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  • View in gallery

    Spatial pattern of AGCM-simulated external variability of 200-mb (top left) DJF seasonal mean height (shading interval: 1000) and (bottom left) DJF seasonal mean rainfall. External variance is computed from the ensemble mean DJFs between 1980 and 2000. Units for height are m2 and for rainfall are mm day−2. (right) The ratio of external variance to (top right) the total variance of DJF seasonal mean height (shading interval: 0.2) and (bottom right) DJF seasonal mean rainfall (shading interval: 0.2). Total variance is computed from the variance of all DJFs in the analysis period. This ratio is proportional to the potential predictability of 200-mb height and rainfall anomalies.

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    (top left) Spatial structure of the first EOF of external variability of 200-mb DJF seasonal mean heights (shading interval: 20) and (top right) the associated time series. For the individual DJFs, the AGCM-simulated height anomalies projecting on this mode can be computed as the scalar product of these two fields. (bottom left) The corresponding rainfall anomalies (in mm day−1) and (bottom right) SSTs (in K) are obtained as a regression with the time series of the first EOF.

  • View in gallery

    (top left) Spatial pattern of 200-mb DJF seasonal mean height external variance as in Fig. 1 not explained by the first EOF (shading interval: 250). Units are in m2. (top right) The ratio of the external variance of height explained by mode 1 and the external variance itself (shading interval: 0.2). The closer the ratio is to one, the larger the fraction of variance explained by the dominant mode of external variability is. (bottom left) The external variance for the rainfall not related to the first EOF of the height. Units are mm day−2. (bottom right) The ratio of external variance of rainfall related to mode 1 of height and the external variance of rainfall itself (shading interval 0.2).

  • View in gallery

    Same as in Fig. 2, but for the second EOF of the external variability.

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    Same as in Fig. 2, but for the third EOF of the external variability.

  • View in gallery

    (left) Spatial pattern of the ratio of 200-mb DJF seasonal height external variance explained by the first three EOFs and the total external variability. (right) Spatial pattern of the ratio of seasonal mean rainfall variance linearly related to the first three EOFs of height and the total external variability of seasonal mean rainfall. The closer the ratio is to one, the larger the fraction of the variance explained by the first three modes of external variability is. The shading interval is 0.2.

  • View in gallery

    (top) Spatial pattern of the nonlinear component of ENSO response for the AGCM-simulated 200-mb heights (shading interval: 10), (middle) observed SSTs (shading interval: 0.5), and (bottom) the AGCM-simulated rainfall. The nonlinear component is estimated as the sum of the warm composite for DJF 1983 and DJF 1998 and the cold composite for DJF 1988 and 1999 [also see Eq. (3)]. Units are m for 200-mb height, K for SSTs, and mm day−1 for rainfall.

  • View in gallery

    (a) (top) AGCM-simulated 200-mb height response for the warm ENSO event of DJF 1998 (in shading; shading interval: 20) superimposed on the atmospheric response reconstructed from the first EOF of external variability (in contours). (bottom) The difference between the AGCM-simulated height response and the response reconstructed from the first EOF as shown in the top panel (contouring interval: 20). The difference is the AGCM-simulated height response that is not explained by the canonical response to EOF (i.e., the first EOF). Units are in m. (b) Same as in Fig. 8a, but for the cold ENSO event of DJF 1999.

  • View in gallery

    AGCM-simulated 200-mb height response for (top two panels, respectively) the cold events of DJF 1989 and DJF 1985 and for (bottom two panels, respectively) the warm events of DJF 1992 and DJF 1983. Anomalies for the warm events are multiplied by negative one. (middle) The spatial pattern of atmospheric response for the first EOF. The sequence of the five panels can be thought of as ENSO atmospheric response progressing from the extreme cold events to the extreme warm events. The straight line across the five panels joins the center of positive height anomalies at 40°N and indicates an eastward shift in the 200-mb height response to ENSO SSTs from cold-to-warm events. Units are in m and contouring interval is 20.

  • View in gallery

    (top) AGCM-simulated 200-mb height response (shading interval: 10), (middle) observed SST anomalies (shading interval: 0.2), and (bottom) AGCM-simulated rainfall response. All the anomalies are averages for DJFs of 1980, 1981, 1982, and 1986. The winters were chosen based on the following: 1) they were not an ENSO year as indicated by the time series shown in Fig. 1, and 2) the height anomaly had a large projection on the third EOF in Fig. 5. Units are m for 200-mb height, K for SSTs, and mm day−1 for rainfall.

  • View in gallery

    (top left) Spatial pattern of temporal anomaly correlation between AGCM-simulated and observed 200-mb height anomalies for DJFs between 1980 and 2000. Anomaly correlation when the AGCM-simulated height anomalies are reconstructed from (top right) the first EOF alone, (bottom left) the first two EOFs, and (bottom right) the first three EOFs of external variability.

  • View in gallery

    (top) Difference in the temporal anomaly correlation between AGCM-reconstructed and observed 200-mb height anomalies where AGCM-reconstructed height anomalies were either based on EOFs 1 and 2 or were based on the first EOF. Difference also corresponds to difference in anomaly correlations shown in the bottom-left and top-right panels in Fig. 11. (bottom) Same as in top, but for the difference in the anomaly correlations where AGCM-reconstructed height anomalies were either based on the first three EOFs or were based on the first EOF alone. Difference also corresponds to difference in anomaly correlations shown in the bottom-right and top-right panels in Fig. 11.

  • View in gallery

    (left) The scatterplot between the anomaly correlations shown in the bottom-right and top-right panels in Fig. 11. The x axis represents the anomaly correlations based on mode 1 alone, whereas the y axis is the anomaly correlations based on modes 1–3. (right) Same as in left, but for anomaly correlations computed over non-ENSO years alone. For all the points above the diagonal line, the anomaly correlation based on added information from the EOF modes 2 and 3 was better than the anomaly correlation based on the EOF mode 1 alone.

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SST-Forced Atmospheric Variability in an Atmospheric General Circulation Model

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  • 1 Climate Prediction Center, NOAA/NWS/NCEP, Camp Springs, Maryland
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Abstract

From ensembles of 80 AGCM simulations for every December–January–February (DJF) seasonal mean in the 1980–2000 period, interannual variability in atmospheric response to interannual variations in observed sea surface temperature (SST) is analyzed. A unique facet of this study is the use of large ensemble size that allows identification of the atmospheric response to SSTs for each DJF in the analysis period. The motivation of this study was to explore what atmospheric response patterns beyond the canonical response to El Niño–Southern Oscillation (ENSO) SST anomalies exist, and to which SST forcing such patterns may be related. A practical motivation for this study was to seek sources of atmospheric predictability that may lead to improvements in seasonal predictability efforts.

This analysis was based on the EOF technique applied to the ensemble mean 200-mb height response. The dominant mode of the atmospheric response was indeed the canonical atmospheric response to ENSO; however, this mode only explained 53% of interannual variability of the ensemble means (often referred to as the external variability). The second mode, explaining 19% of external variability, was related to a general increase (decrease) in the 200-mb heights related to a Tropicwide warming (cooling) in SSTs. The third dominant mode, explaining 12% of external variability, was similar to the mode identified as the “nonlinear” response to ENSO in earlier studies.

The realism of different atmospheric response patterns was also assessed from a comparison of anomaly correlations computed between different renditions of AGCM-simulated atmospheric responses and the observed 200-mb height anomalies. For example, the anomaly correlation between the atmospheric response reconstructed from the first mode alone and the observations was compared with the anomaly correlation when the atmospheric response was reconstructed including modes 2 and 3. If the higher-order atmospheric response patterns obtained from the AGCM simulations had observational counterparts, their inclusion in the reconstructed atmospheric response should lead to higher anomaly correlations. Indeed, at some geographical regions, an increase in anomaly correlation with the inclusion of higher modes was found, and it is concluded that the higher-order atmospheric response patterns found in this study may be realistic and may represent additional sources of atmospheric seasonal predictability.

Corresponding author address: Dr. Arun Kumar, Climate Prediction Center, NOAA/NWS/NCEP, 5200 Auth Road, Rm. 800, Camp Springs, MD 20746. Email: arun.kumar@noaa.gov

Abstract

From ensembles of 80 AGCM simulations for every December–January–February (DJF) seasonal mean in the 1980–2000 period, interannual variability in atmospheric response to interannual variations in observed sea surface temperature (SST) is analyzed. A unique facet of this study is the use of large ensemble size that allows identification of the atmospheric response to SSTs for each DJF in the analysis period. The motivation of this study was to explore what atmospheric response patterns beyond the canonical response to El Niño–Southern Oscillation (ENSO) SST anomalies exist, and to which SST forcing such patterns may be related. A practical motivation for this study was to seek sources of atmospheric predictability that may lead to improvements in seasonal predictability efforts.

This analysis was based on the EOF technique applied to the ensemble mean 200-mb height response. The dominant mode of the atmospheric response was indeed the canonical atmospheric response to ENSO; however, this mode only explained 53% of interannual variability of the ensemble means (often referred to as the external variability). The second mode, explaining 19% of external variability, was related to a general increase (decrease) in the 200-mb heights related to a Tropicwide warming (cooling) in SSTs. The third dominant mode, explaining 12% of external variability, was similar to the mode identified as the “nonlinear” response to ENSO in earlier studies.

The realism of different atmospheric response patterns was also assessed from a comparison of anomaly correlations computed between different renditions of AGCM-simulated atmospheric responses and the observed 200-mb height anomalies. For example, the anomaly correlation between the atmospheric response reconstructed from the first mode alone and the observations was compared with the anomaly correlation when the atmospheric response was reconstructed including modes 2 and 3. If the higher-order atmospheric response patterns obtained from the AGCM simulations had observational counterparts, their inclusion in the reconstructed atmospheric response should lead to higher anomaly correlations. Indeed, at some geographical regions, an increase in anomaly correlation with the inclusion of higher modes was found, and it is concluded that the higher-order atmospheric response patterns found in this study may be realistic and may represent additional sources of atmospheric seasonal predictability.

Corresponding author address: Dr. Arun Kumar, Climate Prediction Center, NOAA/NWS/NCEP, 5200 Auth Road, Rm. 800, Camp Springs, MD 20746. Email: arun.kumar@noaa.gov

1. Introduction

In recent decades, increased understanding of atmospheric teleconnnections forced by the interannual variability in the sea surface temperatures (SSTs), particularly in the equatorial tropical Pacific, has provided a firm physical basis for operational seasonal climate predictions (Trenberth et al. 1998; Goddard et al. 2001). Initial successes in the emerging practice of seasonal climate prediction, for example, during the 1997/98 El Niño (Goddard et al. 2003; Frederiksen et al. 2001; Mason et al. 1999), has also led to a search for sources of seasonal climate predictability above and beyond what is attributable to the SST anomalies related to the El Niño–Southern Oscillation (ENSO) phenomenon. For example, suggestions have been put forward that an understanding of atmospheric variability related to different flavors of ENSO, or related to SST variability in ocean basins other than the tropical equatorial Pacific (i.e., non-ENSO SST variability), would lead to improvements in our ability to predict seasonal climate variations (Mathieu et al. 2004; Kumar and Hoerling 1997; Trenberth 1993). Similar to our current understanding for the atmospheric responses forced by the canonical ENSO SSTs (Horel and Wallace 1981; Hoerling and Kumar 2002), this requires documenting atmospheric responses to SST forcings beyond the canonical ENSO SSTs.

Atmospheric responses to SST forcings can be obtained using two broad approaches. An empirical approach depends on the analysis of historical data and searches for relationships between the anomalous SSTs and the corresponding atmospheric circulation anomalies. Indeed, such an analysis first led to documenting global teleconnections forced by ENSO SSTs (Barnett 1981; Horel and Wallace 1981; Halpert and Ropelewski 1992). However, the historical observational record of SSTs and atmospheric circulation is not long enough to identify relationships between flavors of ENSO, or between the non-ENSO SST forcings and the seasonal climate anomalies. This is because not enough samples of such SSTs exist to statistically infer corresponding atmospheric circulation anomalies reliably.

An alternate, and complementary approach is to identify atmospheric response to different SST anomalies based on atmospheric general circulation model (AGCM) simulations. A particular advantage of ACGMs is that a large ensemble of simulations can be generated for any spatial structure of SST anomaly. In such experiments, AGCM simulations only differ in their specification of initial atmospheric conditions but are forced by identical SSTs. A shortcoming of the AGCM approach is that the inferences about the atmospheric responses to different SST forcings can be influenced by the AGCM biases. Such shortcomings notwithstanding, the AGCM approach to understand and document atmospheric responses for SSTs other than those due to the canonical ENSO has been used frequently (Hoerling et al. 1997, 2001; Sardeshmukh et al. 2000).

Previous studies, however, are generally based on either small ensemble sizes over a large number of years or are with large ensemble sizes for few specific cases of SST anomalies. In the present study, we analyze atmospheric responses derived from an 80-member ensemble for December–January–February (DJF) seasonal means between the 1980–2000 period.1 In doing so, our analysis is based on a large ensemble for each DJF and at the same time analyzes atmospheric responses over 21 different renditions of observed SSTs.

Our methodology anchors on the analysis of the interannual variability of the ensemble mean of AGCM simulations. Specifically, we document the dominant spatial modes of atmospheric responses and identify to which SSTs they are related. In contrast to previous studies of a similar kind, we also assess if the spatial modes of atmospheric responses obtained from the AGCM simulations have any bearing on what occurs in nature. This assessment is based on reproducibility of interannual variability (as estimated by the correlation skill) between the AGCM-simulated and the observed anomalies, where AGCM-simulated anomalies are reconstructed by adding progressively higher-order spatial modes of atmospheric responses to SSTs. The AGCM data and the analysis procedures used in this study are described in section 2. Analysis of the dominant modes of atmospheric response to SST variability for DJF winters between 1980–2000 is presented in section 3. An assessment of the realism of spatial modes of atmospheric responses from the AGCM simulations is also outlined in section 3. Summary and conclusions are presented in section 4.

2. Data and analysis procedure

Analysis in this paper is for DJF seasonal means, although for the datasets available to us, it could be extended to other seasons also. Boreal winter is the most studied season for atmospheric responses to interannual variations in SSTs because 1) interannual variability in SSTs is maximum for this season (Trenberth et al. 1998), and 2) in the Northern Hemisphere tropical–extratropical interactions are also most prominent during this season (Newman and Sardeshmukh 1998).

In our analysis, AGCM simulations from a seasonal forecast model that was operational at the National Centers for Environmental Prediction (NCEP) are used. Details of this model and the prediction system are described in Kanamitsu et al. (2002a). Briefly, the AGCM is a spectral model with T62 horizontal resolution and it has 28 vertical levels and includes detailed parameterization for physical processes, for example, convection, radiation, etc.

For dynamical seasonal forecasts at NCEP, each month a set of seasonal hindcasts for the 1979–99 period is first made. The purpose of the hindcast simulations is to assess the simulation skill of the seasonal means and to generate a set of climatologies from which the anomalies for the seasonal forecasts can be computed. All the hindcasts are of approximately 7-month duration and are forced with the observed SSTs (Reynolds and Smith 1994). An ensemble of hindcasts from 10 different atmospheric initial conditions but with the same observed SSTs is made. For example, for each November between 1979 and 1999 (i.e., 21 yr), an ensemble of 10 AGCM simulations, starting from 12-hourly-apart atmospheric initial conditions between the first and fifth of the month, is made, and hindcast simulations are run until the end of May. Atmospheric initial states are taken from the NCEP–Department of Energy (DOE) Atmospheric Intercomparison Project (AMIP-II) reanalysis (R-2) dataset (Kanamitsu et al. 2002b).

From the above set of hindcast simulations, for all DJFs between 1980 and 2000, 10 AGCM simulations from November initial conditions are available. Within this setup, DJF seasonal means are approximately 1 month from the start of the simulations. Additional sets of 10 DJF simulations each, although with longer lead times, are also available from October, September, and August initial conditions. If all the simulations from different initial conditions are pooled, then for each DJF in the period 1980–2000, an ensemble of 40 AGCM simulations is available. Furthermore, as the seasonal forecast system at NCEP was operational for more than 2 yr, and the hindcasts repeat each month, we also pool the hindcasts for DJFs over a full 2-yr period, resulting in an 80 member ensemble for each DJF between 1980 and 2000.2 We have analyzed and confirmed that the statistical characteristics of DJFs from different lead times (and for different years of hindcasts) are similar (see also Phelps et al. 2004; Peng and Kumar 2005; Chen 2004), and therefore AGCM simulations from different lead times can be pooled together. The analysis in this study is for the AGCM-simulated DJF seasonal mean 200-mb heights and rainfall. The anomalies are computed with respect to the seasonal mean DJF climatology for the 1980–2000 period, and model and observed anomalies are obtained from their respective climatologies.

The ensemble mean anomaly from 80 simulations for each DJF represents the SST-forced atmospheric response for that year, and the variance of ensemble means over the 1980–2000 period is the “external variability” forced by the interannual variations in the specified SST forcing (Kumar and Hoerling 1995; Rowell et al. 1995). Based on individual DJFs, one can also estimate the total variance of DJF seasonal means, and a comparison of the external and the total variance provides an estimate of potential predictability of seasonal means. We should point out that the estimate of potential predictability is entirely an AGCM-based estimate and can be influenced by the AGCM biases.

The preferred spatial modes of 200-mb height atmospheric responses are obtained from the empirical orthogonal function (EOF) analysis of ensemble means. EOF analysis is for the global domain, and a latitudinal weighting prior to the EOF analysis is applied. The time series for different EOFs is also regressed against the global observed SSTs and the AGCM-simulated rainfall to understand the spatial structure of the SST responsible for forcing the respective atmospheric patterns. Furthermore, all the results are presented as regressions normalized to one standard deviation of the EOF time series.

To assess the realism of modes of variability obtained from the AGCM simulations, we also compare the 200-mb ensemble mean height anomalies with the observed 200-mb heights obtained from the NCEP–National Center for Atmospheric Research (NCAR) reanalysis. This assessment is based on the computation of temporal anomaly correlations, and different estimates, with different information content, for AGCM-simulated atmospheric responses are used. For example, the atmospheric response could be the ensemble mean itself, or by its construct, it could be the atmospheric response reconstructed from selective EOFs. In the anomaly correlation approach, higher anomaly correlations between the AGCM-simulated ensemble mean and the observed anomalies imply that AGCM-simulated interannual variability has increasing similarity to the observations. On the other hand, if the AGCM ensemble mean simulated pattern of interannual variability does not correlate with the observed anomaly, that would imply that the AGCM-simulated atmospheric response is erroneous and does not have an observed counterpart.

An aspect to keep in mind following the analysis of anomaly correlations approach is that while the ensemble mean minimizes the influence of atmospheric internal variability unrelated to SSTs, the observed anomalies are a combination of atmospheric response to SSTs and the atmospheric internal variability. Depending on the relative magnitude of the atmospheric response and the atmospheric internal variability in the observed seasonal means, the anomaly correlation between the AGCM-simulated ensemble mean and the observed seasonal mean has an upper bound (Kumar and Hoerling 2000; Sardeshmukh et al. 2000), and because of small (large) internal variability in the Tropics (extratropics), it is expected that the anomaly correlation is higher (smaller) in tropical (extratropical) latitudes (Peng et al. 2000).

3. Results

a. Dominant modes of atmospheric response to SSTs

In Fig. 1 the AGCM-simulated external variance for the DJF seasonal mean 200-mb height and rainfall is shown. This variance is computed from the ensemble mean anomalies for the period 1980–2000. By definition, this variability is a result of the interannual variations in the external boundary conditions, that is, global observed SSTs.

Spatial structure of 200-mb height external variability has maximum amplitude in the tropical and subtropical latitudes east of the date line, with a wave train–like structure extending in the extratropical latitudes of both the hemispheres. Furthermore, as will be evident later, the extension into the extratropical latitudes is reminiscent of the global atmospheric response to ENSO SST anomalies. Although the amplitude of height variability is stronger in the Northern Hemisphere, symmetry of response around the equatorial latitudes suggests a tropical origin. For the spatial structure of external variability, a particular feature to note is the geographical preference.

Spatial structure of seasonal mean rainfall variability (Fig. 1, bottom left) is mainly confined to a narrow latitudinal band in the equatorial tropical Pacific, a region where interannual variability in SST also maximized (Trenberth et al. 1998). Equatorial confinement of maximum in external variability for seasonal mean rainfall provides further credence to the hypothesis that the equatorial symmetric nature of 200-mb height external variability is of tropical origin.

To contrast the AGCM-simulated atmospheric variability forced by SSTs with the total seasonal variability, Fig. 1 (right panels) show the ratio of external variability to the total variance of DJF seasonal means. If this ratio is close to one, it implies that a large fraction of seasonal mean variability is due to the interannual variations in the SST anomaly. On the other hand, if this fraction is near zero, it implies that the atmospheric variability unrelated to SSTs dominates. In terms of the potential predictability of seasonal mean anomalies, while higher values indicate larger potential predictability, smaller values imply that the internal variability dominates, and potential predictability is also smaller.

Consistent with earlier results, for both 200-mb height and rainfall the spatial pattern of fraction of the total variance explained by the interannual variations in SSTs is largest in the Tropics and decreases (almost) monotonically toward the extratropical latitudes (Kumar and Hoerling 1995; Rowell et al. 1995; Peng et al. 2000). For 200-mb height, this decrease is not the result of a decrease in the amplitude of the external variability (Fig. 1, top left) but is the result of a monotonic increase in the amplitude of seasonal mean variability unrelated to SSTs (e.g., see Kumar et al. 2003). For the seasonal mean rainfall, the largest fraction is further confined to a narrow latitudinal band in the equatorial tropical Pacific west of the date line, and furthermore, in contrast to the 200-mb height, meridional decrease is mainly a result of the corresponding decrease in the external variance (Fig. 1, bottom left). From the standpoint of assessment of potential predictability of seasonal mean atmospheric states, the results imply a high potential predictability in the tropical latitudes and a much smaller potential predictability in the extratropical latitudes.

The results (and the accompanying discussion) shown in Fig. 1 are merely a reconfirmation of analysis of seasonal predictability from a host of previous studies. The primary focus of our analysis, however, is to determine the dominant spatial patterns of external variability of 200-mb height in Fig. 1, and to identify the SST forcing these patterns are associated with. This analysis is based on the EOF technique applied to the ensemble mean 200-mb anomalies for DJFs of 1980–2000.

The spatial pattern of the first EOF of ensemble mean variability, together with its time series, is shown in Fig. 2 (top). This pattern explains 53% of the external variability in Fig. 1; however, as will be discussed in Fig. 3, its local contribution could be much higher. The spatial structure of this mode bears some similarity to the global teleconnection pattern related to SST anomalies (Horel and Wallace 1981). This is further confirmed by the associated patterns of rainfall and SST anomalies shown in the Fig. 2 (bottom). The SST pattern has the largest amplitude in the equatorial tropical Pacific and corresponds to the dominant mode of SST variability for the DJF winters between 1980 and 2000 (not shown). The time series for this pattern also relates to well-documented warm and cold ENSO events during this period.

Shown in Fig. 3 (top right) is the percentage of local 200-mb height external variance that is explained by the first mode. Although this mode explains 53% of the global variance, regionally it can account for more than 80% of variance at selected locations. The hemispheric symmetry of the explained variance is even more striking than the hemispheric symmetry of the total external variance shown in Fig. 1. In the top-left panel, the remaining external variance of 200-mb height not accounted for by the first mode is also shown and is mostly concentrated in the extratropical latitudes in the Northern Hemisphere.

The corresponding plots for the rainfall are shown in Fig. 3 (bottom). As described above, the rainfall signal related to mode 1 of 200-mb height was obtained based on linear regression and only captures the rainfall variance that is “linearly” related to the interannual variability of mode-1 time series of 200-mb heights. This is likely the reason that fraction of external rainfall variance (Fig. 3, bottom right) related to the mode 1 of 200-mb height is not as high as one would have expected. For example, near the date line and in the equatorial tropical latitudes, only 60%–70% of SST-forced variability of rainfall is associated with the variability of mode 1 of 200-mb heights.

A surprising result of this analysis is that the most well documented atmospheric response pattern related to SST variability explains only 53% of global external variability of 200-mb heights, indicating that a considerable amount of atmospheric height response to interannual variations in SSTs projects on the higher modes, and these modes of external variability are discussed next.

Shown in Fig. 4 is the second dominant mode of atmospheric response to interannual variations in SSTs. On a global basis, this mode explains 19% of external variability. In contrast to mode 1, the spatial structure of height anomalies has a zonally symmetric pattern of response. Similarly, the associated SST anomalies shown in the bottom panel also have the same sign anomalies over most of the tropical and the extratropical oceans of the Northern Hemisphere. This implies that in response to uniform SST anomalies in the tropical ocean basins, for example, a tendency for the tropicwide increase in SST anomalies from 1996 onward; the 200-mb height anomalies also trend toward increased heights. This mode is similar to mode 2, identified in Hoerling and Kumar (2002).

The spatial structure of mode 3 of the external variability is shown in Fig. 5 and explains 12% of external variance. Similar to mode 1, the spatial structure of this mode has considerable regionality. The corresponding time series tends to have a large amplitude during the extreme ENSO years, for example, during the warm events of DJF 1983 and DJF 1998 and the cold events of DJF 1989 and DJF 1999. Furthermore, unlike for the time series for mode 1, which has opposite sign during the warm and cold phases of ENSO, time series for mode 3 has the same sign during extreme but opposite phases of ENSO. This hints at the possibility that this mode is similar to the nonlinear atmospheric response to ENSO discussed by Hoerling et al. (1997). Indeed, this is demonstrated in the next section.

The SST structure corresponding to mode 3 has an east–west dipole structure in the tropical equatorial Pacific with opposite-sign SST anomalies located at the date line and near the west coast of South America. Similar to the anomalous SSTs, corresponding rainfall anomalies also have an east–west structure.

Together, the first three modes account for 84% of external height variance in Fig. 1. The spatial structure of the fraction of the explained variance of height is shown in Fig. 6 (left), and it is clear that over a wide region of the globe, the first three modes together explain, in excess of 80%, of the interannual variability in the atmospheric response to SSTs. The corresponding plot for the fraction of external rainfall variance (Fig. 6, right) linearly related to the first three modes of 200-mb heights indicates that globally approximately 70% of variance is accounted for. However, the spatial structure of fractional variance for rainfall has more complex spatial structure than for the height. We emphasize once again that the fractional rainfall variance shown is only the component of SST-forced rainfall variability that is linearly related to the first three modes of external variability of 200-mb heights and was found to be smaller than the variance explained by the first three dominant EOFs of external variability of rainfall itself (not shown).

Because of consideration of sampling variability, and possible contamination from the atmospheric internal variability on the ensemble means that could exist even for an ensemble size of 80, we have not analyzed the EOFs beyond mode 3.

One interesting feature to note among the three modes analyzed is that while the spatial structure of heights and the SSTs differs considerably from one mode to another, the spatial structure of the tropical rainfall anomaly does not have such variations. For all three modes, the associated rainfall anomaly is mostly confined to the equatorial tropical Pacific, with opposite-sign rainfall anomalies in the eastern and western equatorial tropical Pacific. Assuming that rainfall anomalies are the conveying mechanism between SST and 200-mb height anomalies, a dynamical explanation for this apparent discrepancy needs to be further explored.

b. Alternate interpretation for the EOF modes

In this section, we discuss alternate views for the spatial modes of atmospheric responses discussed in the previous section and also establish connections with results obtained from the traditional analysis of atmospheric response to ENSO. One conventional approach to analyze atmospheric responses to ENSO SST variability is the compositing technique, namely, based on some SST index (e.g., the Niño-3.4 index), warm and cold ENSO years are first selected. The averaged atmospheric circulation anomaly for the selected warm and cold years then provides an estimate for the atmospheric response during the respective phases of ENSO.

Another widely used technique to assess global impact of ENSO SSTs is to compute regression between the Niño-3.4 SST index and global atmospheric anomalies. If ΔSST is the Niño 3.4 index, the regression approach can be formally represented as
i1520-0442-18-19-3953-e1
where Z is some meteorological variable (e.g., 200-mb heights or global SSTs) and a and b are the regression coefficients. The majority of previous studies have focused on obtaining the linear response in the atmospheric climate variability to ΔSST, that is, the coefficient a. In an implicit manner, some previous studies have also assessed the second-order atmospheric response to ΔSST (often referred to as the “nonlinear” response; e.g., see Hoerling et al. 1997; Hannachi 2001; Wu and Hsieh 2004).
In the composite technique, warm (Z+) and cold (Z) composites are obtained for an average warm SST index (ΔSST+) and an average cold SST index (ΔSST). If the distribution of the warm and cold SST index was symmetric, then the regression coefficients a and b can also be written as
i1520-0442-18-19-3953-e2
and
i1520-0442-18-19-3953-e3
Hoerling et al. (1997) assessed the linear and nonlinear component of ENSO SST response following Eqs. (2) and (3). A more formal analysis of regression coefficients and their relationship to linear and nonlinear composites can be found in Monahan and Dai (2004).

In the EOF analysis of 200-mb height atmospheric response to SSTs presented here, the first EOF corresponds to the linear response to the Niño-3.4 (5°N–5°S, 120°W–170°W) SST index in the equatorial tropical Pacific (not shown). The third EOF in our analysis corresponds to the nonlinear component of the atmospheric response to ENSO. This is confirmed in Fig. 7, where similar to Eq. (3), the atmospheric response based on extreme warm (DJF 1983 and DJF 1998) and extreme cold (DJF 1989 and DJF 1999) is shown. The spatial pattern of all three fields shown, that is, 200-mb heights, SSTs, and precipitation, is very similar to the spatial pattern derived using the EOF analysis (Fig. 5) and lends validity to the hypothesis that while the atmospheric response pattern related to the first EOF corresponds to the average (or linear) atmospheric response to ENSO, the third mode of the external variability is the modulation of this response for the extreme ENSO events.

To provide a better visual illustration of how the atmospheric response to extreme ENSO events varies to give rise to two separate modes of variability, the ensemble mean atmospheric responses for DJF 1998 and DJF 1999 (in shading), together with the response constructed from the first mode alone (in contours), is shown in Figs. 8a,b (top). By definition, the spatial pattern of the response reconstructed based on mode 1 is the same for both winters, and only the amplitude varies. Also shown in the bottom panels is the difference between the ensemble mean response and the response reconstructed from mode 1 alone, that is, the atmospheric response not explained by the EOF1.

For DJF 1998, an extreme warm ENSO event, the AGCM-simulated atmospheric response is shifted eastward of the atmospheric response explained by mode 1 alone (Fig. 8a, top). In contrast, for the cold ENSO event of DJF 1999, the ensemble mean response is shifted westward of the response explained by mode 1 (Fig. 8b, top). As a consequence, for both years (or for both phases of ENSO) the component of atmospheric response not explained by mode 1, shown in Figs. 8a,b (bottom), has a similar spatial structure, and furthermore, is also similar to the spatial structure of EOF mode 3. To summarize, in an EOF-based analysis, the average response for different ENSOs is captured by mode 1, while the spatial variations around the average for the ENSO extremes are captured by mode 3.

Another depiction of atmospheric response to ENSO SSTs for different amplitude warm and cold ENSO events is shown in Fig. 9. In this figure, the top two panels are the AGCM-simulated 200-mb height response for DJF 1989 (a strong cold ENSO event) and DJF 1985 (a moderately cold ENSO event), respectively. The bottom two panels are the same, but for DJF 1992 (a weak warm ENSO event) and DJF 1983 (a strong warm ENSO event), respectively. For the sake of comparison, negative one multiplies the response for the warm events. The middle panel is the spatial pattern of the first EOF. It is clear that proceeding from the strong cold to strong warm cases, the atmospheric response to ENSO SSTs shifts eastward (as indicated by the straight line drawn across the five panels connecting the positive center at 40°N). In an EOF (or regression and the compositing) technique for inferring the atmospheric response to SSTs, the mean response for the cold and warm SST events is represented by the dominant EOF, while the gradual eastward shift in the atmospheric response is manifested as the nonlinearity in the atmospheric response, or in our case, as the third mode in the EOF analysis.

The time series for the third EOF in Fig. 5 has a large projection on some non-ENSO winters, for example, DJFs of 1980, 1981, 1982, and 1986, among others. This suggests that this spatial structure may also be an atmospheric response to those years when tropical Pacific SST anomalies project onto the SST anomalies for this mode in Fig. 5. To show that this is indeed the case, the 200-mb height and rainfall response together with the SST anomalies composited for these four winters are shown in Fig. 10. The similarity between the responses for all three variables in Fig. 10 and the corresponding patterns in Fig. 5 confirms our hypothesis.

Returning to our basic motivation behind this study, that is, the understanding of atmospheric variability related to different flavors of ENSO, or related to SST variability in ocean basins other than the tropical equatorial Pacific, analysis up to this point allows us to reach the following conclusions. Regarding the atmospheric response to flavors of ENSO, analysis for this particular AGCM indicates a small sensitivity beyond the dominant first mode. From strong cold to strong warm ENSO events, the atmospheric response has a small eastward shift that is manifested as the third mode in our analysis. This is consistent with previous results (Hoerling et al. 1997). Beyond this sensitivity, changes in the tropical Pacific SST anomalies from one ENSO to another do not seem to matter. Possible dynamical reasons for this were discussed in Trenberth et al. (1998) and can be summarized as follows: the geographical pattern of atmospheric response to tropical Pacific SST anomalies (that are communicated to the atmosphere via the resulting rainfall anomalies) are spatially phase locked because of the climatology of the atmospheric mean state, for example, the wintertime jet and the climatological stationary waves. The climatological mean state, and its dynamical characteristics, provide the selection mechanism through which tropical–extratropical interaction is manifested. As a consequence, even though the ENSO SST anomalies may vary from one event to another, the resulting extratropical atmospheric response has a (nearly) spatial invariant pattern.

As for the atmospheric response patterns related to SST variability in ocean basins other than the tropical equatorial Pacific, analysis for this period and for this AGCM results in a dominant pattern of height variability that corresponds to an almost uniform increase or decrease in the 200-mb heights in phase with a similar increase or decrease in the sea surface temperatures. If the analysis is performed for a different period when such variations did not exist, or were weaker, the importance of this mode would also be smaller. The interannual variance of the atmospheric response (Fig. 1) in such a scenario would itself be smaller, and modes 1 and 3 may become the dominant modes of variability. Needless to say, analysis spanning a longer time period and with large ensembles remains a desirable proposition. Our analysis does not exclude atmospheric sensitivity to some very special cases of SSTs and corresponding atmospheric responses during specific years that are not part of the analysis period.

c. Are the higher-order EOFs real?

In model-based analysis of atmospheric response to SSTs, doubt always exists as to whether the inferred atmospheric response is something that also happens in nature or whether our inferences are an artifact of AGCM biases. We attempt to address this question from the analysis of anomaly correlation between the model-simulated and the observed anomalies with the construct that model-simulated anomalies can be (i) ensemble mean anomalies, (ii) anomalies reconstructed based on mode 1 alone, or (iii) anomalies including higher modes also, for example, modes 2 and 3, etc. If the atmospheric responses of different modes are realistic, then their inclusion in the model-simulated anomaly (which is correlated with the observed anomalies) should lead to an increase in the anomaly correlations (ACs).

Shown in Fig. 11 are the spatial maps of the anomaly correlation between different model-based estimates for the DJF 1980–2000 atmospheric response and the observed 200-mb height anomalies. The top-left panel is the correlation between the ensemble mean and the observed anomaly and represents ACs based on the use of the most complete model information available. The top-right panel is the AC between the model information based on the first EOF mode alone and the observations, the bottom-left panel is the AC between the model information based on modes 1 and 2 and the observations, and finally, the bottom-right panel is the model information based on modes 1–3 and the observations.

A comparison between the top two panels clearly indicates that the AC based on full ensemble means has better skill than the AC based on mode 1 alone, that is, the information in the atmospheric response to SSTs in the ensemble means other than what is in mode 1 alone leads to improved simulation of interannual variability. This can only happen if the atmospheric responses beyond mode 1 have something in common with the observed interannual variability and its relationship with SSTs.

A comparison of the AC between the top-right panel and bottom-left panel indicates that inclusion of information because of mode 2 leads to an overall increase in the AC, particularly in the subtropical latitudes. This is confirmed in Fig. 12, where the difference in correlation is shown. At almost all subtropical locations, the inclusion of interannual variability due to mode 2 leads to an increase in the AC, implying that a general increase (decrease) in the model-simulated height response due to a general increase (decrease) in SSTs is also part of the observations.

The change in AC due to interannual variability related to mode 3 when added to the interannual variability of modes 1 and 2 is shown in Fig. 12 (bottom). For this case, the change in the AC is not as unanimous as was the case for mode 2 (Fig. 12, top). For example, in the Southern Hemisphere polar latitudes, inclusion of interannual variability due to mode 2 leads to degradation in the ACs, implying that the AGCM-simulated response is clearly erroneous. On the other hand, there is some increase in AC in the Northern Hemisphere extratropical latitudes, for example, the west coast of North America and the North Atlantic basin. Of particular interest to note is the increase in AC over the North Atlantic basin that corresponds to a strong nonlinear signal during the cold phase of ENSO (Fig. 8b, bottom), a fact also noted by Sardeshmukh et al. (2000) and Lin and Derome (2004).

A final analysis of anomaly correlations is shown in Fig. 13 (left), where a scatter diagram between the AC based on mode 1 alone (x axis) and the AC based on all three modes (y axis) is plotted. For points located above the diagonal, the AC based on three modes is better than the AC based on mode 1 alone. As the majority of points are above the diagonal, it implies that the information contained in modes 2 and 3 is indeed realistic, although most of the improvements are a result of the addition of the atmospheric response due to mode 2. We have also repeated the same analysis but for AC computed only over the non-ENSO years in the 21-yr time series. Results shown in Fig. 13 (right) are similar to the analysis of AC over all the years and indicate that inclusion of modes 2 and 3 also improves potential predictability in non-ENSO years. To summarize, an overall assessment from the inclusion of atmospheric response due to higher modes on the AC is that it indeed leads to improvement in the representation of interannual variability due to SSTs, and therefore, the atmospheric response patterns contained in the higher modes discussed here, to a certain degree, are realistic.

4. Summary and conclusions

Based on the ensemble of 80-member AGCM simulations for DJFs between 1980 and 2000, this study focused on the analysis of the dominant modes of 200-mb height response to SSTs. The motivation for our analysis was to understand the atmospheric responses other than what is the “average” response forced by ENSO. Specifically, we attempted to diagnose what may be the atmospheric response due to flavors of ENSO, and what the atmospheric response to SSTs in the ocean basins other than the equatorial tropical Pacific may be. If such deviations in the atmospheric response beyond the canonical ENSO response exist, their documentation and understanding is of importance to further seasonal prediction efforts.

The analysis approach in this study was the EOF decomposition of interannual variability in the 200-mb ensemble mean height response. The first EOF of the height pattern, and the associated SST pattern, was the familiar pattern of tropical–extratropical teleconnection pattern forced by the ENSO SSTs, also obtained in earlier studies based either on the regression or the composite analysis techniques. This pattern of variability, however, explained only 53% of the variance of AGCM-simulated external variability, implying that for this AGCM, and for this analysis period, there are higher-order modes of variability with a substantial amount of variance explained.

The second mode obtained using EOF analysis explained 19% of external variance and was associated with a tropicwide warming (cooling) in SSTs leading to a general increase (decrease) in 200-mb height anomalies. The third mode explaining 12% of variance was identified as the departure from the ENSO response contained in mode 1 that occurs for extreme cases for ENSO. It was also shown that even for some non-ENSO years when the SST anomalies themselves project on the spatial structure of SSTs related to the EOF mode 3, 200-mb height response does mimic the spatial structure similar to that of mode 3.

To assess that the dominant modes of variability identified were not an artifact of AGCM biases, spatial maps of temporal anomaly correlation between the AGCM-simulated anomalies (based on different levels of information content) and the observed anomalies were compared. It was shown that when the AGCM-simulated 200-mb height response was reconstructed based on modes 1 and 2, the anomaly correlation was clearly superior to the anomaly correlation based on 200-mb height reconstructed based on mode 1 alone. Inclusion of anomalies reconstructed from mode 3, however, led to mixed results, with ACs being larger only over some geographical locations. In general, however, the results imply that the inclusion of atmospheric response beyond mode 1 leads to an increase in the anomaly correlations, and, therefore, the higher-order responses may indeed be realistic.

To summarize, the analysis of AGCM simulations does indicate that atmospheric responses other than the canonical response to ENSO exist. The relative dominance of mode 2 in the analysis may be an artifact of the analysis period used in this study and may decrease for the analysis periods when trends in the tropical SSTs are not pronounced.

The difference in the anomaly correlation obtained using the ensemble-averaged anomaly and the anomaly correlation obtained based only on the information from mode 1 (i.e., the two top panels in Fig. 11) is indicative of the increase in potential predictability due to atmospheric responses other than what is solely due to ENSO SSTs. However, actual realization of this predictability poses considerable challenges, because these responses also depend on the prediction of SSTs beyond the capability of the current generation of coupled prediction systems, that is, the ENSO. Furthermore, whether these SST anomalies themselves are predictable or not remains to be seen.

Acknowledgments

This research was partially supported by NOAA’s Climate Dynamics and Experimental Prediction Program.

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Fig. 1.
Fig. 1.

Spatial pattern of AGCM-simulated external variability of 200-mb (top left) DJF seasonal mean height (shading interval: 1000) and (bottom left) DJF seasonal mean rainfall. External variance is computed from the ensemble mean DJFs between 1980 and 2000. Units for height are m2 and for rainfall are mm day−2. (right) The ratio of external variance to (top right) the total variance of DJF seasonal mean height (shading interval: 0.2) and (bottom right) DJF seasonal mean rainfall (shading interval: 0.2). Total variance is computed from the variance of all DJFs in the analysis period. This ratio is proportional to the potential predictability of 200-mb height and rainfall anomalies.

Citation: Journal of Climate 18, 19; 10.1175/JCLI3483.1

Fig. 2.
Fig. 2.

(top left) Spatial structure of the first EOF of external variability of 200-mb DJF seasonal mean heights (shading interval: 20) and (top right) the associated time series. For the individual DJFs, the AGCM-simulated height anomalies projecting on this mode can be computed as the scalar product of these two fields. (bottom left) The corresponding rainfall anomalies (in mm day−1) and (bottom right) SSTs (in K) are obtained as a regression with the time series of the first EOF.

Citation: Journal of Climate 18, 19; 10.1175/JCLI3483.1

Fig. 3.
Fig. 3.

(top left) Spatial pattern of 200-mb DJF seasonal mean height external variance as in Fig. 1 not explained by the first EOF (shading interval: 250). Units are in m2. (top right) The ratio of the external variance of height explained by mode 1 and the external variance itself (shading interval: 0.2). The closer the ratio is to one, the larger the fraction of variance explained by the dominant mode of external variability is. (bottom left) The external variance for the rainfall not related to the first EOF of the height. Units are mm day−2. (bottom right) The ratio of external variance of rainfall related to mode 1 of height and the external variance of rainfall itself (shading interval 0.2).

Citation: Journal of Climate 18, 19; 10.1175/JCLI3483.1

Fig. 4.
Fig. 4.

Same as in Fig. 2, but for the second EOF of the external variability.

Citation: Journal of Climate 18, 19; 10.1175/JCLI3483.1

Fig. 5.
Fig. 5.

Same as in Fig. 2, but for the third EOF of the external variability.

Citation: Journal of Climate 18, 19; 10.1175/JCLI3483.1

Fig. 6.
Fig. 6.

(left) Spatial pattern of the ratio of 200-mb DJF seasonal height external variance explained by the first three EOFs and the total external variability. (right) Spatial pattern of the ratio of seasonal mean rainfall variance linearly related to the first three EOFs of height and the total external variability of seasonal mean rainfall. The closer the ratio is to one, the larger the fraction of the variance explained by the first three modes of external variability is. The shading interval is 0.2.

Citation: Journal of Climate 18, 19; 10.1175/JCLI3483.1

Fig. 7.
Fig. 7.

(top) Spatial pattern of the nonlinear component of ENSO response for the AGCM-simulated 200-mb heights (shading interval: 10), (middle) observed SSTs (shading interval: 0.5), and (bottom) the AGCM-simulated rainfall. The nonlinear component is estimated as the sum of the warm composite for DJF 1983 and DJF 1998 and the cold composite for DJF 1988 and 1999 [also see Eq. (3)]. Units are m for 200-mb height, K for SSTs, and mm day−1 for rainfall.

Citation: Journal of Climate 18, 19; 10.1175/JCLI3483.1

Fig. 8.
Fig. 8.

(a) (top) AGCM-simulated 200-mb height response for the warm ENSO event of DJF 1998 (in shading; shading interval: 20) superimposed on the atmospheric response reconstructed from the first EOF of external variability (in contours). (bottom) The difference between the AGCM-simulated height response and the response reconstructed from the first EOF as shown in the top panel (contouring interval: 20). The difference is the AGCM-simulated height response that is not explained by the canonical response to EOF (i.e., the first EOF). Units are in m. (b) Same as in Fig. 8a, but for the cold ENSO event of DJF 1999.

Citation: Journal of Climate 18, 19; 10.1175/JCLI3483.1

Fig. 9.
Fig. 9.

AGCM-simulated 200-mb height response for (top two panels, respectively) the cold events of DJF 1989 and DJF 1985 and for (bottom two panels, respectively) the warm events of DJF 1992 and DJF 1983. Anomalies for the warm events are multiplied by negative one. (middle) The spatial pattern of atmospheric response for the first EOF. The sequence of the five panels can be thought of as ENSO atmospheric response progressing from the extreme cold events to the extreme warm events. The straight line across the five panels joins the center of positive height anomalies at 40°N and indicates an eastward shift in the 200-mb height response to ENSO SSTs from cold-to-warm events. Units are in m and contouring interval is 20.

Citation: Journal of Climate 18, 19; 10.1175/JCLI3483.1

Fig. 10.
Fig. 10.

(top) AGCM-simulated 200-mb height response (shading interval: 10), (middle) observed SST anomalies (shading interval: 0.2), and (bottom) AGCM-simulated rainfall response. All the anomalies are averages for DJFs of 1980, 1981, 1982, and 1986. The winters were chosen based on the following: 1) they were not an ENSO year as indicated by the time series shown in Fig. 1, and 2) the height anomaly had a large projection on the third EOF in Fig. 5. Units are m for 200-mb height, K for SSTs, and mm day−1 for rainfall.

Citation: Journal of Climate 18, 19; 10.1175/JCLI3483.1

Fig. 11.
Fig. 11.

(top left) Spatial pattern of temporal anomaly correlation between AGCM-simulated and observed 200-mb height anomalies for DJFs between 1980 and 2000. Anomaly correlation when the AGCM-simulated height anomalies are reconstructed from (top right) the first EOF alone, (bottom left) the first two EOFs, and (bottom right) the first three EOFs of external variability.

Citation: Journal of Climate 18, 19; 10.1175/JCLI3483.1

Fig. 12.
Fig. 12.

(top) Difference in the temporal anomaly correlation between AGCM-reconstructed and observed 200-mb height anomalies where AGCM-reconstructed height anomalies were either based on EOFs 1 and 2 or were based on the first EOF. Difference also corresponds to difference in anomaly correlations shown in the bottom-left and top-right panels in Fig. 11. (bottom) Same as in top, but for the difference in the anomaly correlations where AGCM-reconstructed height anomalies were either based on the first three EOFs or were based on the first EOF alone. Difference also corresponds to difference in anomaly correlations shown in the bottom-right and top-right panels in Fig. 11.

Citation: Journal of Climate 18, 19; 10.1175/JCLI3483.1

Fig. 13.
Fig. 13.

(left) The scatterplot between the anomaly correlations shown in the bottom-right and top-right panels in Fig. 11. The x axis represents the anomaly correlations based on mode 1 alone, whereas the y axis is the anomaly correlations based on modes 1–3. (right) Same as in left, but for anomaly correlations computed over non-ENSO years alone. For all the points above the diagonal line, the anomaly correlation based on added information from the EOF modes 2 and 3 was better than the anomaly correlation based on the EOF mode 1 alone.

Citation: Journal of Climate 18, 19; 10.1175/JCLI3483.1

1

Throughout the paper, the year corresponding to DJF is identified according to the year for which the month of January corresponds. For example, DJF 1980 implies seasonal average from December 1979 to February 1980.

2

Although the hindcasts for two different years started from the same atmospheric initial conditions, simulations for the second year of hindcasts differed because of incremental changes in the computing architecture on which forecasts were made. Such changes did not influence the statistical characteristics of AGCM-simulated fields, but they act as pseudorandom perturbations to effectively generate independent seasonal realizations.

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