Distinguishing Between the SST-forced Variability
and Internal Variability in Mid-Latitudes:
Analysis of Observations and GCM Simulations
David M. Straus and J. Shukla
Center for Ocean-Land-Atmosphere Studies
4041 Powder Mill Rd., Suite 302
Calverton, MD 20705 USA
phone: (301) 595-7000
April 1999
Abstract
It is shown that the dominant structure of the seasonal mean mid-latitude circulation (500 hPa height) pattern over the Pacific - North America region forced by tropical SST-related diabatic heating is distinctly different from the seasonal mean internal variability pattern that occurs in the absence of ENSO-related SST anomalies. The separation of these two patterns is accomplished by utilizing ensemble general circulation model (GCM) integrations in conjunction with reanalyses.
Ensemble simulations made with the GCM of the Center for Ocean-Land-Atmosphere Studies (COLA) are compared to the reanalyses of the National Centers for Environmental Prediction (NCEP) for the 16 winters 1981/82 - 1996/97. The GCM ensemble for each winter consists of nine integrations initialized from analyses, and utilizing the observed time varying sea-surface temperature (SST). A signal to noise ratio is defined and found to exceed 3.0 (4.0) in the eastern North Pacific (over Mexico).
A number of techniques are used to calculate the SST / heating forced patterns and the internal variability patterns. The SST-forced mid-latitude circulation pattern is calculated in seven ways, namely (1) as the leading empirical orthogonal function (EOF) of the ensemble mean GCM height field for the 16 winters; (2) as the leading mode of a singular value decomposition (SVD) analysis of height with tropical diabatic heating from the GCM, (3) as the leading EOF (as above) for NCEP reanalyses for the same 16 winters; (4) as the leading SVD mode (as above) for the NCEP reanalyses for the same 16 winters; (5) as the leading EOF of height from reanalyses for the 10 winters having the five strongest warm and five strongest cold tropical SST anomalies in the last 39 years; (6) as the leading SVD mode (as above) from reanalyses for these same 10 strong SST winters; and (7) as a regression of GCM simulated height on a tropical SST time series obtained from the first EOF mode of reanalysis tropical diabatic heating. It is found that the results of all of these techniques agree extremely well with each other, and that the leading modes in the EOF (SVD) analyses explain large amounts of variance (covariance), about 50% (90%). We draw two conclusions: first, that the GCM ensemble means simulate the observed anomalies with high accuracy; and second, that the observed and simulated anomalies were indeed forced by tropical diabatic heating.
The internal variability pattern was calculated in six different ways: (1) as the leading EOF of height of the deviations of each seasonal mean from the corresponding ensemble mean for that winter, (2) as the leading height EOF from a 26-year GCM integration forced by climatological, annually varying SST, and (3) as the leading height EOF from reanalyses for 29 winters not associated with strong warm and cold tropical SST, (4) - (6), as above but for a teleconnectivity analysis for each of the three data sets. The patterns derived from these analyses have a common structure. It is found that it is this internal variability pattern, and not the SST-forced pattern described above, that closely resembles the "PNA" pattern of Wallace and Gutzler (1981). The SST-forced pattern is characterized by strong northward wave action flux across the subtropics in the central Pacific, as well as strong northeastward flux across the northeastern Pacific into Mexico, both of which are not associated with the internal variability pattern.
1. Introduction
The paradigm of mid-latitude response to tropical variations of sea surface temperature (SST) is a confident one from the point of view of seasonal predictability, as the time scale of SST variation is so long compared to that of the atmosphere. This ideal is best realized in the case of the strong winter mid-latitude response in the Pacific / North American region to tropical Pacific SST variations associated with the El-Niño Southern Oscillation (ENSO) phenomenon (Bjerknes, 1966, 1969; Horel and Wallace, 1981; Hoskins and Karoly, 1981; Simmons, 1982: Shukla, 1984). While both the nature of the tropical forcing and the dynamics of the remote response have been studied extensively, there is still a fundamental disagreement regarding the relationship of the remote response to the "internal" variability which occurs independently of the tropical SST forcing. This internal variability in the region of interest is dominated by the Pacific North-America ("PNA") pattern, defined in terms of monthly mean teleconnection patterns (Wallace and Gutzler, 1981) or in terms of leading rotated principal component analysis (Barnston and Livezey, 1987). The "PNA" pattern, clearly shown in Fig. 17c of the former paper and Figs. 3d and 3e of the latter, is obtained from consideration of all winter months in the record regardless of the state of the tropical Pacific SST. It is similar in some ways to the tropically forced ENSO response, as estimated (for example) in Zhang et al., 1996 (hereafter Z). However, the subtle structural differences between these two patterns (as emphasized by Z) is indicative of a different origin. In their coupled analysis of Pacific SST (tropical and mid-latitude) with mid-latitude height, Z show that by removing the influence of ENSO SST via linear regression, the remaining variability is dominated by the "PNA" pattern (compare their Figs. 5 and 6). The strong relationship of the "PNA" pattern to North Pacific extratropical SST anomalies, and the evidence that the latter represents the oceanic response to internal atmospheric variability, are reviewed in detail in Z.
However, another point of view interprets the ENSO mid-latitude response pattern as a natural mode of the atmosphere (usually taken to be represented by the "PNA" pattern) which has been excited by the tropical forcing, much as beating a drum excites its "natural" normal modes. What really distinguishes ENSO and non-ENSO winters in this view is the strength and consistency (or probability) of the response, not its structure. This point of view has been recently expressed in modeling studies (Lau and Nath, 1994; Lau, 1997; Saravanan, 1998) and from a more theoretical approach (Palmer, 1993). Lau and Nath (1994) present the first coupled mode of the observed "nearly global" SST field (40oS-60oN) with the Northern Hemisphere extratropical 500 hPa height field for 42 winters. The leading SST pattern encompasses not only tropical Pacific ENSO-like variability but also extensive variability in the North Pacific. The associated height pattern (their Fig. 3a) is similar to observational results presented by Z.
The GCM simulation results of Lau and Nath (1994) are, however, difficult to interpret. The first coupled mode of the GCM integration using global SST variations prescribed from observations ("GOGA") yields a pattern similar to the "PNA" pattern of Wallace and Gutzler (1981), while the first mode of the GCM integration using observed SST variations only in the tropics ("TOGA") yields a different pattern, one much closer to the ENSO-related pattern diagnosed in Z and in many earlier studies (e.g., Horel and Wallace, 1981; Ferranti et al., 1994; Graham et al., 1994; Kumar et al. 1996; and Chen and van Den Dool,)(1997). We note in this context that the GCM response to ENSO is very weak in the GCM used by Lau and Nath.
Saravanan (1998) shows evidence (his Fig.1) that the regional wintertime variability of simulations made with either observed tropical or observed global SST is dominated by the same pattern which is seen in a long integration made with climatological SST (i.e. SST having an annual cycle but no interannual variation). This pattern, obtained by regional empirical orthogonal function analysis in each case, seems to resemble the "PNA" pattern more than the ENSO-response pattern found in the studies quoted above(1). Since in the case of the climatological SST run, the mode in question is seen only as the second empirical orthogonal function, it is not clear what role sampling errors may play here(2).
The effects of ENSO- related SST variations on the occurrence of the "PNA" pattern was studied by Renshaw et al. (1998) who identified this pattern from a rotated EOF analysis of filtered daily data. They compute the probability distribution function (pdf) for the amplitude of this pattern for all ElNiño years, all LaNiña years, and all years pooled together. The LaNiña pdf shows a modest but significant shift compared to the all-years pdf, but the ElNiño pdf is not significantly different than the all-years pdf. This finding is not in agreement with the significant pdf shift shown in Shukla et. al. (1999, this volume), who project five-day mean data onto the leading EOF of ensemble, seasonal means.
Unless assumptions are made, it is in general not possible from observations (analyses) alone to distinguish between the variability of seasonal means due to forcing by SST anomalies and the internal variability, which is due to the sensitivity of the non-linear dynamics to initial conditions. A common assumption made in analyzing observations is that the mid-latitude height seasonal mean response to tropical Pacific SST is linear, and can be estimated by linear regression of individual grid points on a SST time series relevant for ENSO (see for example Z). Implicit in this approach is linearity in both the dependence of deep tropical diabatic anomalous heating on SST anomaly, and the linearity of the mid-latitude response to the diabatic heating. Furthermore, since only a single spatial pattern is obtained, only that part of the seasonal mean response which is symmetric in the sign of SST anomaly is captured.
In order to overcome these difficulties, we suggest an alternative approach in which one integrates a GCM a number of times utilizing the same observed SST for a given season of a specific year, starting from different initial conditions. In this ensemble approach, the signal forced by the SST anomalies for that specific season is given by the ensemble average of the individual seasonal means. This process filters out the internal variability; in the limit of very large ensemble size, this filtering is complete. The internal variability itself is estimated by the set of deviations of the individual seasonal means about the ensemble average. A collection of such ensembles for different calendar years (with distinct observed SST) allows for a general and robust estimation of SST-forced signal and of internal variability.
The validity of this method is critically dependent upon at least two characteristics of the GCM: it must respond in a realistic manner to the dominant year-to-year SST variations of interest, and the overall variability of seasonal means in the GCM must be comparable to those in analyses. The COLA GCM satisfies these criteria quite well. The overall accuracy of the GCM in responding to fixed SST anomalies was assessed in a companion paper (Shukla et al.,1999; hereafter S) by comparing the anomalies of the ensemble means with analyses. Over the Pacific / North America region, the agreement was good, and it was outstanding during strong ENSO events. Note that while the comparison of the ensemble mean to analyses is useful when the SST-forced signal is large, it ignores the role of internal fluctuations in the analyses. In terms of overall seasonal mean variability in this region, the COLA GCM is also comparable to analyses, as we will show.
The purpose of this paper is to assess the mid-latitude variability of seasonal means in the Pacific - North America (PacNA) region due to ENSO-related SST variations for 16 recent winters (1981/82 - 1996/97), and to contrast it with the chaotic internal variability, both in terms of magnitude and characteristic patterns. What is new here is the use of the full GCM ensemble to clearly separate the dominant regional pattern of internal variability due only to sensitivity to initial conditions from the response forced by ENSO-dominated SST.
The ensemble integrations of the COLA GCM (described in S) are used in conjunction with reanalyses from NCEP, hereafter referred to as "observations." Strictly speaking, the COLA integrations give an unambiguous depiction of the variability due to global SST variations vis-a-vis internal variability, as described above. We present evidence to show that, during this period the, ENSO-related SST signal is dominant in terms of its importance to mid-latitude height variations in the PacNA region. The role of the analyses is not only to assess the accuracy of the GCM ensemble mean "best" seasonal forecast (thus ignoring internal variability in the observations), but more importantly to provide an observational estimate of ENSO vs. non-ENSO-related variability. This is obtained by contrasting a longer record of 29 winters in which ENSO-related SST (tropical Pacific) anomalies were absent with a record of 11 winters in which these anomalies were strong. This segregation approach to the ENSO signal in observations avoids the assumptions inherent in the regression-based approach described above. We will show that the PacNA variability during non-ENSO winters from observations is quite similar to the internal GCM variability obtained from the deviations about the ensemble mean, thus suggesting that the importance of non-ENSO SST anomalies in forcing the PacNA region is quite small during winter. Finally, the variability of seasonal means in a 26-year continuous integration of the COLA GCM forced by climatological SST will provide another estimate of the chaotic noise.
The GCM integrations and reanalysis data sets used are described in Section 2. The overall magnitude of SST-forced and internal variability is discussed in Section 3. Section 4 describes in detail the dominant patterns associated with SST-forced variability, and Section 5 describes those associated with internal variability. Some salient points about the differences between these two patterns are highlighted in Section 6. A summary is given in Section 7, a discussion in Section 8, and conclusions in Section 9.
2. COLA GCM Integrations and Data
(a) DSP GCM Integrations
The Dynamical Seasonal Prediction (DSP) framework and the COLA GCM are described in detail in S. Briefly, the GCM is a global spectral model with horizontal rhomboidal 40 (R40) resolution, and 18 vertical levels. The prognostic variables are vorticity, divergence, virtual temperature, specific humidity, and log of surface pressure. Prognostic cloud cover is used for the radiative transfer calculations. A realistic land surface model, realistic orography and a full, updated suite of physical paramaterizations are included. In particular, the adoption of the relaxed Arakawa-Schubert convection scheme has greatly improved the simulation of the response to tropical SST variations (DeWitt, 1996; DeWitt and Schneider, 1999).
The GCM integrations consist of 16 ensembles, corresponding to the 16 winters of 1981/82 through 1996/97. The weekly observed optimal interpolation SST (OISST) for each winter was utilized. Each ensemble consists of nine integrations started from the twice-daily sequence of analyzed initial conditions from 00 UTC 13 Dec. through 00 UTC 17 Dec. Each integration was carried out until the end of March. Climatological soil moisture was used as an initial condition for the land surface model in each case, with the subsequent evolution of soil moisture being predicted. Unless otherwise stated, the definition of winter in this paper is the100-day period starting at 00 UTC 20 December.
(b) Climatological SST Integration
The integration, which used the same GCM as in the DSP integrations, was initialized from National Meteorological Center (NMC) analysis valid for 00 UTC 1 Jan, 1977, and with climatological soil moisture, and was integrated for 26 years. The prescribed SSTs used as boundary conditions possess the annual cycle seen in observations, but have no interannual variability: each month's SST was obtained as a climatological average obtained from Reynolds, 1988.
(c) NCEP Reanalyses (Observations) and GCM Data
The reanalyses of the National Centers for Environmental Research (NCEP; Kalnay, et al. 1996) were obtained from the archive at the National Center for Atmospheric Research for the 39 winters 1958/59 through 1996/97, the winter season being defined as the 100 days starting on 00 UTC 20 Dec. The 500 hPa height field was interpolated from the original 2.5o x 2.5o to a 4o x 5o (latitude x longitude) grid, and was further interpolated to an equal area grid (Molteni, et al. 1988) extending over the PacNA region [defined to be 150oE-30oW , 20oN - 80oN] for the empirical orthogonal function (EOF) and singular value decomposition (SVD) analyses in Section 4. The calculations of the stationary wave action fluxes in Section 6 used 500 hPa and 200 hPa heights and winds interpolated to a Gaussian grid consistent with a T42 truncation (128 x 64 grid points). The total diabatic heating rates used in the SVD analysis were obtained on the original reanalysis forecast model T62 horizontal Gaussian grid (192 x 94 grid points). The original 28 levels of diabatic heating were vertically integrated (not averaged) into six layers, with mid-points approximately equally spaced between 1000 hPa and 100 hPa. For SVD analysis, the six-layer heating was interpolated to a 5o x 5o grid extending over the Pacific tropical region [120oE-80oW , 20oS- 20oN]. Throughout the paper, the height, wind and heating data from the reanalyses are referred to (for convenience) as observations.
The GCM data are all originally on the R40 Gaussian grid (128 x 102 grid points) with 18 levels in the vertical. For the empirical orthogonal function analysis in Section 4, the 500 hPa height fields are interpolated first to a 4o x 5o (latitude x longitude) grid and further interpolated to an equal area grid over the PacNA region in the same manner as the observations. Similarly, the GCM winds and heights used in the stationary wave action fluxes were interpolated to a T42 grid. The diabatic heating fields are first vertically integrated over six layers (as with the observations), and then interpolated to a 5o X 5o grid extending over the Pacific tropical region.
(d) Sea Surface Temperature Data Sets
In order to have a definition of strong warm and cold ENSO events, which we collectively refer to as strong ENSO events, the NINO3 SST anomaly index(3), averaged for the three month period of Jan.-Mar., was computed from the first version (1.1) of the global sea ice and sea surface temperature (GISST) data set (Parker, et al.. 1995) for the 39 winters 1958/59 through 1996/97. The five strongest warm events (positive NINO3 anomaly) are the winters of 1965/66, 1972/73, 1982/83, 1986/87 and 1991/92. The five strongest cold events (negative NINO3 anomaly) are the winters of 1970/71, 1973/74, 1975/76, 1984/85 and 1988/89. The 29 winters which exclude these 10 winters are referred to as non-ENSO winters.
(e) Nomenclature
In order to distinguish the many data sets, both from observations and from the GCM, that are used in this paper, it is useful to define the following nomenclature for seasonal means:
OBS 16 refers to the seasonal means for the 16 winters of 1981/82 through 1996/97 from the observations (NCEP reanalyses) which correspond to the DSP period.
OBS 39 refers to the seasonal means for all 39 winters 1958/59 through 1996/97 from the observations (NCEP reanalyses).
OBS 10 refers to the seasonal means for the subset of 10 winters from OBS 39 that include all strong ENSO events (see previous subsection).
OBS 29 refers to the seasonal means for the subset of 29 winters from OBS 39 that exclude all strong ENSO events (see previous subsection). These are the non-ENSO winters.
GCM 16 refers to the ensemble average of GCM seasonal means for the16 winters of 1981/82 through 1996/97.
GCM 16x9 refers to all 144 GCM seasonal means, that is, nine seasonal means for each of the 16 winters of 1981/82 through 1996/97.
GCM D 16x9 refers to the deviations of GCM seasonal means about the ensemble average for the nine ensemble members for each of 16 winters of 1981/82 through 1996/97.
GCM Cli-SST refers to the 26 seasonal means from the GCM integration using climatological SST.
3. SST-Forced and Internal Variability: Overall Magnitude
In this section, the overall variability of seasonal means in the GCM and the corresponding observations is compared, as well as the variability that can be ascribed to ENSO SST forcing and that due to internal variability. The variance of observed seasonal means for the 16 winters 1982/83 - 1996/97 (data set OBS 16) is compared with the variance of all 144 GCM seasonal means (data set GCM 16x9) in Fig.1. It is important to note that the variances in this figure (as in all mid-latitude results presented in this paper) are calculated using an equal-area grid (as in Molteni et al. 1988), so that high latitude, high zonal wavenumber features are necessarily filtered out. In Fig.1, the strong Pacific maximum near 160oW and 45oN is well simulated, as is the broad band of high variance over Canada. The major difference occurs just over the western coast of Canada, where the model over-predicts the variance.
Estimates of the internal variability are given in Fig.2 which shows the variance of the GCM from (a) the GCM D16x9 and (b) GCM Cli-SST data sets. These purely internal variances are compared to (c) the observed non-ENSO variance obtained from the 29 winters not considered to be ENSO events (OBS 29; see Section 2 for the definition of an ENSO event). The two GCM estimates of internal variability look nearly identical. However there are differences with the observed non-ENSO variance: the distinct observed North Pacific maximum is weaker (but broader) in the GCM. This difference is due both to unrealistic behavior in the GCM and to SST variations not related to ENSO which contribute to the observed variance. We can not separate these effects.
The variances shown in Figs. 1 and 2, as well as all further results to be shown in this paper, were calculated after removing the North Atlantic / Arctic oscillation in the 500 hPa height field from both the observational and model the model data sets. This oscillation is hemispheric-wide, and is fairly similar in it manifestations in the GCM and the observations. It is also strongly related to the annular mode discussed by Thompson and Wallace (1999). Details relating to the North Atlantic / Arctic oscillation and its removal from the various data sets are given in the Appendix.
An important fundamental result is obtained by comparing the GCM SST-forced signal, defined as the variance of the GCM 16 data set, with the GCM estimates of internal variability or noise, defined as the variance of the GCM D16x9 data set. The ratio of the former to the latter variance is given in Fig.3. This "signal to noise" ratio exceeds 3.0 in the eastern Pacific, and is even larger over Mexico (> 4.0). This basic result implies that SST forcing is responsible for much of the variance that is observed in these regions.
4. SST Forced Variability: Dominant Pattern
In order to determine the dominant patterns associated with the SST forcing, we employ EOF analysis of the 500 hPa height of GCM 16 restricted to the PacNA region. Section 2 discusses the grid utilized. Since the leading hemispheric EOF has been removed (see Section 2 and the Appendix), there is no need to rotate these regional EOF modes in order to achieve stable, localized patterns. In fact, Table 1 gives the explained variance and associated uncertainty (North et al. 1982) of the first two regional EOF modes for the GCM 16 data set. It is clear that the first mode, explaining 46% of the spatially integrated variance, dominates the spectrum. The uncertainty gives an indication of the sampling error. Since this error is less than the difference in explained variance between the first two modes, the distinction between them is statistically significant.
The homogeneous correlation height pattern associated with the first mode is given in Fig.4(a). This is defined as the temporal correlation of the variation of the height field at each grid point with the variation of the time series (principal component) associated with the first mode (Bretherton et al. 1992). The pattern consists of broad centers in the mid-latitude (45oN) Pacific between 140oW and 160oW, between (and just west of) the Great Lakes and Hudson Bay, and over the Gulf of Mexico (25oN) extending across Florida eastward into the Atlantic. It strongly resembles the SST - 700 hPa height correlation presented by Horel and Wallace (1981, their Fig. 9a), and the ENSO warm event composites of Kumar et al. (1996, their fig. 5a), and Chen and van Den Dool (1997, their Fig. 3).
In order to establish a connection between major fluctuations of the GCM 16 tropical Pacific diabatic heating field and the 500 hPa height field for the PacNA region, we have also carried out an SVD analysis of these two fields(4) (see Section 2 for details of the regions and grids). The SVD technique identifies modes in a pair of fields which maximize the (squared) covariance between the fields (Bretherton et. al. 1992). We have chosen to use the three-dimensional tropical diabatic heating rather than the (more conventional) SST anomaly field in the SVD analysis for two reasons. It is, after all, the diabatic heating and the associated changes in tropical circulation that are directly responsible for the Rossby wave train response into mid-latitudes (Hoskins and Karoly, 1981; Sardeshmukh and Hoskins, 1988). The SST anomaly will only be effective if it can create a suitable diabatic heating anomaly. Diagnosing the three-dimensional structure of the diabatic heating anomaly that is associated with ENSO is the second goal in using the heating. The price that we pay for this choice is that in the case of the "observations", the diabatic heating in fact does not come from observations, but directly from the numerical forecast model.
The squared covariance explained by the first two SVD modes for the GCM 16 data is given in Table 1. Again, the first mode (explaining 88%) dominates the second (explaining 11%). The normalized explained squared covariance (which tends to be more robust statistically, see Wallace et al. 1993) is also given for the first mode in Table 1. The spatial structure of the 500 hPa height component of the first SVD is given by the heterogenous correlation, which is defined as the temporal correlation of the height field variation at each grid point with the leading SVD tropical heating time series. The heterogeneous correlation, shown in Fig. 4b, is quite similar to the pattern associated with the first EOF (Fig. 4a).
The three-dimensional GCM 16 tropical Pacific diabatic heating pattern which is associated with the first SVD mode is shown in Fig. 5, which has been scaled so that the time coefficient associated with this mode is 1.0 for the winter of 1982/83. Vertically integrated, it consists of equatorial heating centered at the dateline, with cooling in a surrounding horseshoe shaped region. The heating indicates an enhancement of precipitation in both the Pacific intertropical convergence zone (ITCZ) and the South Pacific convergence zone (SPCZ), in agreement with the ENSO-related variations of precipitation estimated from outgoing long wave radiation and from the microwave sounding unit satellite data (Yualeve and Wallace,1994; Straus and Shukla, 1997). The maximum cooling at about 150oE, 15oN lies somewhat to the east of the observed suppression of precipitation in the above studies. The vertical structure of the GCM heating, with a maximum at 500 hPa, is distinct from that shown in the GCM study of Straus and Shukla (1997), who found a maximum at 300 hPa. In that study, the GCM utilized a very different parameterization scheme for cumulus convection.
This three-dimensional structure is the same as that of the first EOF of GCM 16 tropical diabatic heating alone, also shown in Fig. 5 and scaled in the same manner as above. The first mode, which explains 42% of the total variance, dominates all other modes, the second EOF explaining only 20% of the variance.
Clearly, the dominant SVD patterns of tropical heating and mid-latitude height capture the dominant patterns present in each field separately, putting to rest any concern that the relatively short number of independent maps in the GCM 16 data set leads to severe sampling problems. That these dominant patterns are related specifically to ENSO is demonstrated in Fig. 6a, which gives the time series associated with both the first EOF and SVD modes for the GCM (solid and dashed curves). These time series are standardized to have zero mean and unit variance. Very sharp maxima of both time series occur for the winters of 1982/83, 1986/87, and 1991/92, corresponding to warm winters as defined from the GISST (see Section 2). The cold events of 1984/85 and 1988/89 lie in (separate) minima of the time series, which however also encompass the non-ENSO winters 1983/84 and 1989/90 also. After 1991/92, the fluctuations are weaker. (We defer a discussion of the differences between the GCM time series and the dotted and dash-dot curves in Fig.6a, derived from observations, until later in the paper.) The diabatic heating time series for the GCM EM EOF and SVD modes, shown in Fig. 6b, again as the solid and dashed curves. Here the warm events are marked by larger amplitudes than the cold ones, which are not well distinguished from other winters. We have chosen to utilize tropical diabatic heating as opposed to SST anomalies in the SVD analysis. However, a comparison of the results in Figs. 4, 5, and 6a and 6b with the corresponding SVD results for height and SST anomalies given in S indicate nearly identical height patterns. The maximum in the SST pattern associated with the first SVD mode in S is shifted considerably to the east compared to the corresponding diabatic heating maximum shown here. This is a reflection of the fact that it is the total SST field and not its anomaly that influences convection and diabatic heating, so that while the largest ENSO SST anomalies lie in the eastern tropical Pacific, the warmest water extends eastward only to the central Pacific (Desser and Wallace, 1990).
In order to demonstrate that the leading height pattern in the PacNA region shown in Figs. 4a and 4b is not very sensitive to the particular 16 winters chosen, we have carried out an EOF analysis of tropical Pacific diabatic heating from the longer OBS 39 (reanalysis) data set. The time coefficients of the leading EOF mode provided an independent extended time series with the last 16 winters corresponding to those of the GCM 16 data set. The temporal correlation of the GCM 16 height at each grid point with the corresponding portion of this extended time series is shown in Fig. 4c. The pattern closely resembles that shown in Figs. 4a and 4b.
We have repeated the entire sequence of GCM analyses discussed above for the observed seasonal means for both the corresponding 16 winter period (OBS 16 data set), and for the 10 winters deemed strong ENSO events in Section 2 (OBS 10 data set). The single record of 16 winters contains a number of strong ENSO events, but non-ENSO SST fluctuations are also present. By repeating the analysis using only the 10 strong events we try to gauge their effect. For the 16 winter period, the first EOF-1 explained variance of 50% (see Table 1) dominates that of the second EOF (15%), and the explained squared covariance of 88% is much larger than the 5% explained by the second mode. These statistics are quite similar to both those of the GCM 16 and the strong ENSO OBS 10 data sets.
That the actual (area-averaged) height variance explained by the first EOF mode for the GCM 16 results (3.24 x 102 m2, see Table 1) is only 64% of the height variance explained in the observations (5.03 x 102 m2) is a reflection of the greater total variance of the observed seasonal means as compared to that of the ensemble mean GCM seasonal means. The former variance contains contributions due both to internal (non SST-related) variability and to non-ENSO SST forced variability, while SST variations do not contribute to the latter.
The mid-latitude height first mode EOF homogeneous correlation patterns and first mode SVD heterogeneous correlation patterns are presented in Fig. 7 for both observed data sets, while the corresponding (vertically integrated) diabatic heating maps are given in Fig. 8. The agreement between the two (overlapping) observed data sets, and between observations and the GCM 16 (Figs. 4 and 5) is quite remarkable. A subtle shift in the positive height maximum over Canada some 5o-10o west is noted in the observations compared to the GCM ensemble mean, as is the presence of a separate maximum over the northwestern Atlantic. Not only do the height patterns for both EOF and SVD modes, and for both OBS and GCM data sets, resemble those found by Horel and Wallace (1981), Kumar et al. (1996), and Chen and van Den Dool (1997), as mentioned above, but they are also in substantial agreement with the leading canonical mode between observed tropical SST and Northern Hemisphere 700 hPa heights presented in Fig. 1(d) of Graham et al. (1994), and with the GCM response to ENSO SST forcing simulated by Ferranti et al. 1994 (their Fig. 12).
The (normalized) height time series associated with the leading EOF and SVD modes in the OBS 16 are given by the dot-dash and dotted lines in Fig. 6a, while the corresponding heating time series are given in Fig. 6b. In all cases, the three warm ENSO winters of 1982/83, 1986/87 and 1991/92 are marked by sharp maxima, but the cold events are not always marked by sharp minima, e.g. 1984/85 (1988/89) in the heating (height) time series. In addition, a large negative value of the height time series is seen in 1981/82, and to a certain extent in 1990/91, both non-ENSO winters. Differences between the observed and GCM time series in Fig. 6a are smallest during warm events, but are not small at other times (1981/82, 1989/90, 1993/94). Although this record of leading modes obtained from the observations is dominated by ENSO related variations, evidence of variability not related to ENSO is also seen.
5. Internal Variability
In this section we determine the dominant patterns associated with variability not forced by SST variations by examining deviations from the ensemble mean in the GCM experiments (GCM D16x9) and 26 years of the climatological-SST GCM run (GCM Cli-SST). In addition, the observed 29 winters not considered to be ENSO events (OBS 29) are analyzed, although this record also includes variability forced by non-ENSO related SST fluctuations. The results of a teleconnection analysis of the anomalies of 500 hPa height (as in Wallace and Gutzler, 1981) is presented for the three data sets in Fig. 9. This analysis consists of computing the correlation of a base point in the PacNA region with all other grid points in the region, and determining the most negative correlation and the remote point with which it is associated. The absolute value of this correlation is assigned to the base point, and the procedure repeated for all points in the region. The resulting teleconnectivity map indicates which points are most closely correlated (for the seasonal mean) with other grid points in the region. Local maxima(5) of this field are used to define the teleconnection patterns. For each maximum, the difference in 500 hPa height anomaly between the local maximum and the associated remote point is used as an index. The anomaly field is averaged for all times (in this case seasons) when the index is either above 1.0 standard deviation or below -1.0 standard devation. The difference between these averages defines the associated teleconnection pattern. Fig. 9 shows these patterns for the three data sets discussed above. In each case, the pair of points used to define the index on which the composite is based are indicated, as is the correlation between the points. All three (dimensional) patterns show strong minima in the North Pacific near 45o-50oN , 160oW-180oW, maxima over the North American continent at 55oN , 110oW-120oW, and a diffuse minima encompassing much of the Southeastern United States, the Gulf of Mexico and the Southwestern Atlantic. Significantly, one of the points involved in the teleconnection index lies in the subtropics near 170oW, 20oN in each case. We return to this point in the discussion.
The teleconnection patterns are compared to the corresponding composite patterns based on the first EOF for the three data sets in Fig.10. Specifically, the anomaly field of 500 hPa height was averaged for times (seasons) when the projection on the first EOF was above 1.0 standard deviation and below -1.0 standard deviation. The difference between the averages is given in Fig.10. In addition, the percentage of explained variance of the first two EOFs are given for each data set in Table 2. Even though the leading EOF explains a modest fraction of the variance (28% to 34%), it is significantly different from the second EOF for both the GCM D16x9 and OBS 29 data sets. More importantly, each EOF composite in Fig.10 strongly resembles the corresponding teleconnection pattern in Fig. 9, although the maxima over the continent and the minima over Florida tend to be stronger in Fig.10. These patterns are fairly close to the classic "PNA" pattern of Wallace and Gutzler (1981, hereafter WG), although a detailed comparison between Figs. 9 and 10 and Fig.17c of WG (based on an index consisting of four grid points) shows a 10o eastward shift of the continental maximum in our results compared to those of WG. Our internal variability patterns also resemble the EOF composite presented by Lau (1997) for his control run, in which SST varied climatologically (his Fig. 5).
6. Comparison Between SST-Forced and Internal Variability Patterns
In this section, we distill the differences between the two distinct patterns that have emerged from the analysis of this paper. The leading EOF of the GCM 16 data set over the PacNA region is shown in Fig.11a. The corresponding homogeneous correlation function appeared in Fig. 4a. Similarly, the leading EOF of the GCM D16x9 data set is given in Fig. 11b; the composite based on this EOF was shown in Fig.10a. In Fig.11, the EOF patterns have been scaled so that they can be approximately interpreted as 500 hPa height fields(6)
. The important point is that these two patterns are normalized in exactly the same manner, so that the difference shown in Fig. 11c (GCM 16 minus GCM D16x9) arises only from changes in shape and not from differences in overall magnitude. The strong minimum in the North Pacific in the "PNA" is shifted to the north and west compared to the SST-forced pattern, while the maximum over Canada in the latter is much broader and extends further eastward compared to the former. Also, the area of negative anomaly over the southeastern U.S. has a distinctly different orientation in the two patterns.
This distinction between the "PNA"-like pattern and the SST-forced pattern can also be emphasized by examining the associated stationary wave activity flux (Plumb, 1985) in each case. Figs. 12a-b, and c-d show the 200 hPa horizontal Plumb flux (vectors) superimposed on the 500 hPa vertical flux (contours) for stationary wave composites based on the first EOF of 500 hPa height for following data sets: (a) OBS 16, (b) OBS 29, (c) GCM 16, and (d) GCM D16x9. The patterns associated with response to ENSO in (a) and (c) indicate upper level poleward wave action flux across 20oN in the central Pacific, strong mid-level upward flux and upper-level poleward and eastward flux in the North Pacific, and strong upper level eastward flux across Mexico. Over the interior of the continental United States, equatorward flux is seen. In contrast, the patterns associated with internal variability (b) and (d) show no poleward flux across the subtropics, weaker mid-level upward flux in the North Pacific, and a complete absence of flux across Mexico.
7. Summary
What is new in this paper is the use of the full GCM ensemble to clearly separate the dominant regional pattern of internal variability due only to sensitivity to initial conditions from the SST-forced response. The COLA GCM has demonstrated the realism necessary to be considered a reliable tool in making this distinction. Once the North Atlantic / Arctic related variability in the observations and the GCM have been accounted for, the remaining GCM variability of seasonal means in the PacNA region (variance of GCM 16x9 integrations) compares very well with the remaining observed variability. Another significant result is that the total GCM (GCM 16x9) variance exceeds the GCM internal variance (GCM D16x9 or GCM Cli - SST), particularly in the eastern Pacific (ratio exceeds 4.0), over Mexico (ratio exceeds 5.5), and over northeastern North America (ratio exceeds 2.5).
Examination of this variability with regional EOF / SVD techniques leads to the identification of a very robust pattern associated with the response to ENSO-related diabatic heating during the 16- year period. This pattern is seen in both the ensemble mean record of GCM integrations (in which non-SST related variability has been averaged out) and in the single record from observations. It arises as the leading (and dominant) EOF pattern, the leading (and dominant) mode in SVD analysis of the regional height field with tropical Pacific diabatic heating, and from regression of the height field on a time series (OBS 39) derived from NCEP reanalysis tropical heating for a long (39-year) record. Furthermore, this ENSO pattern is the same as that which arises from consideration of 10 strong ENSO winters obtained from observations solely on the basis of tropical Pacific SST data. It also agrees well with previous studies (e.g., Horel and Wallace, 1981).
This pattern explains about 50% of the regional variance for both (ensemble-averaged) GCM and observations, and between 80% and 90% of the covariance with tropical diabatic heating. Because the observations include internal as well as SST-forced variability, the total observed regional variability is somewhat greater than in the simulated ensemble mean; hence the actual area- averaged explained variance for the ensemble-averaged GCM is only about 64% that of the observations. The area-averaged covariance of height with diabatic heating (see Table 1) in the GCM, in contrast, is 40% larger than in the observations, indicating a stronger degree of coupling between heating and response in the model.
Deviations of GCM seasonal means about the ensemble mean are used to identify internal variability due only to sensitivity to initial conditions. Again, the hemispheric North Atlantic / arctic hemispheric modes are excluded. Composites based on the value of the time series associated with the first regional EOF are compared to the results of teleconnection analysis for (a) the deviations of the nine GCM ensemble members about the ensemble mean for 16 winters (GCM D16x9), (b) the 26 winters of the climatological SST GCM integration (GCM Cli-SST), and (c) the 29 non-ENSO winters from observations. There is consistent agreement among the two techniques for all three data sets: the dominant pattern is closely related to the classical "PNA" pattern of WG. While there has been a suggestion (see Z) that this pattern is associated with extra-tropical North Pacific SST anomalies in the observations, the notion that the extra tropical SST anomalies do not cause (but are rather a response to) atmospheric variations is consistent with the occurrence of the "PNA" in the GCM D16x9 and GCM Cli-SST data sets.
The teleconnection analysis indicates that a subtropical Pacific point (20oN) is consistently one of the most highly correlated pairs of points, suggesting that diabatic heating unrelated to SST variations can excite this internal mode, as in Simmons et al. (1983) and Sardeshmukh and Hoskins (1988).
8. Discussion
The distinction between ENSO-forced and internal variability presented here is supported by the observational results of Livezey and Mo (1987). They find that the simultaneous correlations of winter tropical SST with their "PNA" pattern (see Barnston and Livezey, 1987) are not as high as the corresponding correlations with the "Tropical/Northern Hemisphere" pattern, which strongly resembles our ENSO pattern of Figs. 4, 5, 6a and b, 7, and 8. The strong correlation found by these authors between outgoing long-wave radiation at 10oN in the eastern tropical Pacific and the PNA pattern is consistent with the involvement of a subtropical point in the teleconnection analysis of the internal variability presented in Fig. 10.
The structural difference between the ENSO response and the "PNA" pattern includes an enhanced wave action flux across Mexico seen in conjunction with ENSO. Previous studies have shown that it is accompanied by increased upper level transient kinetic energy (Straus and Shukla, 1997) and related transient height variance (Trenberth and Hurrell, 1994).
The methods of analysis used in this study to relate tropical Pacific diabatic heating with mid-latitude dynamics capture only the linear part of the relationship. Some evidence of the real asymmetries between the response to warm and cold events (Hoerling et al., 1997) is seen in the disparity between the amplitudes of these events in the EOF and SVD time series of Figs. 6a and 6b. However, since the methodology tries to fit one pattern for both cold and warm responses, it does not distinguish between them adequately. The present approach was necessitated by the modest number of calendar winters (16) for which ensemble GCM integrations have been made - only two cold events and three warm events are included. Future plans for carrying out ensemble integrations for a much larger number of calendar winters will enable a better resolution of the asymmetries between warm and cold events.
While the structure of the diabatic heating fields in the dominant ensemble mean SVD patterns presented here (as well as the corresponding SST structure explored in S) makes it clear that this mode is related to ENSO forcing, the simulations were carried out with realistic SST boundary conditions globally. The role of non-ENSO SST, and in particular North Pacific SST forcing on the height variations over the PacNA region is not resolved. Many studies have addressed this question, and it is not even clear that specifying SST in the North Pacific improves model simulations (see for example Ferranti et. al. 1994; Graham et al. 1994; Zhang et al. 1996). Resolution of this issue awaits the future.
9. Conclusions
The results presented here call into question a set of fairly fundamental tenets previously held. One is that the temporal variability of the mid-latitude atmosphere is not noticeably enhanced in the presence of SST fluctuations (Lau, 1985, 1997). This assertion is contradicted by the current simulations using the COLA GCM, in which the presence of varying SST makes a large difference regionally in the mid-latitude variance of seasonal means. Another is the belief that the ENSO mid-latitude response pattern is dominated by an internal mode of the atmosphere (the PNA pattern) which would exist even in the absence of external (SST) forcing. We have demonstrated unambiguously in the context of the COLA GCM that the response forced by global SST and strongly linked to ENSO-related diabatic heating is quite distinct from the internal variability pattern that dominates regionally. The applicability of these GCM results to the real atmosphere is supported by the fact that the COLA GCM has a realistic response to ENSO both in terms of the strength and patterns of the anomalies, and also possesses realistic variability on the seasonal mean time scale. These findings are also strongly supported by consideration of the observed winters not considered to be strong ENSO events.
Acknowledgments. We would like to acknowledge many stimulating and helpful discussions with Professor J. M. Wallace and with Dr. Ben Kirtman. This work was supported by the National Science Foundation (under grant ATM 93-21354), by the National Oceanic and Atmospheric Administration (under grant NA76GP0258) and by the National Aeronautics and Space Administration (under grant NAG5-4977).
10. Appendix - The North Atlantic / Arctic Oscillation
A hemispheric EOF analysis of the seasonal mean 500 hPa height for the full Northern Hemisphere (20oN - 80oN) was carried out for the following data sets: (a) GCM 16, (b) GCM D16x9, (c) GCM Cli-SST, and (d) OBS-39. Table 4 shows the percentage variance explained for the first three modes, and the associated uncertainty (according to North et al. 1982). In the GCM D16x9 and GCM Cli-SST data sets, the separation between the first and second modes is large compared to the uncertainty; for the OBS 39 and GCM 16, the separation is not as significant.
The homogeneous correlation patterns associated with the first mode for each data set are shown in Fig.13, plotted so that each contour corresponds to a correlation of 0.20. The GCM 16 pattern (Fig.13a) is basically a hemispheric version of the SST-forced pattern described in the paper, with a westward extension over the Pacific. The leading EOF of the data sets GCM D16x9 and GCM Cli-SST, shown in Figs. 13b and 13c, are dominated by a large arctic center, with less intense features over North America, Europe, Asia and (for GCM Cli-SST) over the Pacific. All the patterns indicate a significant zonal mean see-saw between high and mid-latitudes. They resemble the first EOF of the OBS 39 data set (Fig.13d), which however has a stronger emphasis on the Atlantic region. For convenience, we refer collectively to the patterns seen in Figs.13b - 13d as the North Atlantic / Arctic pattern. Since this pattern appears in the GCM only when climatological SST is used, or when the ensemble mean is removed, we can say that this pattern is not related to SST forcing in the GCM.
Removal of this mode from all the OBS data sets considered in this paper is achieved by subtracting the EOF spatial pattern scaled by the coefficient (principal component) for the relevant year. Similarly, this mode can be removed from the GCM D16x9 and GCM Cli-SST data sets using the appropriate GCM spatial pattern and principal components in each case.
Table 1. ENSO-forced variability
| Dataset | EOF 1 % var
EOF 2 % var |
EOF 1 exp var | SVD 1 % sqcov
SVD 2 % sqcov |
SVD 1 exp cov |
| OBS 10 | 59 (26)
13 ( 6) |
671 | 91
5 |
217 |
| OBS 16 | 50 (18)
15 ( 5) |
503 | 88
5 |
134 |
| GCM EM 16 | 47 (17)
25 ( 9) |
324 | 81
11 |
188 |
OBS 10 refers to 10 strong ENSO episodes from reanalysis (see text); OBS 16 to the 16 winters 1981/82 through 1996/97 from reanalysis; GCM 16 to the ensemble mean for 16 winters 1981/98 through 1996/97. Column marked % var gives the EOF percentage of explained variance, with numbers in parentheses giving uncertainty as in North et al. (1982). Column marked exp var gives the actual explained variance averaged over PacNA area in units of m2. Column marked % sqcov gives the SVD percentage of explained squared covariance. Column marked exp cov gives the actual explained covariance averaged over PacNA area in units of W m-1 (see text for details).
Table 2. Internal variability
| Dataset | EOF 1 % var
EOF 2 % var |
EOF 1 exp var* | SVD 1 % sqcov
SVD 2 % sqcov |
SVD 1 exp cov** |
| OBS 29 | 34 ( 9)
18 ( 5) |
327 | 56
17 |
512 |
| GCM D 16 | 27 ( 3)
17 ( 2) |
159 | 41
14 |
155 |
| GCM CLI-SST | 37 ( 9)
25 ( 7) |
176 | 48
29 |
454 |
OBS 29 refers to 29 "normal" winters from reanalysis (see text); GCM D 16 to the deviations about ensemble mean for 16 winters 1981/98 through 1996/97;(see text). Column marked % var gives the EOF percentage of explained variance, with numbers in parentheses giving uncertainty as in North et al. (1982). Column marked exp var gives the actual explained variance averaged over PacNA area in units of m2 . Column marked % sqcov gives the SVD percentage of explained squared covariance. Column marked exp cov gives the actual explained covariance averaged over PacNA area in units of W m-1 (see text for details).
Table 3. SVD Calculations (Leading Modes)
| Dataset | Total SqCov | Expl. Sq Cov | Norm. Sq Cov | Norm Ex SqCov |
| OBS 10 | 2.71 x 1010 | 2.47 x 1010 | 0.57 | 0.54 |
| OBS 16 | 1.06 x 1010 | 0.94 x 1010 | 0.41 | 0.40 |
| GCM 16 | 2.28 x 1010 | 1.85 x 1010 | 0.41 | 0.37 |
OBS 10 refers to 10 strong ENSO episodes from reanalysis (see text); OBS 16 to the 16 winters 1981/82 through 1996/97 from reanalysis; GCM 16 to the ensemble mean for 16 winters 1981/98 through 1996/97. Total SqCov is the total squared covariance summed over all grid points in units of W / m. Expl. SqCov is the fraction of Total SqCov explained by the first mode. Norm. Sq Cov is the normalized squared covariance (see Wallace et al. 1993). Norm. Ex Sq Cov is the fraction of normalized squared covariance explained by the first mode (see Wallace et al. 1993).
Table 4. Hemispheric EOFs
| Mode | GCM 16 | GCM D 16x9 | GCM Cli-SSt | OBS 39 |
| 1 | 35 (12) | 28 ( 4) | 39 (11) | 26 ( 6) |
| 2 | 24 ( 8) | 14 ( 2) | 15 ( 4) | 19 ( 4) |
| 3 | 16 ( 6) | 9 ( 1) | 13 (3) | 10 ( 2) |
Percentage of explained variance for each of the first three hemispheric EOFs of 500 hPa height for the data sets listed. The numbers in parentheses indicate the uncertainty according to North et al. (1982).
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12. Figure Captions
Fig. 1. Variance of winter mean 500 hPa height in the region 150oE-30oW, 20oN-85oN. The North Atlantic / Arctic oscillation has been removed. (a) From OBS 16 (Reanalyses for 16 winters 1981/82 - 1996/97) (b) From GCM 16x9 (all GCM integrations). (c) Difference of (b) minus (a). Contour interval is 1000 m2. Dashed lines are negative in (c).
Fig. 2. Variance of winter mean 500 hPa height for: (a) GCM D16x9 (seasonal mean deviations about the ensemble mean). (b) GCM Cli-SST (26 winters from the GCM integration using climatological SST). (c) OBS 29 (reanalysesfor the 29 "non-ENSO" winters). The North Atlantic / Arctic Oscillation has been removed. Contour interval is 1000 m2.
Fig. 3. Ratio of the variance of GCM 16 (GCM seasonal ensemble means) to the variance of GCM D 16x9 (seasonal mean deviations about the ensemble mean). The North Atlantic / Arctic Oscillation has been removed.
Fig. 4. Correlations of 500 hPa height from GCM 16 (ensemble-seasonal means for 16 winters). (a) Homogeneous correlation of EOF-1. (b) Heterogeneous correlation of SVD-1 coupling the height field with tropical Pacific diabatic heating field. (c) External correlation with tropical Pacific diabatic heating time series derived from a 39-winter SVD analysis of OBS 39 (NCEP reanalyses). See text for details. All correlations have been multiplied by 10. Contour interval is 2, with the zero contour omitted.
Fig. 5. Tropical Pacific diabatic heating fields from GCM 16 (ensemble-seasonal means for 16 winters). (a) Vertically integrated diabatic heating from EOF-1. (b) Vertically integrated diabatic heating from SVD-1 of 500 hPa height coupled with heating. (c) Longitude/pressure section (averaged 10oS-10oN) of EOF-1. (d). Longitude/pressure section (averaged 10oS-10oN) from SVD-1. Contour interval is 125 Wm-2 in (a) and (b), 20 Wm-2 in (c) and (d). Fields are normalized so that the associated time EOF (or SVD) time series have a value of +1.0 for the winter of 1982/83. See text for details.
Fig. 6. (a) Time series of 500 hPa height associated with first EOF (first SVD) of GCM 16 (ensemble/seasonal means for 16 winters), given by the solid (short dashed) lines. Also shown are the time series of 500 hPa height associated with the first EOF (first SVD) of OBS16 (16 winters from reanalyses), given by the dot-dashed (dotted) lines. All time series are standardized to have 0 mean and a standard deviation of 1.0. See text for details. (b) Time series of tropical Pacific diabatic heating. Otherwise as in (a).
Fig. 7. Correlations of 500 hPa height from OBS 16 (NCEP reanalyses).(a) Homogeneous correlation of EOF-1 for 16 winters (1981/82 - 1996/97). (b) Heterogenous correlation of SVD-1 coupling the height field with tropical Pacific diabatic heating for the same 16 winters. (c) Homogeneous correlation of EOF-1 from OBS 10 10 (strong ENSO winters). (d) Homogeneous correlation of SVD-1 coupling the height field with tropical Pacific diabatic heating for the same 10 strong ENSO winters. See text for details. All correlations have been multiplied by 10. Contour interval is 2, with the zero contour omitted.
Fig. 8. Vertically integrated tropical Pacific diabatic heating fields from NCEP reanalyses. (a) From EOF-1 for 16 winters (1981/82 - 1996/97). (b) From SVD-1 of 500 hPa height coupled with heating for 16 winters. (c) From EOF-1 for 10 strong ENSO winters. (d). From SVD-1 for 10 strong ENSO winters. Contour interval is 100 W/m2 in (a) and (b). Fields are normalized so that the associated time EOF (or SVD) time series have a value of +1.0 for the winter of 1982/83. See text for details.
Fig. 9 Composites of 500 hPa height based on teleconnection analysis. In each case, the composite is the difference between the average of all seasonal means for which the teleconnection index (defined by the difference in height between the indicated points) is above 1.0 standard deviation, and the average of seasonal means for which the index is below -1.0 standard deviation. (a) From GCM D 16x9 (deviations from the ensemble means for 16 winters). (b) From GCM Cli-SST (26 winters taken from GCM climatological SST integration). (c) From OBS 29 (reanalyses for 29 non-ENSO winters). See text for details. Contour interval is 30 m.
Fig. 10. Composites of 500 hPa height based on the first EOF. In each case, the composite is the difference between the average of all seasonal means for which the principle component associated with the first EOF mode is above 1.0 standard deviation, and the average of seasonal means for which the principle component is below -1.0 standard deviation. (a) From GCM D 16x9 (deviations from the ensemble means for 16 winters). (b) From GCM Cli-SST (26 winters taken from GCM climatological SST integration). (c) From OBS 29 (29 non-ENSO winters from reanalyses). See text for details. Contour interval is 30 m.
Fig. 11. (a) EOF-1 pattern for 500 hPa height from GCM 16 (GCM ensemble means). (b) As in (a) but for GCM D16x9 (deviations of seasonal means about ensemble means). (c) Difference, (a) minus (b). Non-dimensional EOF patterns have been multiplied by 1000, so that the sum of grid point values is 1000.
Fig. 12. Stationary eddy Plumb fluxes (Plumb, 1985) obtained from composites as in Fig.11. The horizontal (vertical) flux is taken at 200 (500) hPa. (a) From seasonal mean OBS 16 (16 winters:1981/82 - 1996/97 from reanalyses).(b) From OBS-29 (reanalyses for 29 non-ENSO winters). (c) From GCM 16 (ensemble means for16 winters).(d) From GCM D 16x9 (deviations about the ensemble mean for 16 winters). See text for details. Standard arrow for 10 m2s-2 is indicated for horiztonal flux. Contour interval is 0.05 m2s-2 in (a) and (c), 0.025 m2s-2 in (b) and (d).
Fig. 13. Homogeneous correlation functions associated with first EOF for seasonal mean hemispheric 500 hPa heights (20oN - 90oN).(a) From GCM 16 (ensemble means for 16 winters) (b) From GCM D 16x9 (deviations about ensemble mean for 16 winters ). (c) From GCM Cli-SST (26 winters of GCM climatological SST integration). (d) From OBS 39 winters (39 winters from reanalyses). See text for details. All correlations have been multiplied by 10. Contour interval is 2, with the zero contour omitted.
1. Since the (unconventional) region used in the analysis of Saravanan does not extend to the east coast of North America, it is hard to make a precise comparison of this pattern with those found by other studies (e.g., Wallace and Gutzler, 1981; Horel and Wallace, 1981; Barnston and Livezey, 1987).
2. Although the difference in variance explained by the first and second empirical orthogonal functions in Saravanan (1998) is marginally significant according to the test of North, et al.(1982), no information is given about the significance of the difference between the second and third modes. Also, the constraint of orthogonality which is inherent in the analysis is especially restrictive when the spatial domain is limited.
3. The NINO3 index is defined as the average SST anomaly in the region: [30oW-90oW , 5oS - 5oN].
4. Since the North Atlantic / arctic hemispheric mode only appears in the GCM D16x9 and GCM 16x9 data sets, no correction to the GCM 16 data was undertaken.
5. These local maxima are obtained by comparing the value of each grid point with those within 1500 km of it. Only correlations with absolute value greater than 0.70 are eligible to be considered maxima.
6. In our EOF analyses, each EOF pattern is normalized so that the sum over all grid points on the equal area grid equals 1.0. Thus in Fig. 11, the sum over all grid points is exactly 1000.0.0.
