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2.2 Understanding and predicting the global impact of tropical SST variations

CDC scientists are using a combination of observational and general circulation modeling approaches to address this problem. The observational studies rely heavily on the 50-year NCEP reanalysis dataset. The GCM studies are conducted by running various versions of the NCEP and GFDL global atmospheric models with prescribed SST forcing, in some cases by coupling to a mixed layer in parts of the world ocean. We have also analyzed 10-12 member ensembles of 50-year runs made by several GCM groups (NCEP, GFDL, NCAR, ECHAM, IRI) with prescribed observed SST forcing, generally for the period 1950-1995, prescribed either globally or in the tropics.

2.2.1 Prediction skill and predictability

Outside the tropics, SST-forced signals account for a relatively small (generally less than 25%) portion of extratropical variability on seasonal to interannual scales. This fundamentally limits the average skill of a deterministic (as opposed to a probabilistic) seasonal forecast, regardless of whether it represents the mean of a large forecast ensemble or even a multi-model ensemble. The limitation arises from a generally small signal-to-noise ratio, and cannot be overcome by improving models. The noise is associated with chaotic (i.e., unpredictable) nonlinear interactions and is intrinsic to the extratropical atmosphere. Still, in extreme individual cases, the signal can exceed the noise, making relatively skillful forecasts possible.

There are two other confounding factors that make it difficult for even sophisticated GCMs to improve upon the forecast skill of simple statistical models based on linear correlations between tropical SST and extratropical circulation anomalies. The first is the approximate linearity of the remote response to ENSO. The other is the relative insensitivity of that response to details of the tropical SST forcing; it appears that knowledge of the area-averaged anomaly in Niño-3.4 alone is almost enough.

Figure 2.4 provides a good illustration of these points. It shows the correlation of observed JFM-mean 200 mb geopotential height anomalies with those predicted, over a 26-year period, using two forecasting systems of vastly different complexity. The top panel shows the skill of a 9-member ensemble-mean forecast by the NCEP atmospheric GCM forced with observed concurrent SST anomalies in the tropical Pacific between 20N and 20S. Consistent with many studies, the correlation of the observed and predicted height anomalies is high in the tropics, and appreciable over North America and the northeast and southeast Pacific oceans. This is encouraging, although it should be noted that the GCM forecasts are not true forecasts. Still, they give an idea of the potential predictability of seasonal anomalies around the globe if the tropical Pacific SSTs were to be predicted accurately. The surprise in Fig. 2.4 is the lower panel. It shows the skill of the simplest conceivable linear regression forecasts for the same cases as in the upper panel, using the regression coefficients of observed JFM 200 mb height anomalies against the area-averaged observed JFM SST anomaly in Niño-3.4. The forecasts themselves are made using the observed Niño-3.4 SST anomaly in the previous 3-month period (OND) as the predictor. These simple forecasts are clearly comparable in skill to the GCM forecasts. They also represent legitimate 1-season `coupled model' forecasts, in that they incorporate a trivial persistence forecast of the Niño-3.4 SST anomalies from OND to JFM.

Local anomaly correlations of predicted and observed JFM-mean 200 mb height anomalies

Fig. 2.4 Wintertime 200 mb height seasonal forecast skill of (a) the NCEP atmospheric GCM with specified observed SSTs in the tropical Pacific basin and (b) a simple linear regression model based on seasonal 200 mb height correlations with Niño 3.4 SSTs. See text for details.

The rough agreement between the two panels in Fig. 2.4 may be interpreted as reflecting either true seasonal predictability limits or the need for further GCM improvement. There is room for both interpretations, although we are more inclined toward the former. GCM error is probably not the main culprit here: several other GCMs analyzed by us yield skill patterns very similar to that in the upper panel. Also, when the NCEP GCM is asked to predict its own behavior, such as when using an 8-member ensemble-mean to predict the 9th member's seasonal anomalies, its skill is again similar to that in the upper panel. One can thus make a case that the modest extratropical values in Fig. 2.4 are mainly a reflection of the limited intrinsic predictability of extratropical seasonal averages associated with tropical SST forcing. As mentioned earlier, this in turn is mainly due to a modest signal-to-noise ratio.

CDC scientists have attempted to clarify the relationship between the expected anomaly correlation skill rho of ensemble-mean forecasts and the signal-to-noise ratio s, defined as the ratio of the ensemble-mean anomaly to the ensemble spread. Figure 2.5 summarizes this general relationship, which is useful in interpreting many GCM results. The rho_infinity and rho_1 curves show the expected skill of infinite-member and single-member ensemble-mean forecasts with a perfect model. The third (blue) curve depicts the expected skill of infinite-member ensemble-mean forecasts with an imperfect model, whose systematic error se (i.e., its error in determining the true s) is of the same magnitude as s. Note that these curves are applicable to any forecast variable, in any forecasting situation, and to any forecasting method, including the regression method used in Fig. 2.4b.

Expected anomaly correlation forecast skill of ensemble-mean forecasts as function of signal-to-noise ratio

Fig. 2.5 Expected anomaly correlation forecast skill of ensemble-mean forecasts as a function of signal to noise ratio s. The red curve is the expected skill of an infinite-member forecast, the black curve the expected skill of a single-member forecast. The blue curve shows the expected skill of an infinite-member ensemble forecast using an imperfect model whose standardized systematic error is of the same magnitude as s.

The rho_infinity curve represents a hard predictability limit with a perfect model, and shows that to produce 'useful' forecasts with anomaly correlations greater than 0.6, s needs to be greater than 0.75. To produce 'excellent' forecasts with anomaly correlations greater than 0.9, s needs to be greater than 2. Given the evidence from several studies that s for ENSO-related 200 mb seasonal height anomalies is approximately between 0.5 and 1 in the extratropical Pacific-American sectors of both hemispheres, and greater than 2 in the tropics, the results in Fig. 2.4 are not surprising. Figure 2.5 is also useful for assessing to what extent the modest skill in Fig. 2.4a might be due to model error or using only 9-member ensembles. The difference between rho_infinity and rho_1 shows the potential gain in skill by using infinite-member ensembles instead of a single member. The maximum gain is 0.25, for s ~ 0.6. However, most of this gain is attainable with about 25 members, and even a rho_9 curve (not shown) is close to the curve. The loss of skill due to model error (blue curve) is probably of greater concern in Fig. 2.4a than not having enough members. However, model error could equally be affecting skill in Fig. 2.4b.

2.2.2 New research challenges

Figures 2.4 and 2.5 together suggest that the modest skill, on average, of deterministic extratropical seasonal forecasts is largely consistent with the predictability limits imposed by the modest local values of s associated with the tropically forced signal. Given also the evidence in Fig. 2.4b that similar skill can also be achieved with simple linear regression models, the question naturally arises as to what further useful predictive information can be extracted by running GCM ensembles.

CDC scientists have spent considerable time pondering this issue, and have come up with several encouraging possibilities. In one way or another, they all involve focusing on the distributional aspects of the ENSO response rather than on the ensemble-mean. For example, as Fig. 2.6a shows, a modest shift in the mean of 0.5 (in units of standard deviation), while not large enough to affect appreciably the expected seasonal mean of an extratropical variable, can still greatly affect the probability of its extreme values. The risk of obtaining an extreme positive value of greater than +1 increases from 16% to 31%, and the risk of obtaining an extreme negative value decreases from 16% to 7%. Thus without ENSO the risks of extreme positive and negative anomalies are the same, but with ENSO, even for a modest s of 0.5, the risk of an extreme positive anomaly becomes 4.4 (=31/7) times the risk of an extreme negative anomaly. Figure 2.6b shows how this risk ratio can be equally strongly affected by modest changes of noise. In this example, a 20% reduction of standard deviation combined with a mean shift of 0.5 changes the risk ratio from 1 (=16/16) to 9 (=27/3).

Illustration of how a shift in the mean or variance of a PDF affects the risk of extreme events

Fig. 2.6 (a) An illustration of how a mean shift of 0.5 of a normal distribution increases the probability of extreme positive values from 16% to 31% and decreases the probability of extreme negative values from 16% to 7%. (b) Illustration of the altered probabilities of extreme values when the mean shift of 0.5 is also accompanied by a reduction of the standard deviation from 1 to 0.8.

When even minor PDF shifts and changes of variance imply large changes in the risks of extremes values, determining them accurately becomes important. It is easy to see how a good GCM might have an advantage over the regression model of Fig. 2.4b in this regard, whose parameters cannot be estimated accurately enough from the limited observational record to have confidence in its predictions of extreme values. Further, one can run as many GCM ensemble members as necessary in individual forecast cases to predict the changes of extreme risks within specified confidence intervals. The regression-model also assumes, in effect, that ENSO-induced mean PDF shifts are strictly linear with respect to the SST forcing and that there are no changes of noise, or variability. CDC scientists have spent considerable effort on ascertaining the extent to which such assumptions are valid, since they have a large bearing on the problem at hand.

2.2.3 Understanding the sensitivity of the atmospheric response to details of the anomalous SST forcing

The regression-model used in Fig. 2.4b always predicts the same signal pattern of the global atmospheric response; only its amplitude varies from forecast case to case in direct proportion to the strength of the Niño 3.4 SST anomaly. As we have seen, this doesn't seem to affect its deterministic forecast skill overmuch, but the question is whether it limits predictions of the risk of extreme anomalies. To what extent does the remote SST-forced signal vary from case to case? To what extent are its variations determined by the nonlinearity of the response to the amplitude and sign of the SST forcing in Niño 3.4, and to what extent by the details of the SST anomaly pattern in the wider tropical Indo-Pacific domain? We have conducted several studies to answer these questions.

Figure 2.7 gives a sense of the signal variation from case to case. Sampling uncertainty is an issue in this problem, given that the number of samples required to establish that s is statistically different from zero is inversely proportional to the square of s. At the 5% level, the number of samples should be greater than 8/s2. To establish the significance of s = 0.5 thus requires 32 samples; to establish the significance of changes of s from case to case, say of order 0.25, would require many more, 128. With this in mind, we ran a very large 180-member seasonal ensemble with the NCEP atmospheric GCM with prescribed observed global SST forcing corresponding to the El Niño of 1987, and another 180-member ensemble for the La Niña of 1989. The right-hand panels of Fig. 2.7 show the ensemble-mean 500-mb height anomalies obtained in these integrations (defined with respect to the ensemble-mean obtained in another set of 180 integrations with climatological-mean SST forcing). To our knowledge this is the most statistically confident determination of the global SST-forced signal ever made for two different observed SST forcing patterns. Note that the sign of the response has been reversed in the lower panel for easier comparison with the upper panel. For comparison we also show in the left panels, in an identical format, observational 500-mb composite anomaly patterns for 10 El Niño and 10 La Niña events based on the Niño 3.4 index, and defined with respect to 10 "neutral" events. Note that the amplitudes of these composite patterns have been scaled by 0.73 and 1.36, in proportion to the observed Niño 3.4 SST anomaly magnitudes during the moderate 1987 El Niño and the strong 1989 La Niña events, respectively. Thus these left panels may be interpreted as the SST-forced 500-mb height signals during 1987 and 1989 as predicted by an empirical method. This method is superior, in principle, to that used in Fig. 2.4b in that it predicts different response patterns in El Niño and La Niña cases, as shown here.

SST-forced 500 mb height signals in JFM

Fig. 2.7The SST-forced signal in 500 mb heights during the El Niño winter of JFM 1987 (top panels) and the La Niña winter of JFM 1989 (bottom panels, with sign reversed) estimated by a GCM (right panels) and an empirical method (left panels). The right panels show the ensemble-mean anomaly fields obtained in 180 seasonal integrations of the NCEP AGCM with prescribed global SST forcing during JFM 1987 and JFM 1989. The left panels show scaled historical composite 500 mb anomaly fields derived from 10 observed El Niño and 10 observed La Niña events in the 1958-1999 period, defined with respect to a Niño 3.4 SST anomaly index. The composite patterns were scaled by factors of 0.73 and 1.36 to account for the moderate Niño 3.4 index magnitude during 1987 and the larger magnitude during 1989, respectively. The contour interval is 10 m in all panels. Positive values are indicated by red and negative by blue shading.

Although the GCM's signal patterns for these individual El Niño and La Niña winters are generally similar to one another, there are some notable differences. The El Niño response is stronger in the PNA sector, despite the weaker SST forcing. This is also true in the empirical forecast. There is little else to compare between the GCM and empirical forecasts because of sampling uncertainty in the empirical forecasts, i.e., the fact that the left panels are derived from only 10 cases each in the historical record. In areas such as the North Atlantic where the left panels predict a strong asymmetric signal of the same sign in 1987 and 1989, the significance of that asymmetry is therefore questionable. The differences between the GCM's predicted signal patterns for 1987 and 1989 are much more reliable in this regard, and though more modest, are large enough that they would have had important implications for predicting the risks of extreme anomalies during these winters.

There is thus evidence of significant signal variation from case to case. To put these results on a stronger footing, one might ideally wish to generate similar 180-member ensembles for each one of the past 50 or so winters. This has not yet been done. However, results from a 46-member multi-model ensemble of four different atmospheric GCMs (NCAR CCM3, NCEP, GFDL, and ECHAM) offer additional evidence of the existence of different response patterns. Between 10 and 12 member ensembles were generated for each model forced with identical evolving observed global SSTs over the past 50 years. For each one of the 50 winters, the SST-forced signal at 500 mb was defined as a weighted average of the ensemble-mean responses of the 4 GCMs. Finally, an EOF analysis of these 50 signal patterns was performed. Figure 2.8 shows the first three EOFs, together with their fractions of the total signal variance explained. The leading EOF alone accounts for 57% of the global signal variance, and as much as 80% over the PNA region. Most elements of this pattern are evident in all the four panels of Fig. 2.7. The dominance of this signal pattern, its strong similarity to the classic observed ENSO teleconnection pattern, and also to the unchanging forecast pattern of the regression model used in Fig. 2.4b, explains why the upper and lower panels of Fig. 2.4 are so similar. Still, there is evidence in Fig. 2.8 of apparently minor but potentially important deviations from this dominant signal pattern from winter to winter. The second EOF is largely zonally symmetric, with out-of-phase anomalies in polar and subtropical latitudes. Locally, it explains a substantial fraction of the signal variability in the subtropics, and its associated Principal Component (PC) time series describes a tropospheric warming trend of lower latitudes over 1950-1999 associated with a long-term tropical SST warming trend. The third EOF resembles a tropically forced wavetrain with centers spatially shifted relative to those of the leading EOF. Its PC time series regressed on the simulated tropical precipitation fields yields a regression map with appreciable magnitudes in the western and central equatorial Pacific. This third EOF may thus reflect a genuine sensitivity of the SST-forced extratropical signal to variations of the anomalous tropical SST pattern from winter to winter.

EOFs of SST-forced 500 mb height signals

Fig. 2.8 The first three EOFs of SST-forced 500 mb height signals in a multi-GCM ensemble of 50-year integrations made with prescribed evolving observed global SST boundary conditions. See text for further details. The values plotted are the correlations of the EOF's Principal Component time series with the local 500 mb height time series of the SST-forced signal. Positive values are indicated by red and negative by blue shading.

It should be stressed that the GCM results in Figs. 2.7 and 2.8 are all for global SST forcing. To what extent can the signal variation evident in these figures be attributed strictly to the tropical Pacific SST forcing, in particular to asymmetric responses to El Niño and La Niña forcing? There is a strong suggestion of a weaker response to La Niña forcing in the lower panels of Fig. 2.7. Such a weaker response (not shown) is also clearly evident in the composite El Niño and La Niña signals in the 4 different ensemble GCM simulations for 1950-1995 described above. Are there also significant differences in the patterns of the response? To what extent do they contribute to the third EOF in Fig. 2.8? Several CDC studies have attempted to address such questions cleanly, by examining the atmospheric response to the first EOF pattern of tropical Pacific SST (very similar to the Pacific portion of the lower panel of Fig. 2.1) with positive ("El Niño") and negative ("La Niña") signs. A weaker response to the negative EOF forcing has indeed been confirmed, but is appreciable only for large amplitude forcing.

Figure 2.9 shows results from a GCM experiment designed specifically to address this issue. A 9-member NCEP GCM ensemble was generated for 1963-1989 by forcing throughout the 27 years with the first SST EOF pattern, varying in magnitude and sign as its associated PC time series. The upper panels of Fig. 2.9 show the ensemble-mean responses during the strongest warm and cold winters of 1983 and 1974, respectively, in this period. The response is clearly weaker for the 1974 event. This is suggestive but not conclusive, since the magnitude of the SST forcing was also weaker in 1974. To settle this, the entire experiment was repeated with the sign of the PC time series reversed. The ensemble-mean responses for the sign-reversed 1983 and 1974 winters are shown in the lower panels. The 1974 response is now stronger than the 1983 response, despite the weaker magnitude forcing. We had noted this effect earlier in Fig. 2.7, but the result here is cleaner. It confirms that the remote atmospheric response to the tropical Pacific SST forcing is appreciably stronger for strong warm than for the strong cold SST forcing. A top-to-bottom comparison in Fig. 2.9 compares the responses to the same SST forcing but of opposite sign, and further confirms this result.

GCM responses to first EOF of tropical Pacific SST forcing for DJF 1982/83 and DJF 1973/74

Fig. 2.9 GCM 200 mb height responses in northern winter (DJF) to the first EOF pattern of tropical Pacific SST forcing, with the observed amplitude during DJF 1982/83 (upper left panel), the observed amplitude during DJF 1973/74 (upper right), the negative of the observed amplitude during DJF 1982/83 (lower left), and the negative of the observed amplitude during DJF 1973/74 (lower right). The contour interval is 10 m. Positive values are indicated by red and negative by blue contours. See text for further details.

2.2.4 ENSO-induced changes of variability

To what extent does ENSO affect the atmospheric noise (i.e., the variability) as hypothesized in Fig. 2.6b? We have addressed this issue in several recent publications. In one study, we examined the standard deviation of seasonal-mean 500 mb heights in our 180-member GCM ensembles for the winters of 1987 and 1989, and found a modest overall increase in the warm (1987) and a decrease in the cold (1989) ensemble compared to that in the neutral 180-member ensemble. This was speculated to be forced partly by the increased variability of seasonal precipitation in the warm (and decreased variability in the cold) ensemble in the Niño-4 area of the central equatorial Pacific, which has been shown to be sensitive region for forcing a large global circulation response. Another study searched for ENSO-induced changes of seasonal noise in the smaller AMIP-style GCM ensembles used in Fig. 2.8, but found little impact in the PNA region. While these findings seem to conflict, a closer look at the published figures shows that the results are not inconsistent in the PNA region. To the extent that the altered extratropical noise is due to the tropical precipitation noise, the effect is also probably both GCM-dependent and ENSO event-dependent. It should be mentioned that sampling uncertainty is of even greater concern here than in Figs. 2.7 and 2.8. The number of samples required to establish the significance at the 5% level of a fractional change Delta of an ensemble's standard deviation is close to 3/Delta
squared. To establish the significance of the Delta of 0.2 (corresponding to a 20% change of standard deviation) in Fig. 2.6b would thus require 75 samples from both the neutral and altered distributions. Any change of smaller than 17.5% would require more than 100 samples.

The effect of ENSO on subseasonal extratropical variability is equally important, and somewhat easier to establish. These effects can be distinct from the effects on seasonal mean quantities, and can have important practical implications. For instance, one may imagine a situation in which El Niño alters the occurrence of both cold waves and warm spells in a winter. The effect is a meaningful change in the risk of extreme weather, even though little seasonal mean signal might be evident. The few published studies on this topic, constrained either by sampling requirements or data availability, have formed composites over several ENSO events to diagnose the effect in limited regions. In an ambitious recent study, we have estimated the effect globally from our large AGCM ensembles for 1987 and 1989, and compared them with observational composites based on 11 El Niño and 11 La Niña events in the recent record. As in Fig. 2.7, the purpose of this comparison was to gauge to robustness of the changes of variability, their predictability, and their variation from event to event.

The most important result from this analysis, depicted in Fig. 2.10, is that the patterns of the SST-forced anomalous height variability are markedly different for the synoptic (2 to 7 days), intraseasonal (8 to 45 days), and monthly (30 -day average) time scales. In contrast, the patterns of the anomalous tropical rainfall variability (not shown) are nearly identical across these time scales. Figure 2.10 shows contours of Delta_sigma, defined as the signed square root of the anomalous variance difference of 500 mb heights on these time scales (where by "signed" we mean that if the anomaly is negative, we depict its square root with a minus sign). The results for La Niña (not shown) are similar and generally of opposite sign. The comparison between the GCM and observational panels in Fig. 2.10 is not clean. Nevertheless, their gross similarity is reassuring, both for the robustness of the changes of variability and this GCM's ability to simulate them. To that extent, their dissimilarity can be attributed to the comparison not being clean (i.e., event-to-event differences) and sampling error, especially in the observations (which is why the observational anomalous monthly variability map has been omitted).

El Niño induced change of 500 mb height variance

Fig. 2.10 El Niño-induced changes of variance on three different subseasonal time scales. The quantity plotted is the square root of the anomalous variance, with red shading for positive and blue for negative anomalous variance. The left panels are based on statistics averaged over 11 observed El Niño and 11 observed "neutral" JFM winters in the NCEP reanalysis dataset. The right panels are derived from a large AGCM ensemble with observed SST forcing for the El Niño winter of JFM 1987. Top panels: Synoptic scale (2 to 6 day periods), Middle panels: Intraseasonal scale (8 to 45 day periods.). Bottom panel: Monthly scale (30-day averages). Contours are drawn at 8 m intervals starting at 4 m in the top panels, and at 16 m intervals starting at 8 m in the middle and lower panels. See text for a fuller explanation.

The main ENSO effect on the synoptic scale is a southward shift of the storm track over the Pacific ocean and North America. On the intraseasonal scale, it is a decrease of height variance over the north Pacific, consistent with a tendency of reduced blocking activity during El Niño. On monthly (and seasonal) scales there is a suggestion of an overall increase of variance. Referring back to Fig. 2.6b, it is evident that these differing ENSO impacts on extratropical noise on different time scales have very different implications for the risks of extreme anomalies on these scales. We believe that three quite distinct dynamical mechanisms are responsible for these sharp differences, and are currently investigating them in a hierarchy of dynamical models.

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