a. Multimodel statistics of variability and decadal potential predictability

We adopt a multimodel ensemble (MME) approach, which pools the statistics of individual models to better estimate population parameters. The justification is that pooled multimodel statistics are generally in better agreement with observation-based estimates for current climate than are the results from individual models. This has been demonstrated, for instance, for climatological mean quantities (Lambert and Boer 2001) and also for the second-order climatological statistics (variances and covariances) that arise in the Lorenz energy cycle (Boer and Lambert 2007). The MME approach is also adopted in seasonal forecasting applications, highlighted in a special issue of Tellus (2005, Vol. 57A, No. 3) devoted to the Development of a European Multimodel Ensemble System for Seasonal to Interannual Prediction (DEMETER) project, and in the climate assessments of M07.

In the 200-yr stabilization period after 2100, Fig. 1 indicates that the rate of climate change decreases markedly as the system adjusts toward a new equilibrium. If we assume that the slow commitment component may be removed by fitting a low-order polynomial to the data, we may calculate the usual variance and potential predictability statistics about this trend and compare them with those of the control simulations. The difference between them gives an indication of how the internally generated interannual variability and the long time-scale predictability is expected to change with global warming. We write X = X_c + X′, where X_c is the committed response to the now-stabilized forcing as the system evolves toward a new equilibrium. It is identified by fitting second-order polynomials, orthogonal in time, to the data at every grid point over the last 150 yr of the simulations. We follow Stouffer and Weatherald (2007) and Vinnikov and Robock (2002), who justify the fitting of a quadratic at each point as a suitable representation of the evolution of the forced component.

The variance of the natural variability component X_i′ that remains after removing X_c, for i = 1 … 150 (the year number), is further decomposed into components following (3) as

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where time is now identified by the decade number j and the “within decade” year number k for i = (j − 1)m + k and m = 10 yr, is the decadal average, and the overbar is the average over all years and decades for the analysis period. Taking the expectations of the sample variances under the assumption that the various components are largely independent (as discussed in Boer 2004) gives unbiased estimators of the variances as

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The decadal potential predictability is estimated as

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following the general approach of Rowell (1998) and Rowell and Zwiers (1999), termed the RZ approach. The statistics are compared with like quantities obtained for the control simulations. Boer and Lambert (2008) discuss the removal of residual drift and the calculation of these quantities for the CMIP3 control simulations.

The usual F test may be applied to the ratio of the variances σ_ω² in the warmer world to those from the control simulations with the view to rejecting the null hypothesis that the ratio is 1. Because of the considerable amount of data (11 realizations of 150 yr each), the hypothesis is rejected in general except for a narrow band about the zero lines (in Fig. 4). For decadal potential predictability, the statistical situation is not so straightforward, but approximate confidence intervals around the ppvf are available following RZ as described in Boer (2004) and we deem the ppvfs to be statistically distinct and plot their differences for probabilities less than 1% (in Fig. 5).

There are only 11 simulations for each of the A1B and B1 scenarios in which simulation results are available for the entire 2000–2300 period and, although there is considerable overlap, the models in the two sets of simulations are not exactly the same. There are two options in comparing the potential predictability of the stabilization and the control simulations. The additional data and the assumption that multimodel statistics are more robust than those for a particular model or group of models suggest the option of comparing the multimodel control statistics based on 27 simulations with the statistics of the 11 particular simulations available for the A1B and B1 scenarios. The alternative is to consider subsets of the control simulations that correspond to the models in the stabilization cases. We adopt the second approach as being more conservative in that data from the same set of models enter the control and stabilization estimates of potential predictability. However, because of the smaller amounts of data involved, the confidence bands about the estimates of potential predictability will be broader, and hence we will be less likely to conclude that there is a difference in potential predictability.

a. Unforced interannual variability

Multimodel estimates of the standard deviations of annual mean temperature σ_T and precipitation σ_P, obtained by pooling the simulated data from the control runs of the coupled climate models in Table 1, are shown in Fig. 2 together with observation-based estimates of these quantities. In each case, trends have been removed to minimize the inclusion of model drift and twentieth-century climate change in the estimates. The observation-based values for temperature are from the 40-yr European Centre for Medium-Range Weather Forecasts Re-Analysis (ERA-40; Uppala et al. 2005), whereas those for precipitation are from the 17-yr Xie and Arkin (1996) dataset. Figure 3 plots the multimodel- and observation-based zonal averages of these standard deviations as solid red and black lines, respectively.

The intent here is not to make a detailed comparison of the simulated and observation-based variances, which has difficulties of its own, but to indicate that the simulated values capture the essential features of the observationally based values as a necessary condition for the analysis of changes in variability. The main area of disagreement is over the very high southern latitudes. Although the area covered is small and not well observed, the source of the differences in standard deviations is puzzling and worthy of further study. Despite these differences, the reasonable correspondence of the multimodel standard deviations with observationally based values over the remainder of the globe supports further analysis.

b. Changes in variability

Figure 3 plots the zonal averages of the observation-based estimates of the standard deviations of annual mean temperature σ_T and precipitation σ_P as black lines and the model-based preindustrial values as solid red lines. The values for the B1 and A1B scenarios are the long- and short-dashed red lines, respectively. The corresponding blue lines are the standard deviations of decadal mean temperature and precipitation. Figure 3 supports Fig. 2 in that the multimodel control-run standard deviations (solid red) are quite comparable to the observation-based estimates (solid black) with the exception of the high southern latitudes.

Figure 3 also indicates that the standard deviation of annual mean temperatures generally decreases with global warming at extratropical latitudes, whereas the reverse is broadly the case in the tropics, although the magnitudes involved in the tropics are much smaller. Standard deviations of annual mean precipitation generally increase everywhere, with larger increases in the tropics. The changes (increases or decreases) are generally larger for the scenario with the largest forcing and warming; that is, changes for the A1B scenario are greater than for the more modest B1 scenario. The situation for the standard deviation of decadal means (the blue lines) is similar, although the changes are typically larger as a percentage of the control-run values.

Figure 4 plots the multimodel standard deviations of annual mean temperature and precipitation for the preindustrial control simulations and the percentage differences for the B1 and A1B stabilization scenarios. For temperature, as anticipated from Fig. 3, there is a general decrease in σ_T at extratropical latitudes and an increase at tropical latitudes. The patterns are not zonal however, especially in the Northern Hemisphere where land–sea differences are notable. It is unnecessary to describe the diagrams, but we may note that σ_T tends to increase over land except for higher Northern Hemisphere land and that σ_T decreases are particularly notable for high-latitude oceans, although increases can be found elsewhere, including the equatorial eastern Pacific. Perhaps not surprisingly, the patterns of change for the two scenarios are very similar.

The patterns of the percentage change in the standard deviation of annual mean precipitation for the two stabilization scenarios are also shown in Fig. 4. Again, as anticipated from Fig. 3, there is a general increase in precipitation variability but there are regions at the latitudes of the subtropical highs that show decreases over both land and ocean. It is generally the case that the percentage change in standard deviation increases with latitude, as does the change in annual mean precipitation itself according to Fig. 10.9 in M07. An increase in σ_P (and σ_T) in the equatorial eastern Pacific is presumably associated with the models’ version of the ENSO mechanism although, according to Merryfield (2006) for example, models do not show consistent ENSO change behavior under global warming.

These results for temperature are broadly similar to those of Räisänen (2002, Fig. 6), who analyzes changes in standard deviation for the climate change forced by doubling atmospheric CO₂ (2 × CO₂) in results from an earlier generation of climate models in the CMIP2 archive. There are several differences, including the larger percentage changes in variability due to, presumably, the stronger forcing, especially for the A1B simulation. There are differences in detail, such as a broader region of increased temperature variability in the southern part of North America and modest increases in temperature variability over India and in the equatorial eastern Pacific, instead of decreases.

Stouffer and Weatherald (2007) investigate the changes in temperature variability with global warming in two versions of the Geophysical Fluid Dynamics Laboratory (GFDL) coupled climate model: an older version (R30) and a more recent version [Climate Model, version 2.1 (CM2.1)], which is included in the multimodel collection in Table 1. Their Fig. 2d shows F ratios, which may formally be transformed into the percentage standard deviation changes of Fig. 4 with δσ/σ = F − 1. There is a broad similarity of their results with Fig. 4 but also some notable differences such as, for instance, the lack of a strong decrease of variability over the southern ocean, which is a feature of the multimodel analysis.

For precipitation, a strong increase in precipitation variability is seen in the equatorial eastern Pacific here and in Räisänen (2002), despite the difference in the changes in temperature variability, and there are differences in other regions, such as over Australia for instance. Nevertheless, the broad agreement of the overall patterns of change in variability despite differences in forcing and in the CMIP3 versus the CMIP2 generation of coupled models indicates the general robustness of the results.

Some of the relationship between the pattern of changes in standard deviation δσ and the pattern of standard deviation in the control simulations σ can be seen in the spatial correlations of Table 2. For temperature, the spatial correlations r(δσ, σ) are negative, indicating that temperature variability, at least as measured by the standard deviation, generally decreases most where it is largest. The correlations are stronger (larger negative) for the more strongly forced A1B scenario compared to the B1 scenario. The reverse is the case for precipitation variability, which tends to increase where it is largest, albeit with a smaller correlation coefficient than for temperature. The correlations are larger for the variability of decadal means of temperature than for annual means and the reverse is again the case for precipitation. The pattern of the changes in standard deviation is similar for the B1 and A1B scenarios, as already apparent in Fig. 4, with spatial correlations r(δσ, δσ) greater than 0.8 in all cases except for the decadal means of precipitation. Finally, the spatial patterns of changes in the variability of temperature are poorly correlated with those of precipitation over the globe.

The implication from these results is that there is not only a shift in mean temperature and precipitation rates, as described in M07, for instance, but also a shift in the widths of the frequency distributions in different parts of the globe. Although it is beyond the scope of the present investigation to identify the mechanisms associated with changes in the variance of annual means, Räisänen (2002) and Stouffer and Weatherald (2007) discuss this briefly and provide some references, whereas M07 provide indirect information largely through a discussion of changes in extremes. In brief, the increase in precipitation variability is consistent with the increase in precipitation intensity, which is a relatively robust feature of the climate projections and is explained as a consequence of the increased moisture capacity of the warmer atmosphere. The decrease of temperature variability at higher latitudes is generally ascribed to the retreat of snow and ice with a resulting less winterlike variability. The replacement of sea ice by open water, for instance, acts to damp temperature variability locally. Increases of temperature variability over lower-latitude land may be linked to generally dryer conditions whereby changes in energy input at the surface are less able to be damped by latent heat fluxes.

c. Changes in decadal potential predictability

Figure 5 plots the multimodel decadal internally generated potential predictability p_ν of the unforced preindustrial control simulation and its difference from the p_ν of the 150-yr stabilization period (nominally 2150–2300) for the two scenarios. Values of p_ν are not plotted unless they are deemed to be significantly different from zero at the 1% level, and differences are plotted only when the probability that the control and stabilization p_ν values are the same is estimated to be less than 1% based on their confidence intervals.

The first result is that differences in p_ν are very similar in the two scenarios and, although a slightly larger area of the globe exhibits statistically significant differences in the more strongly forced A1B case, the results are not strongly scenario dependent, which also attests to their general robustness. The main result is an overall decrease in decadal variability and potential predictability in a warmer world. The decrease tends to be largest where the ppvfs of the unforced preindustrial control climate are largest.

For temperature, decadal potential predictability is largest over middle-to-high-latitude oceans but small over land. The smallness of the ppvf over land is due not so much to the smallness of σ_ν² but rather to the small signal-to-noise ratio there. Over higher latitudes, the longer time scales of the oceans provide larger values of p_ν and these are also where decreases in decadal potential predictability are largest in the warmer world.

The potential predictability of precipitation is small to begin with and only a pale reflection of that for temperature. This is because the decadal variability σ_ν² for precipitation is comparatively small and the noise variance σ_ε² is generally large, giving a small signal-to-noise ratio so that p_ν = γ/(1 + γ) is small almost everywhere. The decrease in p_ν for precipitation occurs despite the modest increase in decadal standard deviation (see, e.g., Fig. 3) because it is outweighed by the overall increase in variability, which implies a reduction in the signal-to-noise ratio γ.

The high-latitude ocean regions of diminished potential predictability are typically those where the surface connects to the deeper oceans and/or where variations in important ocean currents, such as the Kuroshio, Gulf Stream, and the Antarctic Circumpolar Current, can provide the long time scales of interest. There is, however, a bewildering array of modes and analyses that may be called upon to provide the long time-scale variability that might change in the warmer world. These are discussed by M07 (sections 10.3.4 and 10.3.5), who also provide copious references. They include the PDO and the related interdecadal Pacific oscillation (IPO) in the Pacific, the meridional overturning circulation (MOC) and the AMO in the Atlantic, as well as decadal components in the strengths and envelopes of mechanisms, such as ENSO, the North Atlantic Oscillation (NAO), and the northern and southern hemisphere annular modes (NAM and SAM, respectively).

The analysis of internally generated decadal potential predictability undertaken here cannot make a direct connection with these modes but does indicate a general decrease of decadal variability (at least in the model world). This is of interest in itself as well as indicating where to look for mechanisms responsible for the decrease. The potential predictability results also connect with some of the results discussed in M07. In the North Atlantic, for instance, the weakening of the MOC and associated changes in heat transports are noted as a general result in simulations of a warmer world. In the South Atlantic, a poleward shift, strengthening and narrowing of the SH westerlies with enhanced equatorward surface transport, and deeper poleward return flows are documented. These are mean changes in circulations but are apparently also associated with changes in long time-scale variability as indicated by the p_ν changes in Fig. 5 for temperature and, to some extent, precipitation.

Parker et al. (2007) argue for a connection between the long time-scale variations of the MOC and the AMO by regressing decadal mean temperatures on a decadal MOC index in results from a long simulation with the third climate configuration of the Met Office Unified Model (HadCM3). The zero-lag regression pattern (their Fig. 7a) resembles the patterns of p_ν difference for temperature in Fig. 5 over both the North Pacific and Atlantic (even though the HadCM3 model does not appear in Table 1). The coherence of these patterns suggests a decrease in this mode of variability in the warmer world as a possible cause of the pattern of p_ν change. However, the corresponding regression for decadal mean precipitation (their Fig. 8) gives a patchy pattern only vaguely reminiscent of that in Fig. 5 for the change in p_ν for precipitation.

For the North Pacific, Kwon and Deser (2007) analyze decadal variability in a version of the National Center for Atmospheric Research (NCAR) coupled model. They note long time-scale variability of temperature associated with the Kuroshio extension region and suggest a coupled mechanism for its existence. If the decadal potential predictability in the North Pacific can be associated with such a mechanism, then Fig. 5 suggests a decrease in this variability in a warmer world.

Actual decadal predictions, as an initial and boundary value problem, are made in Smith et al. (2007) and Keenlyside et al. (2008). These predictions include the externally forced signal as well as the internally generated decadal component. To the extent that p_ν reflects the behavior of the coupled climate system, the results in Fig. 5 give some indication as to where we may hope to find predictive skill at long time scales for the internally generated long time-scale component and how it might change as a consequence of changes in climate process and feedbacks in a warmer world. In other words, a prediction of the mean temperature anomaly for the next decade will include contributions from both forced and internally generated components of variability. The general decrease of p_ν implies an expected loss of decadal predictability in this latter component in a warmer world.