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Impact of Tropical Subseasonal SST Variability on Seasonal Mean Climate Simulations BEN P. KIRTMAN, DAN A. PAOLINO, JAMES L. KINTER III,
AND
DAVID M. STRAUS
Center for Ocean–Land–Atmosphere Studies, Institute of Global Environment and Society, Inc., Calverton, Maryland (Manuscript received 27 January 2000, in final form 24 August 2000) ABSTRACT The purpose of this study is to examine the impact of subseasonal sea surface temperature (SST) variability on the simulation of the seasonal mean extratropical circulation using a state-of-the-art high-resolution atmospheric general circulation model (AGCM). The format is a case study for January through March 1989 (JFM89) and the primary emphasis is on regional scales over North America. The SST boundary conditions in the AGCM simulations were prescribed using observed weekly data. Experiments were made in which the week-to-week (subseasonal) SST variability was suppressed. In terms of the largest spatial scales, the subseasonal SST variability has only a modest impact; however, statistically significant modifications to the 500-mb height anomalies over North America were detected. Consistent with these changes in the height field, the seasonal mean North American rainfall anomalies were particularly sensitive to the subseasonal SST variations, especially over the Pacific Northwest. Two possible mechanisms for this sensitivity were investigated with additional AGCM experiments and model diagnostics. The first mechanism, referred to as a ‘‘stochastic’’ effect, is defined by the hypothesis that the weekto-week SST variability only serves to enhance the amplitude of tropical precipitation variability, which, in turn, modifies the midlatitude response. With this stochastic effect, the details of the subseasonal SST evolution do not matter. In contrast, the second mechanism is a ‘‘deterministic’’ effect in that the details of the evolution of the subseasonal SST matter. The experiments presented here indicate that the stochastic effect is small and that the details of the subseasonal SST produce significant differences. This conclusion is supported by experiments with very large ensembles using a somewhat lower-resolution AGCM and a nonlinear barotropic model. Finally, some implications of these results for real-time forecasting are discussed.
1. Introduction Recently, a number of atmospheric general circulation modeling (AGCM) studies have demonstrated that during El Nin˜o–La Nin˜a events there are certain elements of the extratropical atmospheric circulation that are predictable (e.g., Shukla et al. 2000). The prevailing hypothesis is that much of this predictability is due to the slowly evolving sea surface temperature anomalies (SSTA). These studies use ensembles of AGCM realizations in order to average out the unpredictable atmospheric noise and isolate the signal forced by the SSTA. There have been a number of studies that have investigated the predictability of the extratropics using this methodology (Palmer 1988; Brankovic et al. 1994; Kumar et al. 1996; Palmer et al. 2000; Straus and Shukla 2000). Typically, these studies use observed SST, there-
Corresponding author address: Dr. Ben P. Kirtman, Center for Ocean–Land–Atmosphere Studies, Institute of Global Environment and Society, Inc., 4041 Powder Mill Road, Suite 302, Calverton, MD 20705-3106. E-mail:
[email protected]
q 2001 American Meteorological Society
by ignoring the uncertainty in the predicted SSTA, which is necessarily present in real-time climate forecasting. On the other hand, Kumar and Hoerling (1997) found only little sensitivity to inter–El Nin˜o variability. It remains an open question how uncertainty in the SSTA affects the seasonal prediction. The purpose of this paper is to examine (in a case study format) how the uncertainty in using predicted SSTA affects the boreal winter season extratropical forecast. While this particular case study focuses on the boreal winter of 1988/89, it was motivated by our experience in attempting to predict the recent 1998/99 La Nin˜a in real time. Before discussing the hindcast and forecast experiments it is worth noting some of the differences between January–March 1999 and 1989 (hereafter JFM99 and JFM89) in the observed circulation and rainfall. Since the forecast was made in real time, the observed differences were not available. Figures 1a,b show the observed differences in global precipitation and 500-mb geopotential height in the Pacific–North American region. Throughout most of the tropical and subtropical Pacific, the rainfall differences are negative. In the
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FIG. 1. (a) Climate Prediction Center (CPC) Merged Analysis of Precipitation (CMAP) difference Jan–Mar 1999 (JFM99) minus Jan– Mar 1989 (JFM89). Contour interval is 1 mm day21 . (b) NCEP reanalysis 500-mb geopotential height difference JFM99–JFM89. Contour interval is 50 gpm.
FIG. 2. (a) Observed sea surface temperature anomaly averaged over JFM89. (b) Predicted minus observed sea surface temperature anomaly averaged over JFM99. In both panels the contour interval is 0.38C. In calculating the anomaly the monthly climatology from 1951–80 has been removed.
Northern Hemisphere extratropics the largest signals are the positive rainfall anomalies in the Pacific Northwest. The 500-mb height differences have three centers of action with negative differences over the Pacific Ocean and the west coast of North America, positive differences over northeast North America, and negative differences over the Atlantic Ocean and the southeast United States. As will be discussed in detail, the modelforecasted differences capture a strong rainfall response in the Pacific Northwest and the three centers of action in the 500-mb height differences. However, the height differences are shifted compared to observations and the rainfall response is more of a dipole as opposed to the single signed structure in the observations. Nevertheless, it is surprising to us that the model and the observations responded so strongly in such a localized region of North America. Moreover, given the similarities in observed and forecasted differences, we believe that the model can be used to understand the source of these differences. With the development of an anomaly coupled ocean– atmosphere prediction system (Kirtman et al. 1997), the Center for Ocean–Land–Atmosphere Studies (COLA) began real-time forecasting of tropical Pacific SSTA (Kirtman et al. 1995). The predicted SSTA for the boreal
winter of 1998/99 (at a lead time of six months) was used to predict extratropical rainfall and circulation using a two-tiered procedure (Bengtsson et al. 1993). In applying this two-tiered process, the SSTA forecast was statistically filtered. This filter produced a seasonal mean SSTA field that closely resembled the SSTA during the earlier 1988/89 cold event (see Fig. 2; the SST climatology was calculated over the 1951–80 period). Because the two seasonal mean SSTA fields were similar, the 1998/99 tier two forecast might be expected to be similar to the earlier 1988/89 hindcast. However, the extratropical forecast over much of the Pacific–North American region was significantly different. Moreover, because the forecast and the hindcast were made with a relatively large ensemble of realizations, it was possible to determine that these differences were not likely to result from ‘‘weather noise,’’ leaving open the possibility that these differences are predictable. The hindcast experiments presented here are aimed at determining the cause for these differences. Moreover, these AGCM experiments establish and quantify how these arguably small SST differences seen in Fig. 1b impact the forecast. Throughout the remainder of this paper we refer to the JFM89 hindcast as H89 and the JFM99 forecast as
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FIG. 3. (a) H89 North American precipitation anomaly, (b) F99 North American precipitation anomaly, and (c) F99–H89 precipitation difference. In all three panels the contour interval is 0.25 mm day21 and values over the ocean have been masked out.
F99. It should be noted that the extratropical SSTA in all the experiments shown here are identical and equal to the SSTA during JFM89. In other words, there are extratropical SSTA, but they are identical in all the experiments. The feature of F99 that was different from H89, and that first caught our attention without prior knowledge of Fig. 1a, was the precipitation anomalies over continental North America. Figures 3a–c show the precipitation anomalies in H89, F99, and the difference, respectively. The precipitation over the ocean has been masked out in Figs. 3a–c, but it will be shown later and discussed in some detail. The feature of Figs. 3a–c that
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was initially surprising was the large difference between H89 and F99 along the Pacific coast. In H89 there are positive anomalies in the Pacific Northwest and negative anomalies along the west coast of Canada. In contrast, F99 has anomalies of the opposite sign in these regions. F99 is also considerably drier than H89 in much of the eastern third of the United States and wetter in the southwest. The observed differences (Fig. 1a) show a strong response in the Pacific Northwest but with a somewhat different structure than that seen in Fig. 3c. The strategy used in this paper to understand the differences between H89 and F99 is to rerun the AGCM with the SSTA modified in some way from the observed 1988/89 SSTA. To isolate signal versus noise, several realizations (ensemble members) of the AGCM simulations are made. The primary result of these experiments is that subseasonal variability in the SSTA has a significant impact on the seasonal mean extratropical response, particularly over North America. This conclusion is based on comparisons to additional AGCM experiments in which we have removed the week-toweek variability in the SSTA. In particular, we show that the rainfall anomaly differences highlighted in Figs. 3a–c are mostly attributable to the subseasonal SSTA differences. We also examine whether the evolution of the subseasonal variability matters. In other words, is the week-to-week variability merely acting as stochastic forcing that enhances the tropical rainfall variability and the associated midlatitude response? Or is the week-toweek SSTA variability producing a deterministic response in the tropical rainfall, which, in turn, produces a midlatitude response via some teleconnection process? Additional AGCM experiments (with a somewhat lower-resolution model) are described that were designed to address this question. Based on the case study presented here, it is concluded that the stochastic effect is relatively small and that the details in the evolution of the SSTA within the season produce significant differences in the seasonal mean. This result is also supported by some barotropic model calculations. These results have a number of implications for real-time climate forecasting that are discussed in some detail. The remainder of the paper is as follows. Section 2 briefly describes the AGCM and how F99 and H89 were made. Differences between F99 and H89 are shown in section 3 with an emphasis on the simulation over North America. The impact of subseasonal variability is examined in section 4. Section 5 discusses the ‘‘stochastic effect’’ results and the concluding remarks are given in section 6. 2. Model The COLA AGCM, which was originally derived from the National Centers for Environmental Prediction (NCEP) numerical weather prediction model (Sela 1980), is used in the experiments described here. Versions of the AGCM have been extensively used for mon-
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soon studies (e.g., Fennessy et al. 1994; Kirtman and Shukla 2000) and for ENSO studies (Kirtman et al. 1997; Kirtman and DeWitt 1997; Kirtman and Zebiak 1997). The AGCM has also been coupled to a slab mixed layer ocean model in Schneider et al. (1997) to study the influence of the tropical oceans on global climate and in Schneider et al. (1999) to examine the climate sensitivity to upper-tropospheric water vapor. The model is a global spectral model with rhomboidal truncation at total wavenumber 40. There are 18 unevenly spaced s-coordinate vertical levels. The parameterization of the solar radiation is after Lacis and Hansen (1974) and terrestrial radiation follows Harshvardhan et al. (1987). The deep convection is an implementation of the relaxed Arakawa–Schubert scheme of Moorthi and Suarez (1992) described by DeWitt (1996). The convective cloud fraction follows the scheme used by the National Center for Atmospheric Research Community Climate Model [Kiehl et al. (1994); see DeWitt and Schneider (1996) for additional details]. There is a turbulent closure scheme for the subgrid-scale exchange of heat, momentum, and moisture as in Miyakoda and Sirutis (1977) and Mellor and Yamada (1982). Additional details regarding the AGCM can be found in Kinter et al. (1988) and DeWitt (1996). Model documentation is given in Kinter et al. (1997). Unless otherwise stated, the AGCM simulations consist of nine-member ensembles initialized with NCEP analysis at 0000 UTC 13 December, 1200 UTC 13 December, 0000 UTC 14 December, . . . , 0000 UTC 17 December 1988. The initial solar date corresponds to the date of the analysis. Each integration is run through the end of March 1989. In all the results shown here, the part of the simulation during December 1988 is ignored. Climatological soil moisture and snow depth were used as initial conditions for the land surface model, with the subsequent evolution being predicted. Throughout the paper, the figures plotted are for the mean of all nine members of the ensemble and anomalies are taken with respect to model climatologies (1982–96). The SSTA in the extratropics (poleward of 158) in all the experiments is the same as H89. 3. JFM99 forecast versus JFM89 hindcast As mentioned in the introduction, Figs. 2a,b show the JFM89 observed seasonal mean SSTA and the difference from the JFM99 SSTA forecast, respectively. Similarly, Figs. 3a–c show the associated rainfall anomalies over North America. In the same format as Figs. 3a–c, Figs. 4a–c show the 500-mb geopotential height. The height anomalies for both H89 and F99 are, in a general sense, consistent with cold ENSO conditions in the tropical Pacific in that there are positive anomalies in the north Pacific and negative anomalies over much of Canada and the northern United States. However, the amplitudes of the 500-mb geopotential height anomalies in H89 are considerably larger than in F99. The North
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FIG. 4. (a) H89 500-mb geopotential height anomaly, (b) F99 500mb geopotential height anomaly, and (c) F99–H89 500-mb geopotential height difference. In all three panels the contour interval is 10 gpm and the shading in (c) indicates regions where the difference is significant at the 95% confidence level.
Pacific high in F99 is about half that of H89. The low in F99 is displaced to the northeast and is considerably weaker than in H89. The shaded regions in the difference maps (Figs. 3c and 4c) indicate regions where the difference is significant at the 95% level according to a local significance test. The differences are also field significant at the 95% level and it is unlikely these differences are due to weather noise. The details of how the significance tests were applied are described in the appendix. A synoptic view of these differences also suggests
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FIG. 5. (a) H89 precipitation anomaly, (b) F99 precipitation anomaly, and (c) F99–H89 precipitation difference. In all three panels the contour interval is 3 mm day 21 and the shading in (c) indicates regions where the difference is significant at the 95% confidence level.
that they are systematic. The rainfall differences noted in Fig. 3c appear to be associated with the height differences in Fig. 4c. For example, the deeper low of the Pacific Northwest is consistent with increased rainfall anomalies in H89. The differences in the height anomalies and the North American rainfall anomalies are significant, yet smaller in magnitude than a typical ENSO response. Nevertheless, the differences may be explained by tropical heating anomalies in the Pacific Ocean forcing a midlatitude response via teleconnections. In other words, the differences in the SSTA lead to differences in tropical precipitation anomalies and associated latent heating anomalies that modify the midlatitude seasonal mean circulation. This teleconnection process, however, is not the only plausible explanation as will be discussed in detail. Figures 5a–c show a tropical wide view of the precipitation anomaly in the same format as Figs. 3 and 4. Precipitation anomalies in the Tropics are a good proxy for heating anomalies and they are shown here as the possible source for the teleconnection patterns seen in Figs. 3 and 4. There are significant heating (precipitation) differences over large regions of the tropical
oceans. For example, there are negative (differences in the western and central Pacific centered along 108N. These differences indicate strong heating anomalies in H89 compared to F99. Conversely, there are stronger heating anomalies in the tropical southwestern Pacific in F99. There are also stronger rainfall anomalies in the eastern tropical Pacific in H89. Given the relatively small amplitude of the seasonal mean SSTA difference seen in Fig. 2b, it is not obvious that the tropical rainfall differences should be as large as those shown in Fig. 4c. On the other hand, as shown below, the SSTA have a relatively large variation within the season. In addition, the tropical precipitation responds nonlinearly to the SST. Therefore, it is possible for the seasonal mean precipitation differences to be larger than expected by consideration of only the seasonal mean SSTA differences. In order to investigate this possibility, the subseasonal variability in the SSTA differences and in the rainfall differences are shown in Figs. 6a and 6b, respectively. Both fields vary over the three-month period; however, the general character is relatively smooth in the sense that the differences do not change sign repeatedly from week to week. From
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FIG. 6. Time–longitude cross section averaged between 158S and 158N of the (a) SST difference between the F99 and H89; (b) same as (a) except for precipitation. In (a) the contour interval is 0.18C and in (b) the contour interval is 1 mm day21 .
Fig. 6 it appears that, even though there is substantial subseasonal variability, it occurs smoothly enough to be adequately described by monthly means. However, the seasonal mean has a large degree of cancellation between monthly mean anomalies of opposite sign. During the first month and a half, the SSTA forecast is warmer than the observed and during the latter part of the period it is colder. The largest differences in the rainfall tend to be in the western Pacific, with generally positive (negative) differences in the first (second) half of the forecast period. In contrast, the largest SSTA differences are in the eastern Pacific. There are small positive differences in the SSTA between 1608E and the date line during the first half of the forecast period that are collocated with relatively large rainfall differences. 4. Subseasonal versus seasonal mean SSTA For the purposes of the work presented here, the SSTA used in F99 and H89 differ in two aspects. First, the seasonal mean SSTA is different, as shown in Fig. 2b. Second, the H89 SSTA has subseasonal variability, whereas the F99 SSTA is nearly constant throughout
the season.1 In this section, we attempt to isolate the impact of these two effects. The simplest way to isolate the impact of the subseasonal variations in the SSTA is to repeat H89, but with the subseasonal variability in the SSTA removed. We refer to this case as EXP1. In EXP1, the SSTA is held constant throughout the simulation and is prescribed to be the same as the seasonal mean SSTA used in H89. Therefore, differences between EXP1 and H89 indicate the impact of observed subseasonal SSTA variability for the JFM89 period. Similarly, the impact of seasonal mean SSTA differences is isolated by examining the differences between EXP and F99. This is because the SSTA in both EXP1 and F99 remain constant throughout the season (i.e.,
1 Strictly speaking, the F99 has month-to-month variability. However, this variability is relatively small and has the same spatial structure as the anomaly. In particular, the maximum subseasonal variability (0.28C between January and March) is in the eastern Pacific where the SSTA is already quite cold. In the western Pacific, the variability is an order of magnitude smaller than the subseasonal variability shown in Fig. 6a. Put simply, the anomaly in F99 is nearly constant throughout the season.
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KIRTMAN ET AL. TABLE 1. Description of AGCM SSTA sensitivity experiments.
Experiment name H89 F99 EXP1 EXP2
SST
Purpose
Observed weekly SST from 15 Dec 1988 to 31 Mar 1989 Forecasted monthly SSTA for Dec 1998–Mar 1999 plus climatological weekly SST Seasonal mean SSTA from Jan 1989–Mar 1989 plus climatological weekly SST Seasonal mean SSTA same as H89 and EXP1, but subseasonal SSTA randomly shuffled plus weekly climatological SST
neither have subseasonal variability). Moreover, the SSTA differences between EXP1 and F99 are the same as the seasonal mean SSTA differences between the H89 and the F99. Symbolically, ^SSTA EXP1 & 2 ^SSTA F99 & 5 ^SSTA H89 & 2 ^SSTA F99 &, where ^ & denotes the seasonal mean average. In summary, EXP1–H89 indicates the impact of subseasonal SSTA differences and EXP1–F99 indicates the impact
Resolution
Hindcast experiment Forecast experiment
R40 R40
Remove subseasonal SSTA variability Randomize subseasonal SSTA variability (i.e., test stochastic impact of subseasonal SSTA)
R40 T30
of seasonal mean SSTA differences. Table 1 summarizes these experiments. a. Seasonal mean fields Figures 7a–c show the precipitation anomalies from EXP1, EXP1–H89, and EXP1–F99, respectively. Figure 7b indicates the impact of subseasonal SSTA differences and Fig. 7c isolates the effect of seasonal mean SSTA
FIG. 7. (a) EXP1 precipitation anomaly, (b) EXP1–H89 precipitation difference, and (c) EXP1– F99 precipitation difference. In (a) and (c) the contour interval is 3 mm day 21 and in (b) the contour interval is 1 mm day21 . The shading in (b) and (c) indicates regions where the difference is significant at the 95% confidence level.
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differences. Comparing Figs. 7a and 5a indicates that, qualitatively, EXP1 and H89 are quite similar in the Tropics. Quantitative differences due to the subseasonal SSTA variability are shown in Fig. 7b. The impact of the subseasonal SSTA variability is quite small compared to the impact of the seasonal mean SSTA differences (Fig. 7c). Based on Figs. 7b,c, it is tempting to conclude that the subseasonal SSTA variability has little or no impact on H89. There are, however, regions in the western Pacific, for example, where the differences in the rainfall are statistically significant. The argument that is made in this paper is that, while these rainfall differences are relatively small, they are systematic enough to modify the forced response over North America, leading to substantial changes in the rainfall anomaly over North America. The changes in the North American rainfall anomalies are highlighted in Figs. 8a–c. Figure 8a shows the rainfall anomaly over North America in EXP1 and Fig. 8b shows the rainfall anomaly from H89. The impact of the subseasonal SSTA variability is shown in the difference between EXP1 and H89 (Fig. 8c). The feature to be noted is the considerably stronger positive rainfall anomalies in H89 in the Pacific Northwest. This enhanced rainfall in H89 (Fig. 8b) is due to the subseasonal SSTA variability; it is statistically significant at the 95% level locally and is field significant at the 95% level (Fig. 8c; the appendix describes how the significance test was applied to the rainfall differences). In terms of real-time seasonal forecasting, this difference would have a substantial regional impact. In the same format as Figs. 7a–c, Figs. 9a–c show the global 500-mb geopotential height anomalies. Similar to Figs. 7b,c, Fig. 9b can be interpreted as the impact of subseasonal SSTA differences and Fig. 9c can be interpreted as the impact of seasonal mean SSTA differences. As with H89 and F99, the general cold event characteristics are captured in EXP 1 (Fig. 9a). Throughout the Tropics, there are low geopotential height anomalies, and, in the North Pacific, there are strong positive anomalies. Over the northern tier of North America, there are negative anomalies and in the southern third of the United States the anomaly is positive. All of these features are consistent with H89 and F99. However, there are differences in the details that are worth noting. First, most of the differences in the Tropics (Fig. 9c) are explained by seasonal mean SSTA differences. The stronger positive anomalies over the North Pacific also appear to be due to seasonal mean SSTA differences. Conversely, the enhanced ridging over western North America is mostly due to the subseasonal SSTA differences. These difference are consistent with the rainfall differences seen in Fig. 8c and are statistically significant at the 95% level. There are at least two possible explanations for the differences between EXP1 and H89 noted in Figs. 7–9. The first possibility is that the week-to-week variability in the SSTA acts as a ‘‘stochastic’’ forcing that enhances
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FIG. 8. (a) EXP1 North American precipitation anomaly, (b) H89 North American precipitation anomaly, and (c) EXP1–H89 precipitation difference. In all three panels the contour interval is 0.25 mm day21 and the shading in (c) indicates regions where the difference is significant at the 95% confidence level.
the variability in the tropical rainfall and the associated midlatitude response. The second possibility is that there is some deterministic subseasonal variability that forces a systematic midlatitude response that can be detected in the seasonal mean. In the following three figures, we show that there is evidence to support both of these hypotheses. It is for this reason that the additional AGCM experiments described in section 5 were made. Figures 10a and 10b compare the precipitation variability within the season for H89 and for EXP1. The standard deviation is calculated from daily values for all nine ensemble members where the seasonal mean of each ensemble member has been removed. The purpose
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in H89 is greater than the variability in EXP1. Coupled with the fact that the seasonal mean precipitation differences are seemingly small, Fig. 10b suggests that the weekly SSTA variability has a stochastic effect on the tropical precipitation, increasing the amplitude of the subseasonal variability, which could possibly enhance the midlatitude response. b. Monthly mean fields
FIG. 9. (a) EXP1 500-mb geopotential height anomaly, (b) EXP1– H89 500-mb geopotential height difference, and (c) EXP1–F99 500mb geopotential difference. In all three panels the contour interval is 20 gpm and the shading in (b) and (c) indicates regions where the difference is significant at the 95% confidence level.
of Figs. 10a,b is to examine whether the variability about the ensemble mean seasonal mean is different between H89 and EXP1. Figure 10a shows the standard deviation for H89 and Fig. 10b shows the difference EXP1–H89. Throughout most of the tropical Pacific, the variability
While the subseasonal rainfall variability in the Tropics suggests that the stochastic effect of weekly SSTA variability is potentially important, examining the individual months that compose the seasonal mean suggests that the details in the evolution of the SSTA may also be important. This can be seen by comparing Figs. 11a and 11b, which show the 500-mb geopotential height differences for January 1989 and March 1989, respectively. Similarly, Figs. 12a and 12b show the same differences for the precipitation. The January monthly mean fields look quite similar to the seasonal mean fields. For example, over the Pacific–North American region, Fig. 11a closely resembles Fig. 9b, except the anomalies have larger amplitude. The location and signs of the centers of action in the region agree quite well. Similarly, Fig. 12a has the same precipitation signal as Fig. 7b along 108N in the western Pacific. Again, the signal is considerably stronger in the January mean compared to the seasonal mean. In contrast, the March 1989 mean (Figs. 11b and 12b) bears little or no resemblance to either the January mean or the seasonal mean. This lack of any similarity is true for both the geopotential height and the precipitation. In particular, the rainfall anomaly along 108N in the western Pacific is of the opposite sign during March 1989 and there is no coherent response over much of North America. These monthly mean results indicate that much of the seasonal mean differences over North America between H89 and EXP1 are due to the January contribution to the seasonal mean. In contrast to the subseasonal variability comparison (Figs. 10a,b), this suggests that the evolution of the SSTA within the season could possibly produce a ‘‘deterministic’’ forcing (as opposed to a stochastic forcing) of the tropical rainfall anomalies, which in turn gives a systematic response over the Pacific– North American region. Based on the results presented thus far, we cannot eliminate either the deterministic or the stochastic explanation for the differences. The experiments described in the next section are specifically designed to address this question of whether the differences over North America are due to deterministic versus stochastic SSTA differences. 5. ‘‘Signal’’ versus ‘‘noise’’ The results of the previous section indicate that the subseasonal SSTA variability contributes to the Pacific– North American seasonal mean in a significant way.
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FIG. 10. (a) Standard deviation of precipitation about seasonal mean ensemble mean for H89 and (b) the difference in the standard deviations EXP1–H89. The contour interval in (a) is 3 mm day21 and in (b) is 1 mm day21 .
Typically, one might expect to see this effect in some large-scale seasonal mean tropical precipitation pattern. This was not the case in the results shown here. Only relatively small-scale features were detected in the seasonal mean. However, results were presented that suggest that details in the subseasonal evolution of the
SSTA are important for determining the forced AGCM response over North America. On the other hand, the stochastic effect of the weekly SSTA also appeared to be important (Fig. 10b). This leads to the question of whether there is some specific detail about the subseasonal SSTA variability that causes the extratropical re-
FIG. 11. (a) Jan 1989 EXP1–H89 500-mb geopotential height difference; (b) same as (a) except for Mar 1989. The contour interval is 10 gpm in both panels.
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FIG. 12. (a) Jan 1989 EXP1–H89 precipitation difference; (b) same as (a) except for Mar 1989. The contour interval is 2 mm day21 in both panels.
sponse or whether the subseasonal variability is acting as stochastic forcing that increases the amplitude of the extratropical response. If the subseasonal SSTA variability is acting as stochastic forcing then the details (or evolution) will not matter. The experiments presented in this section examine whether the evolution of the weekly SSTA has a significant effect on the seasonal mean response. The experiments described in this section use an AGCM of somewhat lower horizontal resolution. The physical parameterizations are identical, but in this case the AGCM is truncated at total triangular wavenumber 30 (T30). The reason for this change in resolution was primarily due to computer time constraints. However, we also felt that obtaining similar results with larger ensembles with the T30 model added further confidence to the results. We have repeated H89, F99, and EXP1 with the T30 version of the model with similar results. In particular, Figs. 13a,b show the same difference maps as Figs. 9a,b except for the T30 model, respectively. We have also increased the number of ensemble mem-
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FIG. 13. (a) T30 version of the AGCM EXP1 500-mb geopotential height anomaly and (b) T30 AGCM EXP1–H89 500-mb geopotential height difference. The contour interval in both panels is 10 gpm and the shading indicates regions where the difference in (b) is significant at the 95% confidence level.
bers to 100.2 The choice of 100 ensemble members was somewhat arbitrary, and similar result are obtained with 50 members, but not 10. Figure 13a compares favorably to Fig. 9a, although the signal is slightly weaker. Similarly, Fig. 13b matches the difference map in Fig. 9b except for the reduced amplitude. Some of the reduction in amplitude can be attributed to the larger ensemble size and some of the reduction is due to the lower resolution in the AGCM. Although it is not shown here, the tropical rainfall difference are also remarkably similar to that produced by the higher-resolution model. We consider this important, because we are arguing that the small rainfall (heating) differences in the subtropical
2 Initial conditions for these ensemble members were obtained using a different method than the experiments with the R40 version of the model. The first initial condition comes from a long simulation with observed SST. The remaining initial conditions are obtained by running the model forward one week and then resetting the calender back one week. In this way it is possible to generate unlimited initial conditions that are synoptically independent (separated by one week) but have the same initial date.
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cific–North American region. Similarly, Fig. 14b shows the difference between EXP2 and EXP1 for the same field. In both figures, the shading indicates regions where the difference is statistically significant at the 95% level. Figure 14b shows a relatively small response compared to Fig. 14a; moreover, the structure is different. The differences between EXP2 and EXP1 over this region do not surpass the 95% confidence level. This suggests that the role of stochastic SSTA forcing is small and that the evolution of the subseasonal SSTA matters. This experiment with randomly shuffling the weekly SSTA has been repeated five different times with largely the same results as presented in Fig. 14b. b. Diagnostic model forced by monthly mean
FIG. 14. (a) T30 AGCM EXP1–H89 500-mb geopotential height difference and (b) T30 AGCM EXP2–EXP1 500-mb geopotential height difference. The contour interval in both panels is 10 gpm and the shading indicates regions where the difference is significant at the 95% confidence level.
western Pacific during January are primarily responsible for the differences seen over North America. a. Role of ‘‘stochastic’’ SSTA forcing The experiment presented here (EXP2) is designed to test the impact of the stochastic nature of the SSTA. In EXP2, the seasonal mean SSTA is identical to H89 and, thus to, EXP1, but week-to-week variability is retained. However, in EXP2 the ordering of the weekly SSTA is randomly shuffled, so that the week-to-week evolution of the SSTA is different. Recall that the difference EXP1–H89 indicates the impact of the observed subseasonal SSTA variability. If the character of the difference fields between EXP2 and EXP1 is significantly different than the character of the difference fields between EXP1 and H89, then the details of the subseasonal SSTA evolution are important, and we can reject the stochastic hypothesis. If, however, the character of the two sets of difference fields is similar, then the evolution of the SSTA does not matter and the stochastic hypothesis is not rejected. Table 1 summarizes these experiments. Figure 14a shows the difference between EXP1 and H89 for the 500-mb geopotential height over the Pa-
The results presented thus far indicate that the SST differences during January between H89 and EXP1 lead to the differences in the rainfall and circulation over North America seen in Figs. 8 and 9. Here we use a simple nonlinear barotropic model that further indicates that the differences in the midlatitude response between H89 and EXP1 is due to monthly mean heating (or divergence) differences during January and March. In other words, the difference in the response over the Pacific Northwest is due to deterministic SSTA differences on the subseasonal timescale. The barotropic model formulation follows Sardeshmukh and Hoskins (1988): ]h 1 Vc · =h 5 2= · (Vx h) 1 damping, ]t
(1)
where h is the absolute vorticity, V c is the rotational component of the wind, and V x is the divergent component of the wind. The first term on the right-hand side of (1) is the so-called Rossby wave source term, which proves to be useful in terms of diagnosing the midlatitude response. There are two components to the damping: (i) linear dissipation with a 60-day e-folding timescale and (ii) biharmonic diffusion with the same diffusion constant as the AGCM. The divergent component of the wind is prescribed from the AGCM and monthly mean values are used. The zonal mean vorticity is also prescribed from the AGCM. The barotropic model is spectral and is truncated at rhomboidal total wavenumber 40, the same as the AGCM. In all the simulations shown here, the barotropic model is integrated for 1000 days and the last 800 days are used to calculate a time mean. With this rather weak damping, the barotropic model does not converge to a steady state and there remains significant transient variability. Four simulations were made with the only differences among the simulations being in the prescribed time mean global divergence and zonal mean vorticity. In the first two simulations the time mean divergence and the zonal mean vorticity are prescribed as the January mean from H89 and EXP1, respectively. Similarly, in the second two simulations the March values of the
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FIG. 15. (a) Jan 1989 R40 AGCM 150-mb streamfunction EXP1– H89 and (b) Jan 1989 barotropic model EXP1–H89. Contour interval is 2.0 3 10 6 m 2 s21 and the contour labels are scaled by 1 3 10 6 m 2 s21 .
divergence and zonal mean vorticity were used. The results from these barotropic simulations are compared to the AGCM in Figs. 15 and 16. Figure 15a shows the time mean January 150-mb AGCM streamfunction difference between EXP1 and H89. Figure 15b shows the same difference using the barotropic model results. The 150-mb level is chosen here because this is the level of maximum response in the AGCM. The barotropic model tends to overestimate the amplitude of the streamfunction difference and fails to capture some of the smaller-scale features. Nevertheless, the barotropic model does reproduce many of the large-scale features of the global response. In particular, it reproduces the relatively large AGCM differences in the Pacific–North American region, especially over the Pacific Northwest where there are relatively large positive differences between EXP1 and H89 in both the AGCM and the barotropic model. In contrast, during March (Figs. 16a,b) the difference between EXP1 and H89 in both the AGCM and the barotropic model is relatively weak over North America.
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FIG. 16. Same as Fig. 14 except for Mar 1989.
We cannot conclude that the tropical forcing (divergence) alone is sufficient to determine the midlatitude response. This can be seen by comparing the Rossby wave source term in Figs. 17a,b. During January, there is significant Rossby wave forcing in the tropical west Pacific along 108N that is collocated with the rainfall differences (see Fig. 7b), and there is significant Rossby wave forcing in the subtropical Pacific centered along 308N. Through experimentation with this barotropic model we have found that both the tropical and subtropical Pacific divergence is required to capture the midlatitude response. The divergence forcing outside the Pacific basin is not required to reproduce the response over the Pacific–North American region. In contrast to the January results, during March (Fig. 17b) there is very little Rossby wave forcing in either the tropical or subtropical Pacific. 6. Discussion A case study was conducted to examine how subseasonal SST variability affects midlatitude seasonal simulations during JFM89. Based on a large number of
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FIG. 17. (a) Jan 1989 and (b) Mar 1989 barotropic model 150-mb Rossby wave source. Contour interval is 3.0 3 10211 s22 and the contour labels are scaled by 1.0 3 10211 s22 .
AGCM and diagnostic model experiments, we found that subseasonal SSTA variability has a significant impact on North American climate anomalies. In particular, the rainfall anomalies in the Pacific Northwest are especially sensitive to subseasonal SST variability. This SSTA variability can be rather small, for example, on the order of 0.2–0.3 K in the western Pacific. This conclusion is based on a comparison of AGCM simulations using observed weekly SST and AGCM simulations in which the week-to-week SSTA variability has been suppressed. Based on this result, we speculated that the response to the subseasonal SSTA was either due to a stochastic effect of the weekly data was deterministic in the sense that the details of the evolution of the SSTA mattered. The stochastic effect contrasts with the deterministic effect in that the details of the week-to-week evolution do not matter, and that the higher-frequency SST variability only serves to enhance the tropical precipitation variability, which, in turn, could possibly increase the amplitude of the midlatitude response. We tested this stochastic effect by randomly shuffling the weekly SSTA and found that this effect
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was relatively small. Further diagnostics and diagnostic model experiments also support the conclusion that the deterministic effect produced the differences in the simulation over North America. As mentioned in the introduction, this work was motivated by our experiences with real-time seasonal prediction over North America using the two-tiered approach during the La Nin˜a of 1998/99, and the results presented here have some interesting implications in terms of applying this approach to real-time midlatitude seasonal forecasting. On the one hand, it is unfortunate that the stochastic effect was not responsible for the differences seen over North America, because this effect would be straightforward to implement in a two-tiered forecast system. On the other hand, the fact that the response to the subseasonal SSTA was deterministic opens the possibility of more detailed and accurate seasonal mean forecasts over North America given improved SSTA forecasts on the month-to-month timescale. In addition to improved seasonal mean forecasts, it may even be possible to accurately predict some subseasonal details. Nevertheless, predicting the subseasonal SSTA evolution remains a daunting challenge for coupled models. However, even if it proves impossible to accurately forecast the subseasonal SSTA variability, it may be possible to make an estimate of the ‘‘steadiness’’ of the SSTA and this information could be used to put additional confidence limits on the extratropical forecast. We also find based on these results that monthly mean SST is sufficient to explain these differences between F99 and H89. At first, we found the sensitivity of the AGCM simulation to rather small SSTA in the western Pacific to be somewhat surprising, but given the relatively large value of the climatological SST in that region, the large response seems reasonable. This sensitivity also represents a daunting challenge for coupled SSTA prediction. Much of the current focus in the experimental SSTA prediction community (e.g., the Experimental Long-Lead Forecast Bulletin) has been on central and eastern tropical Pacific SST. In the future, the emphasis may have to be broadened to include the western Pacific. Conversely, based on this case study only, we found that the midlatitude SSTA has little effect on the North American climate forecast. Finally, it should be noted that these results only apply to this particular case study. For example, there is evidence to suggest that the response over North America to warm ENSO events is not as sensitive to the SSTA details as during cold events. It is also not clear that the response would be the same during other seasons or other cold events. While this AGCM has considerable skill at predicting the North American response to ENSO, it is possible that it may be overly sensitive to small SSTA in the west Pacific. Similar experiments with another AGCMs may help to resolve this question. We should also note that the impact of the subseasonal
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SSTA differences on the midlatitude circulation is localized to North America. Acknowledgments. We are grateful for some early discussions with J. Shukla, E. Schneider, and L. Marx regarding this work. We received constructive criticism from three anonymous reviewers that improved this paper; we acknowledge their assistance. The authors acknowledge support from the following: NOAA NA86GP0258 and NA96GP0056, NSF ATM9814295, and NASA NAG5-8202. APPENDIX Significance Tests In the results presented here, we have relied on the Student’s t-test for statistical significance. In the case of the geopotential height, we have assumed that the sample distribution is normal, whereas, in the case of the rainfall, we have assumed a lognormal distribution. In both case, we have assumed that the degrees of freedom equals the number of ensemble members, and the test has been applied to the seasonal mean at each grid point in the domain. Assuming a particular distribution is potentially problematic. In order to examine how the assumed distributions impact the results, we have also applied the Wilcoxon rank-sum test (Devore 1982), which is a nonparametric test of whether two samples have different means. The regions of significance at the 95% level show little difference from the original Student’s t-test and the same conclusions apply. To calculate the field significance test (Livezey and Chen 1983), the effective spatial degrees of freedom of the seasonal mean 500-mb geopotential height and precipitation needs to be estimated. In estimating the spatial degrees of freedom a Monte Carlo approach is used. Using the nine ensemble members from the H89 simulation all possible seven-member ensemble means are calculated (i.e., 36 ensemble means). From these 36 ensemble means, there are 36!/2 possible pairs of ensemble means on which to perform a Student’s t-test. Using all possible pairs of seven-member ensemble means is too computationally intensive. Instead, 10 000 pairs were randomly selected to calculate the local significance test. The average percent of grid points that pass the local significance test at the 95% level defines the 95% field significance level. For the 500-mb geopotential height in the Pacific–North American region, 16.6% of the points must pass the Student’s t-test for a field significance level of 95%. Similarly, for precipitation, 0.08% of the land grid points over North America must pass the local significance test for a field significance at 95%. Effectively, there is almost no reduction in the spatial degrees of freedom in the JFM89 precipitation over land points in North America.
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