma.Hy referred as the ergodicity prohlem) (Yang, 1996). To alleviate the deficiency of the single-variabfe series, we apply multi -variable se­ries (or t.he spati(}-temporal series analytic and predic­llve met.hod by which the observed series from various spatial positio'ns are combined) to reconstruct the dy­namical system and to carry out the nonlinear regional predictio1J (Yang, 1995; Yilong ct aI., 2000). In this pa­per, such nonlinear prediction is made through incor­poratioll of the zonal mean series on different positiollt; (i.e., Gi\uss-Iatitudes of the T42L9 model). Certainly, such incorpOT(l.tion is based on the premi:;e that the se­ries composed of different positions are all controlled by one dynamical system.

lip to now, a commonly-accepted technique does not exiot for determining the scope of a domain and associa.ted spatial point:; that helong to the same dy­naUlic system. In this paper, by using the above­mentioned pentad zonal-mean height historical series, calculating the minimum completely-embedding di­mension of the series at all Gauss-latitudes of the T12L9 lIIodel, ariel comparing the uniformity of their wavelet transformation (Bian, 1999; Chen, 2000) , we partit.ion the nonlinear preeliction region into three parts: 200-70oN, 200S- 20oN and 200- 70 0 S,

The: basis of the prediction is to find how thc hig.. torical st.ates similar to the current state evolve, i.e., to detcrmiJle the neighhorhood close to the I'urrent state (a point in phase spae:e) and then to make best use of the information of the adjacent points inside the llf~ighborhood to predic:t the coming 8tate (trajectory or po.<;it.ion in phase space) of the current state. It

should be emphasized that the adjacent points could be dlUsen from series at different latitudes.

We take {ll.hj(t j )} as the pentad-mean spati(}­temporal series of the zonal mean height departure at Gauss-latitudes over the domains where j = 1,2, .. . ,.J (J is equal to 61, the number of meridional points of T42L9), and i = 1,2, ... , N (N is the length of the se­ries). Assuming tha.t the dynamics of t.he system have been reinstated ill an embedding phase space wiLh di­mension m (here the atmosphere is approximately re­garded as a dynamical system) , we can obtain its :;tate trajectory in the following,

Hj(t; ) = {ll.hiti-(m-I)T ), ... ,ll.hj(ti -T ),ll.hiti)}' (1)

We further take Ilj(lN) = {ll.hj(tN - (m _l) r ), "" ll.h.](tN _T),ll.hj(tN)} and Hj (tNld respectively as its current state (or initial state) and corning st.at.e k pentads later, in which ll.hj( t,y) is component 171

of ll.H.i(tN), also the initial value of the zollal mean height departure (t.he l!L5t pentad value of a month in the paper) and ll.hj(tJ\'+k) as the coming valne of ll.hj(tN) (here k is the step number of prediction and k = 1, 2,., .,6, implying the longest leading time of 6 pentads for the monthly prediction), Hence the pre­diction model to be constructed is a.~ follows,

(2)

where Fk.) representoR t.h(' projection relation of the two statcf'.,

III practice, only ll.hj(tNH,), the component 7n of Hj (fN+k), should be predicted, so Equation (2) is re­placed by

- ,(1") ~ ll.hj(tN+k) = 1-1;,j (HJ{tN) , (3)

where F~:;) is the component 171 of Fk,j and i8 t.he key of l'reriictlon.

The adjacent point set inside the neighuorhood {Hj ,/(tN),I= I,2 , .. . , q ncar the current state Hi(tN )

is determined and then the information (or evolution) of all the adjacent points is used for the construction of the proje('.tion Fk']). Such a method to construct

F~'J) is also called local approximation (Yang, 1996). 13eing different from single variable prediction, here the adjacent points can be from series of different .Uauss­latit.udes, By expanding ~quation (3), the Ilonlinear predicting models of ll.hj(lN+k) with zero order, and the first-order projection relations are obtained as:

1 m

ll.h j( tN +k) = L' L ll.hj.!( tN+kl, (4) 1= 1

m

~hJ(tN-tk) = ao + Lap ll.h,1(tN- (P - l)T)' (.5) p",l

The value of the coefficients ao and a'J in the first-order relation (5) is obtained frolll the following equation

20 ADVANCES IN ATMOSPH~;HIC SCIENCES VOL. 20

which describes the evolution of the adjacent points of the current state.

m

l:lh) ,l(tNtk) = aO + r Upl:lhj,I(tN-(P-l)T) , (6) p= l

whew l:lhj ,l(tN _(p_l)T) (p = 1,2, ... ,m) denotes the cumpunent of the ad.jacent state points to the CUTTent state point and l:lh) ,I(tNtk} , its components of the !-\tate k-pentads later, where l = 1, 2, . .. , L , and L is the nnmber (or size) of the adjacent points, and L'the number of the pointtl densely distributed inside L.

Here the higher order (say the second order) pre-

dieting models are Hut given for reason that their fure­cast skills arc even lower than that of the zero and the first -order relation.

The twelve months of 1995 are used as the training cases b'y which the above nonlinear prediction models are adjusted, and all of the 36-year data closely pre­ceding each tuning case (month) used as the sample dataset for selecting the adjacent points of the current state. Finally, the optimal value of parameters in the nonlinear model 011 four levels and the formula of pre­diction (extrapolation) are determined as a result of a great deal of training (Table 1).

Table 1. The parameters of the pentad zonal-mean height departure nonlinear prediction model at 500 hPa, 700 hl'a, 300 hPa, aud 200 hPa. over t.he domain (here the direct predictiol\ manner means directly constituting the projection relationship between the current. ~tate and coming state)

LeV.,! Domain m T Projection relation PTedir.tion manne:r Adjacent point 5i7 . ., (L, U)

SOo hPa 200- 70oN 6 2, :i zur<HJrner

:WoS- 20oN 5 3 first-order 700 hPa

20°5- 70° 5 6 3 zero-order

20o-700N 6 4 zero-order

300 hP" 200S 200N 5 4 first-or~er

20oS- 70oN 6 4 zero-order

20o- 70oN I) 4 ?ero-order

200 hP" 20°8 200N 5 4 first-order

20° - 70°5 6 4 zero-order

3.2 The comparison of forecast skill of the pen­tad zonal·mean height by nonlinear predic­tion method with those by persistent predic­tion and by climatic prediction

The predicting experiments for each mouth of 1996 (12 cases) are performed by using the nonlinear mod­els. Table 2-3 demonstrates the skill of the three kinds of prediction at 500 hPa.

Firstly, we can sec that the pentad wnal-mean height ACC of nonlinear method is higher than those of persistent prediction (here the persistent prediction Illeans that the zonal mean height departure of ini­tial pentad is lIsed as the forecasts of the coming 6 pentoos) over the three regions. In oodition, over the southern hemisphere the ACC skill by the persistent prediction is slightly higher than that by the nonlinear prediction on the first twu pentads, which is probably attributed to the persistency of the motion there and should be analyzed from more case forecasts.

ThE' RMSEs of the nonlinear prediction are consid­erably smaller than those of both of the persisteut pre­diction and the climatic prediction (here the climatic prediction means that all of the zonal-mean heights on the coming pentad arc the corresponding climatic V'dl­ues) over the high and mid latitude of the northern and

direct /, = 100, L' = fiO

dirL'Ct L ~ lOn

direct L = 100, L' - 50

direct. L = 120. L' -c 60

direct L = 80

direct L = 120, L' - 60

direct L ~ 140. J,' = 70

direct L = lDO

direct L ~ ].10, II = 70

southern hemisphere. That is to Hay, the nonlinear pre­diction mudel presents better skill, in terms of RMSE, than the persistent prediction and climatic prediction as a whole. Nevertheless the RMSE differences of the nonlinear forecast with the persistent fore<',asts are in­creased with the prediction time (steps) anti thooe with the climatic forecasts are rcla.tively large at the first two steps and then tend to approach each other with tite prediction time. As for the tropic, due to the fact that the large-scale flow is relaUvely stable, few diffN­ences of the RMSEs of three kinds of prediction exist.

Synthesizing all of the above forecast skill and tak­ing account of that the climatic prediction c,an not supply the pentadly depature of the zonal-mean height snggests that the nonlinear forecast is better thl'lIl both of the persistent prediction and the climatic predic­tion.

3.3 The comparison of the forecasts of the pen­tad zonal-mean height by the nonlinear method with those by the T42L9 model

Figure 2 is a comparison of the forecast error dis­tribution of the above 12-case-average monthly-mean zonal height of 500 hPa hy the nonlinear model and by the T42L9 modeL We can see that the zonal mean

NO. I CIIEN BOMIN, JI L1REN, YANG PEICAI, AND ZHANG DAOMIN 21

height of the T42L9 model is lInder-pff~dicted over a majority of the domains except in the north polar re­gion where the reduction in ronal height reaches a magnitude of - 40 to - 80 gpm, whereas the nonlin­ear model is very close to reality, with error totally le~s than ± to gpm over the mid latitudes and tropics. The [ot\~casts at other levels are mustly analugous to the 500 hPa ones and hence, are not shown.

4. Combination of dynamic prediction of the T42L9 model with the nonlinear regional forecast of the pentad-mean zonal height

4.1 Nonlinear correction to the 500 hPa total height predicted by the T42L9 model

To predict the ~ollal height hy the nonlinear method is to improve the forecast of the IIWIlerical model. Hence we replace the 500 hPa :7.0nal height produced by the T42L9 model with the correspond­ing nonlinear results (hereafter post-correction). As a result, the systematical forecasting error of the T42L9 model is significantly reduced. After post­correct iOIl, the 12-ca.~e average 500 hPa monthly anomaly-correlation coefficient (ACC) of the total height field by the T42L9 model is increased iIi com­parison with that before correction (Table 4). The

changes of the ACCs are from 0.306 to 0.312 over the high and mid latitudes of the Northern Hemisphere, from 0.304 to 0.429 over the high and mid latitude re­gions of the Southern Hemisphere , from 0.739 to 0.746 over the tropics, and from 0.360 to D.400 (a relative change of 11%) over the globe (Table 4) . The corre­sponding root-mean-square error (RMSE) is distinctly decreased (Table 1), with a relative change of 30.35%, 26.6%, 82.6% and :l9.4% over the respective four ar­eas. In addition, the useful predictability (days) with the post-correction is prolonged by 1.4, 2.0, and 1.8 days respectively over the high and mid latitudes of the Northern Hemisphere, over the high and mid lati­tudes of the Southern Hemisphere, and over the globe (not shown). Here the useful predictability (days) is referred to as the day number X with ACe of the height averaged for day-l to day-X not less than 0.5.

4.2 Nonlinear nudging for the T42L9 model (correction during integration)

We expect further that the non-axisymmetric com­ponents (wave components) of the height field could be influenced positively with the improvements of the predicted zonal-mean componentH. Hence the nonlin­ear pentad-mean zonal heights are transformed step by step into the corresponding variables of the T42L9

Table 2. The anomaly-correlation coefficient (ACC) of thc pentad zonal-mean height ovcr the domain of the persistent and Ilonlinet'r forecB.'lts (12-= average of 1996)

Step of prediction (pentad) I 2 :3 4 fi 6

Northern Hemisphere. Persistent forecast 0.644 0.361 0.091 0.102 - 0.071 0.269

(200 - 70"N) Nonlinear forecast 0.652 0.354 0.102 11.052 0.062 0.456

Southern Hemisphere Persistent forecast 0.747 1l.549 0.431 0.:\:18 0 .158 - 0.207

(200 -700 S) Nonlinear for"cu.st 0.719 0.539 OAIl4 0.414 0.2()9 -0.045

Tropics Persistent forecast O.51l0 0.000 - O.mH 0.087 -O.O:lO -0.072

(20"S- 20°)\;) Nonlinear forecast 0.608 0.132 0.101 0.05 0.022 0.109

Table 3. The root-mea.n-sqllare error (RMSE, units: gpm) of the pcntasJ 'ZOnal-mean height nvlc" the domain by the pcrsistent, dimatic , and nonlinear forecasts (12-ca.~e average of 1996)

Step of prediction (pentad) 2 3 4 5 6

'lol'thern Hemisphere Per8i~\cllt forecflSt 24.6 a2.7 36.7 :n.9 39.1 29.2

(20° 70°1';) Climatic forecast 30.4 30.3 27.1l 29.2 25.a 29.1

Nonlinear forecast 23.6 28.2 26.7 29.1 25.5 28_0

Southern Hemisphere Persistent forecast 22.3 29.5 32.5 31.6 39.4 46.8

(20 0 - 700 S) Climatic forecast 32.0 al.2 30.2 29.2 29.1! 29.4

Nonlinear forecast 2:1.1 26.8 26.9 26.9 30.0 ~1).8

Tropics Persistent forecast 6.8 9.4 9.2 8.9 9.3 9.4

(20C 8 20c N) Climatic forecast 6.9 5.7 6.2 05.8 6.4 6.2 Nonlinear forecast 6.2 6.4 6.9 6.4 6.3 6.9

22 ADVANCES IN ATMOSPHERIC SCIENCES VOL. 20

0) b)

... teo<

JON ... [0 [0

J05 ,.. 105 ...

to -10 ..

Fig. 2. The 500 hPa forcca.~ted zonal-mean height minus the actual field, (a) of 'l'42L9 model, (b) of t.he nonlinear model (12-case average of 1996 from , Chen et al. (2003)) .

Table 4. The 12-case-avcrage ACC and RMSE of the monl.hly-mean 500 hPa height of 1996 predicted by the T42L9 model llnd with the post-correction of t.he nOnlillt-'ar method

Forecast Rkill 20° 700 N 20° - 70"8 20o-70oN The Globe

T12L9 COR' T42L9

Ace 0.306 0.312 0.304

RMSE (gpm) 71.2 52. a 73.2

'COR denotes po~t-correction

model that are the spectrum coefficients of the temper­ature (hydrostatically-extracted) (Zhang et aI., 1995) , and then the correction during integration (nudging) is made to the counterpart of the T42L9 model. The proces~ of nudging is as follows.

(a) The pentad zonal heights at all 12 initial-vallie­input isobar levels from 50 hPa to 1000 hPa except 200, 300, 500, and 700 hPa are derived from nonlinear forecasb of the four levels by means of a good correlation between neighbor­ing levels.

(b) The above pentad zona.l heights at t.he 12 iRD­bar levels are transformed to the spectrum coef­ficients of the temperature at each integration step of the T42L9 model, and the nudging is then made.

(c) The pentad zonal components of the monthly height at isobar levels outputted by the T42L9 model are replaced by the corresponding non­linear results once more, 011 account of the va.­rkty of error accumulat ion.

The three cases of 1996 (February, June, and Octo­bcr, representing winter, summer, and the transitional season of the year, respectively) are chosen for nudging experimonts.

COR T42L9 COR T4ZL9 con 0.429 0.739 0.746 0.360 0.400

51.0 68.5 11.9 71.7 43.4

After nudging, the monthly 500-hPa height ACCs of all three cases hy the T42L9 model over the South­ern and Northern Hemispheres get largC'f (Figs. 3 5), except for case 2 over the Southern Hemisphere, the average being 0.357 with a change rate of 28%. The useful predictability (X) is also prolonged by 23 days (Table 5). At the same time, the corresponding RM· SEs are obviollsly reduced, with a change of 44 .3% compared to the re.sults without any correction and of 4.7% to the results with the post-correction. All this implies that the nudging process doe.-; affect and improve the wavc components as well.

Concretely, the wave 4- 9 components of the height are given more reasonably. Almost all the monthly ACCs of these components of the three cases are en­hanced to a great extent (Figs. 3- 5). Their values of X over the Southern Hemisphere, the Northern Hemi­sphere and the globe are cnlarged with factors of 1.0, 2.7, and 1.3, respectively. In correspondence, the RM­SEs of the components after nudging arc consistently reduced, the rates of the reduction being 19.8%, 16.4%, and 17.5% over the above thrce regions.

The impact of the nudging process 0/1 wave 1-3 varies wit-h different ca,o;es and region:;. By and large, the RMSs with nudging are less than those without nudging, their relative change being about 7.5%. Hut the corresponding ACCs get smaller than the JaHer

NO. I CHEN HOM IN. JI LlREN, YANG T'EICAI, AND ZHANG DAOMIN

a) Northern Hemi sphere

Might Waye 4-9 .. .. •• .. ... •• OJ

al .. , . , • -0.' ., '"

-'l ",J '. .. ,

" ,. .. .. It " .. .. JI

b) Southern Hemisphere

... height

... . , u

... •• 0..\ , Q.l .. OJ

., .. ... , " .. " 51 .. " .. .. ...... It " It .. ..

c) Tropics

Might .ove 1-3 wave 4-9 0.' .. ...

OJ .. u

0.> ~--- - - -- ---- .. --- ------- - .. --- -- ....... ---- -

de •• .. ... OJ OJ

oJ .. .. .. , .. .,

It " .. .. 1t 1t .. .. ,. • " .. It .. .. d) Globe

0" ., .... , II " .. ~-y--~~~---:--~ .. ---1 .. ~~-.---:It--~--~ .. ~~ .. ~~ ..

Fig. 3. ACe of day I-X average 500 hPa hcight /;IS well lI8 its wavc I 3 and wave 4··9 components of February 1996 over the North Hemisphere (a), the South Hemisphere (b), the tropics (e) Ilnd the glob" (d). Dotted . dot-dashed and solid lines respectively dCl\(\te the results of T42L9 model, post-correctioll and nndging, respectively.

23

24 ADVANCES IN ATMOSPHEl-UC SCIENCES VOL. 20

a) Northern Hemisphere

OJ ruoi9hl ... WQ'If'II t ... J

.. .... T42 model ... ._. carrected ., - nudging

OJ

• A ... ... .. ------

•• •• OJ ,~ .. ' OJ

u u .. '.1 .' ~I

" " .. ,. I. Il ,. .. ., • I, " .. .. " b) Southern Hemisphere

o • tloi9h1 . ~ .. , u .. •.. •• OJ OJ .., OJ .... . f.! U

1.1 ., '"

" " lei ,. .. " u ,. " .. • I, " "' " ..

c) Tropjcs

hoight

•.. ... .. .. ... ---~---~--- ... -- ~ --------- .. - - -~- -~ ~ -- ~

I.' ~. .. OJ U OJ

... U OJ

" .' ., lei .. .. " " .. ,.

" • " " .. 1O

d) Globe

u hoight IIIIQve 1-J W'OV,," 4-9

...

.. , u .. .. ,- u - - ~ -- ~- ~ - - ...

-.... ' •• u OJ

OJ U OJ .. ,

U ILl

'.1 .' -4.,

" .. .. .. .. " 10 " ,,'" " " '" .. " Fig.4. As in Fig. 3 hut for June 1996.

NO . I

Q.T

OJ

OJ ..

CHEN BOMJN, .JJ LII{EN , YANG PEIC AI , AND ZHANC DAOMIN

0) Northern Hemi sphere

heiQht

.. .. 142 model

._. co«ec ied

" - "l.Idgi"9 -, -- - - - ~-..,,,:<.-

~\ . ' ~' .

"-: :

b) Southern Hemi sphere

~.

OJ

., ~ .

If .. " IS JO 0

c) Tropics

~.i9ht ..

" "

" " " IS

wave 1-J .. ""

..

~- ------ ----- U --- - ------- . ~ ------- ----

D.' 0,4 ... D.J D.J OJ

OJ OJ

'.1 .. "

d) Globe

u - - - --U

OJ D.2

~,

OJ D.2

•• ~, .. , to " " " .. .. .. " IS

-., .. " .. IS

Fig. 5. As ill Fig. 3 but for Octuber 1996.

25

JIl

..

26 ADVANCES IN ATMOSPHERIC SClENCES VOL. 20

Table 5. The \IReful predicto.bilily (days) of the f,IlO hl'a average height forecast (the day nUl1lbnr X with ACC of height averaged for day 1 to day X larger than 0.5)

HE!ight Wave 1-;; Wav" 4 ·9 Domain

T42L9 COR !\Judging T42L9 Nudging Ti21.9 Nudging

SOllt

Nort

jwru HcmiBphp.re

herB HcmiRphel'f!

The Globe

17.7

In.1l lIi.:J

18.0 18.0

16.0 18.7

18.:1 18.6

(Figs. 3 5), ana naturally. the corresponding value of X is !-Ihortcned (Table 5) . In a word, the efrect of nudg­ing on the wave 4 ··9 COlllponent.s reJllaill~ inconclusive, find lIlore CI\SCS anu furt.her analysis is needeJ.

5. Conclusion and remark The paper puts forward a.u approach to applying

the nonlinear spatio-temporal serie~ based on phHSC­space reconstruction theory for the reduei,ion of sys­tematic furecast error of the ;wnal component. in nu­merical models. The forecast experiments uemon­strate that. the pentad 7.Onal height given by the nOll­linear dynamical regional model includes more u~efu\ information than that given by the numerical model itself. The combination of the two prediction ap­proaches not only reduces the above syHt.ematical fure­cast errur, but also modifies the forecasts of parts of the wave cOIllponents. This implies that the practical predictability of the synoptic wave can indeed be ex­tended if the zonal mean {low (here the zonal height) is amcnded, which can, in turn, make an improvement in the height of the monthly mean field. Such a hybrid approach can partly reuuee the deficiency of pre\llii/ing dynamical cxtenJed-range (monthly) prediction and be used to supplement it.

Acknowledgments. The study WIIS financed by the Natiollal Key Project for Devp.\opment of Science and 'l~ch­

nology (96-908-02), by the National Natural Science Foull­dation of China under Grant No. 4017:;013, and parl.ly by the Project. of the Chinese Academy of Scieuce;; (ZKCX2-SW-21O). The allthors arc grateful to Profs. Chou Jifan and Wu Guoxiong for their invaluable suggestions.

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