A mechanism for the multi-decadal climate oscillation in the North Pacific

Transcription

1 Theor. Appl. Climatol. 91, (2008) DOI /s Printed in The Netherlands Department of Atmospheric Sciences=Global Environmental Laboratory, Yonsei University, Seoul, Korea A mechanism for the multi-decadal climate oscillation in the North Pacific Soon-Il An With 6 Figures Received February 14, 2006; revised June 15, 2006; accepted November 4, 2006 Published online February 28, 2007 # Springer-Verlag 2007 Summary Analysis of both instrumental and proxy climate records indicates the existence of multi-decadal climate variations (about years) over the northern hemisphere. A simple model for the midlatitude ocean-atmosphere coupled system is presented to discuss a possible mechanism for this multi-decadal variation. Slow dynamic adjustments of the ocean due to the Rossby wave coupled with the meridional heat exchange through the thermal advection in the upper layer of the ocean play an important role in inducing this multi-decadal oscillation. 1. Introduction Using instrumental data and tree-ring records for more than 200 years, it has been shown that there are not only decadal but also multidecadal climate variations over the North Pacific and North America (Minobe, 1997; D Arrigo et al., 1999; Ware and Thomson, 2000). Instrumental observations also reveal the decadalto-interdecadal (20 40 years) variation in the Northern hemispheric ocean and atmosphere (Nitta and Yamada, 1989; Trenberth and Hurrel, 1994). Various coupled general circulation models (CGCM) simulated the decadal-to-interdecadal climate variations (e.g. Latif and Barnett, 1996). The decadal-to-bidecadal time scale (10 20 years) in the North Pacific may be related to dynamic adjustment of the ocean due to the slowly propagating Rossby wave in the midlatitude ocean (Jin, 1997; Neelin and Weng, 1999) or the tropical-extratropical ocean atmosphere interaction (Gu and Philander, 1997; Kleeman et al., 1999). However, the origin of the multi-decadal timescale (here, years) remains unknown so far. The multi-decadal variability might be a part of the red spectra of climate noise. However, the research during the past decade concluded that the interaction between the atmospheric circulation and the subtropical oceanic gyre circulation could produce the interdecadal variability (referring about years) (Latif and Barnett, 1994, 1996). We thus hypothesize that a similar coupled process, with an emphasis on the meridional thermal advection, may be responsible for this multi-decadal oscillation as well. In Sect. 2, the observation analysis is performed. Based on the results, a hypothesis for the multi-decadal oscillation is proposed, and the observed evidence follows. In the Sect. 3, a simple model for the multi-decadal oscillation is introduced. The quantitative analysis of this simple model is facilitated by eigen-mode analysis. Concluding remarks are presented in the Sect. 4.

2 78 S.-Il An 2. Analysis The air sea interaction over the midlatitudes, especially the physical relationship between sea surface temperature (SST) and surface wind anomalies, is the subject of much debate. On the one hand, the atmospheric transient waves are so active in the midlatitudes that they contaminate the atmospheric response to the slow change in the SST, of which the spatial pattern is not associated with the current SST pattern. On the other hand, external factors such as El Ni~no also may influence the midlatitude atmosphere strongly (An and Wang, 2005). Thus, the atmospheric response associated with the local SST anomaly in the midlatitudes rarely is defined in a simple dynamical frame. For example, the dynamical relationship between the surface zonal wind and SST anomalies adapted by Jin (1997) s simple formulation is not consistent with the first singular value decomposition (SVD) mode shown in Fig. 1. For this reason, the empirical method, which is based on observations, has been used widely for studies of North Pacific decadal variability (e.g. Xu et al., 1998; Kleeman et al., 1999; Neelin and Weng, 1999). To illustrate the interaction between surface zonal wind and SST anomalies, we applied the singular value decomposition (SVD) method (Bretherton et al., 1992) to the observed surface zonal wind and SST anomalies obtained from the Comprehensive Ocean Atmosphere Data Set (COADS) as compiled by da Silva et al. (1994). In total, 46 years of monthly-mean data are analyzed. In order to remove short-time scale variations, a 5-year running average has been computed after SVD method applied to the anomalous Fig. 1. First SVD vector between the (a) surface zonal wind and SST anomalies over the north Pacific obtained from COADS data. Data used are for Panel (b) is the same as in (a) except for the second SVD vector. First and second SVD modes explain 61 and 19% of total variance, respectively. Positive values are shaded. Units are non-dimensional. Solid and dotted lines in the lowest panel indicate the corresponding principal components (PCs) for SST and surface zonal wind, respectively

3 A mechanism for the multi-decadal climate oscillation in the North Pacific 79 monthly-mean data. The SVD method produces mostly coherent patterns between two different variables. Figure 1 shows the spatial pattern of the leading SVD modes. The SST pattern of the first SVD mode and the corresponding principal component (PC) time series are almost the same as the general Pacific decadal oscillation (PDO) pattern and the PDO index, respectively. This is expected, since by definition the PDO index is derived from the leading PC of monthly SST anomalies in the North Pacific Ocean, poleward of 20 N (Zhang et al., 1997). The first SVD mode exhibits a negatively correlated relationship between zonal wind and SST anomalies in their spatial patterns (also see An and Wang (2005)). The dominant zonal structure is a monopole pattern having a center near 40 N, while both zonal wind and SST patterns of the second SVD mode are dominated by the north south dipole pattern. As in the first SVD mode, the region of the positive (negative) SST anomalies almost overlaps that of the negative (positive) surface zonal wind anomalies, as if the same mechanism rules in the formation of two modes. Note also that zonally symmetric features dominate both SST and zonal wind patterns. The time series in Fig. 1 associated with SST and zonal wind anomalies are well correlated to each other. The correlation coefficient between the two principal component (PC) time series of the first and second SVD modes are 0.83 and 0.54, respectively. Both are statistically significant at the 99% confidence level. The oscillation feature is unclear due to the short data period. In order to show the multi-decadal variation and the relationship between the two modes using much longer time frames, each SVD mode of the SST has been projected on the longer SST data obtained from the U.K. Meteorological Office (UK- GISST) (Rayner et al. 1996). This produces two sets of time series spanning 130 years. To obtain the slowly varying part of the time series, singular spectrum analysis (SSA) is applied to both sets of time series. As shown in Fig. 2, the time series during the recent decades (since 1950) are well matched to those in Fig. 1. Since 1930, the lead=lag relationship between the two time series is dominated by a 90-degree difference, while before 1930 it is somewhat unclear. During the most recent several decades, the variation of the time series associated with Mode 1 (Fig. 2a) Fig. 2. Time series (thin line) obtained by projecting (a) the first SVD mode and (b) the second SVD mode of SST as shown in Fig. 1 onto SST anomalies obtained from UK-GISST. The thick line indicates the first SSA (Singular Spectrum Analysis) mode of the above time series, which explains 39% of total variance for Mode 1 and 51% for Mode 2 leads that of Mode 2 (Fig. 2b), and both time series show dominant interdecadal to multi-decadal variations. The lead=lag relationships between two modes shown in Fig. 2 are manifested by obtaining the lagged correlation between the two time series of Fig. 2. As shown in Fig. 3, in the raw data, Mode 1 is positively correlated to Mode 2 with a lag of about 18 years (Mode 1 leads Mode 2), and Mode 2 is negatively correlated to Mode 1 with a lag of about both þ5 to 10 years and þ25 to 30 years (Mode 2 leads Mode 1). Thus, the oscillatory behavior is completed by the interaction Fig. 3. Lagged correlations (thin line) between two time series obtained by projecting the first SVD mode and the second SVD mode of SST onto the UK-GISST anomalies (i.e. thin lines in Fig. 2 (a) and (b)). The thick line indicates the lagged correlations between each associated first singular-spectrum mode (i.e. thick lines in Fig. 2 (a) and (b)). Positive-lag (negative-lag) indicates that Mode 1 leads (lags) Mode 2

4 80 S.-Il An Fig. 4. Schematic diagram of the evolution feature of SST, surface zonal wind, wind stress curl, and upper-layer meridional current anomalies representing the multi-decadal oscillation. The positive and negative wind stress curls are marked as (þ) and ( ), respectively. Time sequence is indicated by the direction of the arrow between the two modes. The lagged correlation between the first SSA PC of Mode 1 and that of Mode 2 also supports the aforementioned result. From the SVD modes shown in Fig. 1, we propose a possible oscillation mechanism (sketched in Fig. 4) for the multi-decadal variation of the SST, surface zonal wind, meridional geostropic current, and surface wind stress curl anomalies over the North Pacific. Suppose the warm SST anomaly over the whole north Pacific (Fig. 4, top left panel) resembles the first SVD mode of SST (Fig. 1a). This provides a favorable condition for the easterly in the zonal wind, as shown in Fig. 1a, under an assumption that the atmosphere can be treated effectively as a fast component that quickly adjusts to SST changes 1. The easterly wind anomaly induces an anomalous northward current in the southern part and an anomalous southward current in the northern part, consistent with the Sverdrup balance (Sverdrup, 1947). Meridional heat advection by meridional currents induces the negative and positive SST tendency in the northern and southern parts of the domain, respectively. Eventually, SST exhibits the northsouth dipole pattern. These SST anomalies drive the zonal wind anomalies with the north south dipole pattern, resembling Fig. 1b (the second panel on the right-hand side). This wind forcing drives the southward current, in which the maximum occurs around the center of the North Pacific. This southward current induces the negative SST tendency and eventually results in the cold SST anomaly, referring to the negative phase of the oscillation. In the same manner, the cold phase reverts to the warm phase. Note that the meridional component of the Ekman current, which is omitted in this figure, plays the role of a positive feedback mechanism in the change of the SST anomaly. For example, the warm SST anomaly causes the easterly surface zonal wind, and the easterly wind drives the northward Ekman current that causes the warm advection. The hypothesis shown in Fig. 4 can be supported by the COADS data (da Silva et al., 1994) and the ocean assimilation data (Carton et al., 2000). As shown in Fig. 5, SST and zonal wind anomalies for the first pentad year ( ) are positive and negative, respectively, over the whole basin, with their maxima at around 40 N, which resembles the first SVD mode in Fig. 1a. For the second pentad year ( ), the northward and southward current anomalies, which might be driven by the easterly wind anomalies during the previous pentad year, are dominant over the southern and northern part of the North Pacific, respectively. For the next pentad 1 It is known that the feedback between the sea surface temperature (SST) and the surface wind anomalies in the midlatitude is uncertain (Lau, 1997). Since we use the statistical atmospheric model in the midlatitudes, our interpretation requires caution (Frankignoul, 1999), especially when the active positive-feedback process is taken into account. However, in this study, the interaction between the atmosphere and ocean through the surface heat flux, as in Neelin and Weng (1999), was not taken into account. The atmosphere influences SST only by the way of changing the ocean dynamics fields, and thus the air sea interaction here is more likely passive.

5 A mechanism for the multi-decadal climate oscillation in the North Pacific 81 The empirical relationship between the observed surface zonal wind and SST anomalies (SSTA) that appeared in the two leading SVD modes (as shown in Fig. 1) is used for the atmospheric model (see details in An and Wang 2000). In this calculation, we used the zonally averaged values (150 E 135 W). The resultant empirical atmosphere model x is written as: x ¼ X ~T ð1þ Fig. 5. Observed zonal-mean SST, zonal wind, and meridional current anomalies. The zonal mean is taken over 160 E 140 W. The meridional current has been vertically averaged from 45 m depth to the ocean surface. Each panel indicates each pentad years. Units for SST and zonal wind anomalies are C and m s 1, respectively, and units for the meridional current are cm s 1 year ( ), the negative SST and positive zonal wind anomalies are dominant over the northern part of North Pacific and the weak signal of the positive SST and negative zonal wind anomalies appears in the southern part of the North Pacific. During , the meridional current anomalies mostly become southerly. During , the phase of the SST and zonal wind anomalies become opposite from those of the pentad year The sequence of each variable from the top panel to the bottom panel is in a good agreement with that in Fig. 4 from the top left panel to the bottom right panel. However, the data record only covers roughly one cycle. 3. A simple model To facilitate further quantitative analysis, a simple possible atmosphere model is proposed based on an empirical relationship between SST and surface wind anomalies. Then, this atmosphere model is coupled with the ocean dynamic model and an embedded mixed layer for SST anomaly. where is the coupling coefficient for the sensitivity test, and is a linear operator establishing the relationship between the surface wind stress and SST anomalies, which had been defined from the leading SVD modes. The arrow superscripted over T indicates that two meridional modes of SSTA are used. On the basis of the Sverdrup balance, indicating a steady state response of ocean dynamic field to a given wind forcing, the zonal-mean geostropic meridional current is described by the following equation: v ¼ x ðt Þ: ð2þ Here, v is the anomalous meridional current; x is the anomalous zonal wind stress; is the sea water density; is the meridional gradient of the Coriolis parameter at the reference latitude (35 N); and H is a constant upper-layer thickness of 100 m. The delay time represents the adjustment time scale of the ocean due to the slow propagation of the oceanic Rossby wave, which has a frequency on the order of half a decade. The variation of SST (and zonal wind) anomalies over the North Pacific is dominated by the zonal structure (Fig. 1). Thus, the changes in the upper-ocean temperature can be assumed to be zonally uniform. The upper layer temperature equation, linearized for the climatological state, can be ¼ " TT ð3þ where T denotes the zonal-mean temperature anomaly in the upper-ocean; v is the meridional current as given in Eq. (2); v E is the Ekman current denoted by x =fh 1 (H 1 is a mixed layer depth of 50 m); " T represents the decay rate due to comprehensive local damping (1=4 year 1 ) such as Newtonian cooling, eddy mixing, and

6 82 S.-Il An diffusion. The value of the decay rate is adopted from Jin (1997). The weak zonal-mean zonal advection by the mean current and thermohaline upwelling are ignored. The relatively weak contribution in the generation of North Pacific SST anomaly by the vertical advection associated with Ekman pumping (e.g. Liu and Wu, 2004; Vivier et al., 2002) is also ignored. Note that the local damping inherently includes the anomalous heat flux effect on the ocean by changes in the surface winds, which mainly plays the role of a positive feedback process in interacting with the changes in SST anomaly. By combining Eqs. (1) (3), we obtain a simple coupled system with ocean adjustment dynamics and ~ Tðt Þþ 1 ~T " T ~T fh 1 ð4þ Except for including Ekman flows and the empirical operator, this equation is somewhat similar to the delayed oscillator proposed in Jin Fig. 6. Contour plots of period (heavy solid contour, in unit of year) and growth rate (dashed contour, in unit of year 1 ) on the parameter plane (, ), with " T ¼ 0.25 (in unit of year 1 ). (a) Control case and (b) non-local SST change case. The contours over 100-year period are omitted. Unstable regime is shaded (1997) for Pacific decadal oscillation dynamics. However, the major difference is that two meridional modes of SSTA are utilized based on the observation. Using Eq. (4), the period and growth rate are calculated on the space (Fig. 6). In this calculation, the two leading SVD modes are used so that the linear operator becomes a 2 2 matrix. First, one can consider an extreme case in which the oceanic memory due to the adjustment is not operative in the coupled system. By defining ¼ 0, the dynamic field of the ocean simultaneously responds to the atmospheric forcing without any slow-adjustment process. In this case, the frequency and growth rate correspond to the bottom line of Fig. 6a. When ¼ 1, the period is about 19 years. Such a near neutral oscillatory mode is induced by the thermodynamic adjustment process through the meridional heat exchange. As shown in Fig. 6a, the increase of the dynamic adjustment timescale (i.e. increase of ) results in the increase of both the period and growth rate, especially for the weak and moderate coupling regimes. For ¼ 5 years and ¼ 1, the system becomes unstable, and the corresponding period is about 56 years, indicating that the combined effects of both the dynamic and thermodynamic adjustments induce a longer timescale oscillation. By removing the SST tendency term in Eq. (3), we can get rid of the influence due to the thermodynamic adjustment in the system. In other words, there is no adjustment time delay due to the SST change, which is similar to Fast SST limit (Jin and Neelin, 1993). As shown in Fig. 6b, the model shows a multi-decadal period only in a limited parameter range (>10 year); otherwise the year period is dominant. For example, the period for ¼ 5 years and ¼ 1 is about 23 years. The leading coupled mode is sensitive to the restoration damping rate " T (not shown here). For a given coupling coefficient, both the period and growth rate decrease as " T increases. When " T is small, the mode becomes unstable and its period change rate with respect to becomes larger. 4. Concluding remarks In summary, this study showed that the internal process of the atmosphere ocean coupled system could cause the multi-decadal oscillation. Either

7 A mechanism for the multi-decadal climate oscillation in the North Pacific 83 the slow dynamic adjustment of the ocean due to Rossby wave propagation or the meridional heat advection alone could induce the decadal-tobidecadal climate oscillation (20 years), but the combined effect of those processes could induce the multi-decadal oscillation. An oscillation mechanism was also provided, such that the meridional thermal advection due to a slowly adjusted geostropic meridional current changes the meridional structure of the SST anomaly. The resulting surface wind anomaly makes the geostropic meridional current reverse direction. There are several aspects about the decadal climate oscillation that deserve some elaboration. For example, it may be viewed as a deterministic midlatitude-coupled mode driven by midlatitude ocean-atmosphere interactions (Latif and Barnett, 1994, 1996); another option is to view it as the natural ocean response, albeit with a long timescale, to stochastic atmospheric forcing (Hasselmann, 1976; Frankignoul and Hasselmann, 1977; Cessi and Louazel, 2001); and yet a third possibility is to see it as generated by the decadal variation in the tropical Pacific via oceanic or atmospheric teleconnection (e.g. An et al., 2006). The atmospheric model used here assumes a linear steady response to the midlatitude SST anomaly, so the coupled model does not take into account the role of the atmospheric stochastic forcing. However, since the possible time scales associated with the slow uncoupled oceanic adjustment in the mid-latitude (usually related to Rossby wave speed) hardly reaches the multidecades, at least the multi-decadal climate oscillation seems to be a deterministic midlatitude ocean atmosphere coupled phenomenon. In general, the atmospheric circulation in the mid-latitudes significantly modifies SST anomalies, rather than the other-way around. However, for the longer-time scale, the air sea coupling becomes important (e.g. Liu and Wu, 2004; Latif, 2006). Moreover, the variance spectrum of the mid-latitude ocean under the white noise of the atmospheric variability tends to be red (e.g. Hasselmann, 1976), and thus the role of the ocean in the generation of the longer time scale variation (for example, longer than a decade) is very important. Initially, atmospheric stochastic forcing may cause the SST variation, but the regulation needed to produce the multi-decadal variability most likely is furnished by the ocean. The regulation process is possible because a particular spatial pattern of the SSTA provides favorable conditions for the corresponding spatial pattern of the atmospheric circulation. As in this study, the first=second SVD mode of SST (T1, T2) is well correlated to the first=second SVD mode of the surface zonal wind (W1, W2). T1 provides a favorable condition for the spatial pattern of W1, probabilistically. At the same time, W1 intensifies T1 via modifying the surface heat flux. On the other hand, T2 is gradually intensified due to the thermal advection generated by W1. Eventually T2 provides a favorable condition for W2, and suppresses W1. By the same process, the transition toward the first mode is also possible. The further study will be helpful to justify this conclusion, and to understand it in greater depth. Acknowledgments This work was supported by grant No. R from the Basic Research Program of the Korea Science and Engineering Foundation and the Brain Korea 21 project. References An SI, Wang B (2000) Interdecadal change of the structure of the ENSO mode and its impact on the ENSO frequency. J Climate 13: An SI, Wang B (2005) The forced and intrinsic low-frequency modes in the North Pacific. J Climate 18: An SI, Kug JS, Timmermann A, Kang IS, Timm O (2006) The influence of ENSO on the generation of decadal variability in the North Pacific. J Climate (accepted) Bretherton CS, Smith C, Wallace JM (1992) An intercomparison of methods for finding coupled patterns in climate data. J Climate 5: Carton JA, Chepurin G, Cao X, Giese B (2000) A simple ocean data assimilation analysis of the global upper ocean Part I: methodology. J Phys Oceanogr 30: Cessi P, Louazel S (2001) Decadal oceanic response to stochastic wind forcing. J Phys Oceanogr 31: D Arrigo R, Wiles G, Jacoby G, Villalba R (1999) North Pacific sea surface temperatures: past variations inferred from tree rings. Geophys Res Lett 26: da Silva AM, Young CC, Levitus S (1994) Atlas of surface marine data 1994, NOAA Atlas NESDIS 6, US Department of Commerce, Washington, DC Frankignoul C (1999) A cautionary note on the use of statistical atmospheric models in the middle latitudes: Comments on Decadal variability in the North Pacific as simulated by a hybrid coupled model. J Climate 12:

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