Abstract

The climatology and trend of atmospheric angular momentum from the phase 3 and the phase 5 Climate Model Intercomparison Project (CMIP3 and CMIP5, respectively) simulations are diagnosed and validated with the Twentieth Century Reanalysis (20CR). It is found that CMIP5 models produced a significantly smaller bias in the twentieth-century climatology of the relative MR and omega MΩ angular momentum compared to CMIP3. The CMIP5 models also produced a narrower ensemble spread of the climatology and trend of MR and MΩ. Both CMIP3 and CMIP5 simulations consistently produced a positive trend in MR and MΩ for the twentieth and twenty-first centuries. The trend for the twenty-first century is much greater, reflecting the role of greenhouse gas (GHG) forcing in inducing the trend. The simulated increase in MR for the twentieth century is consistent with reanalysis. Both CMIP3 and CMIP5 models produced a wide range of magnitudes of decadal and interdecadal variability of MR compared to 20CR. The ratio of the simulated standard deviation of decadal or interdecadal variability to its observed counterpart ranges from 0.5 to over 2.0 for individual models. Nevertheless, the bias is largely random and ensemble averaging brings the ratio to within 18% of the reanalysis for decadal and interdecadal variability for both CMIP3 and CMIP5. The twenty-first-century simulations from both CMIP3 and CMIP5 produced only a small trend in the amplitude of decadal or interdecadal variability, which is not statistically significant. Thus, while GHG forcing induces a significant increase in the climatological mean of angular momentum, it does not significantly affect its decadal-to-interdecadal variability in the twenty-first century.

1. Introduction

The long-term coupled model simulations archived by the Climate Model Intercomparison Project (CMIP) have served as an important basis for climate research and prediction. The two most recent phases of CMIP, phase 3 (CMIP3; Meehl et al. 2007) and phase 5 (CMIP5; Taylor et al. 2012), gathered the simulations of climate models that incorporated many key techniques unavailable to previous generations of models. For example, starting from CMIP3, the majority of the coupled models can produce a reliable long-term climatology without invoking a flux correction for air–sea interaction. The transition to CMIP5 saw the emergence of “earth system” models with dynamic treatments for the global biogeochemical cycle, among other processes.

The scope of the multimodel intercomparison has also continued to expand, with a notable new focus being the validation and intercomparison of decadal-to-interdecadal variability. It is now recognized that a correct representation of decadal-to-interdecadal variability in the model is important for climate projection in the near term (e.g., Meehl et al. 2009a), over which the trend induced by greenhouse gas forcing does not yet fully overwhelm internal variability. Thus, it is useful to combine the intercomparisons of the trend and decadal-to-interdecadal variability for major climate variables. The validation of decadal-to-interdecadal variability in climate model simulations has seen limited progress, partly because one can extract only a small number of degrees of freedom for decadal/interdecadal oscillations from the short observational record. The recent construction of the Twentieth Century Reanalysis (20CR) dataset (Compo et al. 2011) presented an opportunity to meaningfully validate the CMIP simulations of decadal-to-interdecadal variability. In a related work, by cross-validating multiple reanalysis datasets for the second half of the twentieth century, Paek and Huang (2012) affirmed the reliability of the decadal-to-interdecadal variability in 20CR using atmospheric angular momentum (AAM). This allows us to confidently adopt the longer record in 20CR for model validation. For completeness, we will also compare the centennial trend in the CMIP simulations with 20CR, but with the caution that [as pointed out by Paek and Huang (2012)] there is less agreement among the reanalysis datasets concerning the trend in the second half of the twentieth century.

Given this background, this study will perform intercomparisons on the centennial trend and decadal-to-interdecadal variability for CMIP3 and CMIP5 simulations and validate them using the 20CR. Specifically, we will focus on the globally integrated atmospheric angular momentum. The variation of AAM reflects the changes in the strength and location of large-scale zonal jets. On shorter time scales, AAM is a well-established index for El Niño–Southern Oscillation (e.g., Black et al. 1996; Huang et al. 2003) and Madden–Julian oscillation (e.g., Kang and Lau 1994; Weickmann et al. 1997). Relevant to this study, the total AAM has been found to increase under global warming in pre-CMIP3 simulations for the twenty-first century (Huang et al. 2001; de Viron et al. 2002; Räisänen 2003). Previous observational studies have also found an upward trend in AAM in the second half of the twentieth century (Abarca del Rio 1999) and a sharp increase in AAM across the climate shift that occurred in 1976/77 (Huang et al. 2003; Paek and Huang 2012). These existing studies provide a useful background for the interpretation of the multimodel intercomparison in this study.

While the validation of the CMIP simulations can only be done for the twentieth century and the beginning of the twenty-first century, the intercomparison of the trend in CMIP3 and CMIP5 will be extended to the whole twenty-first century using the runs under strong greenhouse gas forcing. We will also include a comparison of the decadal-to-interdecadal variability in the twentieth and twenty-first centuries in CMIP simulations to determine if it is affected by greenhouse gas forcing. Since the change in AAM largely reflects the variation of atmospheric circulation in the upper troposphere (e.g., Kang and Lau 1994; Huang and Sardeshmukh 2000), our analysis will complement those that focus on surface climate variables such as the global-mean surface temperature. To aid the interpretation of the trend in AAM, we will also analyze the trend in zonal-mean zonal wind.

2. Data and methodology

a. CMIP and reanalysis data

Tables 1 and 2 list the models in CMIP3 (Meehl et al. 2007) and CMIP5 (Taylor et al. 2012), respectively, that are used in this study. All models in CMIP3 are used. Because some simulations are still ongoing for CMIP5, we use only those that are currently available from the standard CMIP5 archive. Nevertheless, they already include the majority of CMIP5 models. For CMIP3, three types of centennial simulations are included: the “historical” or “climate of the twentieth century” (20C3M) runs that incorporate the aerosol and greenhouse gas (GHG) forcing for the twentieth century; the “preindustrial control” (PICNTRL) runs under a fixed preindustrial level of GHG concentration, and the twenty-first-century simulations based on the “720-ppm stabilization” [Special Report on Emission Scenarios (SRES) A1B] scenario. For CMIP5, we likewise include those three types of runs. The historical and preindustrial control runs are straightforward counterparts of CMIP3, while for the twenty-first century we analyze mainly the simulations under the representative concentration pathway 8.5 (RCP8.5) scenario [detailed in Taylor et al. (2012)]. While the 20C3M group in CMIP3 and most members of the historical and RCP8.5 groups in CMIP5 include multiple runs from each model, most of the SRES A1B simulations in CMIP3 have only one run for each model. To give all models equal weight in the intercomparison, we choose only one run per model for all groups. A quick analysis of the multiple runs using the same model indicates that the ensemble members behave similarly such that adding them would not significantly alter our conclusion.

Table 1.

The CMIP3 models used in this work.

The CMIP3 models used in this work.
The CMIP3 models used in this work.
Table 2.

The CMIP5 models included in this study.

The CMIP5 models included in this study.
The CMIP5 models included in this study.

To validate the climate model simulations for the twentieth century, the 20CR (Compo et al. 2006, 2011) is used as the observation. Since we have recently found some differences in the climatological mean and trend in atmospheric angular momentum for the second half of the twentieth century between 20CR and other reanalysis datasets (Paek and Huang 2012), we will also use the information from those additional datasets to partially address the uncertainty in reanalysis.

b. Calculation for atmospheric angular momentum

The global AAM, the main climate index used in this study, consists of two components: the relative angular momentum MR related to the three-dimensional (3D) zonal wind and the omega or “mass” angular momentum MΩ related to the distribution of surface pressure (e.g., Peixoto and Oort 1992). They are calculated by

 
formula

and

 
formula

where a = 6.371 × 106 m is the mean radius of the earth; Ω is the rotation rate of the earth; g = 9.81 m s−2 is gravitational acceleration; u is the 3D zonal wind as a function of latitude θ, longitude λ, and pressure p; and ps is the surface pressure as a function of latitude and longitude. The vertical integral for MR is performed using the archived zonal wind at pressure levels from 10 to 1000 hPa.

The centennial trend of AAM (or the MR or MΩ component) is evaluated in a straightforward manner as the difference between the 20-yr means of the last and first 20 yr of a century. For the CMIP3 20C3M and CMIP5 historical runs, the twentieth century is considered. For the CMIP3 SRES A1B and CMIP5 RCP8.5 runs, the twenty-first century is considered, except that a slightly shorter record from 2006 to 2099 is used for the latter since the RCP8.5 runs start from 2006. (In that case, the trend is calculated as 2080–99 minus 2006–25.) For the PICNTRL runs in CMIP3 and CMIP5, we only choose the last century of each run to evaluate the trend.

To quantify the decadal-to-interdecadal variability in the numerical simulations and observation, we perform spectral analysis on the angular momentum (focusing on MR) using a centennial time series from the model output or reanalysis data. Because the CMIP5 RCP8.5 simulations cover only 2006–99 (some models have extended the runs beyond 2099 but those outputs are not considered here), to apply the same analysis to all four groups of CMIP3 and CMIP5 runs we choose to use only 94 yr of data for each run (or observation): 1906–99 for the twentieth century and 2006–99 for the twenty-first century. Each time series of MR is linearly detrended first and then transformed to frequency space using Fourier analysis. The decadal and interdecadal variances are defined as the sum of the power within the frequency bands with 7–15-yr and 16–35-yr periods, respectively,

 
formula

where ω is frequency (wavenumber in time) and Φ(ω) is the Fourier component of the angular momentum with frequency ω. The variance or standard deviation is then used for the multimodel intercomparison and validation.

3. Trend in relative angular momentum

a. Climatology and trend of MR

Figure 1a shows the climatological value versus centennial trend of the relative angular momentum MR for the CMIP3 20C3M and SRES A1B simulations. Since we have previously found some differences in the long-term mean of MR for the second half of the twentieth century among the reanalysis datasets (Paek and Huang 2012), to address the uncertainty in the reanalysis data we also add an extra point (a circle) to Fig. 1a with an adjustment on the climatological value for 20CR (but no alteration in the trend). The adjustment was deduced from the difference in the 1979–2007 climatology of MR between 20CR and the ensemble mean of five reanalysis datasets used in Paek and Huang (2012). Compared to the spread in the multimodel ensemble for either group of runs in Fig. 1a, the adjustment (or uncertainty in the reanalysis) is very small and does not affect our later discussions.

Fig. 1.

(a) The climatological value (abscissa) vs the centennial trend (ordinate) of MR for the CMIP3 20C3M (square) and SRES A1B (triangle) simulations. (b) As in (a), but for the CMIP5 historical (square) and RCP8.5 (triangle) simulations. Each model is given a distinctive color, as labeled at right. The multimodel ensemble means of the twentieth- and twenty-first-century simulations are shown as a saltire and a cross, respectively. The observation for the twentieth century from 20CR is shown as an asterisk. The adjusted observation (see text) is shown as an open circle. The unit for MR is 1025 kg m2 s−1.

Fig. 1.

(a) The climatological value (abscissa) vs the centennial trend (ordinate) of MR for the CMIP3 20C3M (square) and SRES A1B (triangle) simulations. (b) As in (a), but for the CMIP5 historical (square) and RCP8.5 (triangle) simulations. Each model is given a distinctive color, as labeled at right. The multimodel ensemble means of the twentieth- and twenty-first-century simulations are shown as a saltire and a cross, respectively. The observation for the twentieth century from 20CR is shown as an asterisk. The adjusted observation (see text) is shown as an open circle. The unit for MR is 1025 kg m2 s−1.

In Fig. 1a, the climatological value of MR for 20C3M ranges from 13.6 × 1025 kg m2 s−1 [we denote 1 × 1025 kg m2 s−1 as 1 angular momentum unit (AMU)] to 19.7 AMU, while its centennial trend for the twentieth century ranges from 0.08 to 0.99 AMU with a multimodel ensemble mean of 0.48 AMU. All CMIP3 models produced a positive trend in MR for the twentieth century. This is qualitatively consistent with the 20CR, which exhibits a positive trend of 0.62 AMU for the twentieth century. At the same time, the CMIP3 simulations all produced a greater climatological value of MR (an ensemble mean of 16.4 AMU) than the reanalysis (13.4 AMU). This indicates the propensity for the CMIP3 climate models to simulate excessively strong westerly zonal jets in the subtropics and midlatitudes, a muted easterly zonal flow on the equator, or both. The total MR can be decomposed into a surface contribution and a baroclinic contribution (Räisänen 2003). The surface contributions are −2.5 and −2.3 AMU for the CMIP3 ensemble mean and 20CR, respectively. In other words, the positive bias in MR in CMIP3 comes mainly from the baroclinic contribution, which indicates that the models systematically exaggerate the meridional temperature gradient associated with the principal zonal jets.

In Fig. 1 we used the difference between 20CR (asterisk) and the average of four other reanalyses (circle) as a measure of the uncertainty of the climatological mean of MR but did not extend this approach to the centennial trend (the ordinate in the figure). This is due to the concern that the trends deduced from the shorter (some cover only a few decades) reanalysis datasets could be part of interdecadal variability, which do not represent the true nature of the centennial trend. We caution that uncertainty exists in the ordinate for the reanalysis in Fig. 1, which remains to be determined.

For the CMIP3 SRES A1B runs, the trend in MR for the twenty-first century ranges from 0.49 to 2.22 AMU with a multimodel ensemble mean of 1.14 AMU. The wide range indicates a still significant level of uncertainty in the projection. Nevertheless, all models produced a positive trend for the twenty-first century, consistent with previous studies using pre-CMIP3 simulations (Huang et al. 2001; de Viron et al. 2002; Räisänen 2003). For most models, the trend in the twenty-first century significantly exceeds that in the twentieth century (the triangle in Fig. 1a is located far above the corresponding square), affirming the dominant role of GHG forcing in producing the centennial trend. The numerical values of the trend in MR are listed in Table 3. Similar quantities calculated from the CMIP3 PICNTRL runs are also listed in that table. Since there is no imposed long-term trend in the external forcing or boundary condition for the PICNTRL runs, the centennial trends from those runs are just the statistical residue of internal variability at a centennial time scale. In some cases, climate drift might also be involved (Sen Gupta et al. 2012). The trends in the 20C3M and SRES A1B simulations clearly rise above this level of statistical residue.

Table 3.

A summary of the centennial trend in global atmospheric angular momentum and the equivalent change in LOD for CMIP3 simulations. Units are 1025 kg m2 s−1 for ΔMR, ΔMΩ, and ΔAAM and μs yr−1 for ΔLOD. The 20C3M and SRES A1B runs are for the twentieth and twenty-first centuries, respectively. The trend for the PICNTRL runs is deduced from the last century of each simulation. An empty entry for the models indicates that the required data for the specific calculation are not available from the CMIP3 archive. The observed values for the twentieth century from 20CR are listed at the bottom.

A summary of the centennial trend in global atmospheric angular momentum and the equivalent change in LOD for CMIP3 simulations. Units are 1025 kg m2 s−1 for ΔMR, ΔMΩ, and ΔAAM and μs yr−1 for ΔLOD. The 20C3M and SRES A1B runs are for the twentieth and twenty-first centuries, respectively. The trend for the PICNTRL runs is deduced from the last century of each simulation. An empty entry for the models indicates that the required data for the specific calculation are not available from the CMIP3 archive. The observed values for the twentieth century from 20CR are listed at the bottom.
A summary of the centennial trend in global atmospheric angular momentum and the equivalent change in LOD for CMIP3 simulations. Units are 1025 kg m2 s−1 for ΔMR, ΔMΩ, and ΔAAM and μs yr−1 for ΔLOD. The 20C3M and SRES A1B runs are for the twentieth and twenty-first centuries, respectively. The trend for the PICNTRL runs is deduced from the last century of each simulation. An empty entry for the models indicates that the required data for the specific calculation are not available from the CMIP3 archive. The observed values for the twentieth century from 20CR are listed at the bottom.

The climatological value and trend of MR for the CMIP5 historical (twentieth century) and RCP8.5 (twenty-first century) runs are shown in Fig. 1b using the same arrangement as Fig. 1a. The numerical values of the trends are listed in Table 4. As a reference, the centennial trends (as a statistical residue of natural variability) of MR from the CMIP5 PICNTRL runs are also listed in that table. For the CMIP5 historical runs, the climatological value of MR varies from 12.84 to 17.33 AMU with an ensemble mean of 14.83 AMU. Just like CMIP3, most of the CMIP5 models produced a climatological value of MR that exceeds the observed value. Nevertheless, it is encouraging that the CMIP5 ensemble has moved much closer to the observation. Also notable is the narrowing of the spread of the CMIP5 historical runs compared to CMIP3 20C3M. (The squares in Fig. 1b are more tightly packed together in the horizontal direction than their counterparts in Fig. 1a.) The surface component of MR is −2.3 AMU and the bias in the baroclinic component is reduced in the CMIP5 models compared to CMIP3. This shows an overall improvement in the simulated climatology of MR from CMIP3 to CMIP5.

Table 4.

As in Table 3, but for CMIP5. The historical and RCP8.5 runs are for the twentieth and twenty-first centuries, respectively. The trend for the PICNTRL runs is deduced from the last century of each simulation.

As in Table 3, but for CMIP5. The historical and RCP8.5 runs are for the twentieth and twenty-first centuries, respectively. The trend for the PICNTRL runs is deduced from the last century of each simulation.
As in Table 3, but for CMIP5. The historical and RCP8.5 runs are for the twentieth and twenty-first centuries, respectively. The trend for the PICNTRL runs is deduced from the last century of each simulation.

The CMIP5 RCP8.5 simulations for the twenty-first century produced a significant centennial trend in MR, which ranges from 0.44 to 3.15 AMU with an ensemble mean of 1.49 AMU, comparable to its counterpart in CMIP3 A1B runs. The anthropogenic GHG forcing in the CMIP5 RCP8.5 and CMIP3 A1B runs are different (see Taylor et al. 2012; Moss et al. 2010). The RCP8.5 scenario is for a more severe increase in GHG concentration, which generally leads to stronger future warming in the climate model projection; the twenty-first-century trends (using the same definitions as those for angular momentum) of the global-mean surface air temperature for the ensemble means of CMIP3 A1B and CMIP5 RCP8.5 are +2.1° and +3.4°C, respectively. The trends in MR from those two ensembles, if normalized by the respective trends in surface air temperature, are 0.54 and 0.44 AMU (°C)−1 for CMIP3 A1B and CMIP5 RCP8.5. Like the twentieth-century runs, the spread of the CMIP5 ensemble of the climatology of MR for the twenty-first-century simulations has narrowed compared to CMIP3. Within CMIP5, because the multimodel ensembles of the twentieth- and twenty-first-century runs have each become more tightly packed together, the separation between the two groups also becomes more distinctive as compared to CMIP3. (In Fig. 1a, the squares and triangles are mixed together while the two groups are more clearly separated in Fig. 1b.) Those quantitative differences aside, the results from CMIP3 and CMIP5 reaffirm the finding from the pre-CMIP3 studies (Huang et al. 2001; de Viron et al. 2002; Räisänen 2003) that GHG forcing induces a robust increase in the relative atmospheric angular momentum in the twenty-first century.

b. Trend in zonal-mean zonal wind

To relate the trend in MR to changes in the upper-level zonal flow, the centennial trends (defined in a similar manner as that for MR) of the annual zonal-mean zonal wind for different groups of the CMIP runs and from reanalysis are shown in Fig. 2. Figures 2c and 2d are for CMIP3 20C3M and SRES A1B runs and are consistent with a similar analysis for the zonal wind in CMIP3 already performed by Ihara and Kushnir (2009). The most robust feature in the twentieth-century simulations from both CMIP3 and CMIP5 (Fig. 2g) and 20CR (Fig. 2a) is the intensification of zonal wind at around 60°S and an accompanying weakening of zonal wind equatorward of it. This pattern is also prominent in the twenty-first-century simulations from both CMIP3 (Fig. 2d) and CMIP5 (Fig. 2h). A similar structure has been identified in pre-CMIP3 simulations with GHG forcing, for example, by Huang et al. (2001) and Kushner et al. (2001), who related it to a poleward shift of the Southern Hemisphere eddy-driven zonal jet. [The vertically deep structure of zonal wind that extends to the surface is a signature of an eddy-driven jet. Note that this structure could be affected by the projected ozone recovery in the twenty-first century. This is beyond the scope of this work, but a useful survey can be found in Son et al. (2008).]

Fig. 2.

The centennial trend (the difference between the 20-yr means of the last and first 20 yr of a century; color shading) and the climatology of the first 20 yr (“starting point”) of the respective century (black contour) of annual zonal-mean zonal wind from the observation and the ensemble mean of model simulations: (a) the observation for the twentieth century from 20CR; (c) the CMIP3 20C3M runs for the twentieth century; (d) the CMIP3 A1B runs for the twenty-first century; (g) the CMIP5 historical runs for the twentieth century; and (h) the CMIP5 RCP8.5 runs for the twenty-first century. (b) As in (a), but the trend is for the second half of the twentieth century as deduced from NCEP-1. The increment of the color shading for the trend is 0.5 m s−1, with the scale shown at right. (e),(f),(i),(j) A measure of the consensus among the models (each corresponds to the panel directly above it). The color scale indicates the percent of models that produced a positive trend. Red (blue) means the majority produced a positive (negative) trend.

Fig. 2.

The centennial trend (the difference between the 20-yr means of the last and first 20 yr of a century; color shading) and the climatology of the first 20 yr (“starting point”) of the respective century (black contour) of annual zonal-mean zonal wind from the observation and the ensemble mean of model simulations: (a) the observation for the twentieth century from 20CR; (c) the CMIP3 20C3M runs for the twentieth century; (d) the CMIP3 A1B runs for the twenty-first century; (g) the CMIP5 historical runs for the twentieth century; and (h) the CMIP5 RCP8.5 runs for the twenty-first century. (b) As in (a), but the trend is for the second half of the twentieth century as deduced from NCEP-1. The increment of the color shading for the trend is 0.5 m s−1, with the scale shown at right. (e),(f),(i),(j) A measure of the consensus among the models (each corresponds to the panel directly above it). The color scale indicates the percent of models that produced a positive trend. Red (blue) means the majority produced a positive (negative) trend.

While the structure of enhanced zonal wind at 60°S appears in both twentieth- and twenty-first-century runs (for both CMIP3 and CMIP5), in the Southern Hemisphere the twenty-first-century simulations additionally produced an enhancement of the subtropical jet with the maximum of the trend confined to the upper troposphere. In the twentieth-century simulations (from both CMIP3 and CMIP5), this structure is much weaker and largely confined to the stratosphere.

In the Northern Hemisphere, the twenty-first-century simulations from both CMIP3 and CMIP5 produced a poleward shift and enhancement of the westerly zonal jet, with a maximum of the trend in the upper troposphere. This poleward shift, along with its Southern Hemisphere counterpart, has previously been identified in the analyses of CMIP3 and often discussed in the context of the poleward shift of storm tracks (e.g., Yin 2005). The twentieth-century simulations from both CMIP3 and CMIP5 also produce an enhancement of the westerly zonal jet in the Northern Hemisphere, but one cannot clearly identify a poleward shift of the jet. In 20CR, one can even see a hint of an enhancement and equatorward shift of the jet. This might have been influenced by the fact that the last 20 yr of the twentieth century includes several very strong El Niño events while the first 20 yr of the century contains very few such events. (Note that an enhancement and equatorward shift of the Northern Hemisphere zonal jet is typical of the atmospheric response to El Niño.) By design, we do not expect the CMIP3 or CMIP5 twentieth-century simulations to capture those specific El Niño events seen in observation. An alternative but related interpretation is that the absence of the equatorward shift of the Northern Hemisphere (NH) zonal jet might reflect a certain common bias in the climate models. Notably, Cai et al. (2009) pointed out that the common bias of a cold equatorial central–western Pacific SST in CMIP3 models generally leads to a muted atmospheric response to ENSO in those models. This might further weaken the footprint of El Niño on the NH zonal jet in the model simulations.

Paek and Huang (2012) have recently found some differences in the long-term mean and trend of atmospheric angular momentum for the second half of the twentieth century between 20CR and other reanalysis datasets that assimilated the 3D observations. In Fig. 2, we use mainly 20CR to validate the twentieth-century simulations because it is the only reanalysis dataset with the centennial coverage. Nevertheless, as a reference we also show in Fig. 2b the trend in zonal-mean zonal wind for only the second half of the twentieth century but from the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) Global Reanalysis 1 (NCEP-1; which has the second longest record next to 20CR; Kalnay et al. 1996; Kistler et al. 2001). Even with the shorter period, the half-century trend has several structures that resemble the centennial trends in 20CR and the model simulations. Most notable among them is the poleward shift of the Southern Hemisphere eddy-driven jet that corresponds to a positive trend at 60°S. Note that this is also the region where the CMIP3 and CMIP5 models show the highest level of consensus, as indicated in Figs. 2e, 2f, 2i, and 2j. The half-century trend in Fig. 2b also shows an overall enhancement of the Northern Hemisphere westerly jet, but its detailed structure differs from its counterpart in 20CR: the equatorward shift of the Northern Hemisphere subtropical jet in Fig. 2a is less pronounced in Fig. 2b. This hints that part of this feature might be a statistical residue of the internal variability and not a robust part of the long-term trend.

The trends in zonal wind in Fig. 2 consist of not only latitudinal shifts but also vertical (mostly upward) displacements of the zonal jets, especially in the twenty-first-century simulations. To visualize the local contributions to the trend of MR, the vertically integrated contributions of different vertical layers (10–200 hPa, 200–1000 hPa, and 10–1000 hPa) as a function of latitude [in the fashion of Fig. 4 in Räisänen (2003)] are shown in Figs. 3a–d for the ensemble means of the four sets of CMIP3 and CMIP5 runs. In all panels, the Southern Hemisphere jet at 60°S is found to be unique in that the local contribution to the trend in MR is dominated by the trend in the zonal wind of the tropospheric column below 200 hPa (which reflects the latitudinal shift of the deep eddy-driven jet as mentioned before). Elsewhere, the increase in MR associated with the subtropical jet in the Southern Hemisphere and the principal zonal jet in the Northern Hemisphere is dominated by the trend in zonal wind above the 200-hPa level. Notably, for the twenty-first-century simulations (Figs. 3b,d), at 30°N the dominating positive contribution from the zonal wind above 200 hPa is accompanied by a smaller negative contribution from below 200 hPa, an indication of an upward shift and intensification of the jet core at that latitude.

Fig. 3.

The contributions to the multimodel-mean centennial trend (the difference between the 20-yr means of the last and first 20 yr of a century) in MR from different vertical layers as a function of latitude: (a) CMIP3 20C3M runs, (b) CMIP3 SRES A1B runs, (c) CMIP5 historical runs, and (d) CMIP5 RCP8.5 runs. The thick solid line is for the whole vertical column from 10 to 1000 hPa, the thin solid line is for the upper levels from 10 to 200 hPa, and the dotted–dashed line is for the lower levels from 200 to 1000 hPa. The unit is 1023 kg m2 s−1 (1° latitude)−1.

Fig. 3.

The contributions to the multimodel-mean centennial trend (the difference between the 20-yr means of the last and first 20 yr of a century) in MR from different vertical layers as a function of latitude: (a) CMIP3 20C3M runs, (b) CMIP3 SRES A1B runs, (c) CMIP5 historical runs, and (d) CMIP5 RCP8.5 runs. The thick solid line is for the whole vertical column from 10 to 1000 hPa, the thin solid line is for the upper levels from 10 to 200 hPa, and the dotted–dashed line is for the lower levels from 200 to 1000 hPa. The unit is 1023 kg m2 s−1 (1° latitude)−1.

4. Trend in omega angular momentum

Figures 4a and 4b show the climatology versus trend, in the same fashion as Fig. 1, for the mass, or omega, angular momentum MΩ for CMIP3 and CMIP5 simulations. While the climatological value of MΩ (from either observation or simulation) is much greater than MR, the trend in MΩ as shown in Figs. 4a and 4b is smaller than its counterpart in MR such that the trend in the total AAM (=MR + MΩ) is dominated by MR. For the climatology of MΩ from the twentieth-century simulations, the spread of the multimodel ensemble has narrowed substantially from CMIP3 to CMIP5 with the latter also moving much closer to the observation from 20CR.

Fig. 4.

As in Fig. 1, but for the climatology and trend of the omega angular momentum: (a) the 20C3M (square) and A1B (triangle) runs from CMIP3 and (b) the historical (square) and RCP8.5 (triangle) runs from CMIP5. Note that the scale on the abscissa in (b) is only a half of that in (a). A model in CMIP3 produced an unusually large climatological value of MΩ (over 1100 AMU) that is outside the range and not shown in (a). The unit for MΩ is 1025 kg m2 s−1 (=1 AMU).

Fig. 4.

As in Fig. 1, but for the climatology and trend of the omega angular momentum: (a) the 20C3M (square) and A1B (triangle) runs from CMIP3 and (b) the historical (square) and RCP8.5 (triangle) runs from CMIP5. Note that the scale on the abscissa in (b) is only a half of that in (a). A model in CMIP3 produced an unusually large climatological value of MΩ (over 1100 AMU) that is outside the range and not shown in (a). The unit for MΩ is 1025 kg m2 s−1 (=1 AMU).

In addition to MΩ, we also calculated the total atmospheric mass, which is proportional to 〈ps〉, where 〈X〉 is the area-weighted global average of X. For the climatology of the twentieth century, the multimodel ensemble mean of 〈ps〉 for the CMIP3 20C3M runs is 985.2 hPa, compared to 985.6 hPa for 20CR. The intermodel standard deviation of 〈ps〉 for CMIP3 20C3M is 1.1 hPa. In contrast, the multimodel ensemble mean of 〈ps cos2θ〉 (which is proportional to MΩ) for CMIP3 20C3M is 661.9 hPa compared to 661.6 hPa for 20CR, and the intermodel standard deviation of that quantity is 2.6 hPa, more than twice its counterpart for 〈ps〉. This suggests that the bias and intermodel variation in MΩ for the climate models are due to not only the variation of total mass but also substantial contributions from the differences in the meridional distribution of ps. This remark also generally holds for CMIP5 historical runs, which otherwise have a smaller bias and ensemble spread for both 〈ps〉 and 〈ps cos2θ〉 compared to CMIP3 20C3M; the (ensemble mean, standard deviation) of 〈ps〉 and 〈ps cos2θ〉 for CMIP5 are (985.1, 0.8) hPa and (661.5, 0.6) hPa, respectively.

The multimodel ensemble means of the trends in MΩ for the twentieth century are 0.07 and 0.11 AMU (1 AMU = 1 × 1025 kg m2 s−1) from the CMIP3 20C3M and CMIP5 historical runs, while the corresponding trend deduced from 20CR is 0.04 AMU. All three are small numbers compared to their counterparts for MR. With the small trend, it is not surprising that the three numbers do not strongly agree with each other (although they are all positive). To see where the difference comes from, Figs. 5a and 5c show the twentieth- and twenty-first-century trend in annual zonal-mean surface pressure weighted by cos3θ from the CMIP3 and CMIP5 runs and from 20CR. The half-century trend from NCEP-1 (see the discussion in section 2b) is also shown. Figures 5a and 5c show an increase in the surface pressure in the tropics in reanalysis that is largely absent in the 20C3M and historical runs (although the latter produced a small positive value across the tropics). On the other hand, the CMIP3 and CMIP5 simulations produced a “ridge” at around 45°S that is missing in 20CR and barely visible in NCEP-1. Qualitatively, the two reanalyses and the CMIP3 and CMIP5 simulations all show a dip in surface pressure south of 60°S and an enhancement of meridional pressure gradient across the midlatitude of the Southern Hemisphere (consistent with the positive trend in zonal wind at 60°S shown in Fig. 2), although the dip is more pronounced for the reanalyses. Qualitatively, we find less agreement among the reanalyses and CMIP runs in the trend of surface pressure for the Northern Hemisphere, a behavior similar to the trend in zonal wind discussed in section 3b. To complement the ensemble mean shown in Figs. 5a and 5c, the multimodel consensus (defined in the same manner as Figs. 2e,f,i,j) on the trend in surface pressure for the CMIP3 and CMIP5 simulations is shown in Figs. 5b and 5d. We find that the level of consensus has increased from CMIP3 to CMIP5.

Fig. 5.

(a) The centennial trend (the difference between the 20-yr means of the last and first 20 yr of a century) in the annual zonal-mean surface pressure weighted by cos3θ from the ensemble mean of the CMIP3 20C3M runs (dark blue) and 20CR (green), both for the twentieth century, and from the CMIP3 A1B runs (red) for the twenty-first century. Also shown is the observed trend for only the second half of the twentieth century from the NCEP-1 (light blue). (b) The measure of consensus among the models as a function of latitude, for the CMIP 20C3M (dark blue) and A1B (red) runs. The ordinate is the percent of models that produced a positive trend as the ensemble mean of the trend. (c) As in (a), but the black and magenta curves are for the CMIP5 historical and RCP8.5 runs, respectively. The two curves for the observation are copied from (a) and imposed to (c) as a reference. (d) As in (b), but the black and magenta curves are for the CMIP5 historical and RCP8.5 runs, respectively. The unit for the surface pressure in (a),(c) is hPa.

Fig. 5.

(a) The centennial trend (the difference between the 20-yr means of the last and first 20 yr of a century) in the annual zonal-mean surface pressure weighted by cos3θ from the ensemble mean of the CMIP3 20C3M runs (dark blue) and 20CR (green), both for the twentieth century, and from the CMIP3 A1B runs (red) for the twenty-first century. Also shown is the observed trend for only the second half of the twentieth century from the NCEP-1 (light blue). (b) The measure of consensus among the models as a function of latitude, for the CMIP 20C3M (dark blue) and A1B (red) runs. The ordinate is the percent of models that produced a positive trend as the ensemble mean of the trend. (c) As in (a), but the black and magenta curves are for the CMIP5 historical and RCP8.5 runs, respectively. The two curves for the observation are copied from (a) and imposed to (c) as a reference. (d) As in (b), but the black and magenta curves are for the CMIP5 historical and RCP8.5 runs, respectively. The unit for the surface pressure in (a),(c) is hPa.

The majority of the CMIP3 and CMIP5 models produce a positive trend in MΩ for the twenty-first century. The multimodel ensemble means of the trend are 0.26 and 0.52 AMU for the SRES A1B and RCP8.5 runs, respectively. They are both significantly greater than their counterparts from the twentieth-century simulations, reflecting the influence of GHG forcing in producing the trends in the twenty-first century. This is qualitatively consistent with some previous studies using pre-CMIP3 simulations (Huang et al. 2001; Räisänen 2003), although a rigorous comparison is difficult since only a small number of the models in the pre-CMIP3 archives have the surface pressure data. As pointed out by Räisänen (2003), the calculation of MΩ can be sensitive to the procedure of converting sea level pressure and temperature to surface pressure. [Another study by de Viron et al. (2002) obtained a more negative trend in MΩ for CMIP2.] The calculations of the MΩ in Figs. 4a and 4b directly used the surface pressure data in CMIP3 and CMIP5 archives and are devoid of the technical ambiguity raised by Räisänen (2003).

The twenty-first-century trends in the zonal-mean surface pressure from the CMIP3 and CMIP5 simulations are shown in Figs. 5a and 5c. They share a similar structure of a pair of ridges in the midlatitude in both hemispheres, in contrast to the twentieth-century simulations, which produced only a ridge in the Southern Hemisphere. This corroborates the structure of the trend in zonal wind in Fig. 2 that the twenty-first-century runs produced a poleward shift of the zonal jets in both hemispheres, while for the twentieth-century runs the poleward shift is robust only in the Southern Hemisphere. For completeness, the level of consensus for the twenty-first-century runs is also shown in Figs. 5b and 5d for CMIP3 and CMIP5, respectively. Again, CMIP5 models exhibit a higher level of consensus in this case.

5. Trend in total atmospheric angular momentum and length of day

Some previous studies have pointed out that the projected increase in the total AAM would imply a slowing down of earth rotation or an increase in the length of day (LOD) (Abarca del Rio 1999; Huang et al. 2001; de Viron et al. 2002). On the interannual and shorter time scales, the total of earth plus atmospheric angular momentum is nearly conserved such that the tendencies of AAM and earth angular momentum are equal and opposite in sign. This is no longer the case on centennial time scale because of the influences of tidal friction and other slow geological processes (such as postglacial rebound) in the long term. Nevertheless, if the GHG-induced trend in AAM is large enough, it can still affect the total trend in LOD (Huang et al. 2001). In that context, we adopted a commonly used empirical formula (Peixoto and Oort 1992),

 
formula

where ΔLOD is in ms and ΔAAM (=ΔMR + ΔMΩ) is in 1025 kg m2 s−1, to convert the change in AAM for the CMIP simulations to an equivalent change in LOD as listed in Tables 3 and 4. Focusing on the twenty-first century, the multimodel ensemble means of the trend ΔLOD are 0.30 and 0.46 ms century−1 for the CMIP3 SRES A1B and CMIP5 RCP8.5 simulations, respectively. They are comparable to previous findings using pre-CMIP3 simulations (e.g., Huang et al. 2001). Since the changes in LOD due to tidal friction and postglacial rebound are about +2.3 and −0.6 ms century−1, respectively [see a survey in Huang et al. (2001)], the impact of the GHG-induced change in LOD is projected to be significant in the twenty-first century but not large enough to overwhelm the secular trend because of the astronomical and geological effects.

6. Decadal-to-interdecadal variability

We next quantify and compare the decadal-to-interdecadal variability in the CMIP3 and CMIP5 simulations by the spectral analysis described in section 2b. The magnitudes of the decadal and interdecadal variability are measured by the cumulative variance of the Fourier modes within the 7–15-yr and 16–35-yr bands. Because the variances of MΩ in the decadal and interdecadal frequency bands are much smaller than their counterparts for MR, we will focus only on MR. [Note that the dominance of MR over MΩ is also well known for interannual and shorter-term variability (e.g., Huang et al. 2003).] To help visualize the behavior of the decadal-to-interdecadal variability of MR in CMIP simulations, Figs. 6 and 7 show the 5-yr running averaged time series of MR (red curve), its linear trend (green line), and the corresponding detrended time series (blue curve) for all available CMIP3 and CMIP5 simulations for the twentieth and twenty-first centuries. From these figures, one can immediately see a very wide range of behavior of the simulated decadal-to-interdecadal variability, in contrast to the more robust upward trend in MR for the twentieth and twenty-first centuries produced by the majority of the models. From Fig. 7, the GHG-induced centennial trend of MR for the twenty-first century is strong enough to overwhelm the background decadal-to-interdecadal variability. This is not so for the twentieth century (Fig. 6), in which decadal-to-interdecadal variability can sometimes override the relatively weak secular trend.

Fig. 6.

(a) Five-year running averaged monthly anomalies of global relative angular momentum MR from the CMIP3 20C3M simulations. The red curve is the time series with the running average, the green line is the linear trend, and the blue curve is the detrended time series. To help visualization, the time series shown are the departure from the long-term mean (which is different for different models) for each individual model. (b) As in (a), but for the historical runs from CMIP5. The unit for angular momentum is 1025 kg m2 s−1, or 1 AMU.

Fig. 6.

(a) Five-year running averaged monthly anomalies of global relative angular momentum MR from the CMIP3 20C3M simulations. The red curve is the time series with the running average, the green line is the linear trend, and the blue curve is the detrended time series. To help visualization, the time series shown are the departure from the long-term mean (which is different for different models) for each individual model. (b) As in (a), but for the historical runs from CMIP5. The unit for angular momentum is 1025 kg m2 s−1, or 1 AMU.

Fig. 7.

(a) As in Fig. 6, but for the CMIP3 A1B runs. (b) As in (a), but for the CMIP5 RCP8.5 runs. Note that the scale on the ordinate is double that in Fig. 6.

Fig. 7.

(a) As in Fig. 6, but for the CMIP3 A1B runs. (b) As in (a), but for the CMIP5 RCP8.5 runs. Note that the scale on the ordinate is double that in Fig. 6.

Figures 8a and 8b are scatterplots of the standard deviation (square root of variance) of decadal variability (abscissa) versus the standard deviation of interdecadal variability (ordinate) of MR. For the convenience of comparing them to observation, the standard deviation of the simulated MR for the decadal or interdecadal band is normalized by its counterpart from the 20CR. The observation (20CR: shown as an asterisk) itself is located at (1.0, 1.0) in both panels in Fig. 8. For the twentieth-century runs from CMIP3 and CMIP5, although the scatterplots show a wide spread of the simulated decadal or interdecadal standard deviation, the bias in the decadal or interdecadal variability is more random compared to the systematic bias in the climatology of MR in Fig. 1. As such, the average over all models brings the ensemble mean of the square root of variance (the saltire or “X” in Fig. 8) close to observation. The spread for both decadal and interdecadal variability is also found to narrow from CMIP3 to CMIP5. Most notably, the outliers in CMIP3 with unusually weak decadal/interdecadal variability (the symbols in the bottom-left corner of Fig. 8a) are absent in CMIP5. Nevertheless, the narrowing of spread for the decadal/interdecadal variability is much less dramatic than the case for the climatology of MR in Figs. 1 and 4. These characteristics about the spread also hold true for the twenty-first-century simulations (triangles) in Fig. 8.

Fig. 8.

(a) The standard deviation of decadal variability (abscissa) vs the standard deviation of interdecadal variability (ordinate) for MR from the CMIP3 20C3M (square) and SRES A1B (triangle) simulations. The multimodel ensemble means of the 20C3M and A1B runs are also shown as a saltire and a cross. The observation from 20CR is shown as an asterisk. To help the model validation, all quantities shown are normalized by their observed values (0.16 and 0.12 AMU for decadal and interdecadal variance, respectively) such that the observation itself is located at (1.0, 1.0) in the plot. Each model is given a distinctive color as labeled at right. (b) As in (a), but for the CMIP5 historical (square) and RCP8.5 (triangle) runs. See text for the definition of the decadal and interdecadal variance.

Fig. 8.

(a) The standard deviation of decadal variability (abscissa) vs the standard deviation of interdecadal variability (ordinate) for MR from the CMIP3 20C3M (square) and SRES A1B (triangle) simulations. The multimodel ensemble means of the 20C3M and A1B runs are also shown as a saltire and a cross. The observation from 20CR is shown as an asterisk. To help the model validation, all quantities shown are normalized by their observed values (0.16 and 0.12 AMU for decadal and interdecadal variance, respectively) such that the observation itself is located at (1.0, 1.0) in the plot. Each model is given a distinctive color as labeled at right. (b) As in (a), but for the CMIP5 historical (square) and RCP8.5 (triangle) runs. See text for the definition of the decadal and interdecadal variance.

Unlike in Figs. 1 and 4, which show a clear change in the climatology from the twentieth to the twenty-first century (a clear separation of the triangles and squares in those figures), in Fig. 8 the twentieth- and twenty-first-century simulations are still mixed together without a clear trend. For both CMIP3 and CMIP5 simulations, using Welch’s t test, we cannot establish a shift in the mean from the twentieth to the twenty-first century at 95% significance level for either decadal or interdecadal variability in Fig. 8. Since the probability distributions of the quantities in Fig. 8 may deviate from Gaussian (due to the presence of significant outliers), we have also used the Kolmogorov–Smirnov test to reconfirm that the ensembles of the twentieth- and twenty-first-century runs are not yet statistically distinguishable. Thus, the GHG forcing in the twenty-first century does not have as significant an influence on the decadal-to-interdecadal variability of MR as it does on the climatological mean of MR.

The scatterplots in Figs. 1, 4, and 8 only summarized the behavior of the CMIP simulations in terms of the temporal mean and variance of MR and MΩ. Certainly, these lower-order statistics alone do not describe every aspect of the time evolution of AAM relevant to climate prediction. A potentially important case is large-amplitude “jumps” of AAM associated with interdecadal climate shifts such as the observed 1976/77 event (Trenberth 1990; Miller et al. 1994) [see recent surveys in Huang et al. (2005), Meehl et al. (2009b), and Paek and Huang (2012)]. A preliminary analysis (using a set of criteria based on the tendency of AAM and optimal fit of a step function to the AAM time series) indicates that a shift in AAM with an amplitude comparable to the observed 1976/77 event almost never happens in the CMIP3 and CMIP5 simulations, despite the fact that many of those runs produced a greater value of the variance of interdecadal variability than the observation. A thorough investigation of such events in the CMIP simulations will have to rely on either higher-order statistics or other methods that do not assume uniformity of statistics in time. We will carry out that investigation in a follow-up study.

7. Conclusions

This study analyzed the centennial climatology, trend, and decadal-to-interdecadal variability of atmospheric angular momentum for the CMIP3 and CMIP5 simulations and validated them using the 20CR. Both CMIP3 and CMIP5 models are found to produce a positive bias in the twentieth-century climatology of MR, but this bias is significantly reduced in CMIP5. The CMIP5 models also produced a narrower ensemble spread of the climatology and trend of both components (MR and MΩ) of angular momentum for the twentieth century. An increase in both MR and MΩ is simulated by both CMIP3 and CMIP5 models and for the twentieth and twenty-first centuries. The trend in the total angular momentum is dominated by the MR component. The simulated increase in MR for the twentieth century is consistent with observation. In all cases, the simulated trend in the twenty-first century is much greater than its twentieth-century counterpart, affirming the role of the GHG forcing in producing the trend.

Both CMIP3 and CMIP5 simulations exhibit a wide range of behavior for the decadal-to-interdecadal variability. Using the standard deviation (square root of variance) of the MR time series within the 7–15-yr and 16–35-yr band to define the magnitude of the decadal and interdecadal variability, it is found that the magnitude of the decadal or interdecadal variability for an individual model can vary from a half to twice of the observed value. Nevertheless, the bias in the decadal and interdecadal variability is relatively random, in contrast to the systematic bias in the climatology of MR. As such, the multimodel averaging brings the ensemble mean of the magnitude of decadal or interdecadal variability to within 18% of the observed value for the twentieth century. The CMIP5 simulations produced a slightly narrower ensemble spread in the decadal or interdecadal standard deviation compared to CMIP3. A notable type of outliers in CMIP3 with very weak decadal-to-interdecadal variability is absent in CMIP5. Otherwise, the CMIP3 and CMIP5 ensemble are close enough that the ensemble means of CMIP3 and CMIP5 are not statistically distinguishable for either the twentieth or twenty-first centuries. More importantly, the twenty-first-century simulations from both CMIP3 and CMIP5 produced only a small trend in the decadal or interdecadal variability, which is not statistically significant. Our results indicate that, while the GHG forcing induces a significant increase in the climatological mean of atmospheric angular momentum, it does not significantly affect its decadal-to-interdecadal variability in the twenty-first century.

Acknowledgments

This study is supported by the Office of Science (BER), U.S. Department of Energy. The 20CR and NCEP-1 data were obtained from the NOAA ESRL/PSD data portal (http://www.esrl.noaa.gov/psd). We acknowledge the World Climate Research Programme’s Working Group on Coupled Modelling, which is responsible for CMIP, and we thank the climate modeling groups (listed in Tables 1 and 2 of this paper) for producing and making available their model output. For CMIP the U.S. Department of Energy’s Program for Climate Model Diagnosis and Intercomparison provides coordinating support and led development of software infrastructure in partnership with the Global Organization for Earth System Science Portals. The authors appreciate detailed comments from three reviewers that helped improve the manuscript.

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