Trend in Atmospheric Angular Momentum in a Transient Climate ...

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Trend in Atmospheric Angular Momentum in a Transient Climate Change Simulation with Greenhouse Gas and Aerosol Forcing HUEI-PING HUANG

AND

KLAUS M. WEICKMANN

NOAA–CIRES Climate Diagnostics Center, Boulder, Colorado

C. JUNO HSU Canadian Centre for Climate Modelling and Analysis, Victoria, British Columbia, Canada (Manuscript received 26 April 2000, in final form 25 July 2000) ABSTRACT The authors investigate the change of atmospheric angular momentum (AAM) in long, transient, coupled atmosphere–ocean model simulations with increasing atmospheric greenhouse gas concentration and sulfate aerosol loading. A significant increase of global AAM, on the order of 4 3 10 25 kg m 2 s21 for 3 3 CO 2–1 3 CO 2 , was simulated by the Canadian Centre for Climate Modelling and Analysis (CCCma) coupled model. The increase was mainly contributed by the relative component of total AAM in the form of an acceleration of zonal mean zonal wind in the tropical–subtropical upper troposphere. Thus, under strong global warming, a superrotational state emerged in the tropical upper troposphere. The trend in zonal mean zonal wind in the meridional plane was characterized by 1) a tropical–subtropical pattern with two maxima near 308 in the upper troposphere, and 2) a tripole pattern in the Southern Hemisphere extending through the entire troposphere and having a positive maximum at 608S. The implication of the projected increase of global AAM for future changes of the length of day is discussed. The CCCma coupled global warming simulation, like many previous studies, shows a significant increase of tropical SST and includes a zonally asymmetric component that resembles El Ninõ SST anomalies. In the CCCma transient simulations, even though the tropical SST and global AAM both increased nonlinearly with time, the ratio of their time increments DAAM/DSST remained approximately constant at about 0.9 3 10 25 kg m 2 s21 (8C)21 . This number is close to its counterpart for the observed global AAM response to El Ninõ. It is suggested that this ratio may be useful as an index for intercomparisons of different coupled model simulations.

1. Introduction Global warming caused by increased concentration of greenhouse gases (GHG) in the atmosphere has been one of the central issues of climate research. Due to the relatively short records of atmospheric and oceanic data available for analyses, long-term general circulation model (GCM) simulations have been widely adopted to investigate the detailed responses of the atmosphere and ocean to anthropogenic forcing. Recent developments in coupled ocean–atmosphere modeling allow researchers to assess more accurately the impact of GHG forcing on atmospheric variables that are sensitive to a change in sea surface temperature (SST). One such variable is the global angular momentum of the atmosphere. Previous work has shown that the global atmospheric an-

Corresponding author address: Dr. Huei-Ping Huang, NOAA–CIRES Climate Diagnostics Center, R/CDC1, 325 Broadway, Boulder, CO 80303-3328. E-mail: [email protected]

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gular momentum (AAM) is highly correlated with circulation changes associated with coherent short-term climate variations, in particular, the Madden–Julian oscillation (MJO; Anderson and Rosen 1983; Madden 1987) and El Ninõ (Rosen et al. 1984). Both MJO and El Ninõ are accompanied by changes in the distribution of tropical convection, which help drive the circulation anomalies. The dynamical mechanisms that produce the AAM changes involve both zonal mean and zonally asymmetric forcing and are best known for the MJO (Weickmann et al. 1997). However, in both cases AAM becomes anomalously high when tropical convection expands zonally from its primary climatological center near Indonesia and becomes anomalously low when convection is concentrated over the Indonesian region. SST anomalies serve to force the redistribution of tropical convection during El Ninõ while internal dynamical mechanisms are more important for the MJO. The sensitive dependence of global AAM on the tropical SST is exemplified by the fact that the highest level

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of global AAM of the last 50 yr occurred during the 1982–83 and 1997–98 El Ninõs. Since recent studies have shown an analogy between El Ninõ and global warming in terms of the change of tropical SST (e.g., Knutson and Manabe 1995; Timmermann et al. 1999; Collins 2000), an analysis of the change of global AAM associated with global warming is of great interest. As a single number that summarizes the net change (vs redistribution) of a fundamental quantity of the atmosphere, global AAM may also serve as a useful index for intercomparisons of climate models. Lambeck and Cazenave (1976) first speculated on the connection between the long-term trend of global AAM and that of global mean surface air temperature. Rosen and Gutowski (1992) studied the change of AAM with doubling CO 2 in uncoupled atmospheric GCMs. Recently, Abarca del Rio (1999) revisited this subject and found an upward trend of observed global relative angular momentum during the second half of the twentieth century, which he also attempted to relate to global warming. One of the unique properties of global AAM is that its time variation is proportional to that of the length of day, provided that the secular terms due to astronomical and geological effects are properly removed (e.g., Peixoto and Oort 1992). Since the earth’s rotation rate can be independently verified by geodetic measurements (Hide et al. 1980; Barnes et al. 1983; Salstein et al. 1993), continued observation of length of day may provide an alternative way to monitor climate change. To examine the feasibility of this idea, one needs to know the relative importance of the contributions to the trend in length of day by atmospheric (changes of zonal wind and airmass distribution) and nonatmospheric (tidal friction, deglaciation) effects. Since in the observations these effects are mixed together, a useful way to estimate the atmospheric effect is to analyze long GCM simulations. In this paper we present, for the first time, the trend in global angular momentum due to increased GHG concentration in a long, transient, coupled atmosphere– ocean GCM simulation. The model used was the Canadian Centre for Climate Modelling and Analysis (CCCma) coupled atmosphere–ocean GCM as described by Flato et al. (2000). Our analysis is based on one control and three GHG 1 A [the ‘‘A’’ denotes the inclusion of sulphate aerosol effects, see Boer et al. (2000a)] runs with different initial conditions as documented by Boer et al. (2000a,b). Each of these long runs simulated the evolution of the atmosphere–ocean state from year 1900–2100, with an increase of GHG concentration following the Intergovernmental Panel on Climate Change scenario IS92a (Houghton et al. 1992). The trends in basic thermodynamic variables (temperature, moisture), key parameters in the hydrological cycle (precipitation, soil moisture), and the oceanic circulation in these simulations have been analyzed by Boer et al. (2000a). Here, we will focus on the trends in global angular momentum and zonal wind. Although

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a detailed intercomparison of the simulated angular momentum by coupled atmosphere–ocean models is not yet available, it is worth noting that in the Atmospheric Model Intercomparison Project the atmospheric component of the CCCma model was among the best performed in the simulation of atmospheric angular momentum (Hide et al. 1997). In the following, we first present the trend in global angular momentum, and the accompanying change of zonal mean zonal wind in the GHG 1 A simulations. Then, the relationship between the trends in tropical SST and global angular momentum in the coupled simulations is analyzed in section 3. A discussion and concluding remarks follow in sections 4 and 5. 2. Trend in angular momentum The total angular momentum of the atmosphere (M) is the sum of the relative angular momentum (MR ) and ‘‘omega’’ angular momentum (MV ) defined by (e.g., Peixoto and Oort 1992) MR 5 MV 5

a3 g

EEE EE

a4V g

2p

pS

0

0

2p

0

p /2

u cos2u du dl dp,

(1)

2p /2

p /2

pS cos3u du dl,

(2)

2p /2

where u and p S are the zonal velocity and surface pressure, l and u are longitude and latitude, g is the gravitational acceleration, and a and V are the radius and rotation rate of the earth. Note that MR is related to the strength and distribution of zonal wind, while MV is related to the distribution of atmospheric mass. Figure 1a shows the relative angular momentum MR from year 1900–2100 in one control (bold) and three GHG 1 A (thin) simulations from the CCCma coupled model experiments. They are calculated from monthly mean zonal winds interpolated onto 17 pressure levels (from 10 to 1000 hPa) from the original hybrid-coordinate model outputs. The curves shown are 5-yr running means with the seasonal cycle (first three harmonics) removed. The three periods 1980–2000, 2040–60, and 2080–2100 that will be used later are roughly related to the 1 3 CO 2 , 2 3 CO 2 , and 3 3 CO 2 regimes (Boer et al. 2000a). A significant increase of MR , by about 2 3 10 25 kg m 2 s21 for 2 3 CO 2–1 3 CO 2 and twice that for 3 3 CO 2–1 3 CO 2 , is clearly shown. Figure 1b is similar to 1a but for the omega angular momentum. The change in MV is much smaller than MR but is still statistically significant (the DMV in the late twenty-first century exceeds many standard deviations of the natural variability in the control run), with an amount of 0.1 3 10 25 kg m 2 s21 for 2 3 CO 2–1 3 CO 2 and roughly twice that for 3 3 CO 2–1 3 CO 2 . The change of total atmospheric angular momentum, DM 5 DMR 1 DMV , is mainly due to DMR . Figure 2 illustrates the change of the zonal mean zonal wind associated with the change of global angular mo-

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FIG. 1. (a) The relative angular momentum for one control (bold) and three GHG 1 A (thin) runs. The time series shown are the 5-yr running means with seasonal cycle (first three harmonics) removed. Units: 10 25 kg m 2 s21 . (b) Same as (a) but for the ‘‘omega’’ angular momentum.

mentum. The time-latitude cross sections show the zonal mean zonal wind at 200 hPa for one control (top panel) and for the three GHG 1 A runs for years 1900–2100. The fields are 5-yr running means with the seasonal cycle (first three harmonics) removed. Note that the angular momentum or zonal wind at 200 hPa is an excellent proxy for its vertically integrated counterpart on a wide range of timescales (correlation 5 0.8 for daily observed anomalies). An overall increase of upper-level westerly wind is shown in all three GHG 1 A runs. The most striking feature is the disappearance of the easterly zone in the Tropics toward the end of the transient simulations. The creation of a superrotational state (i.e., westerly everywhere) in the tropical upper troposphere has been shown previously in idealized atmospheric GCM simulations when the strength of tropical heating was increased beyond a certain threshold (Suarez and Duffy 1992; Saravanan 1993). These models were highly idealized and their ‘‘threshold behavior’’ (a sudden collapse of the midlatitude westerlies to the lower latitudes after the destruction of critical lines) is much more dramatic than in the fully coupled model analyzed here. Both Suarez and Duffy (1992) and Saravanan (1993) had used two-level atmospheric models. As remarked by Saravanan (1993), the transition to super-

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rotation could be much less dramatic in a multilevel GCM. The aforementioned papers had not considered the prospect of a superrotational state being created by global warming. However, recently I. M. Held (1999, Bernhard Haurwitz Memorial Lecture) pointed out this possibility and suggested a search for tropical superrotational states in global warming simulations. Figure 2 is, to our knowledge, the first demonstration of such a possibility in a long coupled simulation. The reason for the gradual disappearance of tropical easterlies in the GHG 1 A runs remains to be investigated. We postpone further remarks on this subject until section 5. Figure 3c shows the vertical structure of the trend in zonal mean zonal wind for 3 3 CO 2–1 3 CO 2 for the winter season (December–February). The difference field in Fig. 3c was constructed by subtracting the 21winter and three-member ensemble mean of year 1980– 2000 from that of year 2080–2100 in the GHG 1 A runs. For reference, the zonal mean zonal wind from these two periods are also shown in Figs. 3a and 3b. The trend is dominated by an overall increase of zonal mean zonal wind in the tropical-subtropical upper troposphere, as can also be inferred from a previous analysis by Fyfe et al. (1999, compare their plates 2 and 3). The detailed pattern in Fig. 3c consists of two distinctive features, namely, a positive region in the tropical-subtropical upper troposphere with two maxima near 308, and a tripole pattern in the Southern Hemisphere extending through the entire troposphere. The doublepeak, tropical–subtropical structure also extends into the midlatitudes in the upper troposphere. However, because of the cos 2 u factor in Eq. (1), zonal winds in the lower latitudes are the main contributors to the global angular momentum. The strengthening of upper-level subtropical jets due to increased tropical SST (see section 3) is not a new idea; it has been extensively investigated in the context of El Ninõ since Bjerknes (1966). As will be shown in section 3, a significant increase of tropical SST—with some similiarities to El Ninõ—occurred in our GHG 1 A simulations. Interestingly, the ‘‘double peak’’ tropical–subtropical upper-tropospheric pattern in Fig. 3c bears some resemblance to the response of upper-level zonal winds to El Ninõ (e.g., Fig. 4 of Hsu 1994; Figs. 1a and 3c of Hoerling et al. 1995). The peak-to-peak meridional scale of our tropical–subtropical response pattern is broader than that of the El Ninõ case, although this broadening actually occurs with time and the initial westerly wind anomalies in the GHG 1 A runs develop near 208 lat (with another westerly signal also developing along 608S). This can be seen in Fig. 4, the time– latitude cross section of the anomalous 200-hPa zonal mean zonal wind in the GHG 1 A runs. Dickey et al. (1992) and Abarca del Rio et al. (2000) show that a similar broadening or poleward propagation of zonal mean relative angular momentum occurs during El Ninõ. Poleward propagation of AAM signals has also been found to accompany MJO (Anderson and Rosen

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FIG. 2. Time–latitude cross sections of zonal mean zonal wind at 200 hPa for (top) one control and three GHG 1 A runs. The time series are 5-yr running means with the seasonal cycle removed. Contour interval is 5 m s21 . Shading scale is shown.

1983; Weickmann et al. 1997). Both these phenomena are episodic with alternating positive and negative phases. As a result, the poleward propagation is captured by the first two empirical orthogonal functions (EOFs) of the zonal mean zonal wind or AAM. Here, in the GHG 1 A simulation there is only one prolonged warming event and the first EOF (DJF) of the undetrended zonal mean zonal wind merely represents the trend itself. This EOF, which explains about 90% of the variance of the undetrended, 5-yr running mean (wintertime) anomalous zonal mean zonal wind, is shown in Fig. 5a. It is similar to Fig. 3c, although the double-peak feature in the subtropical upper troposphere is smeared in the EOF, which is likely because the peak-to-peak meridional scale keeps increasing with time. A double-peak, tropical–subtropical upper-tropospheric pattern has also been shown as the leading structure of the internal variability of zonal wind that covaries with global angular momentum in long GCM simulations (e.g., Fig. 4 of Feldstein and Robinson 1994; and Fig. 1a of von Storch 1999). Von Storch (1999) showed that this pattern appears as the ‘‘reddest’’ mode of internal variability, that is, on average it possesses

the longest decorrelation time. The ‘‘internal modes’’ obtained in these studies show a shorter (as compared with the forced response in our Fig. 3c) peak-to-peak scale for the double-peak feature. Figure 5b shows the first EOF (winter season; DJF) of the anomalous zonal mean zonal wind from the coupled CCCma control run. It explains 25% of the variance (compared to 15% for the second EOF, not shown). Interestingly, it also shows two off-equatorial maxima in the tropical–subtropical upper troposphere, with the peak-to-peak scale shorter than that in the forced response (Fig. 3c). The difference between Figs. 5a and 5b in the Northern Hemisphere suggests the broader forcing in the global warming case leads to circulation anomalies that do not project strongly onto the dominant mode of internal variability from the control run. The tripole structure (with a positive maximum at around 608S) in the Southern Hemisphere in Fig. 3c is a robust feature that has been produced in previous coupled global warming simulations (Stephenson and Held 1993). It is consistent with the observed trend of zonal mean zonal wind in the Southern Hemisphere troposphere during the late twentieth century (e.g., Thompson

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shorter timescales (e.g., Yoden et al. 1987). The locations of the three-sheet equivalent barotropic structures in the Southern Hemisphere are the same for the forced response (Figs. 3c or 5a) and the first unforced EOF (Fig. 5b), an interesting coincidence whose implication remains to be investigated. Curiously, while our response pattern shows an acceleration of westerlies at 608S, the ‘‘typical’’ Southern Hemisphere response of zonal wind to El Ninõ is in the opposite sense with a deceleration of westerly at 608S (Fig. 3a of Hoerling et al. 1995; Fig. 4 of Hsu 1994). This could be due to the different meridional extent of the tropical SST warming in El Ninõ versus our global warming runs (with the former confined to near the equator, and the latter relatively broader, see section 3). Consequently, the location of the nodal lines of the midlatitude responses for the two phenomena could be different. 3. Tropical SST and global angular momentum

FIG. 3. (a) Twenty-one winter (Dec–Feb, hereafter DJF) mean latitude-height cross section of zonal mean zonal wind from year 1980 to 2000 (corresponding to the 1 3 CO 2 regime) in the GHG 1 A simulations. (b) Same as (a) but for years 2080–2100 (3 3 CO 2 regime). (c) The trend, (b) minus (a). Contour interval is 4 m s21 for (a) and (b), and 1.5 m s21 for (c). Negative values are shaded.

et al. 2000, their Table 10). This pattern (regardless of the sign) also appears as the ‘‘second reddest’’ mode of internal variability in the coupled simulation of von Storch (1999), and the leading Southern Hemisphere EOF in various uncoupled simulations (e.g., Feldstein and Robinson 1994), and as the observed first EOF of the Southern Hemisphere zonal mean zonal wind on

The discussion in section 2 calls for a more detailed analysis of the relationship between the trends in tropical SST and global AAM. Recent coupled simulations have shown evidence of an El Ninõ–like asymmetric structure of SST change superimposed on a general increase of tropical SST under global warming (e.g., Knutson and Manabe 1995; Timmermann et al. 1999; Collins 2000). In the context of El Ninõ, global AAM is known to be sensitive to tropical SST changes. Here, we explore this analogy in the context of global warming. The 21winter and three-member ensemble mean SST from the 1 3 CO 2 and 3 3 CO 2 regimes are shown in Figs. 6a and 6b, with their difference 3 3 CO 2–1 3 CO 2 shown in Fig. 6c. Figure 6c shows an increase of SST everywhere in the Tropics and subtropics, with a relatively strong warming in the central Pacific and relatively weak warming in the subtropical Pacific. These characteristics are similar to those in the aforementioned studies of coupled simulations of global warming [in particular, the Hadley Centre coupled simulations by Collins (2000), see his Fig. 14]. To quantify the overall increase of tropical SST, we define an index, DSST as the average of the change of SST in Fig. 6c over all ‘‘ocean’’ grid points between 138N and 138S (which covers eight Gaussian latitudes). Note that because the warming of tropical SST in the simulated case is more uniform (in both meridional and longitudinal directions) than in an El Ninõ, our index is not very sensitive to the choice of the averaging domain. Figure 7 shows the evolution of DSST for one control (bold) and three GHG 1 A simulations from year 1900–2100. An increase of more than 48C is shown for all GHG 1 A cases over the 201yr period [also see Boer et al. (2000a) for related discussion]. A summary of the changes of global angular momentum (DM) and tropical mean SST (DSST) for 2 3 CO 2–1 3 CO 2 and 3 3 CO 2–1 3 CO 2 , averaged from three GHG 1 A runs, is shown in Table 1. Here, the

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FIG. 4. Time–latitude cross section of anomalous zonal mean zonal wind at 200 mb. The anomaly is defined as the departure from the time average (over 201 yr) and ensemble average of the zonal mean zonal wind of the three GHG 1 A runs. Shown are the ensemble average of the three runs. The time series are 5-yr running means with seasonal cycle (first three harmonics) removed. The contour interval is 0.5 m s21 and shading scale is shown.

mean values of SST and AAM for the 1 3, 2 3, and 3 3 CO 2 regimes were estimated from the 21-yr average of years 1980–2000, 2040–2060, and 2080–2100. As mentioned in section 2, the change of total AAM is dominated by that of the relative angular momentum. The most interesting result in Table 1 is that, although both global AAM and tropical SST change nonlinearly with time, the change of AAM scales roughly linearly with that of tropical SST and thus the ratio DM/DSST is approximately a constant (bottom row of Table 1) DM ø 0.9 3 10 25 kg m 2 s21 (8C)21. DSST

FIG. 5. (a) The first EOF of the winter season (DJF) anomalous zonal mean zonal wind on the meridional plane for the three GHG 1 A runs. The anomaly is defined as the departure from mean seasonal cycle (first three harmonics plus annual mean) and is subject to a 5-yr running mean. (b) The first EOF (DJF) for the control run, defined in the same manner as (a). The EOF calculations in (a) and (b) use the monthly mean data of the full 201-yr records of the model runs, with the zonal mean zonal wind weighted by (Dp cosu)1/2 , where u is latitude and Dp is the (pressure) thickness represented by a pressure level.

(3)

This number stays roughly the same if we define DSST as the average over the zonal band between 16.78N and 16.78S (which covers 10 Gaussian latitudes). It decreases to about 0.8 3 10 25 kg m 2 s21 (8C)21 if DSST is defined as the average over a box bounded by 138N, 138S, 1808E, and 1008W. This change does not affect our discussion. Few previous works have discussed the ratio in (3) theoretically or in models, although it may be relevant to compare our result with Satoh and Yoshida’s (1996) estimate using an aquaplanet atmospheric model with imposed DSST. In an experiment with DSST imposed in a relatively narrow box, they found a change of DU ø 10.3 m s21 (their ‘‘equivalent’’ zonal velocity U is related to our relative angular momentum by MR 5 mRU, where m and R are the total mass of the atmosphere and the radius of the Earth) associated with an increase of 18C in tropical SST. This corresponds to a ratio of DM/DSST of about 0.97 3 10 25 kg m 2 s21 (8C)21 , which is on the same order of magnitude as in our coupled model. We suggest that, given a set definition of DSST and DM, the ratio in (3) may be a useful index for quantifying the strength of the atmospheric zonal wind response to tropical SST forcing. It may therefore be used for intercomparisons of climate models. It is also useful to compare (3) with its counterpart for El Ninõ. During the peak season (boreal winter) of a strong El Ninõ, the seasonal mean increase of global

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FIG. 6. (a) Twenty-one winter (DJF) mean SST from year 1980 to 2000 (1 3 CO 2 regime) in the GHG 1 A simulations. Contour interval is 18C. The thick contour is the 288C isotherm. (b) Same as (a) but for years 2080–2100 (3 3 CO 2 regime). (c) The trend, (b) minus (a). (d) The asymmetric component of the trend, i.e., the zonally averaged SST was removed from (c). Contour interval is 0.58C for (c) and (d). Shading scale for (c) is shown below panel c. Negative contours are dashed in (d).

AAM is on the order of 2–3 3 10 25 kg m 2 s21 , while the DSST averaged over central-eastern Pacific is about 28–38C. This gives a ratio of DM/DSST on the order of 1 3 10 25 kg m 2 s21 (8C)21 , which is close to its counterpart for the model-simulated global warming. We should caution, however, that in the case of El Ninõ the DSST is more sensitive to the domain chosen for spatial averaging, and the DM is somewhat sensitive to the

TABLE 1. Changes of global angular momentum and tropical mean SST (defined in text) averaged from three-member ensembles of the GHG 1 A simulations. 2 3 CO22 3 3 CO22 1 3 CO2 1 3 CO2 FIG. 7. The evolution of tropical mean SST (defined as the average over all grids over the ocean between 138N and 138S) for one control (bold) and three GHG 1 A (thin) runs. The time series shown are 5-yr running means with seasonal cycle (first three harmonics) removed.

DMV DM R DM 5 DM R 1 DM V DSST (tropical mean) DM/DSST

0.07 1.35 1.42 1.56 0.91

0.11 3.03 3.14 3.50 0.90

Units 10 kg m 2 s21 0 0 8C 10 25 kg m 2 s21 (8C)21 25

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period for time averaging. The reason is that the zonally asymmetric components of SST anomalies are much larger for El Ninõ than for the global warming simulation. Figure 6d shows the asymmetric global warming component constructed by removing the zonal average from Fig. 6c (note that in the Tropics this zonal average varies slightly with latitude with a typical value of about 13.38C). The 18C east–west difference over the Pacific basin in Fig. 6d is about four times smaller than that observed during a strong El Ninõ. On the other hand, the zonally symmetric component of SST anomaly associated with global warming is stronger than its counterpart for El Ninõ. (The average warm-minus-cold difference in the zonal mean tropical SST is about 0.68C for observed El Ninõ from 1950 to 2000.) These differences obviously have implications for which dynamical mechanisms produce the circulation response given a pattern of SST and tropical convective forcing due to El Ninõ or global warming. The zonal symmetry or asymmetry of the forcing may also affect the dynamics of poleward propagation of the angular momentum signal. In the context of MJO, Weickmann et al. (1997) found that the interaction of the wavy component of circulation anomaly and the climatological stationary wave contributes substantially to the poleward propagation. However, Chang (1998) was able to produce poleward propagation of AAM anomaly by applying a zonally symmetric heating to an idealized atmospheric model. These interesting dynamical problems deserve further investigation. 4. Discussion Although our focus has been on the model simulations, it is useful to remark on the related observations from the second half of the twentieth century. Figure 8 shows the total (MR 1 MV ) AAM for the control (bold solid) and GHG 1 A (thin solid) simulations as the sum of Figs. 1a and 1b. Superimposed on the figure is the 5-yr running mean (dashed, seasonal cycle removed) of the total AAM in the National Centers for Environmental Prediction (NCEP) reanalysis from 1958–98. [A detailed analysis of the budget of angular momentum for the NCEP reanalysis data is in Huang et al. (1999).] Here, the AAM was directly calculated from the 28 sigma-level spectral coefficient data. Because there is a difference between the long-term means of the NCEP reanalysis and the CCCma control run [MV , MR , and M (5MV 1 MR ) are 1017.17, 14.28, and 1031.45 for the former, and 1017.97, 15.94, and 1033.91 for the latter], in Fig. 8 we shifted the curve of NCEP reanalysis upward to compare the trends more easily. The increase of total AAM over the past 50 yr, as deduced from NCEP reanalysis, is more than twice that of the CCCma GHG 1 A simulations. As short-term (interannual to interdecadal) trends can be caused by internal variability unrelated to global warming, the difference between the two is not necessarily surprising. However, the relatively

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FIG. 8. The total angular momentum (MR 1 MV ) from one control (bold solid) and three GHG 1 A (thin solid) runs. The same quantity derived from NCEP reanalysis (1958–98) is shown as the dashed curve. An upward shift of 2.46 units (1 unit 5 10 25 kg m 2 s21 ) was applied to the NCEP time series to compensate the difference between the long-term means of the NCEP data and CCCma control run. The time series shown are 5-yr running means (the first and last 2.5 yr are not shown) with seasonal cycle removed. On the right is a scale, in milliseconds, for the equivalent change of length of day as defined in text.

small, but still significant, increase of global AAM in the GHG 1 A simulations from year 1950–2000 suggests that global warming may be partially responsible for the observed trend of AAM. Also of interest is the fact that the observed increase of AAM is not uniform in time but is particularly concentrated in a short period in the 1970s. The rate of change of AAM is much smaller if this period is removed. [See also Rosen and Salstein (2000) for a discussion on the trend of AAM in the twentieth century and its relationship with observed SST.] There has been speculation (e.g., Trenberth 1990) that a transition from one atmosphere–ocean flow regime to another occurred in the middle 1970s. While it is beyond the scope of this paper, the results shown here suggest the need for further investigation of this aspect. The fluctuation of global AAM is known to be highly correlated with that of the length of day (LOD) on intraseasonal to interannual timescales, on which the total angular momentum of the atmosphere and solid earth is approximately conserved (e.g., Peixoto and Oort 1992). The change of length of day, DLOD, and that of global AAM, DM, can be related by the formula DLOD ø 0.168DM, with DLOD in milliseconds and DM in 10 25 kg m 2 s21 (Peixoto and Oort 1992). On decadal to centennial timescales, the secular changes of the atmosphere–earth’s angular momentum due to astronomical (tidal friction) and geological (postglacial rebound) effects are not negligible (e.g., Munk and McDonald 1960; Lambeck 1980; Wahr 1988). Thus, on the timescale of global warming DLOD needs not be proportional to DM. However, to show how atmospheric effects due to global warming may change LOD, we marked the ‘‘equivalent’’ DLOD on the right margin of Fig. 8 based on the aforementioned linear relationship. In the GHG 1 A simulations, the increase of AAM is

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equivalent to a tendency of 10.3 ms century21 for LOD over the entire 201-yr period. This number increases to about 10.5 ms century21 if only the second century (2000–2100) is considered. Note that the tendency of the length of day due to tidal friction is about 12.3 6 0.1 ms century21 (e.g., Yoder et al. 1983), and that due to the postglacial rebound process is about 20.6 6 0.2 ms century21 based on various observational and theoretical estimates summarized by Peltier and Jiang (1996). With these estimates, the net astronomical and geological effect on the length of day is about 11.7 ms century21 with an uncertainty around 0.2–0.3 ms century21 . Thus, on the centennial timescale, secular astronomical/geological terms dominate the tendency of LOD even under strong global warming. On the other hand, the DLOD due to projected warming of the twenty-first century is not negligible and it eventually rises above the uncertainty in the astronomical/geological terms toward the end of the twenty-first century. If in the future the atmosphere evolves into the 2 3 or 3 3 CO 2 regime it might be possible to extract the signal of global warming from the budget of the length of day. 5. Concluding remarks In this paper we have shown the trends in global angular momentum and zonal mean zonal wind in coupled CCCma simulations with increasing concentration of greenhouse gas and sulfate aerosol loading. A significant increase of total atmospheric angular momentum (dominated by that of the relative angular momentum), on the order of 4 3 10 25 kg m 2 s21 for 3 3 CO 221 3 CO 2 , accompanies the simulated global warming. A significant increase of tropical SST was also shown in the coupled GHG 1 A simulations as previously discussed by Boer et al. (2000a). Although both global AAM and tropical SST increased nonlinearly in the transient simulations, the ratio of DM/DSST remains roughly a constant. This ratio, as deduced from the coupled global warming simulations, is also on the same order of magnitude as its counterpart in observed El Ninõ. We suggest this ratio may be useful for intercomparison of climate models. The local change of zonal mean zonal wind associated with the increase of global AAM is characterized by a positive tendency in the tropical–subtropical upper troposphere with two maxima near 308, and a tripole pattern in the Southern Hemisphere with a maximum at 608S. A particularly interesting feature, shown here for the first time in a long coupled global warming simulation, is the eventual disappearance of tropical uppertropospheric easterlies and the creation of an equatorial superrotational state. The causes for this phenomenon remain to be investigated. A detailed analysis of the zonal mean angular momentum budget for the 1 3 CO 2 and 3 3 CO 2 regimes may shed some light on this issue. This requires calculations of the surface torques and the momentum transport by transient/stationary eddies and

the Hadley circulation [in the context of El Ninõ, Oort and Yienger (1996) showed an enhancement of the Hadley cell with an increased SST]. We hope to acquire more model data to complete this analysis. Short-term climate variations such as El Ninõ and Madden–Julian oscillation have conventionally been investigated as ‘‘anomalies’’ that evolve around a fixed (or seasonally recurring) mean climate state. Recently, there is an emerging thought that events like El Ninõ and MJO actually leave a residual contribution to the maintenance of the mean climate state (Lee 1999; Sun 2000). Lee (1999) showed that the transient eddy momentum flux associated with intraseasonal and interannual variability contributes to a net or rectified acceleration of upper-level zonal mean zonal wind in the Tropics. Lee (1999) speculated that with an increasing strength of the MJO and/or El Ninõ, an equatorial superrotational state may become possible for the earth’s general circulation. Since the MJO is closely related to organized tropical convection in the Indian and west Pacific Oceans (e.g., Knutson and Weickmann 1987; Madden and Julian 1994), and since the SST over these regions increases significantly under global warming (Fig. 6c), Lee’s hypothesis is worth investigating as an explanation for the formation of a superrotational state in the CCCma coupled simulations. The monthly mean model data used in this study did not provide sufficient temporal resolution to analyze the change of transient eddy momentum flux associated with a possible change of MJO activity. We therefore leave this particular problem to a follow-up study, in which the change of momentum fluxes on the intraseasonal and interannual timescales in the coupled simulations will be analyzed using the daily model outputs. Acknowledgments. We thank the CCCma climate modeling team and Dr. Francis Zwiers for their generous offers of the coupled model data used in this study. The comments of Dr. Rick Rosen and three anonymous reviewers helped to improve the manuscript. REFERENCES Abarca del Rio, R., 1999: The influence of global warming in Earth rotation speed. Ann. Geophys., 17, 806–811. , D. Gambis, and D. A. Salstein, 2000: Interannual signals in length of day and atmospheric angular momentum. Ann. Geophys., 18, 347–364. Anderson, J. R., and R. D. Rosen, 1983: The latitude-height structure of 40–50 day variations in atmospheric angular momentum. J. Atmos. Sci., 40, 1584–1591. Barnes, R. T. H., R. Hide, A. A. White, and C. A. Wilson, 1983: Atmospheric angular momentum fluctuations, length-of-day changes and polar motion. Proc. Roy. Soc. London, 387A, 31– 73. Bjerknes, J., 1966: A possible response of the atmospheric Hadley circulation to equatorial anomalies of ocean temperature. Tellus, 18, 820–829. Boer, G. J., G. Flato, and D. Ramsden, 2000a: A transient climate change simulation with greenhouse gas and aerosol forcing: Projected climate for the 21st century. Climate Dyn., 16, 427–450.

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