Seasonal and Long-Term Atmospheric Responses to Reemerging ...

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Seasonal and Long-Term Atmospheric Responses to Reemerging North Pacific Ocean Variability: A Combined Dynamical and Statistical Assessment* ZHENGYU LIU

AND

YUN LIU

Center for Climatic Research, University of Wisconsin—Madison, Madison, Wisconsin

LIXIN WU College of Physical and Environmental Oceanography, Ocean University of China, Qingdao, China

R. JACOB Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Illinois (Manuscript received 1 December 2005, in final form 12 June 2006) ABSTRACT The atmospheric response to a North Pacific subsurface oceanic temperature anomaly is studied in a coupled ocean–atmosphere general circulation model using a combined dynamical and statistical approach, with the focus on the evolution at seasonal and longer time scales. The atmospheric response is first assessed dynamically with an ensemble coupled experiment. The atmospheric response is found to exhibit a distinct seasonal evolution and a significant long-term response. The oceanic temperature anomaly reemerges each winter to force the atmosphere through an upward heat flux, forcing a clear seasonal atmospheric response locally over the Aleutian low and downstream over the North America/North Atlantic Ocean and the Arctic regions. The atmospheric response is dominated by the early winter response with a warm SSTequivalent barotropic ridge and a wave train downstream. Starting in later winter, the atmospheric response weakens significantly and remains weak throughout the summer. The seasonal response of the atmosphere is then assessed statistically from the control simulation. It is found that the major features of the seasonal response, especially the strong warm SST–ridge response in early winter, are crudely consistent between the dynamical and statistical assessments. The statistical assessment is finally applied to the observation, which also suggests a strong seasonal atmospheric response locally over the North Pacific dominated by a warm SST–ridge response in early winter. One important conclusion is that the atmospheric response becomes more significant at annual and longer time scales, with the signal/noise ratio increasing up to 4 times from the monthly to the 4-yr mean response. This increased signal/noise ratio is caused by a much faster reduction of the atmospheric internal variability toward longer time scales than that of the response signal. The slow decrease of the response signal is due to the long persistence associated with the subsurface ocean. This suggests that the subsurface extratropical oceanic variability could have a much stronger impact on the extratropical atmosphere (and climate variability) at interannual–interdecadal time scales than at monthly–seasonal time scales.

1. Introduction Atmospheric response to extratropical oceanic variability remains a challenging problem in climate study. Previous works have focused on the winter atmospheric response to a prescribed SST (e.g., Kushnir et al. 2002)

* Center for Climate Research Contribution Number 897.

Corresponding author address: Z. Liu, 1225 W. Dayton St., Madison, WI 53706. E-mail: [email protected] DOI: 10.1175/JCLI4041.1 © 2007 American Meteorological Society

JCLI4041

or heat flux (Yulaeva et al. 2001; Sutton and Mathieu 2002) forcing with idealized AGCM experiments. This has produced diverse results. Recently, Liu and Wu (2004, hereafter LW04) studied the early winter atmospheric response in a coupled ocean–atmosphere GCM. Furthermore, the dynamical atmospheric response in their coupled sensitivity experiments is compared against an independent statistical estimation of the atmospheric response from the coupled control simulation. Their results suggest that the correct atmospheric response to oceanic forcing is more likely to be simulated in the coupled model. This study is partly motivated by the question: How

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does the atmosphere respond to extratropical oceanic variability at seasonal and longer time scales? Most previous studies have considered the atmospheric response in the entire winter season as a whole. One exception is Peng et al. (1995, 1997), who found that the atmospheric responses to an extratropical SST anomaly differ dramatically between the early and later winters. Their result illustrates the potential complexity of the seasonal evolution of the atmospheric response. Furthermore, most studies so far have considered the atmospheric response to be generated by a prescribed climate forcing of either SST or heat flux. This approach may have two deficiencies: the prescribed forcing may distort air–sea interaction, and perhaps the atmospheric response (LW04), and the prescribed forcing may prevent us from studying the natural long-term evolution of the coupled response, including the atmospheric response, because the time scale of the response is prescribed. The other important motivation of this study is how to verify the model-simulated seasonal atmospheric response. Given the model deficiencies, all previous AGCM studies are idealized in their nature and are not straightforward comparisons with the observation. The lack of a true “target” from the observation or the control simulation of a model, in our opinion, has contributed significantly to the confusion of previous modeling studies. A statistical method is needed to assess the atmospheric response, without which it is impossible to assess the true atmospheric response in the observation. Here, as an extension of LW04, we study the atmospheric response using a combined dynamical and statistical approach. The dynamical assessment is accomplished by using an ensemble coupled simulation in response to an initial ocean temperature anomaly in the North Pacific Ocean. Different from previous works, we will focus on the response at seasonal and longer time scales. Then, the simulated seasonal dynamic atmospheric response will be tested against an independent statistical assessment of the atmospheric response from the control simulation. It is found that the coupled experiment exhibits a distinguishable seasonal cycle. The seasonal oceanic response is associated with the SST reemergence (Alexander and Deser 1995; Deser et al. 2003). The seasonal atmospheric response is dominated by a warm SST–ridge response in early winter, which weakens substantially and may even reverse its sign toward late winter, and remains weak throughout the summer. One key finding of this work is that a subsurface ocean temperature anomaly in the midlatitudes is able to generate a persistent long-term mean

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climate response that is much more robust than the monthly and seasonal responses. This implies a potentially critical role of thermocline variability in determining the atmospheric response at annual and longer time scales. The simulated seasonal atmospheric response is found to be reasonably consistent with a crude statistical estimation of the atmospheric response from the control simulation. This suggests the potential usefulness of the combined dynamical and statistical approach. Finally, an application of the statistical estimation to the observation suggests a substantial seasonal evolution of the atmospheric response to North Pacific SST variability, with some resemblance to the model simulation. The paper is arranged as follows: The coupled model and its control simulation are described in section 2. The coupled ocean–atmosphere response to a North Pacific oceanic anomaly is studied in a set of coupled experiments in section 3, with the evolution of the seasonal cycle response further analyzed in section 4. Section 5 discusses the enhanced atmospheric response signal at annual and longer time scales. An independent statistical assessment of the atmospheric response is then used for comparison with the dynamic atmospheric response and is also applied to the observation in section 6. A final summary is given in section 7.

2. The model We use the Fast Ocean Atmosphere Model (FOAM: Jacob 1997; Jacob et al. 2001) (version 1.5, as in LW04). FOAM is a fully coupled ocean–atmosphere model without flux adjustment. The AGCM component uses the parallel Community Climate Model version 2 (CCM2) dynamics [Parallel Community Climate Model version 3 (PCCM3); Drake et al. 1995] and CCM3 physics; it has a horizontal resolution of R15 (7.5° longitude ⫻ 4.5° latitude) and 18 vertical sigma levels. The OGCM component has a horizontal resolution of 2.8° longitude ⫻ 1.4° latitude and 24 vertical levels in the z coordinate. Some features of the midlatitude ocean–atmosphere interaction can be inferred from the lead–lag correlations between the atmosphere and ocean. In the midlatitude, as suggested by Frankignoul et al. (1998), the simultaneous correlation between the SST and atmosphere is dominated by the atmospheric forcing on SST, while the atmospheric response to SST variability is better inferred from the SST-led covariance. Figures 1a and 1b show the seasonal evolution of the lagged correlation between SST and the atmospheric geopotential height (GPH) at 250 (Z250) and 850 hPa (Z850), respec-

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FIG. 1. Seasonal evolution of lagged correlation between KOE SST and atmospheric GPH anomalies over the Aleutian low at (a) 250 hPa and (b) 850 hPa from the 300-yr control simulation of FOAM (contour interval 0.1; negative in dash contours; shading indicates 95% significance level). Correlations between the SST and surface wind over the KOE are also plotted, vectors in (b). (c) The regression corresponding to (b), which emphasizes the stronger winter activity relative to the correlation (contour interval: 10 m °C⫺1). The ordinate is the atmospheric calendar month, while the abscissa is the lag: positive (negative) for ocean (atmosphere) leading atmosphere (ocean). (d), (e), (f) As in (a), (b), (c) but for the NCEP–NCAR reanalysis. The Aleutian low GPH indices are averaged in the region of 30°–60°N, 150°E–150°W; the KOE SST index is averaged in the region of 30°–50°N, 140°E–180° for FOAM and SST and 35°–45°N, 140°E–180° for the reanalysis. Positive contours are solid, negative are dashed, and zero are suppressed.

tively. The data are monthly output from a 300-yr control simulation (CTRL), with the SST averaged over the Kuroshio–Oyashio Extension region (KOE) (30°– 50°N, 140°E–180°) and the GPH over the Aleutian low region (30°–60°N, 150°E–150°W). For each atmospheric month, the correlations at both levels are dominated by a maximum positive correlation when the atmosphere leads SST (negative lags) by 1 month. This reflects the dominant equivalent barotropic atmospheric forcing on SST variability, with a reduced Aleu-

tian low (and, in turn, a reduced surface westerly wind, as shown by vectors in Fig. 1b) warming the ocean through the reduction of upward turbulent heat flux and southward Ekman advection. The maximum atmospheric forcing on SST occurs in winter from December to March, as seen both in the maximum atmospheric lead correlation and (most clearly) in the lagged regression (Fig. 1c). In comparison, the SST-lead correlation (positive lags) is much weaker (Figs. 1a–c). This reflects the fact

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that, in the midlatitudes, the monthly atmospheric response to SST is much weaker than the atmospheric internal variability. Nevertheless, there is a significant positive correlation and regression in the midwinter (January and February) at both levels when the SST leads by 1–2 months. This is an indication that the atmosphere may respond to winter SST most significantly, with a warm SST–equivalent barotropic ridge response. The major features of the model correlation/regression are reasonable when compared with the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis (Kalnay et al. 1996; Figs. 1d–f; also see LW04). In spite of the much shorter record and, in turn, less significant correlations in the reanalysis, both the model and reanalysis are dominated by the atmospheric forcing on SST (negative lag) in the winter half-year. Both also show an atmospheric response (positive lag) around the winter. This suggests that FOAM is relevant to the observations for the study of North Pacific ocean–atmosphere interaction.

3. Coupled response in the atmosphere and ocean To examine the seasonal evolution of the atmospheric response to a North Pacific Ocean temperature anomaly, we performed a 160-member ensemble coupled experiment with an initial warm ocean temperature anomaly (WARM). In addition to producing the correct ocean–atmosphere coupling (LW04), the coupled model simulation has the advantage of reproducing the natural evolution of SST and the associated atmospheric response. The latter enables us to examine the long-term response of the atmosphere to the initial oceanic temperature anomaly.

a. Experimental design The WARM experiment is designed following LW04. A 160-yr section of the CTRL is used for the initialization of the sensitivity experiments of WARM, each year providing the initial condition (of both the atmosphere and ocean) for each ensemble member. A bell-shaped warm ocean temperature anomaly is added in the oceanic component of the initial coupled state, with the center maximum temperature of ⫹2°C located in the KOE region. For each member of WARM, the experiment is integrated for four years. Its corresponding control is the part of CTRL of the same model years. [For example, if the member m starts from 1 September of year m of CTRL (after the addition of the

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warm anomaly) to 30 August of year m⫹4,1 the corresponding control is the CTRL from 1 September of year 1 to 30 August of year m⫹4.] The anomalous response of each ensemble member is defined as the difference between the member and its corresponding control; the ensemble mean response is derived as the 160-member ensemble mean of the anomalous response. The first September is included in all of the analysis, which turns out to have little influence on the entire analysis. This is because, in the first September, the SST anomaly decays rapidly due to the deepening of the mixed layer in late fall; the atmospheric response, however, remains weak as in Septembers of later years (see discussions later). Unlike in LW04, where the initial temperature anomaly is confined in the surface mixed layer (the model winter mixed layer depth in this region is about 150 m), the warm temperature anomaly now extends uniformly from the surface to 560 m, well into the permanent thermocline. The deep structure of the oceanic temperature anomaly is motivated by the observed deep temperature anomaly of decadal variability in this region (Miller et al. 1998; Deser et al. 1999; Zhang and Liu 1999). For example, in the far western North Pacific, the decadal temperature anomaly in the upper 1000 m has the same sign, with a maximum about 2°C at the depth of 300 m (Fig. 8 of Deser et al. 1999). This deep anomaly is contributed partly by the deep winter convection and the associated mode water formation (Xie et al. 2000) and partly by the first baroclinic Rossby wave response to decadal surface Ekman pumping forcing (Liu 1999). Physically, it is conceivable that the deep ocean temperature anomaly would allow us to study the atmospheric response beyond the seasonal time scale because it allows for the reemergence of the thermocline temperature anomaly, as will be seen later.

b. Evolution of the coupled response The ensemble mean response exhibits a distinguished seasonal cycle, as well as a significant long-term persistence. In the first year, initially in September, the SST anomaly (SSTA) is damped quickly because of the shallow mixed layer in the fall. Starting in November, the SSTA reemerges through the deepening of the mixed layer. In early winter [November–January (NDJ; hereafter, multimonth periods are denoted by the first letter of each month)], the reemerging SSTA is characterized by a primary center in KOE resembling the initial SSTA (Fig. 2a), which releases heat into the atmo1

Each model month is 30 days.

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FIG. 2. Ensemble mean response for the early winter (NDJ) of the first year: (a) SST (contour interval: 0.1°C) and surface wind stress (vector); (b) upward turbulent heat flux (latent plus sensible) (contour interval: 5 W m⫺2); (c) Z250; and (d) Z850 (contour levels: ⫾2, 5, 10, 15 . . . m). Positive contours are solid, negative are dashed, and zero are suppressed. Shading indicates the area above the 95% significance level.

sphere (Fig. 2b). The maximum SST and heat flux anomalies are about 1.2°C and 25 W m⫺2, corresponding to a heat flux damping rate of 20 W m⫺2 °C⫺1, consistent with the observational study of Frankignoul and Kestenare (2002). The atmospheric response is characterized by an equivalent barotropic high over the North Pacific, with a magnitude of about 30 m and 15 m for Z2500 and Z850 hPa, respectively (Figs. 2c,d). The associated surface wind is dominated by an easterly anomaly (Fig. 2a). This easterly anomaly tends to increase the SST by reducing the mean westerly and, in turn, the turbulent heat flux (Fig. 2b) and cold Ekman advection there. The easterly anomaly is confined mainly downstream of the initial SSTA, which generates a secondary positive SSTA downstream around 160°W (Fig. 2a) (also see LW04). The KOE SST also excited a remote atmospheric response through a ridge–trough–ridge wave train that propagates through northern Canada to the eastern North Atlantic (Figs. 2c,d). This wave train response is reminiscent of the winter Pacific–North America (PNA) atmospheric teleconnection both in the observation (Wallace and Gutzler 1981) and in this model—a point to be resumed later.

The vertical structure of the coupled response in early winter is seen more clearly from the longitude– height plot of the oceanic temperature, atmospheric temperature, GPH, and diabatic heating across the midlatitude North Pacific (Fig. 3). The deep ocean temperature anomaly (Fig. 3b) in the KOE region remains little changed from its initial state; the downstream ocean warming centered at 160°W, however, is confined in the surface because it is forced by the surface heat flux (Fig. 2b) and Ekman advection. The lower atmospheric temperature shows a maximum warming over the KOE (Fig. 3a), due to the maximum diabatic heating (Fig. 3d) there. The warm temperature and diabatic heating are advected downstream with height. The GPH is dominated by an equivalent barotropic high locally over the North Pacific (Fig. 3c). Downstream east of the date line is a diabatic cooling caused by the reduction of precipitation and, in turn, latent heating associated with weakening of the Aleutian low. The diabatic warming/cooling tends to be balanced by the adiabatic ascending/descending there. All of these features are similar to those in the early winter response of LW04. Later in the winter season (FMA), the SSTA remains

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FIG. 3. Vertical structure of the ensemble mean response across the midlatitude North Pacific in the early winter (NDJ) of the first year for (a) atmospheric temperature (contour interval: 0.1°C), (b) oceanic temperature (contour interval: 0.1°C), (c) atmospheric GPH (contour interval: 3 m), and (d) diabatic heating (contour interval: 0.05 K day⫺1). The atmospheric and oceanic variables are averaged in the latitude belts of 30°–60°N and 30°–50°N, respectively.

similar to the early winter (Fig. 4a), but the atmospheric response weakens significantly. In addition, the wave train response appears to be replaced by a more circumpolar response, with the North Pacific ridge shifted into the Arctic and the North Pacific region now dominated by a surface low. This somewhat annular response is reminiscent of the Arctic Oscillation (AO) in the observation (Thompson and Wallace 2000) and model—a point to be resumed later. In spite of a similar ocean temperature anomaly in the surface (Fig. 4a versus Fig. 2a) and subsurface (Fig. 5b versus Fig. 3b) in the early and late winters, the vertical structure of the atmospheric response differs significantly. There is a broad atmospheric warming across the entire Pacific

(Fig. 5a), a baroclinic GPH with a surface low (Fig. 5c), and a diabatic heating/cooling confined below 700 hPa (Fig. 5d). The different atmospheric responses between the early and late winters have been noticed by Peng et al. (1995, 1997) and Peng and Robinson (2001) in AGCM studies. As suggested by Peng and her colleagues, it is highly likely that the different atmospheric responses are caused by the different background atmospheric states. In the mean time, we note that the result here seems to be also consistent with LW04 in that the stronger early winter warm SST–ridge response is accompanied by a weaker upward surface heat flux. Indeed, the upward heat flux above KOE is increased from about

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FIG. 4. As in Fig. 2 but for later winter (FMA) of the first year.

25 to 35 W m⫺2 from early to late winter (Fig. 2b versus Fig. 4b). An upward surface heat flux forcing may favor a warm-low response (Yulaeva et al. 2001; Sutton and Mathieu 2002; LW04) and therefore may also contribute to the weaker ridge response in late winter, as speculated by LW04. However, we caution that the corresponding heat flux could also be the result of different atmospheric responses. For example, a stronger ridge response in early winter reduces the westerly wind in midlatitudes, leading to a reduced turbulent heat flux. Therefore, the correspondence between a ridge atmospheric response and a weaker surface heat flux may not indicate a simple causality. Much study is still needed to understand the dramatic change of the atmospheric response during the winter. In the following summer season, the SSTA diminishes rapidly due to the seasonal shoaling of the mixed layer. The atmospheric response remains weak as in the late winter. This seasonal cycle of the coupled response is repeated in the succeeding years, and is discussed below.

4. Seasonal cycle and long-term evolution a. The total response The full 4-yr evolution of the local response over the North Pacific is more clearly seen in a time–height plot,

Fig. 6. In the KOE, the ocean temperature anomaly reemerges each winter, leading to a surface warming (Fig. 6, bottom); the surface warming heats the lower atmosphere over the KOE (Fig. 6, middle) and generates a statistically significant equivalent barotropic high over the Aleutian low (Fig. 6, top). This warm SST– ridge response peaks in early winter (NDJ), preceding the SST peak by 1–2 months. Later in the winter, the ridge response weakens significantly and reverses sign to a weak low near the surface (contributed mainly by southern part of the domain, see Figs. 4c,d). The atmospheric response remains weak in the summer season in spite of a modest warm SST anomaly. The changing atmospheric response throughout the year appears to be caused mainly by the change of the atmospheric response to SSTA with season, rather than the diminishing SSTA forcing itself. Next early winter, the ridge response occurs first in the upper atmosphere and penetrates downward to the surface, consistent with the transient AGCM simulation of the initial establishment of the ridge response (Li and Conil 2003). The overall evolution of the coupled response can also be seen in the leading EOFs of the ensemble mean response. Figure 7a shows the EOF patterns and principal components (PCs) of the two leading SSTA modes. EOF1 resembles the SSTA in the winter (Figs.

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FIG. 5. As in Fig. 3 but for later winter (FMA) of the first year.

2c, 4c) with a primary center over KOE and a secondary center downstream. The PC1 shows a clear seasonal reemergence with the maximum and minimum occurring each February and October, respectively. EOF2 shows a dipole with a cooling in the KOE and warming in the northeast, reflecting the downstream SSTA propagation, which is caused by the downstream atmospheric response and ocean dynamics. The two leading EOFs of the turbulent heat flux (Fig. 7b) correspond well to the two leading SST EOFs, with the EOF1s representing the heat loss of the initial warm SST over the KOE. In addition to the seasonal cycle, the PCs of these leading SST modes also show a significant persistence into succeeding years with an e-folding time of 2–3 yr—a long persistence originating from the thermocline temperature anomaly (Deser et al. 2003). The latter is seen in the slow decaying of the PC1 and PC2 of the upper-ocean heat content, with a slow decay of

the initial anomaly (EOF1) and its slow northeast propagation (EOF2; Fig. 7c). The evolution of the atmospheric response can be seen in the two leading EOFs of Z250 (Fig. 7d) and Z850 (Fig. 7e). Although the EOF1 and EOF2 on each level are spatially orthogonal, both exhibit an equivalent barotropic response over the North Pacific and a wave train into the North Atlantic. The PCs of these modes exhibit a significant seasonal cycle but with different phasing: the PC1 tends to reach a maximum in winter and minimum in summer, while the PC2 switches the sign rapidly from the early to late winter. A more careful observation of the PCs suggests that the PC1s show a significantly positive long-term mean throughout the 4 yr, implying a ridge–trough–ridge response in the long-term mean response. In contrast, the PC2s are dominated by a seasonal cycle with little long-term mean, corresponding to a ridge in early winter and a

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trough in late winter over the North Pacific. It then appears that EOF1 captures mostly the annual and long-term mean response, while the EOF2 represents the dominant seasonal cycle response—an impression that will be confirmed later. In terms of the two leading EOFs, therefore, both modes reinforce each other in early winter, generating a strong warm SST–ridge response over the North Pacific and a wave train downstream (Figs. 2c,d). Later in the winter, however, the reversal of the sign of the EOF2 leads to a strong cancellation of EOF1. This cancellation reduces the North Pacific ridge response substantially, especially in the southern part where it reverses the sign of the response to a low near the surface (Figs. 4c,d). Therefore, the atmospheric response at a particular time is dominated by different EOF modes.

lent barotropic wave train from the North Pacific into the western Atlantic, especially in the upper atmosphere (Figs. 8a,b). Following Thompson and Wallace (2000), the AO index is derived as the PC1 of Z850 north of 20°N of the CTRL of the entire winter halfyear (ONDJFMA). The AO patterns are obtained as the projections of the ONDJFMA Z250 and Z850 of CTRL on the AO index. These AOs show a largely annular feature in a midlatitude/Arctic dipole, with an equivalent barotropic structure (Figs. 8d,e), again consistent with the observation. The PNA (AO) atmospheric response in the anomalous experiment WARM is obtained as the spatial regression of the ensemble mean Z250 and Z850 on each corresponding PNA (AO) pattern. The evolution of the PNA response peaks as a ridge over the Aleutian low in deep winter (JFM) and diminishes in late summer on both levels (Fig. 8c). The AO atmospheric response, however, exhibits a dipole response with a ridge in midlatitudes (negative regression coefficient) in early winter, and a dramatic reversal of the dipole response in late winter for both levels (Fig. 8f). Therefore, the strong ridge response in early winter wave train response (e.g., Figs. 2c,d) can be thought of as the dominance of the PNA response reinforced by the AO response. The weaker and more annular atmospheric response in late winter (e.g., Figs. 4c,d) is caused by a weakening of the PNA response and a reversed AO response, leading to a poleward shift of the ridge response. This way, the seasonal evolution of the total atmospheric response can be viewed as the excitation of different atmospheric internal variability modes in different seasons. Finally, the PNA response has a positive tendency over the 4 yr (Fig. 8c), while the AO response has little annual mean (Fig. 8f). This suggests that the PNA response could contribute significantly to the long-term mean response, in addition to the seasonal cycle; while the AO response contributes mainly to the seasonal cycle. This impression is confirmed in following discussions. The discussion here is roughly consistent with that on Figs. 7d and 7e because of the resemblances between PNA and EOF1, and between AO and EOF2, of the spatial and temporal features.

b. Relationship with internal atmospheric modes

c. The long-term response

It is also interesting to examine the evolution of the atmospheric response discussed above in terms of intrinsic atmospheric modes, notably the PNA and AO. Following Wallace and Gutzler (1981), the PNA index is derived as the PC1 of the winter (NDJ) Z250 north of 20°N in CTRL. The projections of the NDJ Z250 and Z850 of CTRL on the PNA index shows a PNA pattern largely consistent with the observation, with an equiva-

To better separate the long-term mean and seasonal responses, the total ensemble mean response at each grid point is decomposed into the long-term mean, the linear trend, and the residual. The long-term mean response shows a warm SSTA spreading across most of the North Pacific, with a maximum SSTA of about 0.3°C over the KOE (Fig. 9a) and an associated heat flux loss of 6 W m⫺2 (Fig. 9b). This gives a surface heat

FIG. 6. Temporal evolution of the vertical structure of the ensemble mean response. (top) Atmosphere GPH averaged in 30°– 70°N, 180°–160°W (contour levels: ⫾2, 5, 10, 15 . . . m), (middle) atmosphere temperature (contour interval: 0.1°C) averaged in 30°–60°N, 140°E–180°, and (bottom) ocean temperature (contour interval: 0.1°C) in the KOE region (30°–50°N, 140°E–180°). Positive contours are solid, negative are dashed, and zero are suppressed; shading indicates regions above the 95% significance level.

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FIG. 7. The two leading EOFs and the PCs of the total ensemble mean response: (a) EOF1 (66%), EOF2 (12%), PC1 (right side, solid curve), and PC2 (right side, dashed curve) for SST (contour interval: 0.02); (b) EOF1 (56%), EOF2 (15%), PC1 (solid), and PC2 (dashed) of the upward turbulent heat flux (contour interval: 0.1); (c) EOF1 (85%), EOF2 (12%), PC1 (solid), and PC2 (dashed) of the upper-ocean (560 m) heat content (contour interval: 0.02); (d) EOF1 (42%), EOF2 (21%), PC1 (solid), and PC2 (dashed) of Z250 (contour interval: 0.05); (e) EOF1 (37%), EOF2 (24%), PC1 (solid), and PC2 (dashed) of Z850 (contour interval: 0.02). (A 3-month running mean is applied before the EOF analysis.) In this paper, all the EOFs are calculated after the data are first weighted by the square root of the cosine of latitude in the calculation of the covariance matrix. The EOF pattern is then calculated as the regression pattern against the corresponding PC (positive contours are solid, negative are dashed, and zero are suppressed). The domain of the EOF calculation is the same as shown in each EOF figure.

flux damping rate of 6/0.3 ⫽ 20 W m⫺2 °C⫺1, which is comparable with the seasonal responses (in Figs. 2, 3). The local atmospheric response over the North Pacific is characterized by an equivalent barotropic high in the northern Aleutian low region (Figs. 9c,d), a weak trough response in the lower atmosphere in the subtropics (Fig. 9d), and a surface easterly over most of the mid and high latitudes (Fig. 9a). The long-term atmospheric response also exhibits a wave train, reminiscent of the early winter response (Figs. 2c,d). Locally over the northern Aleutian low, the long-term mean response reaches 10 and 4 m in Z250 and Z850, respectively. In addition to the wave train response, the longterm mean response also features an equivalent barotropic high over northern Europe (Figs. 9c,d), which seems to be related to the late winter annular response over the Arctic region (Figs. 4c,d). Overall, as discussed in Figs. 7 and 8, the long-term mean response appears to be contributed more by the PNA wave train response than the AO annular response.

The atmospheric response also decreases with a significant linear trend, reflecting mainly the weakening and northward shifting of the ridge response over the Aleutian low (Figs. 10c,d). This atmospheric trend may correspond to the weakening trend of the heat content (Fig. 7c) and, in turn, the SST (Fig. 10a) and heat flux (Fig. 10b) forcings.

d. The seasonal cycle response The residual response is dominated by the seasonal cycle. The standard deviation of the residual response, which is a crude measure of the amplitude of the seasonal cycle response, shows a maximum in the KOE for the SST and heat flux, associated with the reemergence (Figs. 11a,b). The atmospheric response is characterized by a local response center over the Aleutian low and a remote response extending across the Arctic into the western North Atlantic (Figs. 11c,d). This pattern of standard deviation resembles that of the internal variability at monthly and longer time scales derived from

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FIG. 7. (Continued)

the ensemble members or the control simulation (not shown), implying a close relationship between the seasonal cycle response and the change of the atmospheric internal variability. The pattern and phase of the seasonal cycle of the atmospheric response are shown in the two leading EOFs of the residual GPH response. The EOF1s in both levels are dominated by the primary response locally over the North Pacific, an Arctic response of opposite sign, and a weak downstream wave train (Fig. 12, left); both PC1s show a rapid reversal from positive to negative peaks each year from early (December) to late (March) winter (Fig. 12, right). This rapid change of the residual EOF1 response is consistent with a reversal from the warm SST–ridge response in early winter (Fig. 2) to a surface trough response in late winter (Fig. 4) over the midlatitude North Pacific. The EOF2s of the residual response show a primary response center around the Arctic, with a positive peak in late winter (March) and negative peak in later summer (July: Fig. 12, middle). Different from the wave train pattern of the EOF1s, EOF2s resemble more the annular re-

sponse, especially in the lower layer. The different seasonal phasing and spatial patterns between the first two EOFs of the residual response suggest a potentially complex response of the seasonal cycle, with different modes contributing to different seasons. For example, it now appears that the wave train response in early winter (Figs. 2c,d) is contributed to largely by the residual EOF1 reinforcing the long-term mean response (Figs. 9c,d), while the more annular response in late winter (Figs. 4c,d) is represented more by the residual EOF2. The two leading EOFs of the residual atmospheric response have comparable explained variances: both are dominated by the annual cycle, but with a phase difference of about a season (Fig. 12, right). This implies that the pattern of the seasonal cycle response may be described approximately as a cycle following ⫹EOF1, ⫹EOF2, ⫺EOF1, and –EOF2 through early winter to late summer. Over the Aleutian low region, first in early winter, a ridge (⫹EOF1) strengthens the long-term mean response there (Figs. 9c,d); toward the late winter season, the ridge migrates into the Arctic (⫹EOF2). The Aleutian low region eventually reverses

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FIG. 8. The PNA pattern on (a) Z250 and (b) Z850 obtained from the CTRL as the projection of the anomaly on the PNA index as explained in the text. The PNA index to be regressed is normalized such that the units in (a) and (b) are gpm. (c) The projections of the ensemble mean response of WARM on the PNA for Z250 (solid) and Z850 (dash). On each level, the PNA pattern is first normalized by its spatial standard deviation, which is then used for spatial regression for the ensemble mean response pattern, such that the regression coefficient reflects the amplitude of the projection. Similar are the AO patterns of (d) Z250 and (e) Z850 derived from the control run, and (f) the projections of the ensemble mean response on AO. The Z250 pattern has a contour interval of 10 m, while the Z850 pattern has a contour interval of 5 m. For the response projection time series, the corresponding correlations have similar temporal evolution with a value ranging from ⫺0.5 to ⫹0.8 in (c) and ⫺0.7 to ⫹0.7 in (f) (not shown).

to a trough (⫺EOF1), reducing the long-term mean response there. Finally toward late summer in the transition, a weak ridge shifts back southward to over the midlatitude North Pacific (⫺EOF2).

5. The signal of long-term climate response In spite of the smaller absolute magnitude of the long-term response (Fig. 9) relative to the monthly and seasonal (Figs. 2, 4, and 7), the long-term response is much more robust and, therefore, potentially more important for climate response. The standard deviation of the atmospheric internal variability (noise) diminishes rapidly as the square root of the averaging time because of its stochastic nature (von Storch and Zwiers 1999). In contrast, the atmospheric response (signal) to the slow oceanic variability persists for years (Fig. 6 and

Figs. 7d,e) and its magnitude therefore decreases slowly with the average time scale. As a result, the signal/noise ratio increases significantly for long-term atmospheric responses, as shown below (also see appendix A for a simple example). We first examine the scatter diagrams of the evolution of the North Pacific monthly SST (Fig. 13a), heat flux (Fig. 13b), upper-ocean heat content (Fig. 13c), and the atmospheric responses of Z250 (Figs. 13d,e) for all ensemble members (dots). The monthly responses for individual members show a dramatic scattering in the atmosphere, the heat flux, SST, and even the heat content, forced mainly by the strong internal atmospheric variability. Visually, the magnitude of the scattering, as measured by its envelope or standard deviation, shows a clear seasonal cycle (except for the heat content). The scattering is the strongest in winter for the atmosphere

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FIG. 9. The 4-yr average of the ensemble mean response: (a) SST (contour interval: 0.1°C) and surface wind stress, (b) upward turbulent heat flux (contour interval: 2 W m⫺2), (c) Z250 (contour interval: 2 m), and (d) Z850 (contour interval: 1 m). Positive contours are solid, negative are dashed, and zero are suppressed; shading indicates regions above 95% significance level.

and heat flux, but in late summer for the SST; the former is due to the strong winter atmospheric internal variability, while the latter is due to the shallow summer mixed layer. The ensemble mean response (solid line) also exhibits a clear seasonal cycle (except for the heat content), similar to those in Fig. 6, but with a long persistence associated with the heat content. Owing to the large noise, however, the monthly atmospheric responses are statistically insignificant in the summer (Figs. 13d,e). To quantify the signal/noise ratio, we first define the signal and noise for an ensemble of monthly time series {Ajt}, where t (1 ⱕ t ⱕ 48) is the tth month and j denotes the jth ensemble member. The ensemble mean response time series is {At} ⫽ {具Ajt典}, from which the signal of time-scale M month as follows. First, each successive M month of {At} is binned together to form the new M-month-mean response time series {As} (1 ⱕ s ⱕ 48/M). Next, the M-month-mean signal is then derived as the 4-yr mean of the absolute value of the new time series { | As| }. The noise of the M-month-mean time series is derived from each member of the ensemble as follows: First, each member time series {Ajt} is binned into a new M-month-mean time series {Ajs} (1 ⱕ s ⱕ 48/M);

then the sth element of the standard deviation time series is calculated from the standard deviation of all the sth elements of the ensemble members as ␴(As); finally, the magnitude of the noise is derived as the 4-yr mean of {␴(As)}. For the atmosphere (Z250 in Figs. 13d,e), calculation shows that the noise decreases rapidly by about 6 times, from the monthly mean (⬃50 m) to the 4-yr mean (⬃10 m). This rapid decrease is expected from an uncorrelated time series {Bl} whose standard deviation decreases roughly as the square root of the average time as

␴

冉

1 L

L

兺B

l

1

冊

⫽

␴共B兲

公L

.

共1兲

In comparison, calculation shows that the signal decreases only slightly, from 9 m for monthly to 8 m for the 4-yr mean, in the northern Aleutian low region where the annual mean response overwhelms the seasonal cycle response (Fig. 13d). As a result, the signal/ noise ratio increases more than four times from the monthly to the 4-yr mean response. Given the ensemble size (degrees of freedom) of 160, the statistic

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FIG. 10. The 4-yr linear trend of the monthly ensemble mean response: (a) SST [contour interval: 0.25°C (4 yr)⫺1] and surface wind stress, (b) upward turbulent heat flux [contour interval: 5 W m⫺2 (4 yr)⫺1], (c) Z250 [contour interval: 2.5 m (4 yr)⫺1], and (d) Z850 [contour interval: 1 m (4 yr)⫺1]. Positive contours are solid, negative are dashed, and zero are suppressed; shading indicates regions above 95% significance level.

significance of the response signal is increased from 95% for monthly to over 99.999% for the 4-yr mean, using a one-sided t test. In the central-southern Aleutian low region, where the seasonal cycle dominates the annual mean response (Fig. 13e), the signal decreases more rapidly from about 5 m for monthly to 2.5 m for the 4-yr mean, mainly because of the cancellation between positive and negative responses within the annual cycle. As a result, the signal/noise ratio increase is only twofold. Overall, in mid and high latitudes (30°–80°N), the signal/noise ratio of the atmospheric response increases substantially with the average time (see appendix A for an example). Figure 14 shows the zonal variation of the signal, noise, and signal/noise ratio of Z250 for four average intervals: 1 month, 3 months, 1 yr, and 4 yr. The noise is largely zonally uniform, although there are two modest peaks corresponding to the two storm tracks over the North Pacific and North Atlantic. The overall magnitude of the noise decreases with the average time, roughly following the square root as in Eq. (1) (Fig. 14a). The signal, however, decreases much more slowly, especially for the local response over the North Pacific

(centered at 180°: Fig. 14b). As a result, the signal/noise ratio increases by almost four times locally over the North Pacific sector, and almost three times downstream in the Atlantic sector. The pattern of the signal/ noise ratio is determined mainly by that of the signal because the noise is relatively spatially uniform. For example, the spatial pattern of the signal/noise ratio of the 4-yr mean response (not shown) closely resembles that of the 4-yr mean response (Figs. 9c,d), centered over the northern Aleutian low, and eastern North America/ western North Atlantic. It is noticed in Fig. 14c that most of the increase of the signal/noise ratio occurred from the 1 to 4 yr mean. This leap of signal/noise ratio is related to the strong seasonal cycle of the response signal, rather than a faster decrease of the noise magnitude beyond the annual time scale. For average time shorter than 1 yr, the signal decreases rather rapidly, with the average time due to the cancellation of opposite signs of responses in different months (e.g., Fig. 13e), leading to a substantial decrease of the signal with the average time. However, for signals longer than a year, the reemergence tends to produce the same sign of responses in succeeding years

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FIG. 11. The standard deviation of the residual response of the monthly data for (a) SST (contour interval: 0.1°C), (b) turbulent heat flux (contour interval: 2 W m⫺2), (c) Z250 (contour interval: 2 m), and (d) Z850 (contour interval: 2 m).

due to the long persistence, resulting in little cancellation of the signal with the average time and, in turn, a much slower reduction rate of the signal with the average time (Fig. 14b). It is important to point out that the long-term response in the coupled model here, in principle, can be realized because the SSTA changes naturally in the coupled system for an initial ocean temperature anomaly of realistic characteristics. This is different from an AGCM simulation with a prescribed SSTA in which the time scale is prescribed by the forcing. Since a SSTA cannot remain unchanged in the coupled system, the AGCM-simulated long-term response will not be realized in a coupled system and, therefore, is of less practical value to the understanding of long-term climate variability in the coupled system. The patterns of the long-term mean, linear trend, and seasonal variability have differences. For example, the primary response center of the North Pacific atmosphere long-term mean response is located at about 60°N (Figs. 9c,d), almost 10° north of the primary center in the linear trend (Figs. 10c,d) and the seasonal cycle (Figs. 11c,d). These different patterns may imply different atmospheric responses at different time scales.

6. Dynamic assessment, statistic assessment, and implications to the observation a. Dynamic assessment The ensemble coupled simulation, with an infinite ensemble, defines a true dynamic assessment of the seasonal atmospheric (and oceanic) response to the initial KOE oceanic temperature anomaly. We assume a linear response of an atmospheric variable A to a SSTA index T as A共t兲 ⫽ ␭AT共t兲 ⫹ N共t兲,

共2兲

with N being associated directly with the atmospheric internal variability. The response efficiency ␭A, that is, the response per unit SSTA, can be estimated dynamically from (2) as

␭A|dyn ⫽

具A共t兲典 , 具T共t兲典

共3兲

where the ensemble mean atmospheric internal variability vanishes 具N(t)典 ⫽ 0, while the ensemble mean SST signal 具T(t)典 is the nonzero anomalous SST forcing. This estimation applies to each month of the ensemble

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FIG. 12. The (left) EOF1, (middle) EOF2, and (right) their PCs (solid for EOF1 and dashed for EOF2) of the residual response of the atmosphere for (a) Z250 and (b) Z850. Positive contours are solid, negative are dashed, and zero are suppressed (contour interval: 0.02).

simulation. The response efficiency of the same calendar month can then be averaged to generate a composite seasonal cycle of response efficiency. Figures 16a and 16b show the seasonal cycle of the response efficiency of the Aleutian low atmosphere to the KOE SSTA for Z250 and Z850, respectively (pluses). This seasonal cycle is estimated as a weighted average of the monthly efficiencies of year 1 (weight 1) and year 2 (weight 0.5). [The weight is roughly proportional to the annual mean KOE SST in each year. Later years are not used because of the diminishing 具T(t)典 in the denominator in (3) and, in turn, larger sampling errors.] Consistent with previous discussions, the dominant atmospheric response is an equivalent barotropic ridge response in early winter (before February). Later in this year, this ridge response weakens substantially when the lower-level response reverses to a low. Into the following early winter, the upper-level ridge reintensifies and then penetrates downward to reverse the surface response to a ridge. (Also see discussion on Fig. 6.)

Some features of the response efficiency are better understood from the response itself (具A(t)典) in the coupled system. For example, the response efficiencies seem to indicate two positive peaks in early winter (November and January at 250 hPa and October and January at 850 hPa). However, only the peak in January is due to a peak in the atmospheric response. This can be seen in the atmospheric responses, which show only a single peak of equivalent barotropic ridge response in January (Figs. 16c,d). The earlier peak is due to the small SSTA in later fall, as seen in the SST signal (具T(t)典) (Fig. 16e), which tends to diminish late fall (except for the September peak of the first-year SSTA, which is caused by the imposed initial SSTA). This minimum SSTA also leads to a peak efficiency of baroclinic response in August (positive at 250 hPa and negative at 850 hPa, in Figs. 16a,b). The true August atmospheric response in the coupled system, however, exhibits only a weak baroclinic response (Figs. 16c,d) because of the weak SSTA (Fig. 16e) at that time.

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FIG. 13. Scatter diagram of the full evolution of the response for all the ensemble members (each member minus the mean of the control) for (a) SST (°C), (b) upward turbulent heat flux (W m⫺2), (c) upper-ocean (560 m) heat content (m°C) (all three in the region of 30°–50°N, 140°E–180°), and the atmospheric Z250 (m) in (d) the northern (50°–70°N, 150°E–150°W) and (e) central-southern (30°–60°N, 180°–150°W) Aleutian low region. At each month, the value of each member is plotted as a dot; the ensemble mean response and the 95% confidence level are plotted in the heavy solid and dashed lines, respectively. A 3-month running mean is applied to each member and the ensemble mean.

FIG. 14. Zonal variation of the magnitude of the (a) atmospheric internal variability (noise), (b) ensemble mean response (signal), and (c) signal/noise ratio for Z250, averaged in the latitude belt of 30°–80°N for 1 month (dotted), 3 months (dashed), 1 yr (dashed–dotted), and 4 yr (solid). The signal and noise at each grid point are first derived as described in the text, and then averaged for the latitude on each longitude.

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b. Statistical assessment We now proceed to estimate the response efficiency statistically from CTRL following Frankignoul et al. (1998) (also Frankignoul and Kestenare 2002; Czaja and Frankignoul 2002). By eliminating the atmospheric internal variability N in Eq. (2) with a SST-lead covariance analysis, this method extracts the response efficiency statistically from a single control simulation. The key is that the SSTA cannot be forced by the atmospheric internal variability of a later time. This assures 具N(t), T(t ⫺ ␶)典 ⫽ 0 in Eq. (2), where ␶ is a time lag longer than the atmospheric response time (usually assumed as 1–2 weeks) and the ensemble mean (angle brackets) is now approximated by a time mean. Multiplying Eq. (2) by T(t ⫺ ␶) and ensemble averaging, we have an estimator for the response efficiency as

␭A|sta ⫽

具A共t兲, T共t ⫺ ␶兲典 . 具T共t兲, T共t ⫺ ␶兲典

共4兲

If the efficiency is truly constant, with an infinite ensemble, estimator (4) should remain unchanged with the lag. With a finite ensemble, in practice, sampling errors tend to increase with the lag because of the diminishing SST autocovariance in the denominator (for a more detailed discussion, see Liu et al. 2006). Therefore, only the very first few lags are usable (Frankignoul et al. 1998). This method has been used for the estimation of a winter month atmospheric response (LW04) and is now extended to the estimation of the entire seasonal cycle of the response efficiency from the 300yr control simulation. Before calculating the covariance, the influence of ENSO is filtered out from the monthly SST (with a 2-month lag) and GPH (at 0 lag) using a regression against the Niño-3 SST index. The response efficiency is then estimated for each calendar month using Eq. (4) at lag 1 and 2, separately. The final response efficiency is a weighted average of lag 1 (weight 1) and lag 2 (weight 0.5). In early winter, the statistic estimation shows an equivalent barotropic ridge response over the Aleutian low region (Fig. 15, left; notice the different contour intervals between Z250 and Z850), with wave train responses downstream and upstream. This pattern is largely consistent with the dynamic response in Figs. 2c and 2d. The maximum local ridge response in the statistical estimation is over 30 m °C⫺1 in Z250 and over 20 m °C⫺1 in Z850. These maxima are therefore somewhat weaker than, but still rather comparable with, their dynamic assessments—about 50 m °C⫺1 for Z250 and 25 m °C⫺1 for Z850. The magnitude of the dynamic assessment is obtained from the WARM response

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Figs. 2c,d, divided by the area mean KOE SST anomaly (0.6 m °C⫺1). This comparison is consistent with LW04, in which only the December response is studied. The statistically estimated seasonal cycle of response efficiency is shown for the Aleutian low region in Figs. 16a and 16b (circles). The statistical estimation is dominated by an early winter equivalent barotropic ridge response, as well as a weaker response in the rest of the year, with even a reversed sign late winter in the lower level. These features are also evident in the dynamic assessment. Furthermore, the magnitude of the statistical estimate is comparable with the dynamic estimate, with the maximum of about 30 and 15 m °C⫺1 for Z250 and Z850, respectively. There are still substantial differences between the two estimates. For example, the winter ridge response occurs about one month later in the statistic assessment (Figs. 16a,b). The responses in late winter and summer tend to be less robust than in early winter, because they are weak in both estimates. As a result, the response patterns in other seasons show less agreement between the two estimates (not shown). These differences between the two estimates are not surprising because there are many reasons that the two estimates could differ significantly. In addition to sampling errors, the discrepancy between the two assessments may result from the nonlinear atmospheric responses (Peng et al. 2003), which cannot be captured by the linear statistical method here. The discrepancy could also be attributed to the nonlocal nature of the response. For the statistical estimate (4), it has been assumed that the atmosphere responds to the SST forcing in the KOE region only. In the control simulation, however, the atmosphere could have responded to SST variability outside the KOE region, such as the other parts of the North and tropical Pacific, and even in the Atlantic. In addition, the regression removal of ENSO impact may not be complete. Finally, even in the dynamic simulation, the initial SST anomaly expands and migrates northeastward such that the SST index based on the KOE SST is no longer a perfect index for the SST forcing. Given these potential deficiencies of the two methods, it is rather interesting that the two independent estimates are consistent in the major features of the responses and give a comparable magnitude of the response. Admittedly crude, this statistical method, we believe, is still useful for providing, for the first time, an order-of-magnitude estimate of the atmospheric response. In spite of a reasonable statistical estimate of the monthly and seasonal atmospheric responses, it is likely to be more difficult to estimate the response at annual and longer time scales. It is, nevertheless, interesting

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FIG. 15. The patterns of the statistically estimated atmospheric response efficiency to the KOE SST index (in m °C⫺1), for (left) the FOAM control and (right) the NCEP–NCAR reanalysis on (top) Z250 and (bottom) Z850. The statistical estimate is a weighted average of lag 1 (weight 1) and lag 2 (weight 0.5) (contour levels: ⫾2, 5, 10, 15 . . . m °C⫺1).

that, locally over the Aleutian low region, a simple annual mean of the monthly response efficiencies from the two methods are comparable: In Figs. 16a,b, the annual mean of the 12-month response efficiencies shows a clear ridge response of ⫹15 and ⫹10 m °C⫺1 for the dynamical and statistical estimates for Z250 (from Fig. 16a), respectively, but nearly zero (⬍1 m °C⫺1) for both estimates for Z850 (from Fig. 16b). In a sense, the simple annual mean of the monthly efficiency is not justified because it assumes the same SST in each month, while the SST varies during the year in the coupled evolution (Fig. 16e). The role of SST change can be included if one compares the annual mean responses instead of the efficiency. For Z250, the annual mean atmospheric response can be calculated at ⫹3.4 and ⫹2.9 m for the dynamical and statistical estimates, respectively. Here, the dynamic estimates of the responses are simply the average of the first two years’

ensemble mean responses in Fig. 16c, while the statistical estimate of the response is the response efficiency in Fig. 16a multiplied by the SSTA seasonal cycle derived from Fig. 16e. A similar calculation of the annual mean responses for Z850 shows a nearly zero response (⬍0.5 m) in both estimates. Either way, the simple annual mean of the monthly statistical estimates seems to be able to provide some useful information about the annual mean dynamic response.

c. Implications to the observation Given the usefulness of the statistical estimate, we believe it informative to apply the statistical estimation to the observation. The response efficiency of the early winter atmosphere to the KOE SST is estimated using the monthly SST, Z250, and Z850 from the 1950–2005 NCEP–NCAR reanalysis (Kalnay et al. 1996; in Fig. 15,

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FIG. 16. Dynamic (plus) and statistical (circles) assessments of the seasonal cycle of response efficiency (in m °C⫺1) of the Aleutian low atmosphere (30°–60°N, 150°E–150°W) to the KOE SST (30°–50°N, 140°E–180°) for (a) Z250 and (b) Z850. The statistical assessments are the weighted average of the lag 1 (weight 1) and lag 2 (weight 0.5) estimates according to Eq. (4), while the dynamic assessments are the weighted average of the responses in year 1 (weight 1) and year 2 (weight 0.5). The monthly coupled responses are also shown for (c) Z250, (d) Z850 (in m), and (e) SST (in °C) for year 1 (solid) and year 2 (dash).

right, notice the different contour intervals between Z250 and Z850). The observation shows a distinct equivalent barotropic ridge response over the Aleutian low region and a wave train downstream. This pattern is reminiscent of the FOAM response (Fig. 15, left). The observed seasonal cycle of response efficiency over the Aleutian low region is estimated in Fig. 17. The inferred atmospheric response shows a dominant early winter response of an equivalent baotropic ridge and a much weaker response in the rest of the year, a major feature also evident in FOAM (Figs. 16a,b). Furthermore, the magnitude of the response efficiency in winter is about 30 and 15 m °C⫺1 for Z250 and Z850, respectively (as shown in Fig. 17). These are also comparable with those in FOAM. Finally, the annual mean response efficiency can be calculated as 8 m °C⫺1 for Z250 and nearly zero (⬍1 m °C⫺1) for Z850, which is also comparable with the FOAM estimate. Admittedly, there are also significant differences between the FOAM estimate and the observational estimate. Nevertheless, the similarity between FOAM and the reanalysis seems to be sufficient to suggest that the FOAM study is relevant to the real world. Taken together, it is possible that the observed

North Pacific atmospheric response to the KOE SST variability does exhibit a dominant early winter warmridge response, which weakens dramatically during the rest of the year, as simulated dynamically in FOAM.

FIG. 17. Statistical assessment of the seasonal cycle of response efficiency of the Aleutian low atmosphere (30°–60°N, 150°E– 150°W) to KOE SST (35°–45°N, 140°E–180°) variability estimated the same as in the model FOAM (circles in Figs. 16a,b), but for the NCEP–NCAR reanalysis for Z250 (solid) and Z850 (dashed).

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7. Summary The atmospheric response to a North Pacific Ocean temperature anomaly is investigated in a coupled GCM with the focus on the response evolution at seasonal to interannual time scales. The coupled response is studied in an ensemble experiment with an initial warm temperature anomaly extending deep into the thermocline in the KOE region. Two issues are addressed: First, how does the atmosphere respond to this KOE oceanic temperature anomaly at seasonal and longer time scales? Second, can the simulated dynamic atmospheric response be assessed statistically from the control climate? The ensemble mean response exhibits a distinguished seasonal cycle as well as a significant long-term persistence in the coupled system. The oceanic temperature anomaly reemerges each winter, generating a SSTA and, in turn, an upward heat flux. Subsequently, the forced atmospheric response exhibits a distinct seasonal evolution locally over the North Pacific, downstream over the North America/North Atlantic sector, and around the Arctic. The maximum atmospheric response occurs in early winter as a warm SST–ridge locally over the Aleutian low region, with a significant wave train response downstream. The atmospheric response weakens substantially toward late winter and later in the summer. The response pattern also tends to change to an annular-like response with a trough in the lower atmosphere over the North Pacific later in the winter. This distinct seasonal atmosphere response is further shown to be largely consistent with an independent statistical assessment of the atmospheric response from the control simulation. Both assessments are characterized by a dominant equivalent barotropic ridge in early winter, and both assessments have a comparable magnitude of the seasonal responses. An application of the statistical assessment to the observation seems to also suggest a distinct seasonal cycle of the atmospheric response, with some resemblance to the model simulation. One important finding of the ensemble coupled simulation is a significant atmospheric response at annual and longer time scales. These long-term responses are much more robust than the monthly and seasonal responses, especially locally over the North Pacific sector where the signal/noise ratio can be increased up to four times. The signal/noise ratio is increased because the atmospheric internal variability is stochastic with time, while the atmospheric response signal has a long persistence associated with the slow subsurface ocean. It is important to point out that the long-term atmospheric response produced here is potentially feasible

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in the coupled system because it is now forced by a naturally evolving oceanic temperature anomaly, rather than by a prescribed time-invariant SST anomaly in an AGCM simulation. One implication of the robust longterm atmospheric response is that the atmospheric response to North Pacific oceanic variability tends to be much more important at interannual to interdecadal time scales than at monthly and seasonal time scales, with subsurface oceanic variability playing a critical role. The North Pacific atmospheric response in the sensitivity experiment appears to be caused dominantly by the SST anomaly in the North Pacific, rather than from other regions, such as the tropical Pacific. In the WARM experiment, a weak warm SST anomaly propagates into the equatorial Pacific, peaking each early summer (AMJ) and diminishing each fall (not shown). This early summer SST anomaly can be traced back to the North Pacific SST in the eastern subtropics of the preceding winter through a rapid equatorward propagation that is caused by the coupling between the surface atmospheric and oceanic processes (Liu and Xie 1994; Vimont et al. 2001; Wu et al. 2007). However, the SST in the tropical Pacific is very weak, less than about 0.2°C even in its peak season (in the second and third year). This secondary SST anomaly, which results from the KOE SST forcing in the coupled system, may have some impact on the North Pacific atmosphere in early summer in the second and third year, but it appears unlikely to be important for the North Pacific atmospheric response in other seasons, and the entire first year. This study has left many questions unresolved. The different atmospheric responses in different seasons are certainly related to the different roles of eddy feedbacks (Peng and Whitaker 1999; Peng and Robinson 2001). The detailed role of the eddy feedbacks, however, still remains to be understood. The long-term response also requires further studies, especially in the context of the coupled system. Furthermore, the statistical assessment method needs to be improved to take into account nonlocal response and, perhaps, nonlinear response. Finally, the role of ocean–atmosphere interaction in the atmospheric response remains one major puzzle to us. The coupled response differs significantly from a 200-member ensemble AGCM experiment [Atmospheric Model Intercomparison Project (AMIP): see appendix B]. Here, each AMIP member is forced by the ensemble mean global SST anomaly of the WARM experiment such that the AMIP ensemble mean response can be compared directly to the coupled WARM experiment. Consistent with LW04, the AMIP

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response exhibits a substantial difference from the coupled WARM experiment (see appendix B): notably, the atmospheric response is overall weaker in AMIP than in WARM. In addition, the response pattern in AMIP can also be distorted in certain seasons (such as the late winter) as well as in the long-term mean. The cause of the difference between AMIP and the coupled WARM remains unclear to us. The consistent result with LW04 does suggest that, at least in FOAM, the correct atmospheric response is more likely to be achieved in the coupled experiment. Acknowledgments. We thank Drs. D. Lorenz and E. DeWeaver for a helpful discussion on the atmospheric dynamics and Mr. M. Marohl for some editorial assistance. We also thank the careful comments of the two anonymous reviewers, which have led to a substantial improvement of the paper. This work is supported by DOE, NOAA. Part of the work is also supported by Chinese NSF 40333030 and 40576009. The computations are performed at NCAR SCD and DOE NERSC.

APPENDIX A Signal/Noise Ratio for Different Average Time The key for the increased signal/noise ratio is that the amplitude (standard deviation) of a random noise decreases with the square root of the averaging time, while a persistent signal decays slower. In general, the time mean of an AR-1 random variable decreases faster with the average period if its persistence is shorter, because of the cancellation of uncorrelated events during the time average. This amplitude reduction can be quantified below. We first define the running mean of a standard random variable q(t) (of a unit variance) as q共t兲 ⫽ 共1Ⲑp兲

冕

⫹pⲐ2

⫺pⲐ2

q共t ⫹ t⬘兲 dt⬘,

where p is the time average period in the unit of month. The q(t) has a persistence time of 1/a such that its covariance is

具q共t兲, q共s兲典 ⫽ e⫺a|t⫺s|.

共A1兲

The standard deviation of the time-mean variable can be shown as

␴q共a, p兲 ⬅ 公具q共t兲, q共t兲典 ⫽ Q共ap兲 ⬅

冑 冉

⫺ap

1⫺e 2 1⫺ ap ap

冊

.

共A2兲

Here Q(ap) decreases monotonically from 1 to 0 as p increases from 0 to infinity, representing the decay of

FIG. A1. (a) The decay of amplitude of four time-mean AR-1 variables R(a, p), as defined in Eq. (A1) (solid), as a function of the average period p. For reference, the amplitude decay of a pure white noise 1/公p is also plotted (dashed). (b) The signal/noise ratio RN(a, p), as defined in Eq. (A5) for the four AR-1 variables in (a). The fastest variable (a ⫽ 4) can be thought of as the atmospheric internal variability and can be seen to be virtually the same as a pure white noise. The slowest variable (a ⫽ 1/50) can be thought of as the heat content, or the part of atmospheric response to heat content.

the time-mean variable with the average time. Since here we are interested in the change of amplitude relative to the monthly data, we will consider the decay relative to the unit period ( p ⫽ 1 month) average R共a, p兲 ⫽ Q共ap兲ⲐQ共a兲.

共A3兲

This amplitude function decays monotonically with p and decays faster with a shorter persistence time (a k 1) (Fig. A1a). In the limit of zero decorrelation time (1/a → 0), R can be shown to decay as the square root of p as R(⬁, p) ⫽ 1/公p, as for a pure white noise. In practice, an atmospheric internal variability N(t) has a

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persistence time of a week (a ⫽ 4); this can be treated virtually as a pure white noise, as shown in Fig. A1a. Figure A1b further plots the ratio of the amplitude of the AR-1 variable relative to the pure white noise as RN共a, p兲 ⫽ R共a, p兲ⲐR共⬁, p兲.

共A4兲

Figure A1b shows that RN increases monotonically with the persistence time 1/a, as expected. With the application to our atmospheric response here, the atmospheric variability consists of the atmospheric internal variability N(t) and a slow signal S ⫽ ␭H(t), where H is the heat content with a persistence time of 4 yr (a ⫽ 1/50): A(t) ⫽ S(t) ⫹ N(t). Figure A1b shows that the signal/ noise ratio can be increased about four times for an average period of 4 yr ( p ⫽ 50). This is roughly consistent with our FOAM simulation (Fig. 14). Indeed, with the aid of Eq. (A2), the signal/noise ratio for a sufficiently slow process (a K 1) after a sufficiently long average time (such that ap k 1) can be estimated as RN共a, p兲 →

冑

2 . a

共A5兲

Therefore, the signal/noise ratio increases with the persistent time as a square root, roughly consistent with Fig. A1.

APPENDIX B The AMIP Experiment To examine the role of ocean–atmosphere coupling in seasonal atmospheric responses, as studied by LW04, an ensemble of the AMIP experiment is performed parallel to the WARM experiment. First, we performed a separate AMIP control. The coupled model is integrated for 250 years in which the global SST to the atmosphere is prescribed as the climatological seasonal cycle of the fully coupled control (CTRL). [This AMIP control experiment is similar to the global partial coupling experiment described in Wu et al. (2003)]. Second, the atmospheric state for each 1 September of the last 200 years is used for the initial condition of each AMIP ensemble member, with a total of 200 members. Third, each ensemble member is forced by a common SST anomaly superimposed on the climatological SST to the atmosphere model; the SST anomaly for the AMIP run is constructed using the monthly mean of the ensemble mean SST anomaly (over the entire globe) of the first 3 ⫻ 12 month ⫽ 36 months of the WARM experiment and is linearily interpolated to each time step in each AMIP member integration for 3 years. The anomalous response of each experiment is the difference between the member and the corresponding years

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of the AMIP control. Therefore, this AMIP experiment represents our best possible AMIP simulation of the coupled WARM experiment. In the following, we present the 200-member ensemble mean response. The winter atmospheric response in the first early winter (NDJ) is shown in Fig. B1a and b for Z250 and Z850, respectively. Compared with the corresponding atmospheric response in the coupled WARM experiment (Figs. 2c, d), the AMIP experiment simulates a similar pattern but with a weaker amplitude. In the center of the Aleutian low, the atmospheric response is weaker by about a half, especially in the lower layer. This weaker AMIP response is consistent with LW04, in which only the December response is studied. In other seasons, the atmospheric response weakens significantly relative to the early winter, as in the coupled response. The response pattern, however, tends to show differences from the coupled run. For example, the AMIP response in late winter (FMA) of the first year (Figs. B1c,d) exhibits a different pattern from the coupled WARM experiment (Figs. 4c,d). The different patterns may also be related to the fact that the weaker atmospheric responses in late winter (and other seasons) are less robust than in the early winter. It is also possible that the role of ocean–atmosphere coupling on the atmospheric response differs for different seasons. The seasonal evolution of the atmospheric response can be seen in the Aleutian low region (Figs. B2a,b). As discussed in Fig. B1, the AMIP seasonal cycle is roughly consistent with the WARM experiment (Figs. 16c,d), with both being dominated by a strong equivalent barotropic ridge response in early winter and a weaker response the rest of the year. The amplitude of the AMIP atmospheric response is, however, weaker by about a half, while the seasonal cycle of KOE SST is virtually identical to WARM (cf. with Fig. 16e) as it should be. Finally, the long-term mean response of AMIP is shown as the 3-yr mean in Fig. B3. The mean SST (Fig. B3a) is virtually identical to the WARM experiment (Fig. 9a), as it should be. The mean atmospheric response, however, is substantially weaker in AMIP (Figs. B3c,d) than in WARM (Figs. 8c,d: the contour interval in the former is half that in the later). The maximum ridge response decreases more than a half, from about 5 m in WARM to less than 2 m in AMIP for Z250. Furthermore, the pattern of the long-term mean response in AMIP differs substantially from that of WARM. For example, the maximum response center over Bering Strait in WARM disappears and is replaced by much weaker centers to the south and east.

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FIG. B1. Ensemble mean atmospheric response of the AMIP simulation in the first year of early winter (NDJ) for (a) Z250 and (b) Z850, and late winter (FMA) for (c) Z250 and (d) Z850. (Contour levels: ⫾2, 5, 10, 15 . . . m). Positive contours are solid, negative are dashed, and zero are suppressed. Shading indicates the area above the 95% significance level. (a), (b), (c), and (d) correspond to the panels of the WARM experiment in Figs. 2c, 2d, 4c, and 4d, respectively.

Accompanying the weaker ridge response, the upward heat flux increases over the KOE. Overall, the AMIP atmosphere exhibits generally a weaker response. The response pattern is reproduced

well only for the early winter, when the response is the strongest. The mechanism for the different atmospheric response between the AMIP and the coupled response has remained unclear to us. LW04 speculated that the

FIG. B2. AMIP seasonal response of the ensemble mean for the Aleutian low region (30°–60°N, 150°E–150°W) in year 1 (solid) and year 2 (dash) for (a) Z250 and (b) Z850 (both in m). The corresponding SST history in the KOE region (30°–50°N, 140°E–180°) is shown in (c) SST (in °C). (a), (b), and (c) correspond to the panels of the WARM experiment in Figs. 16c, 16d, and 16e, respectively.

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FIG. B3. The 3-yr average of the ensemble mean AMIP response for (a) SST (contour interval: 0.1°C), (b) upward turbulent heat flux (contour interval: 2 W m⫺2), (c) Z250 (contour interval: 1 m), and (d) Z850 (contour interval: 0.5 m). Positive contours are solid, negative are dashed, and zero are suppressed; shading marks the regions of 95% significance level. This figure corresponds to Fig. 9 of the WARM experiment, but the contour intervals for Z250 and Z850 are only half those in Fig. 9.

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