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Southern Hemisphere midlatitude atmospheric variability of the NCEP-NCAR and ECMWF reanalyses

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Southern Hemisphere midlatitude atmospheric variability of the NCEP-NCAR and ECMWF reanalyses
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  Southern Hemisphere midlatitude atmospheric variabilityof the NCEP-NCAR and ECMWF reanalyses Alessandro Dell’Aquila, 1 Paolo M. Ruti, 1 Sandro Calmanti, 1 and Valerio Lucarini 2 Received 6 April 2006; revised 5 July 2006; accepted 25 August 2006; published 25 April 2007. [ 1 ]  We compare the representation of the Southern Hemisphere midlatitude winter variability in the NCEP-NCAR and ERA40 reanalyses by using the Hayashi spectraltechnique. We find important discrepancies in the description of the atmospheric waves at different spatial and temporal scales. ERA40 is generally characterized by a larger variance, especially in the high-frequency spectral region. Compared to the NorthernHemisphere, the assimilated data are relatively scarce particularly over the oceans, andthey provide a weak constraint to the assimilation system even in the period when satellitedata are available. In the presatellite period the discrepancies between the two reanalysesare large and randomly distributed; after 1979 the discrepancies are systematic. Thisstudy suggests that, as for the winter midlatitude variability in the Southern Hemisphere,a well-defined picture to be used in the evaluation of climate model simulations is stilllacking because of the nonconsistency of the reanalyses. Citation:  Dell’Aquila, A., P. M. Ruti, S. Calmanti, and V. Lucarini (2007), Southern Hemisphere midlatitude atmospheric variabilityof the NCEP-NCAR and ECMWF reanalyses,  J. Geophys. Res. ,  112 , D08106, doi:10.1029/2006JD007376. 1. Introduction [ 2 ] In the Southern Hemisphere (SH), the absence of mountain chains that lock the phase of planetary-scalewaves implies that most part of the atmospheric variabilityis accounted for by eastward propagating wave trains at  both high and low frequencies [  James , 1994].[ 3 ] At high frequencies, (periods shorter than 10 days) themidlatitude atmospheric flow is dominated in both hemi-spheres by the growth and decay of baroclinic disturbances,which convert available potential energy into kinetic energy[  Holton , 1992]. In the SH, the baroclinic activity is stronger than in the Northern Hemisphere (NH) and peaks around50  S. Regionally, high-frequency disturbances are strongest in the southern Indian Ocean [ Trenberth , 1991;  Frederiksenand Frederiksen , 1993;  Cuff and Cai , 1995], where themeridional heat fluxes maximize.[ 4 ] At low frequencies (periods between 10 and 50 days),the eastward propagating wave trains feature characteristicspatial structure, often referred to as Pacific South American(PSA) patterns, which are characterized by ultralong spatialscales [  Robertson and Mechoso , 2003]. A standing patternassociated to the zonal wave number 3 and often related to blocking events is also observed [ Trenberth and Mo , 1985;  Raphael  , 2004].[ 5 ] Recently, a great interest has arisen regarding the skillof NCEP and ERA40 reanalyses [  Bromwich and Fogt  ,2004]. Our aim in the present paper is to analyze quantita-tively the differences in the midlatitude SH winters as portrayed by those reanalyses in their description of intra-seasonal variability at different time and spatial scales. For this purpose, we adopt the spectral analysis techniqueintroduced by  Hayashi  [1971, 1979]. This was employedin a companion study that focuses on the NH [  Dell’Aquilaet al. , 2005] (D05 henceforth), where the winter variabilitywas analyzed in terms of standing and propagating waves.Moreover, we introduce measures of the bulk spectral properties of the waves, which have proved useful for thedefinition of benchmarks for the assessment of the reliabil-ity of climate models [  Lucarini et al. , 2007].[ 6 ] The intercomparison of the description provided bythe reanalyses for the SH atmospheric variability constitutesan appealing issue for several different reasons.[ 7 ] 1. Fewer observational data are available for theassimilation system in the SH. Unlike in the NH, the scarceamount of rawinsondes data in the SH does not provide astrong constraint to the observed three-dimensional thermalstructure of the tropospheric disturbances. Instead, the most relevant data source is the remote-sensing observationalsystem, which represents a weaker constraint to the atmo-spheric vertical structure.[ 8 ] 2. The SH midlatitudes troposphere is strongly cou- pled to the ocean and to the stratosphere.[ 9 ] 3. The absence of a major topographic forcing rulesout the possibility that observed discrepancies between thereanalyses can be attributed to significant differences in thedescription of interaction between atmospheric flow andtopography.[ 10 ] All of these issues bear relevance for the initializa-tion of operational and research weather forecast models at various spatial scales. Another study that intercompares the JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 112, D08106, doi:10.1029/2006JD007376, 2007 Click Here for Full A rticle 1 Progetto Speciale Clima Globale, Ente Nazionale per le NuoveTecnologie, l’Energia e l’Ambiente, Roma, Italy. 2 Physics and Applied Statistics of Earth Fluids (PASEF), Dipartimentodi Matematica ed Informatica, Universita` di Camerino, Camerino (MC),Italy.Copyright 2007 by the American Geophysical Union.0148-0227/07/2006JD007376$09.00 D08106  1 of 11  reanalyses in the SH [  Hoskins and Hodges , 2002] employsa tracking method that provides a detailed description of thespatial distribution of the synoptic systems. Our spectralapproach, following several studies in the 1980s [  Mechosoand Hartmann , 1982;  Fraedrich and Kietzig  , 1983;  Hansenet al. , 1989], complements the work of   Hoskins and Hodges [2002] by providing a more detailed description of the wavekinematics, while the information about their geometry isessentially lost.[ 11 ] The paper is organized as follows. In section 2 wereview the main differences between the NCEP and ERA40reanalysis systems, describe the data sets used, and present the Hayashi spectral technique and the notation adopted. Insection 3 we show the results of Hayashi spectral analysisfor the two data sets and discuss their outstanding differ-ences. In section 4 we compare the spatial distribution of the variability for the two data sets before and after theintroduction of satellite observations. In section 5 wesummarize the results obtained and present our conclusionsand outlook for future studies. 2. Data and Methods 2.1. Reanalysis Data Sets [ 12 ] We use the freely available 500hPa daily geopoten-tial height fields for the SH provided by the National Center for Environmental Prediction (NCEP data set;  Kistler et al. [2001]) and by the European Center for Medium-RangeWeather Forecasts (ERA40 data set;  Simmons and Gibson [2000]) for the period from 1 September 1957 to 31 August 2002. Both reanalyses are released with spatial resolution of 2.5     2.5  , corresponding to a resulting horizontal grid of 144    73 points. We select the June–July–August (JJA) period and we average the data over the latitudinal belt 30   –75  S (similarly to what is done in D05 for the NH),where the bulk of the baroclinic and of the low-frequency planetary waves activity is observed [ Simmonds and Keay ,2000;  Trenberth , 1991].[ 13 ] The principal inhomogeneity in the assimilated datais given by the introduction of satellite observations whichhas dramatically improved the amount of available dataover the last 3 decades [ Sturaro , 2003]. The availability of satellite data may deeply affect the description of the life-cycle of baroclinic eddies and the associated heat fluxes, particularly in the SH [  Mo et al. , 1995].[ 14 ] The first source of satellite data for reanalysis is theVertical Temperature and Pressure Radiometer (VTPR),available from 1973 to 1978. However, whereas the NCEPreanalysis uses raw satellite radiances at low spatial resolu-tion to extract vertical temperature profiles, the ERA40reanalysis assimilates directly the raw radiances at fullresolution Such a discrepancy in the assimilation of satellitedata could be important in the SH, where the ground basedobserving system is coarser than in the NH. Since 1979, theTIROS Operational Vertical Sounder (TOVS) data fromsatellite are available, and they are handled in a rather different way in the two assimilation systems. ERA40system assimilates satellite radiance directly; instead, NCEPassimilates retrieved profiles of temperature and humidity.See also D05 for more details about the other source of data.[ 15 ] Moreover, in the SH the misplacing of PAOBS(Australian Surface Pressure Bogus data for the SouthernHemisphere) data in NCEP [  Kistler et al. , 2001] for the period 1979–1992 are known to produce an error in thedescription of wintertime synoptic-scale features polewardof 40  S over the oceans that is comparable to the basicuncertainty of the analyses [  Kistler et al. 2001 ;  Simmondsand Keay , 2000].[ 16 ] In order to provide a rough estimate of the effect of this bug, we also consider the NCEP-DOE AMIP (Atmo-spheric Model Intercomparison Project) II reanalysis (here-after NCEP2) that fixes this mistake and other processingerrors present in NCEP (see  Kanamitsu et al.  [2002] for adetailed description of NCEP2). NCEP2 has been releasedfor the period 1979–2002, and should be regarded as anupdated and error–fixed version of NCEP. The physical parameterisations are the same used in NCEP, with the samespatial and temporal resolution, and the satellite data aretreated in the same way. 2.2. Spectral Analysis [ 17 ] In a recent paper (D05), we have compared thewinter midlatitude variability of the 500 hPa geopotentialfield of the NH using the space-time spectral analysistechnique introduced by  Hayashi  [1971]. This techniqueallows us to discriminate the variance associated witheastward/westward propagating waves and standing waves.[ 18 ] The information may be obtained by firstly Fourier analyzing the spatial field, and then computing the time- power spectrum of each spatial Fourier component. Thedifficulty here lies in the fact that in a straightforward space-time decomposition a standing wave will give two spectral peaks corresponding to waves travelling eastward andwestward at the same speed and with the same phase. The problem can only be circumvented by making assumptionsregarding the nature of the wave. For instance, we mayrequire complete coherence between the eastward andwestward components of standing waves and attribute theincoherent part of the spectrum to bona fide travellingwaves [  Pratt  , 1976;  Fraedrich and Bottger  , 1978;  Hayashi ,1979].[ 19 ] For each winter (considered of length  t   = 90  d  ), weexpress the meridionally averaged 500 hPa geopotentialheight   Z  ( l ,  t  ) in terms of its zonal Fourier harmonics:  Z   l ; t  ð Þ¼  Z  0  t  ðÞþ X 1  j  ¼ 1 C  k   j   t  ðÞ cos  k   j  l   þ S  k   j   t  ðÞ sin  k   j  l    :  ð 1 Þ where the zonal wave number is  k    j   = 2  j  p  .The power spectrum  H   E/W  ( k    j  ,  w  m ) for the eastward andwestward propagating waves at zonal wave number   k    j   andangular frequency  w  m  = 2 p  m /  t  , is given by:  H   E   k   j  ; w  m   ¼ 14  P  w  m  C  k   j    þ  P  w  m  S  k   j     þ 12 Q w  m  C  k   j   ; S  k   j     ð 2a Þ  H  W   k   j  ; w  m   ¼ 14  P  w  m  C  k   j    þ  P  w  m  S  k   j      12 Q w  m  C  k   j   ; S  k   j     ð 2b Þ where  P  w  m and  Q w  m are the power and the quadrature spec-tra, respectively, of zonal Fourier harmonic of the 500 hPageopotential height   Z  ( l ,  t  ) [  Hayashi , 1971]. D08106  DELL’AQUILA ET AL.: S.H. VARIABILITY IN NCEP AND ERA402 of 11 D08106  The total variance spectrum  H  T  ( k    j  ,  w  m ) is given by the sumof the eastward and westward propagating components:  H  T   k   j  ; w  m   ¼ 12  P  w  m  C  k   j    þ  P  w  m  S  k   j      ð 3 Þ while the propagating variance  H   P  ( k  ,  w  ) is given by theabsolutevalueofthedifferencebetweenthecomponents(2a)and (2b):  H   P   k   j  ; w  m   ¼  Q k   j  ; w  m   :  ð 4 Þ So, the standing variance spectrum  H  S  ( k  ,  w  ) is given by:  H  S   k   j  ; w  m   ¼  H  T   k   j  ; w  m     Q k   j  ; w  m   :  ð 5 Þ We emphasize that, to simplify the notation, in the precedingdefinitions an index corresponding to the winter analyzed isnot included. It is customary to represent Hayashi’s spectra by plotting the quantities  j   m   H  T  ( k    j  ,  w  m ),  j   m   H  S  ( k    j  ,  w  m ),  j   m   H   E  ( k    j  , w  m ),and  j   m   H  W  ( k    j  , w  m ),inorderforequalgeometricalareas in the log-log plot to represent equal variance. With thisdefinition, the Hayashi spectra presented in this paper areexpressed in unit of   m 2 , as done by  Blackmon  [1976], Speranza  [1983], and  Lucarini et al.  [2007], and can becomparedtothosegiveninD05afteramultiplicationby a =1/ (8  86,400 s).[ 20 ] In order to characterize the different portion of thespectrum, and their temporal evolution, we introduce thefollowing integral quantities:  E  nt   W ð Þ¼ X m ¼ m 2 ;  j  ¼  j  2 m ¼ m 1 ;  j  ¼  j  1  H  nt   k   j  ; w  m   ;  with  t   ¼ T  ; S  ;  E  ; W  ;  ð 6 Þ where  n  indicates the winter analyzed; and the integrationextremes,  m 1,2  and  j  1,2 , determine the spectral region of interest   W  = [ w  m 1 ,  w  m 2 ]    [ k    j  1 ,  k    j  2 ]. The quantity  E  t n ( W ) inequation (6) represents the portion of variance of thespectrum associated to a given subdomain  W and to a givenwinter   n  and is expressed in unit of   m 2 . The averaging process defined in equation (6) overcomes the well-knowninstability of the Fourier analysis in describing small-scalespectral features. Having normalised the  H  t n ( W ) by the factor  a , the quantities  E  t n ( W ) correspond to a more consistent definition of the spectrum than those presented in D05. 3. Hayashi Spectra 3.1. Climatological Average [ 21 ] The Hayashi spectra express the power density of thewave field with respect to frequency and zonal wavenumber, and define the decomposition between the standingand propagating components. Figure 1a shows    H  T  ( k    j  ,  w  m ),the total power spectrum; Figure 1b shows    H  S  ( k    j  ,  w  m ), the power spectrum related to standing waves; Figure 1c shows   H   E  ( k    j  ,  w  m ), the power spectrum related to eastward propa-gating waves; and Figure 1d shows    H  W  ( k    j  ,  w  m ), the spec-trum of the westward propagating waves. The overbarsindicate averaging over the 45 JJA periods.[ 22 ] The lobes of westward propagating components(Figure 1d) are less intense and bounded than in the NHon the planetary scale (zonal wave numbers 2–3 with periods longer than 20 days), as expected in a region wherethe effects of large-scale topography are small. The standingvariance (Figure 1b) is comparable with that in the NH,and has a sharper peak for k = 3. This lobe of standingvariance has been usually associated with blocking epi-sodes [ Trenberth and Mo , 1985;  Raphael  , 2004]. How-ever, in the SH the total variability (Figure 1a) is mainlyexplained by the eastward propagating component, whichislargerthanthecorrespondingoneintheNH(seeFigure1cinD05) and also extends to the planetary scales (k = 3–4 and periodaround15daysormore),asillustratedinFigure1c.Noteinparticular that theamplitude ofthevariabilityassociated tok=4istwiceaslargeasintheNH.Theeastwardpropagatingcomponent with zonal wave number 4 could be related to thePacific/South America pattern PSA-1 and PSA-2 [  Lau et al. ,1994].Recently,thenatureofthesepatternsoflow-frequencyvariability has been debated in literature [  Mo and Higgins ,1998;  Robertson and Mechoso , 2003]. Also in the spectralregion of the baroclinic activity (zonal wave numbers greater than 5 and periods less than 10 days) we observe a larger variance than in the NH. These results are in good agreement with previous analyses that used shorter data sets [  Fraedrichand Kietzig  , 1983;  Hansen et al. ,1989].[ 23 ] Following D05 we show in Figure 2 the differences between ERA40 and NCEP in the climatological spectra of the eastward propagating component. It is apparent that ERA40 has a dramatically larger variance than NCEP. Thediscrepancy corresponds to more than 25% of the signal.The other components (standing and westward propagating)do not show any substantial differences in the climatolog-ical averages and are not reported here. The discrepanciesare most evident for zonal wave number k = 5 with a periodof about 7 days, which is in the domain of baroclinicdisturbances. The difference in the climatologies of thewinter atmospheric variability in the SH is about 1 order of magnitude larger than in the NH. The agreement does not improve significantly when comparing ERA40 with NCEP2for the period 1979–2002 (not shown). 3.2. Interannual Variability [ 24 ] Following D05, we inspect the temporal behaviour of the previously observed discrepancies by using theintegral quantities  E  t n ( W ), which represent the portion of variance associated to the spectral subdomains  W  for eachwinter ( n)  and for each component ( t   =  T, S, E, W  ). The first two columns of Table 1 present     E  t  ( W ) for the two reanal-yses, computed over the whole wave number and frequencydomain for the period 1957–2002. As in D05, we estimatethe standard error of the time-averaged value with theinterannual variability of the signal  D  E  t  ( W )  =  s   E  j   W ð Þ  ffiffiffi   N  p   , where  N   is the number of winters considered in the averaging process. This is consistent with the hypothesis that theconsidered winters are assumed to be statistically indepen-dent from each other. Most of the variance is due to theeastward propagating component, as can be inferred alsofrom Figure 1. The time average of the ERA40 signal isconsiderably larger and the discrepancies between theaveraged values for NCEP and ERA40 largely exceed theerror bar related to the standard error   D  Ej  ( W ) , especially for the eastward propagating waves. D08106  DELL’AQUILA ET AL.: S.H. VARIABILITY IN NCEP AND ERA403 of 11 D08106  [ 25 ] These features are confirmed by inspection of thetime series of   E  t n ( W ) for the two reanalyses (Figure 3). The biases for the eastward propagating and, less markedly, for the standing waves are apparent. In particular, Figure 3reveals significant discrepancies in the 1958–1972 period.There is a sudden jump in 1973, when the propagatingeastward variance in ERA40 abruptly decreases with respect to NCEP. Another abrupt jump can be observed in 1978.Afterward, ERA40 exhibits a systematic larger variance.Moreover, the ERA40 data feature a robust positive trend inthe variability of the signal, especially for the eastward propagating waves, while in NCEP this property is lessevident. However, recent studies stress the dubious correct-ness in the detection of ultra-long-term trends starting fromreanalysis data [  Bengtsson et al. , 2004].[ 26 ] The differences in  E  t n ( W ) for the total, standing andeastward/westward propagating components (Figure 4) dis- play more clearly the positive bias of ERA40. However, inthe presatellite period the signal-to-noise ratio of the dis-crepancies between the two reanalyses is small. Moreover,there is no clear shift in the standing and westward prop-agating components. This result does not change if weconsider a different latitudinal belt (30–50S or 50–70S,not shown).[ 27 ] The abrupt change in the description of the variabil-ity corresponds to the onset of the assimilation of the VTPR data, as largely discussed in D05. This result suggests that the different use of satellite data (NCEP system assimilatesretrieved profiles of temperature and humidity, ERA40assimilates directly satellite radiance) corresponds to a verydifferent capability in describing atmospheric variability, principally the travelling disturbances. This effect is partic-ularly evident in the Southern Hemisphere where a weaker constraint on the models is provided by the sparsely avail-able land-based vertical soundings.[ 28 ] In order to compare homogeneously derived data weskip the VTPR period 1973–1978. We show in Table 1averaged values    E  t  ( W ) for the presatellite and postsatellite periods, 1958–1972 and 1979–2002, respectively. Mainlyin the second period, mean values for ERA40 are clearlylarger than for NCEP with differences significantly greater than the corresponding standard error   D  E    j  ( W ). The abrupt change in    E  T,E  ( W ) between the first and the second period in Figure 1.  Climatological average over 45 winters of Hayashi spectra for 500 hPa geopotential height (relative to the latitudinal belt 30–75  S) from NCEP data: (a) total variance    H  T  ( k    j  ,  w  m ); (b) standingcomponent     H  S  ( k    j  ,  w  m ); (c) eastward propagating component     H   E  ( k  ,  w  ); and (d) westward propagatingcomponent     H  W  ( k    j  ,  w  m ). Hayashi spectra have been obtained multiplying the spectra by  j   m . The unitsare m 2 . D08106  DELL’AQUILA ET AL.: S.H. VARIABILITY IN NCEP AND ERA404 of 11 D08106  ERA40 is evident, as already pointed out by  Bengtsson et al.  [2004], although they analysed different climatologicalvariables. In NCEP the time averaged values seem to bemore temporally homogeneous. Nevertheless, a positivetrend in the variance can be recognized by comparing thetime averages for two periods, as also noted by  Renwick and  Revell   [1999].[ 29 ] In order to analyse the effects on the description of the midlatitude variability of the bugs found in the srcinalversion of the NCEP data, we also compare the differencesin  E  t n ( W ) for NCEP and NCEP2 for the period 1979–2002.The discrepancies are more pronounced in the first years,when NCEP data are affected by the well-known PAOBS bug, and all the components  E  t n ( W ) feature similar biases, asshown in Figure 5. However, the discrepancies between thetwo releases of the NCEP-NCAR reanalysis cannot affect our comparison since they are 1 order of magnitude smaller than those between NCEP and ERA40.[ 30 ] Following D05, Table 2 presents the clear-cut divi-sion of different spectral subdomains W into four categories,on the basis of the results reported in Figures 1a–1d. This partition can help identifying discrepancies in the capabilityof the two reanalyses in describing phenomena occurring ona given spatial and temporal scale. As in the NH, in theaustral winter most of the variance can be attributed tothe low-frequency–low-wave-number (LFLW) and high-frequency–high-wave-number (HFHW) waves (values not shown). However, the division is slightly different from that adopted for the NH because of the differing spectralcharacteristics of the ultralong and synoptic waves in SH.[ 31 ] In Figures 6a–6b we plot the time series of thedifference between the quantities  E  t n ( W LFLW ) and  E  t n ( W HFHW )forNCEP and ERA40 reanalyses. The qualitative propertiesshown in Figure 4 are largely confirmed. Regarding thediscrepancy for the LFLW domain (Figure 6a), the signal-to-noise ratio is small in the presatellite period when ERA40has, on average, a standing and westward propagatingcomponent of the variance smaller than NCEP. Instead, thedifferences become systematic after a sudden jump duringthe VTPR period and ERA40 has a larger variance for all thecomponents. In the HFHW spectral subdomain (Figure 6b)the discrepancies are noisy in the earlier period, but ERA40has systematically more variance than NCEP. After 1979, thesignal-to-noise ratio becomes larger and the bias is almost constant. 4. Spatial Distribution of Variability Before 1973and After 1979 [ 32 ] In Figures 7a–7d, we map the low-frequency (LF)variability of NCEP for the periods 1958–1972 (Figure 7a)and 1979–2002 (Figure 7b), and the corresponding differ-ences with the same data for the ERA40 reanalysis (Figures7c–7d, respectively). The LF atmospheric variability isobtained by discarding the frequencies  w   > 2 p  /11 day  1 (see also Table 2) in the Fourier transform of the 500hPageopotential height. The two maps of NCEP variance showthat the LF atmospheric variability has a more zonalcharacter than in the NH (D05). There are, however, twolocal maxima over the South Pacific and the south IndianOcean. In particular, in the South Pacific, the lobe associ-ated to the PSA  1/   2 pattern is clearly evident [ Trenberthand Mo , 1985;  Lau et al. , 1994;  Robertson and Mechoso ,2003]. In this region the major discrepancies between thetwo reanalyses can be observed. In particular, before 1973(Figure 7c) discrepancies in the location and intensity of  blocking episodes and PSA are evident. This suggests azonal shift between NCEP and ERA40 in the maximum of the LF variability. A similar shift, but oriented in the north-south direction, is present over the Atlantic basin. In theIndian sector, ERA40 has significantly larger LF variancecompared to NCEP. In south of Australia, the differencesare almost comparable with the signal itself. After 1979,ERA40 has systematically more variance than NCEP, espe- Table 1.  Time Mean of   E    j  ( W ) With  j   =  T, S, E, W   for the JJA Period of the Whole Record, 1957–1972 and 1979–2002 a  W  = ALL ERA 1957–2002 NCEP 1957–2002 ERA 40 1957–1972 NCEP 1957–1972 ERA 40 1979–2002 NCEP 1979–2002   E  T  ( W ) 5100 ± 100 4690 ± 70 4610 ± 90 4480 ± 90 5600 ± 100 4900 ± 100   E  S  ( W ) 1350 ± 50 1270 ± 40 1250 ± 40 1240 ± 50 1430 ± 70 1230 ± 70   E   E  ( W ) 3740 ± 70 3360 ± 60 3430 ± 80 3220 ± 70 4040 ± 90 3490 ± 80   E  W  ( W ) 1360 ± 40 1330 ± 40 1180 ± 50 1260 ± 50 1520 ± 70 1340 ± 60 a  We consider the standard error of the time-averaged value as a function of the interannual variability of the signal:  D  E    j   ( W )  = s   E  j   W ð Þ  ffiffiffi   N  p   . As in Figure 3,  W corresponds to the whole wave number and frequency domain. The units are  m 2 . Figure 2.  As in Figure 1c, but for the difference betweenERA40 and NCEP Hayashi spectra    H   E  ( k  ,  w  ) associated tothe eastward propagating component. We do not plot thezero contours. In the standing and westward propagatingcomponents there are no significant differences and theseare not reported here. D08106  DELL’AQUILA ET AL.: S.H. VARIABILITY IN NCEP AND ERA405 of 11 D08106
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