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In this study, daily atmospheric variables, including the wind speed, geopotential height, and air temperature, were used to calculate the metrics of storm track activity and associated energy conversion terms, which were provided by the ECMWF (European Centre for Medium-Range Weather Forecasts) Interim (ERA-Interim) reanalysis during the period 1982–2017 with a spatial resolution of 0.75° × 0.75° (Dee et al., 2011). The monthly surface air temperature (SAT) was obtained from the ERA-Interim reanalysis. The monthly SST data, obtained from the National Oceanic and Atmospheric Administration (NOAA) Optimum Interpolation Sea Surface Temperature (OISST) with a spatial resolution of 0.25° × 0.25° (Reynolds et al., 2007), were mainly adopted to calculate all the oceanic indices used. We also used the ERA-Interim SST product to investigate the imprints of the KE multi-scale oceanic variations on SST, consistent with the spatial resolution of relevant atmospheric responses. The daily satellite altimetry data are offered by the Archiving Validation and Interpretation of Satellite Oceanographic (AVISO) product (Ducet et al., 2000) on a 0.25° × 0.25° grid from 1 January 1993 to 31 December 2017. The mean seasonal cycle of all variables is removed by subtracting the climatological monthly means. A cubic polynomial is also removed from each variable by employing a least squares fit to eliminate the influence of trends and ultra-low frequencies.
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Following Qiu et al. (2007), the KE large-scale variation can be measured by an index defined as the average SSTA over the KE region of 32°–38°N, 142°E–180° (Fig. 1a, black box). Although this region is located to the south of maximum SST variance (Fig. 1a), the KE region possesses the strongest ocean circulation variability over the North Pacific (Fig. 1b) that primarily drives the KE SST changes (Qiu et al., 2007). Considering that the diameters of mesoscale eddies are generally less than 5°, we used a 5° × 5° spatial boxcar to filter the mesoscale SSTA from large-scale signals before calculating the KE SSTA index (Zhang et al., 2019).
Figure 1. (a) Climatological mean North Pacific SST (°C; black contours) in the cold season during 1982–2017. Color shading indicates the root-mean-square amplitude of SST (°C). (b) Root-mean-square amplitude of the North Pacific SSH signals (cm) in the cold season during 1993–2017. (c) Climatological mean of the magnitude of horizontal SST gradient [°C (100 km)‒1] in the cold season during 1982–2017. (d) Climatological mean surface EKE (cm−2 s−2) in the cold season as calculated from the SSH anomalies of 1993–2017. The black boxes in four subplots denote the regions used to define the indices of the KE multi-scale oceanic variations (see text for details).
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The KEF is detected from the position of the maximum horizontal SST gradient between 32°–37°N at each longitudinal grid point from 142° to 180°E (Chen, 2008). The present paper only considers the upstream KEF position because this oceanic front becomes weak and shows obvious bifurcation in its downstream area (Kida et al., 2015). Therefore, following Seo et al. (2014), we searched the KEF in the region of 32°–37°N, 142°–155°E (Fig. 1c, black box), and the zonally averaged oceanic front position between 142°E and 155°E is defined as the KEF position (KEFP) index.
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We used an index to depict the intensity of the KE mesoscale eddy activity proposed by Yu et al. (2020). First, the eddy kinetic energy (EKE) in the western North Pacific is calculated according to Qiu and Chen (2005). The formula is as follows:
where
$ h^{\prime} $ denotes the high-pass filtered SSHAs that only retain changes below 300 days,$ {g} $ is the acceleration of gravity, and$ f $ is the Coriolis parameter. From the distribution of the EKE (see Fig. 1a of Yu et al., 2020), it can be observed that the KE EKE is the strongest in the region of 31°–38°N, 142°–155°E (Fig. 1d, black box), thus, we focus on the eddy activity in this region. Then, the KEEA index is constructed based on the KE EKE-related SSTA distribution:$\alpha {T_{\text{A}}} + \beta {T_{\text{B}}} + \gamma {T_{\text{C}}}$ , where TA, TB, and TC denote the normalized SST anomalies averaged over regions A (36.875°–38.375°N, 143.875°–146.125°E), B (33.625°–34.875°N, 138.375°–140.875°E), and C (34.125°–35.625°N, 148.125°–150.625°E), respectively. The coefficients α, β, and γ are obtained by the least-squares method. Specifically, the estimated EKE from the AVISO SSH data is regressed onto the normalized SSTAs from the OISST dataset, and both span the period from January 1993 to December 2017. This quantifies the EKE–SST relationship and gives a 103.98 cm−2 s−2 EKE increase per standard deviation increase in TA, a 52.99 cm−2 s−2 EKE decrease per standard deviation increase in TB, and a 60.25 cm−2 s−2 EKE decrease per standard deviation increase in TC. This index actually reflects the anomalous poleward transport of warm water modulated by the KE eddy activity and highlights its climatic effects. More details about this index can be referred to in the work of Yu et al. (2020).The temporal variations of all above-mentioned KE indices during 1982–2017 are shown in Figs. 2a–c, respectively. These indices all show obvious oscillations on interannual and decadal time scales. To focus on the cold season and increase the sample size, we selected these KE indices for September–April (SONDJFMA) (Figs. 2a–c, black dots) since the NPST responses are estimated between November and April from the KE oceanic forcings two months earlier (see details in section 2.6).
Figure 2. Time series of the normalized (a) KE SSTA index, (b) KEFP index, and (c) KEEA index during 1982–2017. The black dots indicate the KE indices in the SONDJFMA season, as used in the GEFA. (d) Correlation coefficients of the KE SSTA index in the cold season with the KE SSTA indices of the preceding 10 months. Dots denote the correlation coefficients exceeding the 95% confidence levels. Panels (e) and (f), as in (d), but for the KEFP and KEEA indices in the cold season, respectively.
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Since baroclinic disturbances in the mid-latitudes extend from the surface to the tropopause, the storm track can be observed at different altitudes (Chang and Fu, 2002; Gan and Wu, 2014). To study the NPST responses to the KE multi-scale oceanic variations in a more stereoscopic way, the NPST is represented by the meridional heat flux at 850 hPa, the root mean square of geopotential heights at 500 hPa, and the variance of the meridional wind velocity at 300 hPa through the use of a Lanzcos bandpass filter to isolate the synoptic-scale (2–8 day) disturbances from daily data. This method is convenient for visualizing and comparing the effects of the KE multi-scale oceanic variations on the NPST activity in the free atmosphere.
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To distinguish the NPST responses to the KE multi-scale oceanic variations, the GEFA method developed by Liu et al. (2008) was adopted in this research, which can effectively exclude the impacts of other external forcings when revealing the atmospheric response to a certain variable (Wen et al., 2010, 2015; Wang et al., 2013; Jiang et al., 2015; Révelard et al., 2018). The basic principle is outlined as follows. Suppose the atmospheric variable
$ A(t) $ is at time$ t $ and the oceanic forcing${\boldsymbol{O}}(t)$ has${\boldsymbol{J}}$ variables, so that${\boldsymbol{O}}\left( t \right){\text{ = }}\left[ {{O_1}\left( t \right),{O_2}\left( t \right), \cdots ,{O_J}\left( t \right)} \right]$ . The relationship between them can be approximately expressed as:where
${\boldsymbol{B}}{\text{ = }}\left[ {{B_1},{B_2}, \cdot \cdot \cdot ,{B_J}} \right]$ is a matrix containing the atmospheric response coefficients to each single oceanic variable and$ N(t) $ is the internal atmospheric variability.Owing to the poor atmospheric memory that only lasts for up to 1–2 weeks, the ocean is not affected by the atmosphere with a time lag
$ \tau $ larger than its intrinsic persistence. Thus, we have${{\boldsymbol{C}}_{ON}}(\tau ) \approx 0$ , where${{\boldsymbol{C}}_{ON}}(\tau )$ represents the lagged covariance matrix between${\boldsymbol{O}}(t)$ and$ N(t) $ . By multiplying Eq. (2) by${\boldsymbol{O}}\left( {t - \tau } \right)$ and calculating the covariance, we can obtainHowever, considering that the atmospheric response to extratropical SSTAs needs a few months to fully develop (Ferreira and Frankignoul, 2005; Deser et al., 2007), the relation in Eq. 2 should take a more complex form. According to Frankignoul et al. (2011),
${\boldsymbol{O}}(t)$ in Eq. 2 can be replaced by${\boldsymbol{O}}(t - d)$ , where$ d $ denotes a characteristic delay time. Then, the relation in Eq. 4 becomes for$ \tau>d $ To estimate the typical amplitude of the NPST response, all the oceanic time series are normalized, and thus
${{\boldsymbol{C}}_{OO}}(\tau - d)$ becomes a lag correlation matrix. Here, we chose$ \tau=2 $ months,$ d=1 $ month. The reasons behind the choice of these value schemes consider two aspects. 1) The atmospheric response to lower boundary forcings reaches its maximum amplitude after at least two months (Frankignoul and Sennéchael, 2007; Strong et al., 2009); 2)$ \tau-d $ should be as small as possible to achieve a better condition on${{\boldsymbol{C}}_{OO}}(\tau - d)$ to reduce the sampling errors in Eq. (5) (Liu et al., 2006). However, it should be noted that the value scheme of$ \tau=d $ is not considered, for which${\boldsymbol{B}}$ is divided by${{\boldsymbol{C}}_{OO}}(0)$ , and the GEFA becomes a lag regression analysis. This is because the contribution to${{\boldsymbol{C}}_{OO}}(0)$ contains two parts, very fast changes and more persistent variability (Frankignoul et al., 2011). Considering that the NPST responses to the slow changes in boundary forcing over the KE region are our focus,$B$ should be calculated by only using the slow contribution to${{\boldsymbol{C}}_{OO}}(0)$ , which is smaller than${{\boldsymbol{C}}_{OO}}(0)$ itself. Hence, the use of${{\boldsymbol{C}}_{OO}}(0)$ will underestimate the amplitudes of NPST responses. Furthermore, Révelard et al. (2018) adopted the GEFA with$ \tau=3 $ months and$ d=1 $ month to estimate the atmospheric responses by using seasonal mean anomalies, but they found that the results remain nearly the same by using monthly anomalies based on$ \tau=2 $ months,$ d=1 $ month. We verified, using the monthly anomalies, that the estimated responses based on$ \tau=3 $ months,$ d=1 $ month are largely similar to the results of the present work. All the action centers of NPST responses in lag$ \tau=2 $ months can be identified in lag$ \tau=3 $ months (figure not shown).Since the tropical El Niño-Southern Oscillation (ENSO) exerts a significant impact on the mid-latitude atmosphere and ocean (Alexander et al., 2002), the first two principal components of SSTAs over the tropical Pacific between 20°S and 20°N (TP1 and TP2) are also added to the oceanic forcing matrix
${\boldsymbol{O}}(t)$ to avoid the interference of ENSO signals on the KE-NPST relationship. In other words, the${\boldsymbol{O}}(t)$ in our study contains the time series of five indices (KE SSTA, KEFP, KEEA, TP1, and TP2). According to Révelard et al. (2018), the GEFA will be invalid if the regressors are strongly correlated, making it hard to separate their influence. Therefore, the multi-collinearity should first be examined. Table 1 shows the lag correlation matrix${{\boldsymbol{C}}_{OO}}(\tau - d)$ used to estimate the NPST responses in the cold season. It can be clearly seen that the correlations among these five regressors are generally weak and insignificant. To better quantify the multi-collinearity, we calculated the variance inflation factors (VIFs) that are equal to the diagonal elements of the inverse correlation matrix${{\boldsymbol{C}}_{OO}}{(\tau - d)^{ - 1}}$ (Kendall, 1946). Generally, VIFs that exceed five indicate the existence of severe multi-collinearity (Judge et al., 1988). Here, it is found that the maximum VIF of the five regressors is only 1.73. Accordingly, there is no strong problem of multi-collinearity in our study. Furthermore, the persistence of the KE large-scale SSTA index, the KEFP index, and the KEEA index is all more than five months, far exceeding the inherent atmospheric memory (Figs. 2d–f), indicating that the persistence of these oceanic forcings is in accordance with the physical basis of GEFA.KE SSTA KEFP KEEA TP1 TP2 KE SSTA 0.81 0.06 –0.03 –0.12 0.11 KEFP 0.19 0.64 0.08 –0.24 –0.09 KEEA 0.00 0.02 0.76 –0.18 0.07 TP1 –0.25 –0.19 –0.15 0.98 0.00 TP2 0.10 –0.06 0.01 –0.06 0.93 Maximum VIF = 1.73. Table 1. Lag correlation matrix of (left to right) the five oceanic regressors used to estimate the NPST responses in the cold season (NDJFMA). Each row and column use monthly anomalies in ONDJFM and SONDJF, respectively. The bold type denotes correlations exceeding the 95% confidence level.
To further prove the validity of the GEFA method, the SST footprints of the KE multi-scale oceanic variations derived in two different ways are compared. Both ways use Eq. (4) to estimate the SST imprint of specific KE oceanic variation (e.g., the KE large-scale variation, KEF meridional shift, or KEEA variation). However, the first way, called univariate feedback analysis, adopts the oceanic forcing matrix
${\boldsymbol{O}}(t)$ that contains just only one regressor associated with this KE oceanic variation, and the second way is the GEFA utilizing the${\boldsymbol{O}}(t)$ that contains all five oceanic regressors in the present study. As shown in Fig. 3 (left panels), the SST footprints derived by the univariate feedback analysis show significant remote signals beyond the definition domain of indices or regressors. For instance, all the KE indices are associated with the equatorial Pacific SSTAs, reflecting the atmospheric bridge between the equatorial and extratropical oceans. In addition, we also note that all the SSTAs associated with these KE indices show warming signals over the mid-latitude central North Pacific. However, these signals are not likely induced by the KE mesoscale oceanic variations that mainly impact the local SST, indicating the indices of KEFP and KEEA may contain the signal of the KE large-scale variation. Hence, it can be inferred that the univariate estimates of the NPST responses will be confounded by the interference of multiple oceanic forcings. In contrast, the GEFA can effectively remove the remote SST signatures of the KE multi-scale oceanic variations and lead to more localized SSTAs (Fig. 3, right panels): the SSTAs over the equatorial Pacific are largely gone, and the mid-latitude central Pacific warming associated with the KEFP and KEEA indices are also significantly weakened. We verified that these changes are mainly caused by the inclusion of ENSO indices (TP1 and TP2) in the GEFA that largely filter out the impacts of ENSO on tropical and mid-latitude SSTs. Furthermore, it is found that the SST footprints of the KE multi-scale oceanic variations derived by GEFA account for 10%–40% of the total variance over the KE region (figure not shown).Figure 3. SST footprints (°C) in the cold season for the (a) KE large-scale variation, (b) KEF meridional shift, and (c) KEEA variation derived by univariate feedback analysis. Panels (d)–(f), as in (a)–(c), respectively, but for the SST footprints derived by the GEFA. The stippled areas denote the 90% confidence levels based on the Monte Carlo test.
The above results indicate that GEFA is a suitable method for isolating the impacts of the KE multi-scale oceanic variations on the local SST and, thus, the NPST. The significance of each atmospheric response coefficient in
${\boldsymbol{B}}$ is examined using a Monte Carlo bootstrap approach (Czaja and Frankignoul, 2002), in which the GEFA is repeated 1000 times using the original oceanic time series with the atmospheric variable scrambled randomly by year, while the order of six months in the cold season of a year is retained. Then, the significance is determined at each grid by the percentage of response coefficients from the scrambled time series that are smaller in magnitude than the response coefficient from the original time series.
KE SSTA | KEFP | KEEA | TP1 | TP2 | |
KE SSTA | 0.81 | 0.06 | –0.03 | –0.12 | 0.11 |
KEFP | 0.19 | 0.64 | 0.08 | –0.24 | –0.09 |
KEEA | 0.00 | 0.02 | 0.76 | –0.18 | 0.07 |
TP1 | –0.25 | –0.19 | –0.15 | 0.98 | 0.00 |
TP2 | 0.10 | –0.06 | 0.01 | –0.06 | 0.93 |
Maximum VIF = 1.73. |