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    Relative angular momentum in the CMIP2 control runs (horizontal axis) and the changes in this at the doubling of CO2 (vertical axis). Individual models are labeled as in Table 1 and the closed circle shows the 16-model mean. The dashed vertical line indicates the value obtained from the ECMWF reanalysis for 1979–93. Note the difference in scale between the horizontal and vertical axis

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    The changes in tropical (13°S–13°N) SST (horizontal axis) and global relative angular momentum MR (vertical axis) in the CMIP2 experiments. Individual models are labeled as in Table 1 and the closed circle shows the 16-model mean. The dashed lines indicate the ratio between the MR and SST changes, with numeric values on the left in 1024 kg m2 s–1 °C–1

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    (a) The 16-model mean zonal mean zonal wind (u) in the control simulations (contours every 5 m s–1; negative values shaded). (b) The 16-model mean change in u at the doubling of CO2 (contours at every 0.5 m s–1). (c) The ratio between the 16-model mean change and the model-to-model std dev (contours and shading at −2, −1, 1, 2, and 3)

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    Contributions of different latitude zones and atmospheric layers to the 16-model mean change in relative angular momentum [unit = 1024 kg m2 s–1 (1° lat)–1]. Solid line = the whole vertical column from 0 to 1000 hPa; dashed line = the layer 0–200 hPa; dotted line = the layer 200–1000 hPa

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    Contributions of different latitude zones (a),(c) to the 16-model means of control run relative angular momentum, and (b),(d) to the greenhouse run minus control run changes. (a),(b) MR and ΔMR (solid line) divided with Eq. (3) to the contributions of the surface wind (dashed) and the baroclinic wind (dotted). (c),(d) As in (a) and (b), but using the geostrophic assumption (see text)

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    (a) Changes in 16-model mean zonal mean virtual temperature at the doubling of CO2 (contours at every 1 K, negative values shaded). (b) The meridional gradient in the 16-model mean virtual temperature change (unit = 10–6 K m–1, contours at every 0.25 units). (c) As in (b), but multiplied by −cos2φ/sinφ to illustrate the effect on the angular momentum change. (d) The ratio between the 16-model mean change and the model-to-model std dev of the field shown in (c) (contours and shading at −2, −1, 1, 2, and 3). The thick dashed line indicates the approximate thermal tropopause (see text)

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CO2-Induced Changes in Atmospheric Angular Momentum in CMIP2 Experiments

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  • 1 Rossby Centre, Swedish Meteorological and Hydrological Institute, Norrkoping, Sweden
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Abstract

The response of atmospheric angular momentum to a gradual doubling of CO2 is studied using 16 model experiments participating in the second phase of the Coupled Model Intercomparison Project (CMIP2). The relative angular momentum associated with atmospheric zonal winds increases in all but one of the models, although the magnitude of the change varies widely. About 90% of the 16-model mean increase comes from increasing westerly winds in the stratosphere and the uppermost low-latitude troposphere above 200 hPa. This increase in westerly winds reflects a steepening of the meridional temperature gradient near the tropopause and in the upper troposphere. The simulated temperature gradient at this height increases partly as an indirect consequence of the poleward decrease in the tropopause height, and partly because convection induces a maximum in warming in the tropical upper troposphere. The change in the omega angular momentum associated with the surface pressure distribution is in most models smaller than the change in the relative angular momentum, although its exact value is sensitive to the method of calculation.

Corresponding author address: Dr. Jouni Räisänen, Department of Physical Sciences, Division of Atmospheric Sciences, P.O. Box 64, FIN-00014, University of Helsinki, Finland. Email: jouni.raisanen@helsinki.fi

Abstract

The response of atmospheric angular momentum to a gradual doubling of CO2 is studied using 16 model experiments participating in the second phase of the Coupled Model Intercomparison Project (CMIP2). The relative angular momentum associated with atmospheric zonal winds increases in all but one of the models, although the magnitude of the change varies widely. About 90% of the 16-model mean increase comes from increasing westerly winds in the stratosphere and the uppermost low-latitude troposphere above 200 hPa. This increase in westerly winds reflects a steepening of the meridional temperature gradient near the tropopause and in the upper troposphere. The simulated temperature gradient at this height increases partly as an indirect consequence of the poleward decrease in the tropopause height, and partly because convection induces a maximum in warming in the tropical upper troposphere. The change in the omega angular momentum associated with the surface pressure distribution is in most models smaller than the change in the relative angular momentum, although its exact value is sensitive to the method of calculation.

Corresponding author address: Dr. Jouni Räisänen, Department of Physical Sciences, Division of Atmospheric Sciences, P.O. Box 64, FIN-00014, University of Helsinki, Finland. Email: jouni.raisanen@helsinki.fi

1. Introduction

In studies of model-projected future anthropogenic climate change, most of the attention has been directed, for obvious reasons, to surface quantities such as temperature and precipitation (Cubasch et al. 2001). However, changes in climate are also expected to occur in the free atmosphere. One aspect of atmospheric climate changes that has recently received increased interest is the change in the atmospheric angular momentum (AAM). In addition to issues related to atmospheric dynamics, this interest has been fed by the fact that AAM affects the rotation rate of the earth and hence the length of day (LOD). Variations in AAM are known to explain much of the LOD variations on intraseasonal to interannual timescales, on which the total angular momentum of the atmosphere and the solid earth is approximately conserved (Peixoto and Oort 1992). Greenhouse-induced changes in AAM might likewise make a measurable contribution to long-term LOD trends in the future, although, on decadal and centennial timescales, other geophysical and astronomical effects are also important (e.g., de Viron et al. 2002).

Model-simulated greenhouse gas–induced changes in AAM were first studied by Rosen and Gutowski (1992, hereafter RG92). They analyzed the equilibrium response of three atmospheric general circulation models (GCMs) to a doubling of CO2, focusing on the relative angular momentum associated with atmospheric zonal winds. The results generally suggested a decrease in angular momentum, although in one of the models increases in stratospheric westerlies reversed this to a slight increase in the boreal winter. The decrease in AAM is, however, not supported by more recent experiments made with coupled atmosphere–ocean GCMs (AOGCMs). Huang et al. (2001, hereafter HWH01) found a significant increase in AAM in an ensemble of three transient greenhouse gas plus aerosol climate change simulations made with the Canadian Centre for Climate Modelling and Analysis model. Most of the change resulted from an increase in the relative angular momentum, that is, increasing westerly winds, with changes in the surface pressure distribution making a smaller positive contribution. Using the database collected for the second phase of the Coupled Model Intercomparison Project (CMIP2; Meehl et al. 2000), de Viron et al. (2002, hereafter dV02) showed that similar results are obtained from other current AOGCMs. In particular, the relative AAM increased in 13 of the 14 models included in their study.

The present study also uses the CMIP2 dataset, aiming to provide more meteorological insight to the CO2-induced changes in AAM in these experiments than was given in the brief report of dV02. After describing the dataset and some of the computational aspects in section 2, the changes in the relative angular momentum and zonal winds are discussed in section 3. Specifically, it is found that the general increase in relative angular momentum mainly results from increases in stratospheric westerlies above the 200-hPa level. The next section uses the thermal wind relationship to investigate the connection of the wind and AAM changes to the distribution of temperature changes. This analysis suggests that much of the increase in stratospheric westerlies results indirectly from the poleward decrease in the tropopause height. Section 5 compares the CMIP2 results with RG92, and discusses the possible causes of the qualitatively different results (increase vs decrease in relative angular momentum). The changes in the “omega” angular momentum associated with changing surface pressure are studied in section 6, and the conclusions follow in section 7.

2. The CMIP2 dataset and calculation of relative angular momentum

Each CMIP2 experiment consists of a control run with constant (“present day”) atmospheric CO2 and of a greenhouse run with a standard gradual (1% yr–1 compound) increase in CO2. We use the set of 16 models (Table 1) that provides 80-yr-long control and greenhouse runs with output including the pressure–latitude distribution of atmospheric winds. Climate changes are here evaluated for the 20-yr period (years 61–80) centered at the doubling of CO2 in the greenhouse runs, by comparing the greenhouse run means during this period with the control run means during the same period. This definition of climate changes helps to minimize the problems associated with control run climate drift in some of the models (see Räisänen 2001). The global mean surface air warming at the doubling of CO2 varies between 1.3° and 2.1°C in these experiments. The recent assessment of the Intergovernmental Panel on Climate Change (Cubasch et al. 2001) includes two models with global temperature change outside this range (MRI2, 1.1°C; and CCSR2, 3.1°C) but the data needed for the present calculations were not available for these.

The axial component of the atmospheric angular momentum is the sum of the relative angular momentum (MR) and the omega angular momentum (MΩ). Neglecting the height of the atmosphere and the small latitude variation in the acceleration of gravity (g) and the radius of the earth (a), these have the expressions (e.g., Peixoto and Oort 1992)
i1520-0442-16-1-132-e1
where u is the zonal wind velocity, Ω the rotation rate of the earth, φ latitude, λ longitude, p pressure, and ps surface pressure.

Most of this paper focuses on the relative angular momentum. As the CMIP2 dataset excludes ps for most models and the wind data are only included as zonal means, MR is estimated by approximating ps with a constant (p0 = 1000 hPa). The errors caused by this approximation are likely to be small, because winds tend to be weak near the surface. The CMIP2 atmospheric data are provided at a model-dependent vertical and meridional resolution. For the present comparison, they were interpolated to a common grid with 10-hPa vertical and 2.5° meridional resolution. In the vertical interpolation, a linear variation with the logarithm of pressure between the original (depending on the model, 9–21) levels was assumed. Above the highest level (varying in different models between 1 and 50 hPa with a mean of 17 hPa), u was assumed to be constant with height.

Estimating the change in MΩ with the CMIP2 data involves some caveats. The surface pressure ps is only available for a few of the models (through an extension of CMIP2 known as CMIP2+; http://www-pcmdi.llnl.gov/cmip/cmip2plusann.html), while for the others, the only source of pressure information is the sea level pressure. In addition, the models show inconsistencies in the conservation of the total atmospheric mass, especially in the treatment of the effect of increasing water vapor. These aspects will be discussed in more detail in section 6.

3. Changes in relative angular momentum at the doubling of CO2

The atmospheric relative angular momentum varies substantially among the CMIP2 models, both regarding the values in the control run and the changes induced by increasing CO2 (Fig. 1). The range in the control run MR is from 94 × 1024 kg m2 s–1 (IAP/LASG) to 193 × 1024 kg m2 s–1 (GISS), with 12 of the 16 models being somewhat above the value 149 × 1024 kg m2 s–1 inferred from the ECMWF reanalysis for 1979–93 (Gibson et al. 1997). The change at the doubling of CO2 varies from −0.8 × 1024 kg m2 s–1 in IAP/LASG to 19.2 × 1024 kg m2 s–1 in HadCM2. However, in accord with the findings of dV02, MR increases in all but one of the models. There is little correlation between the control run MR and the simulated CO2-induced changes, even though the IAP/LASG model with a CO2-induced decrease in MR is also well below the others in control run MR. Like all aspects of climate change, the changes in MR and the model-to-model differences therein are to some extent affected by internal variability (“noise”) in the simulations. However, the method used in Räisänen (2001) suggests that this factor only explains about 20% of the intermodel variance in the MR change, which implies that most of this variance arises directly from model differences.

In the experiment analyzed by HWH01, there was an apparent linear relationship between the changes in AAM and tropical sea surface temperature (SST) averaged over the zone 13°S–13°N. For a 1°C increase in SST, the sum of MR and MΩ increased by 9 × 1024 kg m2 s–1, and MR alone by about 8.7 × 1024 kg m2 s–1 (their Table 1). These authors also suggested using this ratio as a diagnostic tool in model intercomparisons. This is done for the CMIP2 simulations in Fig. 2, which shows that the ratio varies widely between the individual models but is in most of them lower than found by HWH01. The 16-model mean changes in MR (7.2 × 1024 kg m2 s–1) and SST (1.47°C) give a ratio of 4.9 × 1024 kg m2 s–1 °C–1.

The changes in tropical SST and MR seem unrelated, with only a very weak positive correlation (r = 0.23) between the intermodel variations in them. This might seem surprising since, as far as tropical convection is one of the key processes affecting the MR changes (which is hinted by the results in the next section), one would in fact expect the SST changes to play a role. However, the absolute increase in tropical SST might not be the most relevant quantity, since temperature changes outside the Tropics also vary widely between the models. For comparison, we also correlated the changes in MR and tropical SST after dividing both with the model-dependent increase in global mean temperature (this gives a rough indication of how the warming in the Tropics compares with the overall response of the model). In this case, a slightly higher (r = 0.47) although still relatively modest correlation was found.

A 1024 kg m2 s–1 increase in AAM would increase the LOD by 1.68 × 10–5 s, assuming that the combined angular momentum of the atmosphere and the solid earth is not changed by variations in oceanic angular momentum (Peixoto and Oort 1992). If acting alone, the 16-model mean increase in MR (7.2 × 1024 kg m2 s–1) would thus increase the LOD by 1.2 × 10–4 s, or by 1.7 × 10–6 s yr–1 if the change takes place in 70 yr. This agrees closely with the trend estimate of dV02 for their set of 14 models. Such a long-term LOD trend is relatively small compared with the trends expected from other astronomical and geophysical factors (Table 2 of dV02), but not completely negligible.

The changes in MR reflect changes in the zonal wind component u. A latitude–pressure plot of the 16-model zonal mean changes in u is shown in Fig. 3b (the corresponding control run mean is given in Fig. 3a). The largest increase occurs in the midlatitude stratosphere, especially in the Southern Hemisphere, where the change reaches 3–4 m s–1. In the higher midlatitudes, the increase extends throughout the troposphere down to the surface, but it is weaker in the Northern than in the Southern Hemisphere. Small decreases in u dominate in most of the lower and midtroposphere from the Tropics to lower midlatitudes and in polar regions.

The relative agreement between the different models in indicated in Fig. 3c by the ratio between the 16-model mean change in u and the model-to-model standard deviation. As a guideline of interpretation, a ratio of 1 or −1 typically indicates that 13 or 14 of the 16 models have the same sign of change, whereas a ratio exceeding 2 in absolute value usually signifies a complete agreement on the sign of the change. The increase in u in both the Northern and the Southern Hemisphere midlatitude stratosphere is quite robust, with a ratio of 2–3. The tropospheric increase around 55°S has a mean-to-standard-deviation ratio slightly below 2, but even in this region at least a small increase occurs in all 16 models. The agreement on the changes in the other parts of the latitude–pressure plane is lower, except for a decrease in u in the lower troposphere near 30°S. The pattern in the Southern Hemisphere midlatitude troposphere, with increasing u in higher and (although below 500 hPa only) decreasing u in lower midlatitudes, indicates that the change projects positively onto the so-called Southern Hemisphere Annual Mode (or Antarctic Oscillation). This feature and issues related to its physical interpretation have been discussed earlier by Kushner et al. (2001), among others.

For MR, low-latitude winds are relatively more important than winds in high latitudes, because the distance from the earth’s rotation axis and the area represented by a constant-width latitude zone are both proportional to the cosine of latitude. The vertically integrated contributions of different latitude zones to the 16-model mean change in MR are shown in Fig. 4. In addition to the whole vertical column, the contributions of the layers 0–200 hPa and 200–1000 hPa are given separately. The upper layer, which includes the stratosphere and the uppermost tropical troposphere, makes a uniformly positive contribution, with maxima at 30°S and 30°N. The tropospheric contribution from 200 to 1000 hPa is of variable sign and generally smaller, excluding the pronounced maximum at 50°–55°S. The dominance of the upper layer makes the 0–1000-hPa vertical integral positive at almost all latitudes.

As shown in the top three rows of Table 2, only 10% of the global 16-model mean increase in MR (0.7 × 1024 kg m2 s–1 of 7.2 × 1024 kg m2 s–1) comes from altitudes below the 200-hPa level. This contrasts with the control simulations, in which 70% of MR resides below this level. The middle and lower troposphere from 400 to 1000 hPa in fact make a slightly negative contribution to the change (−0.3 × 1024 kg m2 s–1). Due to differences in both the stratosphere and the troposphere, wind changes in the Southern Hemisphere have a three times larger net effect on the average global MR increase than those in the Northern Hemisphere (5.4 vs 1.8 × 1024 kg m2 s–1).

The importance of the stratospheric wind changes for the change in MR immediately raises the issue of whether the vertical resolution of current climate models is adequate for addressing climate changes in this part of the atmosphere. A rigorous answer would require comparison with models with (much) better vertical resolution, but the CMIP2 results themselves suggest that this is not the dominant uncertainty. The vertical resolution of the CMIP2 models varies substantially, in particular above 200 hPa, where eight of the 16 models have only 2–4 levels and the other eight 6–9. Comparison between these two groups reveals, on the average, a slightly larger increase in both the tropospheric and the stratospheric MR in models with high stratospheric resolution, but the difference is small compared with the within-group variability.

4. Connection between the changes in relative angular momentum and temperature

The relative angular momentum MR can be divided into a surface contribution MRs (which is here calculated by approximating ps with 1000 hPa) and a baroclinic contribution MRb:
MRMRsMRb
where the two components
i1520-0442-16-1-132-e4
are obtained by rewriting in (1) u as u(ps) + [uu(ps)]. The physical motivation for making the division in this way, rather than by replacing u(ps) with the wind at some upper level, relates to the fact that the exchange of angular momentum between the atmosphere and the solid earth takes place at the surface. As discussed in the following, this tends to restrict MRs and the CO2-induced changes in this to relatively small values. The division (3) is therefore dominated by MRb, the changes of which are closely related to the distribution of temperature changes.

The fourth and fifth rows in Table 2 show the 16-model mean and the model-to-model standard deviation in the two components of (3), both for the control runs and the greenhouse run minus control run climate changes. It is clear that MRb is the dominating part of the division. The 16-model means of the control run MRs and the change ΔMRs are both slightly negative, in contrast with large positive values of MRb and ΔMRb. The intermodel differences in MR and ΔMR are also mostly due to the baroclinic term.

The relative smallness of MRs and ΔMRs is only partly explained by the fact that winds are weaker near the surface than higher up in the atmosphere. While MRb and ΔMRb are positive at almost all latitudes, there is with both MRs and ΔMRs a substantial cancellation between positive and negative values in different latitude zones (Figs. 5a,b). This is as expected from the requirements of the global angular momentum balance. The time tendency of atmospheric angular momentum can be written as (Madden and Speth 1995)
i1520-0442-16-1-132-e6
where TF is the friction torque and TM the mountain torque. Observational studies (e.g., Swinbank 1985; Madden and Speth 1995; Huang et al. 1999) indicate that the two torques tend to act in the same sense. They both generally make the atmosphere lose (gain) angular momentum where the surface zonal wind, and thus the integrand of (4), is positive (negative). Thus, if the surface zonal wind had the same sign in all latitude zones, this would most likely lead to a large rate of change of M. In the long-term means considered here, however, the actual time tendency of M must be very small, notwithstanding the slow CO2-induced trends in the greenhouse runs. This prevents the surface zonal wind (and changes in this between different model runs) to be uniformly westerly or easterly. For the baroclinic part of the wind field, no such constraint exists.
Apart from the immediate vicinity of the surface and the equator, the time-mean atmospheric flow is close to geostrophic balance. For such a flow, (3) is replaced with
MR(G)MRs(G)MRb(G)
where (G) indicates that u is replaced with its geostophic value, uG. The latter component of this division can be rewritten by using the thermal wind relationship. The geostrophic wind at level p is determined by the geostrophic wind at the surface and the distribution of virtual temperature Tυ (Rogers and Yau 1989, p. 17) via
i1520-0442-16-1-132-e8
where Rd = 287 J kg–1 K–1 is the gas constant of dry air. A partial integration of this over the whole atmospheric column yields, by noting that [uG(p) − uG(ps)]p is zero at both the upper and the lower boundaries
i1520-0442-16-1-132-e9
so that
i1520-0442-16-1-132-e10
The result (10) implies that, when the winds are near geostrophic balance, a poleward decrease in virtual temperature is accompanied by positive (baroclinic component of) relative angular momentum. However, since cos2φ increases and the absolute value of the Coriolis parameter 2Ω sinφ decreases toward the equator, a given virtual temperature gradient is much more influential in low than in high latitudes.

Here, MRb(G) is evaluated by using the zonal means of atmospheric temperature and absolute humidity in the CMIP2 dataset. The surface geostrophic wind needed for MRs(G) is estimated from sea level pressure and virtual temperature at 1000 hPa. The integrands at the equator, where the Coriolis parameter is zero, are interpolated linearly from the values at 2.5°S and 2.5°N.

The resulting global 16-model mean values and latitude distributions of control run MR(G) agree quite well with MR (compare the solid lines is Figs. 5a and 5c, and the values in the first and last row in Table 2). The agreement for the greenhouse run minus control run climate changes is somewhat worse, ΔMR(G) being generally slightly more positive than ΔMR especially in low latitudes (Figs. 5b,d and Table 2). The extent to which the disagreement reflects computational errors and true ageostrophy of the simulated wind changes, respectively, is not easily resolved (height fields are not included in the CMIP2 dataset). The gross features of the meridional distributions of ΔMR and ΔMR(G) are nevertheless quite similar.

The division between the surface contribution and the baroclinic contribution is also reasonably similar between (3) and (7). The geostrophic assumption tends to exaggerate the magnitude of the 1000-hPa wind, which makes MRs(G) and the changes in this somewhat larger than MRs, especially at low latitudes. However, the conclusion that the increase in global MR results essentially from changes in the baroclinic part of the wind field remains unchallenged even when basing the division on the geostrophic assumption.

Sixteen-model means of the simulated change in virtual temperature are shown in Fig. 6a. The humidity correction has a nonnegligible effect in the lower troposphere in the Tropics, where ΔTυ exceeds ΔT by 0.2–0.3 K, but the difference decreases poleward and is even in low latitudes well below 0.1 K above 500 hPa. The basic features of ΔTυ are therefore familiar from earlier studies of temperature change. In the lower troposphere, there is a maximum in warming in high northern latitudes and a minimum over the Southern Ocean near 60°S. In the upper troposphere, the strongest warming occurs in the Tropics. In the lower stratosphere, the warming turns into a cooling that increases upward. To facilitate further discussion, Fig. 6a also includes the thermal tropopause identified from the 16-model mean control run temperatures as the level where the vertical lapse rate of temperature falls below 2 K km–1 (WMO 1957). The inferred tropopause is close to 100 hPa in the Tropics and at 200–250 hPa in polar regions, with the steepest meridional gradients at 30–40°S/N. These features agree with observations (Hoinka 1998), except that the observed time-mean tropopause in high latitudes is lower, at 270–300 hPa. The limited vertical resolution of the models makes them unable to capture the true sharpness of the instantaneous tropopause, but it is not clear if this is important for the multimodel time-mean results.

The meridional gradient of the 16-model mean virtual temperature change (∂ΔTυ/∂y = a–1∂ΔTυ/∂φ) is shown in Fig. 6b, and in Fig. 6c the gradient is multiplied by the factor −cos2φ/sinφ. Comparing with (10), the latter representation allows a look at how much the changes in the Tυ gradient in the different parts of the latitude–pressure plane contribute to the change in MRb(G) (a unit change of 10–6 K m–1 in the whole vertical plane would yield ΔMRb(G) ≈ 103 × 1024 kg m2 s–1). It is obvious from Fig. 6c that the major positive contribution comes from the Tropics, subtropics, and lower midlatitudes, from near the tropopause level and the uppermost troposphere. In fact, the change in the Tυ gradient in the region (50°S–50°N, 100–400 hPa) alone yields ΔMRb(G) = 8.0 × 1024 kg m2 s–1, which coincides closely with the actual values of ΔMRb(G), ΔMRb, and ΔMR in Table 2. Thus, one may argue that the 16-model mean increase in global relative angular momentum is essentially due to the equatorward increase in warming in this region (the humidity contribution to ΔTυ above 400 hPa is negligible). Furthermore, this increase in the upper-tropospheric-tropopause level pole-to-equator temperature gradient is quite robust to model differences. It is present in all 16 models, and in midlatitudes the ratio between the mean change and the model-to-model standard deviation exceeds two (Fig. 6d).

Why does the upper-level meridional temperature gradient increase in the models? A probable key factor is the decrease in tropopause height from the subtropics to high latitudes. The efficient vertical mixing that mediates the radiative heating due to increased CO2 and water vapor from near the surface to the bulk of the troposphere, extends higher up in low than in high latitudes. Conversely, the temperature decrease in the stratosphere, which is only weakly connected with the surface–troposphere system and where increasing CO2 leads to radiative cooling, extends lower in the polar regions (changes in planetary wave propagation might also affect the temperature response in polar stratospheres but are unlikely to be the primary cause of the cooling). Near the tropopause, this leads to an equatorward gradient in the temperature change (Shindell et al. 2001). In Fig. 6b, the largest simulated increase in the Tυ gradient coincides, in both latitude and pressure, with the steepest gradient in the tropopause height.

The high low-latitude tropopause is ultimately maintained by deep tropical convection. Convection also has another, more direct effect, which helps to explain why the simulated equatorward increase in ΔTυ extends well below the time-mean tropopause, especially in the subtropics. It tends to keep the tropical temperature profile near moist adiabatic. With increasing surface temperature, the moist adiabatic lapse rate decreases, which leads to an upward increase in the simulated warming. In the midlatitudes, where the temperature profile is less tightly controlled by moist thermodynamics, the upward increase in warming is weaker or absent. The expected net effect of this is a maximum of warming in the tropical upper troposphere, as seen in Fig. 6a.

5. Comparison with RG92

The increase in MR found in almost all the CMIP2 experiments differs markedly from the results of RG92. They studied the changes in MR in three atmospheric GCMs coupled to a slab ocean model and run to equilibrium with doubled atmospheric CO2. The changes in MR for the whole atmosphere were approximately −3, 1, and −18 × 1024 kg m2 s–1 in the GFDL, GISS, and NCAR models, respectively. These values are all more negative than the changes in MR in the GFDL, GISS, and NCAR models in the present study (see Table 3), despite the fact that all these models simulate a MR increase somewhat below the 16-model mean. The interpretation of these differences is complicated, because the model versions used by RG92 differ from those used here. In particular, the huge differences in the NCAR results probably mainly reflect the substantial improvements made to this model since the study of RG92. However, this might not be the case for the GFDL and GISS models, whose atmospheric components have been changed less extensively. The different nature of the experiments may also play a role. The CMIP2 models simulate the transient climate response to increasing CO2, whereas the models used by RG92 simulated the equilibrium response to doubled CO2. Because of the thermal inertia of the oceans, the warming in the transient experiments is smaller and its geographical patterns are partly different from those in equilibrium experiments. The differences in temperature change may, in turn, affect the wind changes.

Comparing the present GFDL and GISS results with those of RG92, both sets of simulations show similar increases in stratospheric MR. The difference mainly arises from the troposphere below 200 hPa, where the experiments used by RG92 indicate larger decreases in MR than the corresponding CMIP2 simulations (Table 3). A detailed comparison between the wind changes in the two cases is difficult, since RG92 only show seasonal results whereas the CMIP2 data are available as annual means. However, one of the main differences appears to occur in the Southern Hemisphere higher midlatitudes. The increase in tropospheric westerlies in this region, which is prominent in the CMIP2 simulations, is either diffuse (GISS) or reversed to an increase in easterlies (GFDL) in the experiments of RG92. This difference is probably related to the large heat capacity of the Southern Ocean, which greatly retards the warming in this area in transient experiments compared with equilibrium experiments (e.g., Manabe et al. 1991), in part via a much smaller reduction in sea ice. This leads to very different changes in atmospheric baroclinicity in the two cases. The possibility that the equilibrium response of the Southern Hemisphere atmospheric circulation to elevated CO2 may differ substantially from the transient response was also recently demonstrated by Stone et al. (2001).

6. Changes in omega angular momentum

Estimating the changes in MΩ from the CMIP2 data involves some caveats. As shown by the values given in Table 4, the results depend on the details of the calculation. In agreement with earlier studies, however, all the methods indicate that the change in MΩ is in most models smaller than that in MR.

The surface pressure ps required by (2) is excluded from the basic CMIP2 dataset and for this study is available for only HadCM2, HadCM3, and NCAR-CSM. The changes in MΩ in these three models, calculated by a direct substitution of Δps to (2), are slightly positive, from 0.9 to 2.8 × 1024 kg m2 s–1 (first row of Table 4).

Sea level pressure (psea) is available for all the CMIP2 models. Substituting the change in this instead of ps to (2) yields the results given in the second row of Table 4. This calculation suggests a very slight 16-model mean decrease in MΩ. However, comparing the results for those three models for which ps is also available, the use of psea instead of ps makes the estimated ΔMΩ more negative by 1–2 × 1024 kg m2 s–1. The explanation is relatively simple. Over the continents, psea is derived from ps with the hydrostatic relationship, using an extrapolated temperature profile below the ground (the details of this calculation are model-dependent). In a warmer climate, the extrapolated temperatures increase, which implies smaller air density and hence a smaller pressure increment between the actual surface and the sea level. The changes in psea over the continents are therefore systematically more negative than those in ps.

To get a first-order estimate of Δps in all 16 models, the approximation
i1520-0442-16-1-132-e11
was used, where T(2m) is the surface air temperature. The term (pseaps)0 approximates the control run sea level minus surface pressure difference, which was unavailable for most models but depends mainly on the surface height and should therefore not be overly model-dependent. In practice, this term was averaged over the three models with ps available and the same value was used for all 16 models. The approximation (11) follows from a linearization of the hydrostatic relationship, which indicates that the pressure increment in a given height interval is inversely proportional to temperature. When substituted to (2), the Δps estimates from (11) reproduce the original ΔMΩ for HadCM2, HadCM3, and NCAR-CSM with an error of at most 0.2 × 1024 kg m2 s–1 (third row of Table 2). The 16-model mean change increases to 1.5 × 1024 kg m2 s–1.

Another caveat concerns changes in the total mass of the atmosphere. With increasing temperature, the simulated amount of water vapor in the atmosphere increases. With no change in the mass of dry air, this should lead to an increase in the atmospheric mass, and hence in the global mean surface pressure. However, the CMIP2 results suggest that this mechanism works in only a few of the models (water vapor increases even in the others, but this has apparently no effect on the global mean surface pressure). In addition, a few models seem to lose or gain mass for purely numerical reasons. As a result, the global mean changes in psea and the inferred ps [from (11)] vary widely between the models, the former from −0.56 to 0.31 hPa (with a mean of −0.16 hPa) and the latter from −0.32 to 0.52 hPa (with a mean of 0.07 hPa). This variation is not negligible. A 0.1-hPa change in ps over the whole earth affects MΩ by 1.0 × 1024 kg m2 s–1.

To filter out the impact of the global mass changes, another estimate of ΔMΩ was derived by subtracting, in each grid box, the global change in ps from the local change (fourth row of Table 4). These values, which reflect changes in the latitude distribution of mass only, show a somewhat smaller 16-model mean increase (0.8 × 1024 kg m2 s–1) and substantially smaller scatter than the previous estimate. However, they neglect the global mass increase associated with increasing water vapor. The latter amounts, on the average, to about 3 kg m–2, which implies a 0.3-hPa increase in the global mean ps. Adding this effect to the estimate shown in the fourth row of Table 4 raises the 16-model mean change in ΔMΩ to 4.0 × 1024 kg m2 s–1 (fifth row), assuming that the change in the total mass does not affect the geographical distribution of the pressure changes.

Considering the change in ΔMΩ alone, the last estimate in Table 4 is the most plausible, since it includes the impact of increasing water vapor but excludes other, artificial mass changes. On the other hand, an increase in atmospheric water vapor implies a decrease in the total water mass of the oceans, the terrestrial hydrosphere, and the cryosphere, at almost the same distance from the center of the earth. Its net impact on LOD is therefore expected to be small.

The results in the last two rows of Table 4 contrast with dV02, who found the combined omega angular momentum of the atmosphere and the ocean to decrease in most CMIP2 models, compensating on the average a third of the increase in MR. The difference probably relates partly to their inclusion of the ocean contribution, and partly to different ways of estimating the surface pressure change.

7. Conclusions

Simulated CO2-induced changes in atmospheric zonal winds and relative (MR) and omega (MΩ) atmospheric angular momentum (AAM) have been compared between 16 coupled atmosphere–ocean GCMs participating in the CMIP2 intercomparison (Meehl et al. 2000). Some of the issues discussed in this paper have been studied before, in particular by dV02, who recently calculated the changes in MR for largely the same set of climate change simulations. However, the meteorology underlying the simulated changes in angular momentum has been investigated here more in depth than was done in the previous studies. The main findings follow.

  1. At the doubling of CO2, which takes 70 yr in the idealized CMIP2 experiments, all but one of the 16 models indicate an increase in MR, although the magnitude of the change varies widely between different models. The 16-model mean change is 7.2 × 1024 kg m2 s–1.
  2. About 90% of the 16-model mean increase in MR results from an increase in westerly winds in the stratosphere and in the uppermost low-latitude troposphere, above 200 hPa. This increase is quite robust to model differences, particularly in midlatitudes, and it is (like the changes in baroclinicity) somewhat stronger in the Southern than in the Northern Hemisphere. The troposphere below 200 hPa only makes a 10% contribution to the average global increase in MR. A substantial and reasonably model-independent increase in westerly winds in the mid- and lower troposphere only takes place in the higher southern midlatitudes, where the wind response is likely related to the increase in baroclinicity associated with the slow warming over the Southern Ocean.
  3. The increase in westerly winds near the tropopause and in the stratosphere is related to an increase in the pole-to-equator temperature gradient near the tropopause and in the upper troposphere. The temperature gradient at this height steepens in part as an indirect consequence of the poleward decrease in the tropopause height, in part as a result of the simulated maximum of CO2-induced warming in the upper-tropical troposphere. These two mechanisms are intertwined by their more or less direct links to tropical convection.
  4. The increase in MR in almost all the CMIP2 simulations contrasts with the findings of RG92, whose results for three atmospheric GCMs run to equilibrium with doubled CO2 rather suggested a decrease in MR. This probably reflects, in part, model improvements since RG92. However, genuine differences between the transient climate response to increasing CO2 and the equilibrium response also likely play a role, in particular in the Southern Hemisphere where the changes in atmospheric baroclinicity are very different in the two cases.
  5. The change in MΩ is in most models smaller than that in MR, but it is sensitive to the methods of calculation and to model inconsistencies related to the conservation of global atmospheric mass. Taking only into account the meridional distribution of surface pressure changes with no change in the global mean surface pressure yields an average increase of 0.8 × 1024 kg m2 s–1. Adding to this mass increase expected from increasing water vapor raises the estimate to 4.0 × 1024 kg m2 s–1.

Considering the implications of these results for the real world, two caveats should be recalled. One is the possibility of systematic model errors. The response of the real climate system to increasing CO2 is not necessarily near the mean of the model results, and in principle it might be outside the range indicated by them. Second, increasing CO2 is not the only forcing agent expected to affect climate in the present century, although, in terms of the surface temperature change, it is expected to be more important than other anthropogenic and natural factors (Houghton et al. 2001). However, it is not self-evident that the relative importance of different forcing agents will be the same even for temperature changes near the tropopause and in the upper troposphere, which in the light of the present results may have a large impact on the AAM changes. For example, looking in the past rather than to the future, Tett et al. (1996) demonstrated that the simulation of recent observed temperature changes in this part of the atmosphere is substantially improved when the simulations include ozone depletion in addition to increasing CO2.

Acknowledgments

All CMIP2 modeling groups are acknowledged for conducting and making available the simulations requested by the CMIP Panel. CMIP is supported and the model data are distributed by the Program for Climate Model Diagnosis and Intercomparison (PCMDI) at the Lawrence Livermore National Laboratory (LLNL). This research has been conducted within the Swedish SWECLIM programme financed by MISTRA and by SMHI. The constructive comments by Steven Feldstein and another reviewer helped to improve the original manuscript.

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Fig. 1.
Fig. 1.

Relative angular momentum in the CMIP2 control runs (horizontal axis) and the changes in this at the doubling of CO2 (vertical axis). Individual models are labeled as in Table 1 and the closed circle shows the 16-model mean. The dashed vertical line indicates the value obtained from the ECMWF reanalysis for 1979–93. Note the difference in scale between the horizontal and vertical axis

Citation: Journal of Climate 16, 1; 10.1175/1520-0442(2003)016<0132:CICIAA>2.0.CO;2

Fig. 2.
Fig. 2.

The changes in tropical (13°S–13°N) SST (horizontal axis) and global relative angular momentum MR (vertical axis) in the CMIP2 experiments. Individual models are labeled as in Table 1 and the closed circle shows the 16-model mean. The dashed lines indicate the ratio between the MR and SST changes, with numeric values on the left in 1024 kg m2 s–1 °C–1

Citation: Journal of Climate 16, 1; 10.1175/1520-0442(2003)016<0132:CICIAA>2.0.CO;2

Fig. 3.
Fig. 3.

(a) The 16-model mean zonal mean zonal wind (u) in the control simulations (contours every 5 m s–1; negative values shaded). (b) The 16-model mean change in u at the doubling of CO2 (contours at every 0.5 m s–1). (c) The ratio between the 16-model mean change and the model-to-model std dev (contours and shading at −2, −1, 1, 2, and 3)

Citation: Journal of Climate 16, 1; 10.1175/1520-0442(2003)016<0132:CICIAA>2.0.CO;2

Fig. 4.
Fig. 4.

Contributions of different latitude zones and atmospheric layers to the 16-model mean change in relative angular momentum [unit = 1024 kg m2 s–1 (1° lat)–1]. Solid line = the whole vertical column from 0 to 1000 hPa; dashed line = the layer 0–200 hPa; dotted line = the layer 200–1000 hPa

Citation: Journal of Climate 16, 1; 10.1175/1520-0442(2003)016<0132:CICIAA>2.0.CO;2

Fig. 5.
Fig. 5.

Contributions of different latitude zones (a),(c) to the 16-model means of control run relative angular momentum, and (b),(d) to the greenhouse run minus control run changes. (a),(b) MR and ΔMR (solid line) divided with Eq. (3) to the contributions of the surface wind (dashed) and the baroclinic wind (dotted). (c),(d) As in (a) and (b), but using the geostrophic assumption (see text)

Citation: Journal of Climate 16, 1; 10.1175/1520-0442(2003)016<0132:CICIAA>2.0.CO;2

Fig. 6.
Fig. 6.

(a) Changes in 16-model mean zonal mean virtual temperature at the doubling of CO2 (contours at every 1 K, negative values shaded). (b) The meridional gradient in the 16-model mean virtual temperature change (unit = 10–6 K m–1, contours at every 0.25 units). (c) As in (b), but multiplied by −cos2φ/sinφ to illustrate the effect on the angular momentum change. (d) The ratio between the 16-model mean change and the model-to-model std dev of the field shown in (c) (contours and shading at −2, −1, 1, 2, and 3). The thick dashed line indicates the approximate thermal tropopause (see text)

Citation: Journal of Climate 16, 1; 10.1175/1520-0442(2003)016<0132:CICIAA>2.0.CO;2

Table 1.

The 16 CMIP2 models included in this study. The first column gives the labels used in Fig. 1

Table 1.
Table 2.

Sixteen-model means and model-to-model std dev in the control run values (CTRL) and simulated CO2-induced changes (GHG − CTRL) of the relative angular momentum MR and various contributions to it. Unit is 1024 kg m2 s–1

Table 2.
Table 3.

Changes in relative angular momentum in the GFDL, GISS, and NCAR models in the present study (CMIP2) and in RG92. The RG92 values are estimated from their Fig. 1 and 2 by averaging the results for Dec–Jan–Feb and Jun–Jul–Aug. For CMIP2, the first NCAR value is for NCAR-CSM and the second for NCAR/DOE-PCM. Unit is 1024 kg m2 s–1

Table 3.
Table 4.

Changes in MΩ, using different estimates of the surface pressure change (see section 6 for the details of the methods). Columns 2 to 4 give the results for the three models with ps data available, and the last two columns give the 16-model mean change and the model-to-model std dev (not available for the first method). Unit is 1024 kg m2 s–1

Table 4.
Save