AO, COWL, and Observed Climate Trends

Transcription

1 1JUNE 2004 WU AND STRAUS 2139 AO, COWL, and Observed Climate Trends QIGANG WU Center for Ocean Land Atmosphere Studies, Calverton, Maryland DAVID M. STRAUS George Mason University, Fairfax, Virginia (Manuscript received 7 May 2003, in final form 12 December 2003) ABSTRACT The linear trends for a number of fields obtained from the reanalyses of the National Centers for Environmental Prediction National Center for Atmospheric Research (NCEP NCAR) are calculated for the Northern Hemisphere winter months (January March) from the 55-yr period of The fields include sea level pressure (SLP); geopotential height at 500 and 50 hpa; temperature at 500 and 50 hpa; zonally averaged height; temperature; zonal, meridional, and vertical velocities from 1000 to 50 hpa; and surface air temperature (SAT). The trend fields are expressed in terms of two alternate expansions: (i) contributions from the Arctic Oscillation (AO) and cold ocean warm land (COWL) patterns, as defined from the leading modes of an empirical orthogonal function (EOF) analysis of sea level pressure; or (ii) contributions from the modified AO (AO*) and modified COWL (COWL*) patterns, defined from the leading EOFs of 500-hPa height. The residuals in each expansion are considered, and the completeness properties of the expansions are discussed. Long-term linear trends of various fields at mid- and lower-tropospheric levels project well onto the AO (AO*) and COWL (COWL*) modes. The AO contribution accounts for most of the SLP falls over the Arctic and half of the SLP rise over the North Atlantic, while the COWL pattern represents the entire negative pressure trend over the Pacific and half of the rise over the Atlantic. In the expansion into AO* and COWL* patterns, the latter represents most of the SLP trend. Similar remarks hold for the height trend at 500 hpa. In each case the residual is a small fraction of the trend. The observed SAT trend (warming over most of North America and Asia, cooling over northeast Canada and the Pacific) is partitioned nearly equally between contributions from the AO and COWL, although the COWL contribution dominates over North America. In the alternate expansion, the COWL* dominates nearly all of the warming over North America and Asia. The midtropospheric (500 hpa) temperature trend is mostly due to the COWL (or COWL*) patterns, with the AO representing only the local cooling over Greenland. The 50-hPa height and temperature trends are not well represented by either set of patterns. The links of the trends in the zonal-mean fields and the AO (AO*) and COWL (COWL*) are weaker than those in the mid- and lower troposphere. 1. Introduction Recently there has been considerable interest in the relationship between the trends and the dominant natural variability modes of the climate system. A number of studies have investigated the projection of recent trends and climate change onto the annular modes [also called the Arctic Oscillation (AO) in the Northern Hemisphere and the Antarctic Oscillation in the Southern Hemisphere] from both the observational record and general circulation model (GCM) output analysis (Thompson and Wallace 1998, 2000). Recent work has suggested that the Arctic Oscillation captures much of Corresponding author address: Dr. David M. Straus, Center for Ocean Land Atmosphere Studies, George Mason University, 4041 Powder Mill Road, Suite 302, Calverton, MD straus@cola.iges.org the geopotential height falls over the polar cap region and the strengthening of the subpolar westerlies from the surface to the lower stratosphere (Thompson et al. 2000, hereafter TWH). In the Southern Hemisphere, the similarity between the Antarctic Oscillation and the trends have been reported by Hurrell and van Loon (1994), Chen and Yen (1997), Randel and Wu (1999), and TWH. In GCM greenhouse gas transient integrations Fyfe et al. (1999) found that the pattern of climate change projects partially onto the AO in the Northern Hemisphere. Similar conclusions have also been documented in the integrations of a coupled GCM forced with increasing concentrations of greenhouse gases (Stone et al. 2001). A strong relationship between GCMsimulated climate change in the Southern Hemisphere sea level pressure and the Antarctic Oscillation were noted by Fyfe et al. (1999), Shindell et al. (1999), Kushner et al. (2001), and Stone et al. (2001) American Meteorological Society

2 2140 JOURNAL OF CLIMATE VOLUME 17 Another dominant mode of natural variability in the Northern Hemisphere is the cold ocean warm land (COWL) pattern. The COWL pattern arises from partitioning the observed winter season time series of monthly mean surface air temperature into a very slowly varying radiative component, and a component exhibiting rapid year-to-year fluctuations, the latter comprising the COWL pattern (Wallace et al. 1995, 1996). Wallace et al. (1996) argued that the COWL is essentially induced by the land sea distribution. From GCM test results, Broccoli et al. (1998) confirmed that the contrast in thermal inertia between land and ocean is the primary factor for the existence of the COWL pattern, whereas dynamical air sea interactions do not play a significant role. The COWL resembles the observed surface air temperature trend during recent decades (TWH). The COWL pattern has also been derived from cluster analyses designed to identify significant deviations from a Gaussian background in the probability distribution function (Corti et al. 1999; Hsu and Zwiers 2001). The occurrence of the COWL pattern seems to be independent of the occurrence of El Niño Southern Oscillation (ENSO) events, and the positive phase of the pattern has become more prevalent in the past few decades. Recently, Wu and Straus (2003) have applied the partitioning cluster algorithm of Michelangeli et al. (1995) to the monthly mean Northern Hemisphere (NH) wintertime (December March) sea level pressure, geopotential height, and zonal wind from the reanalyses of the National Centers for Environmental Prediction National Center for Atmospheric Research (NCEP NCAR). They found that the AO and COWL regimes coexist in the NH wintertime variability and that both AO and COWL regimes can be reproduced from conditional one-point correlation maps. [Wu and Straus (2003) refer to the AO pattern as the Northern Hemispheric annular mode (NAM)]. Knowledge of projections of climate change onto the preexisting natural modes of variability would greatly enhance our understanding of climate change. The dynamical importance of the AO to the Northern Hemisphere climate change has recently been extensively documented, whereas the role of the COWL has been little investigated. The purpose of this paper is to examine the role played by the COWL pattern in NH wintertime climate change. This will be accomplished by projecting the linear trends in a number of fields from the 55-yr winter record of the NCEP NCAR reanalysis onto the AO and COWL patterns. Our results for the AO projections are very similar to those reported in TWH (although we use a longer period: versus in TWH). Our results for the COWL pattern are new. The paper is arranged as following. Section 2 describes the data sources and the analysis techniques. Section 3 presents the structures of the AO and COWL modes embedded in the observed sea level pressure (SLP) and 500-hPa geopotential height (Z 500 ). In this section AO and COWL indices based on both SLP and Z 500 calculations are also defined. In section 4, we examine to what extent the observed trends in various fields in the NH can be represented by trends in the AO and COWL patterns. Section 5 contains a summary and discussion. 2. Data and analysis techniques a. Data The primary dataset used in this study is the NCEP NCAR reanalysis (Kalnay et al. 1996) obtained from the National Oceanic and Atmospheric Administration s Climate Diagnostics Center. The zonal and meridional winds, temperature, geopotential height, and vertical pressure velocity were obtained on a 2.5 latitude 2.5 longitude grid at 15 pressure levels: 1000, 925, 850, 700, 600, 500, 400, 300, 250, 200, 150, 100, 70, 50, and 30 hpa. The vertical velocity reported in the figures was obtained from the vertical pressure velocity by using the hydrostatic equation. The time period covers January 1948 to December We use January March (JFM) monthly data here. Other datasets are SLP (Trenberth and Paolino 1980) and SAT (Jones 1994; Parker et al. 1995). The choice of JFM for winter is motivated by the results of Thompson and Wallace (2000), who concluded that JFM forms the most active season in the NH lower stratosphere. All results in this paper are little changed if the months of November and December are also included in the analysis. b. EOF analysis Empirical orthogonal function (EOF) analysis is applied to the JFM monthly mean fields of SLP and Z 500 for the period The climate (55-yr mean) of each month is removed separately, and the domain is N. In the EOF analysis, area weighting is accomplished by multiplying each field by the square root of the cosine of latitude before computing the covariance matrix. The leading two EOFs of SLP are readily identifiable as being the AO and COWL patterns, respectively, as we discuss in section 3. This is also true for the leading two EOFs of Z 500. All physical fields have been divided by the square root of the cosine of latitude before plotting. c. Trend projections Following Straus (1983), we can expand any time series in a Legendre series, which is a complete and orthogonal expansion. The leading term is just the climate for that series, and the second term represents the trend. (For more details see the appendix.) The trend calculated in this manner is completely equivalent to

3 1JUNE 2004 WU AND STRAUS 2141 that obtained by a least squares fit to a straight line. We have applied this expansion to the 55-yr time series consisting of one calendar month only as a way to compute the trend as part of a formally orthogonal expansion. The first two terms represent the climatology for that month and the 55-yr trend for that month. Performing this temporal expansion separately for the months of January, February, and March at each grid point leads to a trend field or map for each month. Trends in zonal cross sections are obtained in exactly the same way. The trends obtained by treating the data record as a single 165-month time series are very close to those obtained as the average of the JFM trends. The former procedure is the one we adopt computationally. Combining the Legendre expansion in time with EOF analysis of the same field, one can in a straightforward way express the trend field as a linear combination of EOFs, with each corresponding temporal coefficient being the trend of the appropriate principal component (PC). In principle this expansion is complete, although in this paper we are concerned only with the leading two terms. However, we will also relate the trend field (or zonal cross section) of one variable to the PCs of a second (distinct) variable. In that case, the trend field can be expressed as a linear combination of component fields, with each corresponding temporal coefficient again being the trend of the appropriate PC. But now the component fields are not EOFs, but are the fields obtained by regression of the first variable on each of the PC time series of the second variable. (Note, that since the PCs are orthogonal, regression on each PC separately is equivalent to multiple regression.) This expansion is not complete because the regression always entails a residual. The mathematical treatment of the above expansions is given in the appendix. Note that our procedure is equivalent to the calculation of linearly congruent components described in TWH, although we feel that the current trend projection approach is conceptually more complete. In particular it is clear that the expansion of a trend field in terms of the EOFs of the same field is in principle complete. Note that this approach is applied to a time series of fields, corresponding to the three winter months (JFM) for each year. Since the climate of each month has been removed separately, the time mean of this field vanishes. 3. The AO and COWL modes in SLP and Z 500 The structure of the leading EOF of NH SLP, shown in Fig. 1a, is virtually identical to the AO obtained in Thompson and Wallace (1998, 2000). The structure of EOF2, shown in Fig. 1b, closely resembles the COWL pattern embedded in SLP, which was obtained by the partitioning cluster algorithm in Wu and Straus (2003). The structure of the leading two Z 500 EOFs are shown in Figs. 1c and 1d. Figure 1c is virtually identical to the annular mode obtained in Corti et al. (1999) and Wu and Straus (2003). Figure 1d is very close to the COWL pattern in Wallace et al. (1996) (their Fig. 5a). This pattern is also very close to the centroid map of the regime obtained by the partitioning cluster algorithm in Wu and Straus (2003). The AO-like and COWL-like structures of NH SLP and Z 500 anomalies shown in Fig. 1 coexist in NH wintertime variability. They can be reproduced by conditional one-point correlation maps for SLP and Z 500, constructed for base points near the Azores (42.5 N, 25 W) and in the North Pacific (45 N, W), as shown in Wu and Straus (2003). The structure of the Z 500 COWL pattern over portions of the Pacific and North America resembles the Pacific North American (PNA) teleconnection pattern (Wallace and Gutzler 1981; Wallace et al. 1996). The interpretation of EOF patterns is questionable when successive patterns explain similar amounts of variance (North et al. 1982). In our case the leading three EOFs of SLP explain 24.9%, 12.9%, and 9.7% of the total variance, while the leading three EOFs of Z 500 explain 19.0%, 13.4%, and 8.8% of the total variance. Applying the guidelines of North et al. (1982) here and using a conservative estimate of 55 degrees of freedom (one per winter), we find that both first and second EOFs are adequately separated from the remaining modes. In the following, we refer to the first two standardized PC time series of SLP as the AO and COWL indices, and the first two standardized PC time series of Z 500 as the AO* and COWL* indices. Similarly, the leading two (dimensional) EOF patterns of SLP are referred to as the AO and COWL patterns, and the leading two EOF patterns of Z 500 as the AO* and COWL* patterns. With each PC time series having unit variance, the corresponding EOF patterns have the units of the original field. The AO, COWL, and COWL* indices have exhibited a tendency toward high index polarity over the past few decades, while AO* has exhibited little overall tendency. These indices are shown in Fig. 2. The linear trends of AO, COWL, AO*, and COWL* indices in JFM of are 0.79, 1.06, 0.14, and 1.32 (55 yr) 1 respectively. From the discussion of section 2, we note that the trend of any particular (standardized) index, multiplied by the appropriate (dimensional) EOF field, yields the total trend field that can be attributed to the corresponding pattern or PC. Although the COWL* pattern is very similar to the regression pattern defined by Wallace et al. (1996), and to the regime-based COWL structure obtained in the cluster analyses of Corti et al. (1999) and Wu and Straus (2003), there are some subtle differences among the three definitions. The regression-based COWL pattern of Z 500 includes, in principle, contributions from all EOFs. In the above-cited cluster analyses, the COWLlike regimes contain contributions from both EOF1 and

4 2142 JOURNAL OF CLIMATE VOLUME 17 FIG. 1. (a) EOF1 and (b) EOF2 of sea level pressure for monthly mean JFM from 1948 to This is the same as the regression of the SLP field on the standardized PCs of the leading two modes (AO and COWL indices, respectively). The 500-hPa geopotential height regressed on the standardized (c) AO* and (d) COWL* indices (leading two PCs of 500-hPa height). Units are hpa and m per std dev of the respective index time series. Contour intervals are 1 hpa for SLP and 10 m for Z 500. EOF2. Because the second EOF of Z 500 strongly dominates the contribution to the regression-based COWL pattern and the COWL-like regimes in the cluster analyses, the COWL mode defined by the second EOF of Z 500 in this study strongly resembles the other two definitions. 4. Trend projections for AO and COWL In this section, the trend components of a number of NH fields are compared to the trend projections based on the leading two EOFs of SLP (AO and COWL patterns) or on the leading two EOFs of Z 500 (AO* or COWL* patterns). The full trend field of SLP is referred to as TP(x), where x denotes a point on the sphere. Following section 3, we can express TP in terms of the EOFs and PCs of SLP: TP(x) TP AO(x) TP COWL(x) TP R (x), (1) where TP AO (x) is the trend projection on the AO pattern, TP COWL (x) is the trend projection on the COWL pattern, and the residual TP R (x) arises only because we truncate the EOF expansion of SLP at two modes. However, if we wish to relate TP(x) to the trends of the PCs of Z 500 (viz., the AO* and COWL* indices), we have TP(x) TP AO* (x) TP COWL* (x) TP R* (x). (2) Here TP AO* (x) is the trend in the AO* index multiplied

5 1JUNE 2004 WU AND STRAUS 2143 FIG. 2. Standardized PC1 of all winter months for (a) SLP (b) PC2 for SLP, (c) PC1 for Z 500, (d) and PC2 for Z 500. These are the AO, COWL, AO*, and COWL* indices, respectively. The abscissa runs over all 165 winter months. by the field obtained by regressing the full SLP field onto the AO* (leading PC of Z 500 ) index, TP COWL* (x) has a similar interpretation in terms of the COWL* index and COWL* field, and now the residual TP R* includes the residuals from the regression as well as the contribution of higher EOFs of Z 500. We will refer to the trend field of Z 500 as TZ, and expanding this trend in terms of the Z 500 EOFs and PCs yields TZ(x) TZ AO* (x) TZ COWL* (x) TZ R* (x), (3) where, for example, TZ AO* (x) is just the leading EOF of Z 500 (AO* field) multiplied by the trend in the AO* index. Similarly, expanding TZ in terms of the PCs of the SLP field yields TZ(x) TZ AO(x) TZ COWL(x) TZ R (x). (4) The temperature trend field will be denoted as TT(x), the trend in zonal mean height field as TZZ(x), the trend in zonal mean temperature as TZT(x), and the trend in zonal mean zonal (u) wind as TZU(x). a. Sea level pressure trend projections The linear trend map of SLP, TP(x), is shown in Fig. 3a. It contains the broad features described by Walsh et al. (1996), TWH, and Gillett et al. (2003): decreasing pressure over the Arctic Ocean [locally as large as 6 hpa (55 yr) 1 ] and the Pacific [locally as large as 7 hpa (55 yr) 1 ], and increasing pressure over the subtropical Atlantic [locally as large as 5 hpa (55 yr) 1 ]. Expanding the trend as in Eq. (1) yields contributions from the AO pattern (same as Fig. 1a but with different magnitude), the COWL pattern (same as Fig. 1b but with different magnitude), and the residual (Fig. 3b). The structural similarities between trends in SLP and the corresponding signatures of the AO in the Arctic and Atlantic, and between trends and the corresponding signatures of the COWL in the Pacific, are remarkable. Virtually all of the SLP decrease over the Arctic Ocean is represented by the AO index and pattern, and nearly all of the SLP decrease over the Pacific by the COWL index and pattern. The SLP increase over the Atlantic is due in nearly equal measure to the AO and COWL. The residual trend field shown in Fig. 3b is much weaker, and its main features are reproduced in response to greenhouse gas and sulphate aerosol forcing in GCMs. The expansion of the SLP trend in terms of the AO* and COWL* indices and patterns, corresponding to Eq. (2), is depicted in Fig. 4. While the pattern of the AO* contribution, shown in Fig. 4a, is highly correlated with

6 2144 JOURNAL OF CLIMATE VOLUME 17 FIG. 3. The 55-yr ( ) linear JFM trend in SLP: (a) total and (b) residual trends. See Eq. (1) in section 4. Contour interval is 1 hpa (55 yr) 1. the AO contribution in the previous figure, the amplitude has been decreased by an order of magnitude, mostly due to the small trend in the AO* index. Here the COWL* pattern reproduces a great deal of the total trend. Virtually all of the SLP decrease over the Arctic basin, all of the SLP rise over the Atlantic, and 90% of the SLP decrease over the Pacific are attributable to the COWL* index. Remarkably, the residual patterns in Figs. 3b and 4c are nearly identical, indicating that for SLP trends the AO and COWL patterns, whether defined from SLP or Z 500, form a kind of subspace of variability. b. Geopotential height trend projections at 500 and 50 hpa Figure 5 shows the total Z 500 trend and its expansion in terms of the AO and COWL patterns of SLP [see Eq. (4)]. Consistent with Schneider et al. (2003), the trend in Z 500 is characterized by falling height over the Arctic and North Pacific [both locally as large as 80 m (55 yr) 1 ], and rise over North America, the Atlantic, and western Europe [all locally as large as 70 m (55 yr) 1 ]. The structural similarities between the trend in Z 500 and the contribution of the AO (TZ AO ) in the Arctic and Atlantic, and between the trend in Z 500 and the corresponding COWL contribution (TZ COWL ) in the Pacific, are striking. The TZ AO component accounts for 75% of the geopotential height fall over the Arctic and 40% of the rise over the Atlantic and Europe. The TZ COWL component accounts for nearly all of the fall over the Pacific and 60% of the rise over North America. The residual TZ R is considerably weaker than the total trend. In the expansion of the Z 500 trend in terms of its own EOF patterns [as in Eq. (3)] the COWL* explains over two-thirds of the trend almost everywhere (not shown). The AO* pattern makes a modest contribution only over Greenland. Not surprisingly, the COWL* contribution resembles the COWL* pattern itself shown in Fig. 1d. The total trend in 50-hPa geopotential height (Z 50 ), shown in Fig. 6a, is dominated by planetary waves 0 2. A negative trend of 250 m (55 yr) 1 is seen over broad regions of the polar cap. Its expansion in terms of the AO and COWL patterns is shown in Fig. 6b and 6c. Clearly the residual component dominates either contribution. (Our definition of residual is simply whatever cannot be explained by projection/regression onto the two dominant patterns, so the residual is not always small.) The AO component, however, locally accounts for 40% of the geopotential height fall over Greenland and parts of the high-latitude polar ocean, while the COWL component accounts for 50% of the rise over western Northern America. When the Z 50 trend is expanded in terms of the AO* and COWL* patterns (not shown), the AO* contribution is very weak, whereas the COWL* contribution strengthens somewhat compared to Fig. 6c, especially over Siberia. (As expected, this COWL* contribution can also be obtained by regressing Z 50 upon the NH-averaged land surface air temperature.) c. Zonal mean geopotential height trend projections The trend in the zonal-mean geopotential height from the surface to 30 hpa, shown in Fig. 7a, is characterized by falling height in the stratosphere poleward of 45 N with a maximum at 70 N, accompanied by rising heights in lower latitudes. The vertical structure is generally equivalent barotropic, with the exception of the polar cap where modest height rises are seen near 500 hpa. As shown in Fig. 7b, the trend component associated with the AO pattern is nearly purely equivalent baro-

7 1JUNE 2004 WU AND STRAUS 2145 FIG. 4. The components of the SLP trend attributed to the Z 500 (a) AO* and (b) COWL* indices, and (c) the residual trend. See Eq. (2) in section 4. Contour interval is 0.1 hpa (55 yr) 1 in (a) and 1 hpa (55 yr) 1 in (b) and (c). tropic, and is also dominated by strong stratospheric height falls at high latitudes and more modest height rises at lower latitudes. However, compared to the total trend, this AO component is shifted nearly 20 in latitude, so that the maximum height fall occurs over the pole. The result is that only between 70 and 80 N does the AO component contribute a substantial fraction of the total stratospheric trend above 300 mb, while between 30 and 40 N the AO component explains about 40% of the positive height trend from the surface to the lower stratosphere. The COWL component in Fig. 7c is relatively quite weak, except in the subtropical stratosphere where it contributes modestly to the positive trend. The net result is that the residual shown in Fig. 7d is nearly as strong as the total trend; in fact, near the pole in the troposphere it is stronger. Interestingly, when the zonal-mean height field is expanded in terms of the 500-hPa AO* and COWL* patterns, the results shown in Figs. 8a and 8b indicate that the AO component (Fig. 7b) and the COWL* component (Fig. 8b) are quite similar. The COWL* component is very highly correlated with the total trend equatorward of about 70 N. The AO* component is quite weak, although in pattern it also strongly resembles the AO component of Fig. 7b. d. Trend projections of temperature at the surface, 500 hpa, and 50 hpa The trend field of surface air temperature shown in Fig. 9a is consistent with previous studies (Jones 1994; Parker et al. 1995; Nicholls et al. 1996; Hurrell 1995, 1996; TWH). It is dominated by strong warming over the high-latitude continents with maximum values as high as 5 K (55 yr) 1 over parts of northwestern Canada and weaker cooling over Greenland and the North Pacific. The trend pattern projects strongly on the AO and

8 2146 JOURNAL OF CLIMATE VOLUME 17 FIG. 5. Fifty-five-year ( ) linear JFM trend in Z 500 : (a) total trend, the components of the trend attributed to the Z 500 (b) AO and (c) COWL, and (d) the residual trend. See Eq. (4) in section 4. Contour interval is 10 m (55 yr) 1. COWL regression patterns over North America and Eurasia, as shown in Figs. 9b and 9c. About half of the SAT trend over Eurasia is attributed to the AO component and half of the trend over western Canada to the COWL component. The corresponding residual shown in Fig. 9d still shows the same pattern as the overall trend, but it is weaker by at least a factor of 2. The large warming over land reflects the response to the increasing greenhouse gas and aerosol sulphate concentrations based on the GCM simulations (Cubasch et al. 1996; Roeckner et al. 1999; Senior and Mitchell 2000; Williams et al. 2001; Voss and Mikolajewicz 2001) and signal detection studies (North and Stevens 1998; Hegerl and North 1997; Scott and Tett 1998; Tett et al. 1999; North and Wu 2001; Zwiers and Zhang 2003). The corresponding results based on the expansion of the SAT trend in components due to the AO* and COWL* patterns are quite similar to those shown in Fig. 9. Table 1 summarizes many of the results for SAT. Spatial averages over various regions of the trend, its components based on the AO and COWL patterns (and the AO* and COWL* patterns), and the corresponding residuals are given. Approximately half of the total trends over NH land are explained by the AO and COWL indices together; this number drops to about 45% when the oceanic areas are included. Expanding the total SAT trend over land and the whole NH in terms of the COWL* and AO* patterns accounts for nearly the same warming as the expansion in terms of COWL and AO patterns. The residuals for land and land plus ocean are the same as above. As we have seen before, it is the COWL* pattern alone that accounts for most of the NH

9 1JUNE 2004 WU AND STRAUS 2147 FIG. 6. As in Fig. 5 except for Z 50. Contour interval is 25 m (55 yr) 1. and land trends, with the AO* pattern contributing little. The residual in the AO* and COWL* expansion is somewhat lower (higher) over North America (Eurasia) than the AO and COWL residual. The trend in 500-hPa temperature (T 500 ) is given in Fig. 10a. As shown in Santer et al. (1999), cooling is seen over Greenland and the North Pacific with warming over North America and the Atlantic Europe sector. The AO component shown in Fig. 10b accounts for about 90% of the cooling over Greenland and 50% of the warming over the Atlantic and Europe. Yet it is the COWL component shown in Fig. 10c that most strongly resembles the total trend over much of the hemisphere, accounting for 90% of the cooling over the Pacific and 90% of the warming over North America. The corresponding residual shown in Fig. 10d indicates that less than 50% of the overall trends are linearly independent of the AO and COWL modes. Expressing the trend in terms of the AO* and COWL* patterns yields maps (not shown) quite similar to Figs. 10b and 10c, respectively, except that the AO* contribution is a factor of 2 3 less than that of the AO. The trend in 50-hPa temperature consists of a strong zonal wave-one pattern with significant cooling over high-latitude Europe (and parts of Asia) and warming over the high-latitude North Pacific, as shown in Fig. 11a. The zonally symmetric AO congruent component in Fig. 11b is very close to that reported by TWH. The shape of the COWL congruent component given in Fig. 11c is similar to the total trend, but with the main centers of change shifted equatorward. The magnitude of the change is about 30% of the total trend. The strong re-

10 2148 JOURNAL OF CLIMATE VOLUME 17 FIG. 7. Fifty-five-year ( ) JFM trend in zonal-mean geopotential height: (a) total trend, components of the trends attributed to the (b) AO and (c) COWL indices, and (d) corresponding residual. Contour interval is 10 m (55 yr) 1 in (a), (b), and (d) and 5 m (55 yr) 1 in (c). FIG. 8. Components of the 55-yr ( ) JFM trend in zonal-mean geopotential height corresponding to the (a) AO* and (b) COWL* indices. Contour interval is 2.5 m (55 yr) 1 in (a) and 5 m (55 yr) 1 in (b).

11 1JUNE 2004 WU AND STRAUS 2149 FIG. 9. As in Fig. 6 but for SAT. Contour intervals is 0.5 K (55 yr) 1 for (a) and (d) and 0.25 K (55 yr) 1 for (b) and (c). sidual seen in Fig. 11d indicates that the components of AO and COWL congruent in T 50 are less important to the total trend than was the case for T 500. As was the case at 500 hpa, explaining the total trend in terms of the AO* and COWL* patterns (not shown) gives similar results with the AO* pattern contribution dropping in magnitude by about a factor of 3. e. Trend projections of zonally averaged temperature and circulation Figure 12a shows the total trend in zonally averaged temperature, which is consistent with the previous observed annual-mean radiosonde studies (Parker et al. 1997; Hanset et al. 1997; Allen and Tett 1999). It is characterized by strong cooling of the Arctic polar middle and upper troposphere [up to 4 K (55 yr) 1 ] and warming of the lower polar troposphere, the subtropical tropopause, and the surface at high latitudes. The warming of the lower polar troposphere is seen to some extent in the COWL component in Fig. 12c. Similarly the highlatitude upper-tropospheric cooling is explained to a certain extent by the AO component shown in Fig. 12b, although the AO-related cooling is too closely confined to the pole and extends too high. In general, the corresponding residual strongly resembles the trend in pattern and in magnitude from N. The residual shown in Fig. 12d is consistent with model simulations of the response to increasing anthropogenic forcings by Hadley Centre GCMs (Allen and Tett 1999). When the zonally averaged temperature is expanded in terms of the AO* and COWL* patterns, the former (although well correlated with the AO contribution) is extremely weak (factor of 5 smaller than the AO contribution).

12 2150 JOURNAL OF CLIMATE VOLUME 17 TABLE 1. Fifty-five-year ( ) linear trends in NH surface air temperature [K (55 yr) 1 ], denoted by TT, averaged over various areas. Land ocean and Land only refer to latitudes N, Eurasia to N, E; and North America to N, W. TT AO and TT COWL are components of the trend explained by the AO and COWL patterns, TT R is the corresponding residual. TT AO* and TT COWL* are components of the trend explained by the AO* and COWL* patterns, TT R* is the corresponding residual. TT TT AO TT COWL TT R TT AO* TT COWL* TT R* Land ocean Land only Eurasia North America The COWL* component shown in Fig. 13a now explains almost half of the high-latitude tropospheric cooling, about one-third of the subtropical tropopause warming, most of the surface warming in the latitude range N, and even a hint of the polar stratosphere warming. The residual shown in Fig. 13b is nearly identical to that in Fig. 12d. The trend in zonal-mean zonal wind shown in Fig. FIG. 10. As in Fig. 6 but for T 500. Contour intervals is 0.5 K (55 yr) 1 for (a) and (d) and 0.25 K (55 yr) 1 for (b) and (c).

13 1JUNE 2004 WU AND STRAUS 2151 FIG. 11. As in Fig. 9 but for T a must of course be consistent with the temperature trend of Fig. 12a and the thermal wind relationship. The enhanced negative temperature gradient in the upper troposphere leads to strong westerly wind trends in midlatitudes in the upper troposphere and lower stratosphere, while the high-latitude easterly trends are consistent with the strong positive temperature gradients near the ground and in the lower stratosphere. The zonally averaged mean meridional circulation is indicated by the arrows in Fig. 14a, with 1 m s 1 of meridional wind corresponding to 1 mm s 1 of vertical velocity. The pattern of upper-tropospheric southerlies in the subtropics and high latitudes, with northerlies in midlatitudes, leads to tendencies (via the Coriolis term) that tend to counteract the zonal wind trends. The enhanced descent in a broad region of the subtropics and enhanced ascent near 60 N may be interpreted as an enhancement of the Ferrell cell. The contribution of the AO pattern, shown in Fig. 14b, reproduces almost half of the easterly (westerly) trend in the upper troposphere, as well as about one-third of the enhanced rising (sinking) motion near 65 N (40 N). (These results agree with those reported by TWH.) However, in the stratosphere the westerly trend due to the AO is displaced nearly 20 N poleward compared to the overall trend. The contribution of the COWL pattern is mainly confined to the troposphere, and here it acts against the total trend as shown in Fig. 14c. When the trend is expanded in terms of the AO* and COWL* pattern, the former is quite weak but is well correlated with the AO contribution; the COWL* contribution, shown in Fig. 15a, shows strong warming in the upper troposphere and lower stratosphere, but shifted considerably poleward compared to the overall trend. The residuals shown in Figs. 14d and 15b are

14 2152 JOURNAL OF CLIMATE VOLUME 17 FIG. 12. As in Fig. 9 but for zonal-mean air temperature. FIG. 13. (a) Component of the 55-yr ( ) JFM trend in zonal-mean temperature attributed to the COWL* index. (b) The residual corresponding to the AO* and COWL* indices. Contour interval is 0.25 K (55 yr) 1 for (a) and 0.50 K (55 yr) 1 for (b).

15 1JUNE 2004 WU AND STRAUS 2153 FIG. 14. Fifty-five-year ( ) linear JFM trend in zonal-mean zonal wind (contours), meridional circulation (vectors): (a) total trend, components of the trend attributed to the (b) AO and (c) indices COWL, and (d) the corresponding residual. Contour interval is 0.5 ms 1 (55 yr) 1 in (a),(d) and 0.25 m s 1 (55 yr) 1 in (b),(c) for the zonal mean wind. Vectors have units of m s 1 in the horizontal and cm s 1 in the vertical. Vector scales shown at bottom of each panel. similar to the total trend, but with the high-latitude easterly trends extended. 5. Summary and discussion We have presented expansions of the trend maps for a variety of fields both in terms of the leading EOF patterns (PC time series) of SLP, which are defined as the AO and COWL patterns, and in terms of the leading EOF patterns (PC time series) of Z 500, which provide alternate representations of the AO and COWL, which we term the AO* and COWL* patterns. The results have verified the remarkable correspondence between the AO pattern (or AO*) and certain elements of the observed monthly mean NH winter climate trends during the last 55 yr in the lower and midtroposphere reported by TWH. But in addition, we have suggested that the COWL (and COWL*) pattern also plays a significant role in representing observed trends. From our results it is clear that in order to represent the main geographical features of the trends in SLP, SAT, Z 500, and T 500 both the AO and COWL patterns must be taken into account, and it is clear that these two patterns taken together account for a great deal of the trend structure. It is also clear that these conclusions hold whether the pattern definitions are based on the SLP or the Z 500 field. In either case, the appropriate residual in the expansion of the trend is relatively small compared to the trend itself for these lower- and midtropospheric fields. This conclusion does not hold in the lower stratosphere. While the Z 50 trend projects well on the AO (AO*) and COWL (COWL*) patterns, the trend cannot be primarily represented as a combination of the AO*

16 2154 JOURNAL OF CLIMATE VOLUME 17 FIG. 15. As in Fig. 14 but for the component of the trend explained by (a) the COWL* index and (b) the residual corresponding to the AO* and COWL* indices. and COWL* (or AO and COWL) patterns. These statements also generally apply to the temperature (T 50 ) field. The structure of the trends in the NH zonal-mean height and temperature fields from the ground to the lower stratosphere generally do not project strongly on the AO and COWL patterns, although the COWL* pattern captures at least some of the global structure of the temperature trend. While the tropospheric structure of the zonal-mean zonal wind field and the mean meridional circulation accounted for by the AO pattern is similar to the overall trend, there are important differences in amplitude and latitudinal position. This becomes even more apparent in the stratosphere. In general there are substantial differences between our results and those of TWH, who consider a much shorter period (the 30 yr from 1968 to 1997) and find that the contribution of the AO pattern to a number of fields dominates the trend. Much of this disparity is related to the trend itself, as in their results for SLP and SAT (their Fig. 2) in which the substantial pressure falls and cooling that we find in the North Pacific are completely missing. Some of the disparity is related to the contribution of the AO pattern, as for example at 50 hpa, where TWH show a much stronger contribution in their Fig. 4c than we obtain in Fig. 6b. We interpret the disparities as being due to the much shorter period chosen by TWH and to the different method used to define the AO pattern, the JFM AO index, and its trend. TWH use the monthly mean NH SLP for all months of the year to define the AO pattern. The JFM AO index is extracted from the first principal component associated with the AO pattern. However, we do not exclude the possibility that some of the differences in data sources play a role, particularly in the stratosphere. The pervasiveness of AO (AO*) spatial structure in the trends for many lower- and midtropospheric fields may be due to its high degree of zonal symmetry, as discussed in TWH. That the COWL (COWL*) structure is also very prominent in these trend fields can be attributed to the influence of the thermal inertia contrast between land and ocean on the lower and midtroposphere. The inability of the COWL or COWL* modes to explain a great deal of the trends in the zonal-mean climate is consistent with the original interpretation of the COWL mode as being due to the indirect effects of atmospheric dynamics (Wallace et al. 1996), distinct from the direct (and presumably more time continuous) response to radiative forcing. How the AO pattern fits into this conceptual scheme is not clear. The long-term trends of SLP and Z 500 were not removed when we defined the AO (AO*) and COWL (COWL*) patterns. So the patterns reflect not just the intermonthly and interannual variability, but also the long-term trends themselves. Since the 55-yr trend accounts for a very small fraction ( 5%) of the total variance of the SLP and Z 500 PC time series, our results are found to be nearly unchanged when the trend decompositions are based on the detrended EOFs and corresponding PCs. The results presented in this paper have considerable relevance to the detection of anthropogenic climate change. The observed climate change in recent years is, in part at least, due to the dynamical effects captured in the COWL (and possibly the AO) patterns. Therefore, it may be necessary to exclude the AO- and COWLrelated warming when we attribute the observed hemispheric mean surface air temperature warming only to a direct forcing by the greenhouse effect. Recently, Gillett et al. (2000) considered the AO-related warming in the detection of a global response to anthropogenic greenhouse gases and sulfate aerosol in the Hadley Centre GCM. They found that the global anthropogenic response is still robust, even though the Second Hadley

17 1JUNE 2004 WU AND STRAUS 2155 Centre Coupled Ocean Atmosphere General Circulation Model (HadCM2) is not able to well simulate the trend of AO. Zwiers and Zhang (2003) find that the detection of global and regional responses to the anthropogenic forcing is also robust after the AO-related warming is excluded. Clearly further studies are needed to remove both AO- and COWL-related warming to detect the influence of anthropogenic forcing on surface air temperature and sea level pressure. Acknowledgments. This research was supported by the Office of Science (BER), U.S. Department of Energy Grant DE-FG02-01ER APPENDIX Trend Projections Following Straus (1983), we note that any finite time series can be expressed as a sum of ordinary Legendre polynomials L (t), which form an orthogonal and complete set. Since the leading polynomial L 1 is just a constant, and the second (L 2 ) a straight line, their respective coefficients simply correspond to the time mean and the linear trend. We may thus express a time-varying field F(x, t) as F(x, t) L (t)t (x), (A1) where x denotes the spatial domain and t the discrete time domain. The patterns T are given by 1 T (x) F(x, t)l (t), (A2) N t where N is the number of discrete times, T 1 (x) isthe time mean field, and T 2 (x) the trend. The trend so calculated is equivalent to the trend obtained by least squares fitting (Straus 1983). Now define an empirical orthogonal function (EOF) expansion of the field F(x, t): F(x, t) P (t)e (x), (A3) where the index labels both the spatial pattern or EOF E (x) and the corresponding orthogonal time series, or principal component (PC) P (t). We will assume that the time mean of any field that we consider vanishes and that the PCs have unit variance: 1 N t P (T)P (t),, (A4) where, 0 if the indices are different, 1 if they are the same. Now taking 2 in Eq. (A2) for the trend and inserting the EOF expansion of Eq. (A3), we obtain [ ] [ ] 1 N 1 1 T 2(x) F(x, t)l 2(t) P (t)e (x) L 2(t) N N t t E (x) P (t)l 2(x) E (x)t, (A5) t where T is just the trend of the th PC. Thus the trend can be uniquely and completely expressed as a sum of the field s EOFs, each weighted by the trend of the relevant PC. However, it may be of interest to expand the trend of one field in terms of the PCs of another field. Writing the set of PCs of the new field as {Pˆ }, we start by regressing the original field F(x, t) on one of the new PCs, say Pˆ (t). The regression is done for each grid point of the original field F(x, t) separately: ˆ F(x, t) P (t)r(x) (x, t), (A6) where is the error field. Minimizing the error variance yields the standard result: [ ˆ ][ ˆ ˆ ] [ ˆ ] R(x) F(x, t)p (t) P (t)p (t) t t F(x, t)p (t), (A7) t where we have assumed that the set of PCs {Pˆ }is standardized. Now this regression can be carried out using more than one PC in the expansion in Eq. (A6): ˆ F(x, t) P (t)r (x) (t). (A8) The sum over need not be complete. (In this paper, the sum only includes two terms.) Since the PCs are orthogonal in time, this is equivalent to a series of simple regressions, and Eq. (A7) holds for each regression field Rˆ (x). Taking 2 in Eq. (A2) for the trend and inserting the multiple regression from Eq. (A8), we obtain [ ] 1 ˆ 2 2 N t T (x) P (t)r (x) (x, t) L (t). (A9) But this can be written as [ ] 1 1 ˆ T 2(x) R (x) P (t)l 2(t) (x,t)l 2(t) N N t t ˆ R (x)t (A10) so that the trend is written as a sum of patterns whose coefficients are Tˆ with a residual given by. The fundamental difference between Eqs. (A5) and (A10) is that in the former case there is, in principle, no residual if all EOF modes are kept; in the latter there is generally a residual arising from the regression. In this paper, only the leading two terms in the PC 1

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