Forcing, feedback and internal variability in global temperature trends

ARTICLE                                    doi:10.1038/nature14117

Forcing, feedback and internal variability in global temperature trends

Jochem Marotzke1 & Piers M. Forster2

 

 

 

The GMST has risen in the past fifteen years at a rate that is only one- third to one-half of the average over the second half of the twentieth century (see, for example, refs 1–5). This hiatus is not reproduced in most simulations with present-generation climate models, which instead over the period 1998–2012 show a larger GMST trend than observed5–14. The difference between GMST observations and simulations is caused in part by quasi-random internal climate variability5–10,13,14, which arises because of chaotic processes in the climate system. But part of the difference is probably caused by errors in the model radiative for- cing5,12,14–16 or in the model response to radiative forcing5,14,17,18. The relative magnitudes of these three contributions are poorly known. Here we quantify how forcing, feedback and internal climate variability con- tribute to spread in simulated historical GMST trends and, hence, to the differences between models and observations.

We use a three-pronged approach. First, we note that, owing to quasi- random internal climate variability, the difference between observed and simulated trends likewise contains quasi-random contributions. To avoid focusing too strongly on the particular period 1998–2012, which contains some climate extremes relevant for GMST19–21 and is hence unlikely to be reproduced in a simulation containing quasi-random contributions, we analyse GMST trends of a certain length for the entire period 1900–201213. Second, we quantify the contributions of forcing, climate feedback, ocean heat uptake and internal variability to simu- lated GMST trends, through a multiple linear regression approach that is physically motivated by the global surface energy balance. And, third, we investigate trends over both 15 and 62 years, representing decadal and multidecadal timescales, respectively. We combine these three as- pects into a new unified conceptual framework, which allows us to put the GMST trends over the 15-year period 1998–2012 into the appro- priate context.

We first create linear trends from an ordinary least-squares fit, and perform all statistical analyses on these trends. This procedure implies that the analysis must be repeated for each trend length, in contrast to previous work aiming at attributing elements in the observed GMST time series itself; such elements include effects of volcanic eruptions,

solar variability, anthropogenic forcing, El Nin˜o events and sources of atmospheric dynamic variability including land–sea contrasts13,14,22–25. Because the amplitude of internal variability decreases with increasing trend length3,26, we expect a clearer breakdown into the individual con- tributions from forcing, feedback and internal variability if we focus on one trend length at a time. We analyse trends over both 15 and 62 years, because these were the trend lengths primarily considered in the Inter- governmental Panel on Climate Change Assessment Report 55 (AR5).

 

Observed and simulated 15-year trends

To gauge whether the difference between simulations and observations is unusual over the hiatus period, we first compare observed and simu- lated 15-year trends over the entire period 1900–2012 (Fig. 1; see also ref. 13). We use the HadCRUT4 observational data set27 and the ‘his- torical’ simulations conducted under the auspices of the Coupled Model Intercomparison Project Phase 528 (CMIP5), extended for the years 2006–2012 with the RCP4.5 scenario runs (Extended Data Fig. 1 and Extended Data Table 1). The simulation output is subsampled using the HadCRUT4 data mask11, to account for the effects of incomplete observational coverage29,30.

Figure 1a contains the joint relative frequency distribution of 15-year GMST trends across the 114 available CMIP5 simulations, as a func- tion of start years since 1900 and trend size. Compared with the CMIP5 ensemble, observed trends are distributed in no discernibly preferred way and occur sometimes at the upper end of the ensemble (for exam- ple, for start year 1927 the best-estimate observed trend is larger than 110 of the 114 simulated trends; Fig. 1b) and sometimes at the lower end of the ensemble (for example, for start year 1998 the best-estimate observed trend is smaller than all 114 simulated trends; Fig. 1c)5,13,26.

In both cases depicted in Figs 1b, c, fewer than 5% of the simulations lie in one of the tails relative to the observed trend. Hence, if a 5% cri- terion for statistical significance were used, one would diagnose formal model–observation inconsistency for 15-year trends with start years 1927 and 199811. But when the comparison is repeated for all start years, the rank that the observed trend would have as a member of the

 

 

1Max Planck Institute for Meteorology, Bundesstrasse 53, 20146 Hamburg, Germany. 2School of Earth and Environment, University of Leeds, Leeds LS2 9JT, UK.

 

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15-year GMST trend against start year: CMIP5 (colour), HadCRUT4 (black/grey)

 

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Figure 1 | Simulated and  observed  15-year GMST trends since 1900. a, Joint relative frequency distribution of GMST trends as a function of start year and trend size, based on the full 114-member ensemble (in bins of 0.025 uC per decade, as shown by colour scale). Circles mark the observed trend from the HadCRUT4 data set27. b, Vertical cross-section of a for start year 1927; vertical line marks the observed trend. c, As b, but for start year 1998. d, Marginal distribution of simulated GMST trend as a function of trend size (purple), obtained by time-averaging the joint

 

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distribution in a, and observed trend distribution (grey). e, Frequency distribution of the rank that the observed trend would have as a member of the

 

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model ensemble (rank 1, observed trend smaller than all simulations; rank 115, observed trend larger than all simulations); bin size is five.

All histograms are normalized such that their area integral is unity. In a, each vertical cross- section is normalized.

 

 

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ensemble of simulated trends31 shows no apparent bias (Fig. 1e), indi- cating that the observed and simulated distributions of 15-year trends are broadly consistent with each other. Any position of the observed trend within the ensemble of simulated trends—including a position at or near the margin—is thus dominated by quasi-random effects (al- though for any particular start year, a non-negligible contribution from systematic errors cannot be excluded).

The marginal distribution of simulated GMST trends as a function of trend size is wider than the observed distribution of trends (Fig. 1d), a finding consistent with that from the previous generation of climate models32. The width is exaggerated owing to contributions arising at three distinct periods. Some simulated trends with start years from around 1950–1960 are more strongly negative than any observed trends since 1900, and some simulated trends with start years from around 1960–1970 and from around 1985–1998 are more strongly positive than any observed trends since 1900 (Fig. 1a). All three periods (1950–1960, 1960–1970 and 1985–1998) are influenced by volcanic eruptions (Mount Agung in 1963 and Mount Pinatubo in 1991). We speculate that some, though not all, models overestimate the cooling induced by an eruption and the subsequent warming recovery (see, for example, ref. 12 con- cerning a confounding role of El Nin˜o).

The mean over all simulated 15-year trends during the period 1900– 2012 is 0.086 6 0.001 uC per decade (mean 6 s.e.m.; n 5 11,186), in

excellent agreement with the observed 0.088 6 0.01 uC per decade (n 5 99). Furthermore, of all 11,186 pairwise comparisons that are possible between simulated and observed trends, the observed trend is higher in 53.6% of cases, which is slightly above the 50% expected for a perfectly unbiased model ensemble. Figure 1 demonstrates that when viewed over the entire period 1900–2012, the 15-year GMST trends simulated by the CMIP5 ensemble show no systematic deviation from the observations. Our interpretation of Fig. 1 tacitly assumes that the simulated multimodel-ensemble spread accurately characterizes internal variabil- ity, an assumption shared with other interpretations of the position of observed trends relative to simulated trends (for example the reduction in Arctic summer sea ice5,33,34). We now test the validity of this assump- tion, by identifying deterministic and quasi-random causes of ensemble spread. We exploit the availability of a large number of simulations— 114  realizations  with 36  different models,  with forcing information

available for 75 realizations with 18 different models35 (Extended Data Figs 1 and 2 and Extended Data Table 1)—and investigate the contri- butions of radiative forcing, climate feedback and ocean heat uptake to all simulated 15-year and 62-year GMST trends during the period 1900–2012.

Energy balance and multiple regression

Our starting point is the globally averaged energy balance for the sur- face layer35–37. An increasing trend DF in effective radiative forcing (ERF) causes an increasing trend DT in GMST. This in turn leads to increased outgoing radiation, which in linearized form is written as aDT, where a is the climate feedback parameter. Furthermore, the GMST increase leads to increased heat transfer from the surface layer to the subsurface ocean, written, again in linearized form, as kDT, where k is the ocean heat uptake efficiency. The thermal adjustment of the surface layer to DF is expected to occur within a few years35–37. This means that for timescales of one to several decades, the surface energy balance is in quasi-steady state and reads

ðazkÞDT~DF

which produces the energy-balance ‘prediction’ for the GMST trend:

 

DT~DFazkÞ                             ð1Þ

Each CMIP5 model simulates its own ERF time series over the his- torical period. These time series were diagnosed previously35; if mul- tiple realizations were available for a model, the ensemble average of the individual diagnosed ERF time series for this model was given35 and is used here. The individual a and k values were previously determined for each CMIP5 model from a regression of global top-of-atmosphere energy imbalance against GMST5,35,38–41, in turn based on simulations in which the CO2 concentration was quadrupled abruptly. The ranges of a and k are 0.6–1.8 and 0.45–1.52 W m22 uC21, respectively. That a and k in the CMIP5 models might vary with time and climate state42,43 is ignored here. There is some positive, though not statistically signifi- cant, correlation between a and k (across the 75-member subensemble, the correlation is 0.17 with P 5 0.14).

 

 

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Each model’s a value is related to its equilibrium climate sensitivity (ECS) by

ECS~F2x=a                                                 ð2Þ

where F2x is the effective radiative forcing from a doubling of the pre- industrial atmospheric CO2 concentration. The reference value for F2x is 3.7 W m22 (see, for example, ref. 44), but F2x varies between 2.6 and

4.3 W m22 across the CMIP5 ensemble5,38. To avoid confounding the uncertainty in model response with the uncertainty from CO2 forcing, we use a and not ECS to characterize model response.

On the basis of the physical foundation of energy balance (equa- tion (1)), we determine the extent to which the across-ensemble varia- tions of DF, a and k contribute to the ensemble spread of GMST trends DT, using the 75-member subensemble of CMIP5 historical simula- tions for which radiative forcing information can be obtained from the CMIP5 archive35 (Extended Data Table 1). The presence of internal

1963 (Fig. 2b; the deterministic ensemble spread is particularly large in these periods; see Extended Data Fig. 4a). The distribution of residuals shows little time dependence, as evidenced by spread that is similar for all start years (Fig. 2c–f). The generally weak time dependence of the spread suggests that we can estimate the magnitudes of deterministic spread and internal variability from the marginal distributions obtained by time-averaging the distributions shown in Fig. 2b and Fig. 2c, re- spectively. The 5–95% range is 0.11 uC per decade for the regression result and 0.26 uC per decade for the residuals; internal variability thus dominates deterministic spread by a factor of 2.5. The dominance of internal variability in the ensemble spread of the 15-year GMST trends indicates that, viewed over the entire period 1900–2012, no systematic model error needs to be invoked when trying to explain differences be- tween simulated and observed trends. In particular, the GMST spread due to feedback a is not systematically larger than the spread from either

 

variability is included in our framework by adding a random term to equation (1), such that our equation is

DT~DFazkÞze                                         ð3Þ

Because equation (3) assumes an increasing trend in ERF, its validity is somewhat questionable following a volcanic eruption (see, for ex-

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15-year GMST trend from regression and from observations

 

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ample, ref. 25). However, Extended Data Fig. 3 shows that overall we see a reliable relationship between ERF and GMST trends in the CMIP5 ensemble, even if the ERF trend is negative.

We make the connection to multiple linear regression by writing each quantity as

xxzx0

where theoverbar marks the ensemble average andtheprime the across- ensemble variation. Linear expansion of equation (3) thus produces

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Prediction from regression

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DT¯ zDT0~  DF¯

¯azk¯

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z

¯azk¯

DF0{       DF¯      a0

ð¯azk¯Þ2

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{      DF¯      k0ze

ð¯azk¯Þ2

This equation holds for each start year separately and suggests the regression model

DTj0~b0zb1DFj0zb2a0jzb3k0jzej,              j~1,:::,75

We thus perform for each start year a multiple linear regression of DT9 against DF9, a9 and k9. The regression residual e is interpreted as the contribution from internal variability. The complete regression-based

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d 1927−1941 e 1998−2012 f All periods
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prediction for GMST trend is obtained by adding the ensemble-mean trend to the regression for the across-ensemble variations:

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DT^reg,j~DT¯zb^0zb^1DFj0zb^2a0jzb^3k0j,    j~1,:::,75        ð4Þ

where the caret marks the regression estimate. We note that for a model that has multiple realizations, the same DF9j, a9j or k9j value is counted multiple times. The regression is performed separately for each period length over which trends are computed. We interpret the ensemble spread of the regression result DT^reg,j, j 5 1, …, 75, as the deterministic spread and the spread ^ej, j 5 1, …, 75, of the residuals as the quasi-random spread.

 

Deterministic versus quasi-random spread

For 15-year GMST trends, deterministic across-ensemble variations are smaller than internal variability, as shown by the comparison of the regression-based ensemble spread with the regression residuals (Fig. 2b and Fig. 2c, respectively). The regression result shows substantial time dependence in ensemble spread only for 15-year periods influenced by major volcanic eruptions, in particular the Mount Agung eruption in

Trend (°C per decade)

Figure 2 | Regression-based and observed 15-year GMST trends since 1900. a, Joint relative frequency distribution of regression-based GMST trends (equation (4)) as a function of start year and trend size (in bins of 0.025 uC per decade, as shown by colour scale), based on the reduced 75-member ensemble for which forcing information is available. The thick red line marks the ensemble average, the thick black line marks the observed trend and whiskers indicate the 5–95% confidence range derived from f. b, Joint relative frequency distribution of regression result (equation (4) minus the ensemble-mean trend) as a function of start year and trend size (in bins of 0.025 uC per decade). The P value of the regression has a median across start years of 0.075, based on the null hypothesis that all regression coefficients are zero. c, Joint relative frequency distribution of regression residual as a function of start year and trend size (in bins of 0.025 uC per decade). d, Vertical cross-section of c for start year 1927. e, Vertical cross-section of c for start year 1998. f, Marginal distribution of regression residual as a function of trend size, obtained by time- averaging the joint distribution in c. All histograms are normalized such

that their area integral is unity. In a–c, each vertical cross section is normalized, and the ordinate ranges are identical.

 

 

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the ERF trend or ocean heat uptake efficiency, and is much smaller than the internal variability (Extended Data Fig. 4 and Fig. 2; see also ref. 12).

a         62-year GMST trends from regression and from observations

0.15                                               Ensemble mean                                                                                          60

 

For any given start year, the residual spread is very similar to the full

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ensemble spread, implying that we can indeed use the ensemble spread as a measure of internal variability (compare Fig. 1b, c with Fig. 2d, e). Furthermore, identifying the ensemble spread of the regression resi-

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duals with internal variability allows us to characterize the component of observational uncertainty that arises from internal variability (Fig. 2a, f). This uncertainty does not concern the construction of the global aver- age from individual station data (which has much smaller uncertainty5) but relates to the question of whether an observed trend is statistically significant (detectable) given serial correlation arising from internal variability18. Our model-based estimate of 0.26 uC per decade for the 5–95% confidence interval for observed 15-year GMST trends is slightly larger than the AR5 serial-correlation-based estimate for the uncer- tainty in the observed GMST trend over the hiatus period (0.2 uC per decade; ref. 4). We deem this an acceptable agreement given that the estimates were obtained through completely different approaches. We further note that the CMIP5 ensemble has been assessed to be generally consistent with observed historical decadal variability in GMST5, al- though on average it somewhat overestimates the global variability in the lower troposphere45.

For most of the historical period, the entire ensemble of regression- based simulated 15-year GMST trends lies within the model-estimated 5–95% confidence interval of the observations (Fig. 2a). The regres- sion-based simulated ensemble partly falls outside this interval during the cooling following the Mount Agung eruption and the subsequent warming recovery, as well as for start dates after 1990, which include the warming recovery following the Mount Pinatubo eruption and the surface warming hiatus (Fig. 2a). Because the phases of volcanically driven cooling and subsequent warming coincide with larger regres-

sion spread due to the ERF trend (Extended Data Fig. 4), we speculate

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that the implementation of volcanic forcing requires improvement in some climate models.

The ensemble spread of 62-year GMST trends is dominated by in- ternal variability for start years early in the twentieth century, but for start years from 1910 onwards, the deterministic spread increases and dominates for start years 1920 and later (Fig. 3). The 5–95% range of the regression residuals is 0.059 uC per decade, compared with a deter- ministic range of 0.032 uC per decade for start year 1900 and 0.093 uC per decade for start year 1951. The 5–95% deterministic range for all 62-year trends is 0.081 uC per decade, which is larger by one-third than the 5–95% range from internal variability. Nevertheless, we see a sub- stantial influence of internal variability even for GMST trends over 62 years.

When observational uncertainty is accounted for—again on the basis of the 5–95% confidence interval derived from quasi-random model spread—the ensemble-mean simulated 62-year GMST trend is consist- ent with the observed trend for all start years after around 1915; before that, the simulations tend to warm too little (Fig. 3a). After around 1945, the ensemble-mean simulated 62-year trend lies above the observed trend, although their difference is smaller than the range of internal variability. From around 1925 onward, both the largest and the smal- lest individual regression-based simulated trends lie outside the range defined by observations plus internal variability and are hence be judged to be inconsistent with observations (Fig. 3a).

The cause of this inconsistency can be traced almost entirely to the contribution to the regression by the ERF trend (Fig. 3). By contrast, the magnitude of the contributions from a and k is around 0.01 uC per decade or less for all start years (Fig. 3e, f). The deterministic ensemble spread in 62-year GMST trend is hence dominated by the spread in ERF throughout the twentieth century (Fig. 3).

 

Discussion

Viewed over the entire period since 1900, the differences between simu- lated and observed 15-year trends in GMST are dominated by internal

1900 1905 1910 1915 1920 1925 1930 1935 1940 1945 1950 0

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Figure 3 | Regression-based and observed 62-year GMST trends since 1900. a, Joint relative frequency distribution of regression-based GMST trends (equation (4); shown by colour scale) as a function of start year and trend size, based on the reduced 75-member ensemble for which forcing information is available. The thick red line marks the ensemble average, the thick black line marks the observed trend and whiskers indicate the 5–95% confidence

range derived from the marginal distribution of c. b, Joint relative frequency distribution of regression result (equation (4) minus the ensemble-mean trend) as a function of start year and trend size. All P values of the regression are below 0.001, based on the null hypothesis that all regression coefficients

are zero. c, Joint relative frequency distribution of regression residual as a function of start year and trend size. d, Joint relative frequency distribution of regression contribution from trend in effective radiative forcing. e, Joint relative frequency distribution of regression contribution from climate feedback parameter a. f, Joint relative frequency distribution of regression contribution from ocean heat uptake efficiency k. In all joint relative frequency distributions, GMST trend is collected in bins of 0.0125 uC per decade, and each vertical cross section is normalized such that its area integral is unity. All ordinate ranges are identical.

 

variability and hence arise largely by coincidence, with a minor con- tribution from volcanic forcing that is sometimes too strong in some models (Fig. 2). Furthermore, we confirm, and extend to all 15-year radiative forcing trends since 1900, the AR5 assessment for the hiatus period5 that the CMIP5 models show little systematic bias when com- pared with the AR5 best-estimate radiative forcing trend46—despite the substantial scatter about the ensemble mean (Extended Data Fig. 2). The generally dominant role of internal variability in shaping simu- lated 15-year GMST trends implies that internal variability also dom- inates the difference between simulations and observations during the hiatus period. This conclusion considerably sharpens the relative roles of internal variability, forcing error and response error, compared with the corresponding AR5 assessment5. Although there is no obvious con- tribution of forcing bias in the CMIP5 models (Extended Data Fig. 2),

 

 

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the diagnosed radiative forcing is uncertain35. Hence, our analysis can- not rule out a small contribution from a systematic forcing bias12,15,16,46–48 in the models. In particular, volcanic forcing is estimated to contribute to the difference between simulations and observations by up to 15% over 1998–201212, with large uncertainty in the magnitude. This is a contribution that our method cannot detect. Furthermore, the period 1998–2012 stands out as the only one during which the HadCRUT4 15-year GMST trend falls entirely outside the CMIP5 ensemble (if only narrowly), suggesting that the CMIP5 models could be missing a cooling contribution from the radiative forcing during the hiatus period12,15,16,46–48, or that there has been an unusual enhancement of ocean heat uptake not simulated by any model19.

For 62-year GMST trends since 1900, the difference between simu- lations and observations is dominated by the spread in the radiative forcing trend in the models, with a smaller yet substantial influence of internal variability (Fig. 3). Our simple regression-based estimate of internal variability in 62-year GMST trends corresponds to a 17–83% range of 60.11 uC for the temperature change over six decades, which is in excellent agreement with the value of 60.10 uC that has been found for the period 1951–2010 using much more sophisticated formal meth- ods of detection and attribution18.

There is scientific, political and public debate regarding the question of whether the GMST difference between simulations and observations during the hiatus period might be a sign of an equilibrium model re- sponse to a given radiative forcing that is systematically too strong, or, equivalently, of a simulated climate feedback a that is systematically too small (equation (2)). By contrast, we find no substantive physical or sta- tistical connection between simulated climate feedback and simulated GMST trends over the hiatus or any other period, for either 15- or 62- year trends (Figs 2 and 3 and Extended Data Fig. 4). The role of sim- ulated climate feedback in explaining the difference between simulations and observations is hence minor or even negligible. By implication, the comparison of simulated and observed GMST trends does not permit inference about which magnitude of simulated climate feedback—ran- ging from 0.6 to 1.8 W m22 uC21 in the CMIP5 ensemble—better fits the observations. Because observed GMST trends do not allow us to distinguish between simulated climate feedbacks that vary by a factor of three, the claim that climate models systematically overestimate the GMST response to radiative forcing from increasing greenhouse gas concentrations seems to be unfounded.

Online Content Methods, along with any additional Extended Data display items and Source Data, are available in the online version of the paper; references unique to these sections appear only in the online paper.

 

Received 6 August; accepted 26 November 2014.

 

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  1. Ridley, A. et al. Total volcanic stratospheric aerosol optical depths and implications for global climate change. Geophys. Res. Lett. 41, 7763–7769 (2014).

Acknowledgements We are indebted to J. Fyfe for making his CMIP5 GMST data set available to us, and to D. Notz, J. Risbey and B. Santer for comments on the manuscript. We acknowledge the World Climate Research Programme’s Working Group on Coupled Modelling, which is responsible for CMIP, and we thank the climate modelling groups (names of models listed in Extended Data Table 1) for producing and making available their model output. For CMIP the US 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. This work was supported by the Max Planck Society for the Advancement of Science (J.M.) and by a Royal Society Wolfson Merit Award and EPSRC grant EP/1014721/1 (P.M.F.).

Author Contributions The authors jointly designed the study. J.M. analysed the data and wrote the manuscript. Both authors discussed the results and the manuscript.

Author Information Reprints and permissions information is available at www.nature.com/reprints. The authors declare no competing financial interests. Readers are welcome to comment on the online version of the paper.

Correspondence and requests for materials should be addressed to

J.M. (jochem.marotzke@mpimet.mpg.de).

 

 

 

 

 

强迫,反馈和全球温度趋势的内部变化

文章doi:10.1038 / nature14117

强迫,反馈和全球温度趋势的内部变化

Jochem Marotzke 1 &Piers M. Forster 2

GMST在过去15年间以20世纪下半叶平均值的三分之一到二分之一的速度增长(参见例如参考文献1-5)。 在现代气候模式的大多数模拟中,这种间断并未被重现,相反在1998 – 2012年期间,GMST趋势比观测到的5-14有所增加。 GMST观测与模拟之间的差异部分是由于气候系统中混沌过程引起的准随机内部气候变率造成的。 但部分差异可能是由模型辐射偏差5,12,14-16或模型对辐射强迫的反应5,14,17,18引起的。 这三个贡献的相对大小是鲜为人知的。 在这里,我们量化强迫,反馈和内部气候变率如何有助于在模拟的历史GMST趋势中扩散,并因此量化模型和观测之间的差异。

我们采用三管齐下的方法。 首先,我们注意到,由于准随机内部气候变率,观测和模拟趋势之间的差异同样包含准随机贡献。 为了避免过分强调1998 – 2012年的特定时期,其中包含与GMST19-21相关的一些气候极端事件,因此不可能在包含准随机贡献的模拟中再现,我们分析整个GMST一定长度的趋势期间1900-201213。 其次,我们量化强迫,气候反馈,海洋热量吸收和内部变率对模拟GMST趋势的贡献,通过一种由全球地表能量平衡驱动的多元线性回归方法。 第三,我们调查了15年和62年的趋势,分别代表了十年和十年的时间尺度。 我们将这三个方面结合到一个新的统一概念框架中,这使我们能够将1998 – 2012年的GMST趋势置于适当的背景下。

我们首先根据普通最小二乘拟合创建线性趋势,并对这些趋势进行所有统计分析。 这个过程意味着必须对每个趋势长度重复进行分析,这与之前针对观察到的GMST时间序列中的元素归因的工作形成对比; 这些要素包括火山爆发的影响,

太阳变率,人为强迫,厄尔尼诺事件和大气动态变化来源,包括海陆对比13,14,22-25。 由于内部变率的幅度随着趋势长度的增加而减小[3,26],如果我们一次只关注一个趋势长度,我们期望从强迫,反馈和内部变率中明确地分解个体贡献。 我们分析了15年和62年的趋势,因为这些是政府间气候变化专门委员会评估报告55(AR5)主要考虑的趋势长度。

观察和模拟15年趋势

为了判断模拟和观测之间的差异在断层期间是否异常,我们首先比较1900 – 2012年整个时期的观测和模拟15年趋势(图1;另见参考文献13)。 我们使用HadCRUT4观测数据集27和在耦合模式比较项目阶段528(CMIP5)的主持下进行的’历史’模拟,在2006 – 2012年与RCP4.5场景运行延伸(Extended Data Fig。 1和扩展数据表1)。 模拟输出采用HadCRUT4数据mask11进行二次采样,以解释不完全观测覆盖29,30的影响。

图1a包含了114个可用CMIP5模拟中15年GMST趋势的联合相对频率分布,作为1900年以来的起始年份和趋势大小的函数。 与CMIP5集合相比,观测到的趋势分布并不明显优选,有时出现在集合的上端(例如,对于开始年份1927年最佳估计观测趋势大于114个模拟趋势中的110个;图1b),有时在整体的低端(例如,1998年开始的最佳估计观测趋势小于全部114个模拟趋势;图1c)5,13,​​26。

在图1b,c所示的两种情况下,相对于观察到的趋势,少于5%的模拟位于一个尾部。 因此,如果使用5%的统计显着性标准,则可以诊断1927年和1998年11年的15年趋势的形式模型观察不一致性。但是,当所有起始年重复比较时,观察到的趋势将作为一个成员

1Max普朗克气象研究所,德国汉堡Bundesstrasse 53,20146。 2利兹大学地球与环境学院,英国利兹LS2 9JT。

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与开始年份相比的15年GMST趋势:CMIP5(彩色),HadCRUT4(黑色/灰色)

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e 4

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图1 | 模拟和观测自1900年以来的15年GMST趋势。a,基于全部114个成员的集合(按照每10年0.025 uC的箱数,GMST趋势作为起始年和趋势尺寸的函数的联合相对频率分布,如彩色标尺)。 圆圈标记了HadCRUT4数据集观察到的趋势27。 b,1927年开始年的垂直横截面; 垂直线表示观察到的趋势。 c,作为b,但是为1998年开始。d,模拟GMST趋势的边际分布作为趋势尺寸(紫色)的函数,通过时间平均关节

0

1900年1910年1920年1930年1940年1950年1960年1970年1980年

开始一年

分布在a和观察的趋势分布(灰色)。 e,观察到的趋势将作为成员的等级的频率分布

b 1927-1941

6

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c 1998-2012 d

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所有时期

Ë

0.1

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频率

模型集成(等级1,观察趋势比所有模拟小;等级115,观察趋势大于所有模拟); bin大小是五。

所有的直方图都进行了归一化处理,以使它们的面积积分为1。 在a中,每个垂直横截面被归一化。

0

-0.2 0 0.2 0.4

0

-0.2 0 0.2 0.4

0

-0.5 0 0.5

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0 40 80 115

趋势(°C /十年)等级

模拟趋势的集合显示没有明显的偏差(图1e),表明15年趋势的观测和模拟分布大致相互一致。 观察到的趋势在整个模拟趋势中的任何位置(包括位于或接近边界的位置)都由准随机效应支配(尽管对于任何特定的开始年份,系统误差的不可忽略的贡献不可能是除外)。

模拟GMST趋势作为趋势尺寸函数的边际分布比观测到的趋势分布更宽(图1d),这与上一代气候模型的结果一致32。 由于在三个不同时期出现捐款,宽度被夸大了。 从1950年到1960年开始的一些模拟趋势比自1900年以来的任何观察到的趋势更为强烈,一些模拟的趋势与大约1960-1970年和大约1985-1998年的开始年相比,自1900年以来的任何观察到的趋势(图1a)。 所有三个时期(1950-1960,1960-1970和1985-1998)都受到火山喷发(1963年的阿贡山和1991年的皮纳图博山)的影响。 我们推测,有些模型(虽然不是全部)高估了喷发和随后的温度恢复所引起的冷却(例如,参见参考文献12关于El Nino的混杂作用)。

1900年至2012年期间所有模拟15年趋势的平均值为0.086 6 0.001 uC每十年(平均值6 sem; n 5 11,186),

与观察到的0.088 6 0.01 uC每十年( n 5 99)的一致性非常好。 此外,在模拟和观测趋势之间可能的所有11,186个成对比较中,所观察到的趋势在53.6%的情况下更高,略高于完美无偏模型集合的50%预期。 图1表明,在整个1900 – 2012年期间观察时,CMIP5集合模拟的15年GMST趋势显示没有系统偏离观测值。 我们对图1的解释默认假设模拟多模式集合传播准确地描述了内部变异性,这个假设与观测趋势相对于模拟趋势的位置的其他解释是一致的(例如,北极夏季海冰减少33,33 ,34)。 我们现在通过确定集合传播的确定性和准随机原因来测试这个假设的有效性。 我们利用大量模拟的可用性 – 具有36种不同模型的114种实现方式,强制信息

可用于75种具有18种不同模型的实现35(扩展数据图1和2以及扩展数据表1),并研究辐射强迫,气候反馈和海洋吸热对所有模拟15年和62年GMST趋势的贡献在1900 – 2012年期间。

能量平衡和多元回归

我们的出发点是地面层的全球平均能量平衡35-37。 有效辐射强迫(ERF)的增加趋势D F在GMST中引起增加的趋势D T。 这又导致出射辐射增加,其以线性化形式被写为D T ,其中a是气候反馈参数。 此外,GMST增加导致从表层到次表层海洋的热传递增加,再次以线性化形式写成k D T ,其中k是海洋热吸收效率。 表面层对D F的热调整预计在几年内发生35-37。 这意味着对于一到几十年的时间尺度,表面能平衡处于准稳态并读取

ða z kÞDT〜D F

这为GMST趋势产生了能量平衡’预测’:

D T〜D F = a a z kÞð1

每个CMIP5模型在历史时期都模拟自己的ERF时间序列。 这些时间序列以前被诊断过35; 如果一个模型有多个实现可用,那么这个模型的单个诊断ERF时间序列的集合平均值就被给出了35并且在这里被使用。 根据全球顶部大气能量不平衡对GMST5,35,38-41的回归,依次基于CO 2浓度突然增加四倍的模拟,对每个CMIP5模型预先确定了个体ak值。 ak的范围分别为0.6-1.8和0.45-1.52 W m 22 uC 21 。 CMIP5模型中的ak可能随时间和气候状态而变化42,43在这里被忽略。 ak之间存在一些积极的,但不是统计上显着的相关性(在75名成员中,相关系数为0.17, P =0.14)。

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每个模型的一个值与其平衡气候敏感度(ECS)有关

ECS〜F 2 x = a                                                  ð2Þ

其中F x是工业化前大气中二氧化碳浓度翻倍的有效辐射强迫。 F x的参考值是3.7 W m 22 (参见例如参考文献44),但F x在2.6和2.5之间变化

整个CMIP5集合53,32的4.3 W m 22 。 为避免模型响应的不确定性与CO 2强迫的不确定性混淆,我们使用a而非ECS来表征模型响应。

根据能量平衡的物理基础(方程(1)),我们确定D F , ak的跨集合变化对GMST趋势D T的集合扩散的贡献程度,使用CMIP5历史模拟的75个成员小组,可以从CMIP5档案35(扩展数据表1)获得辐射强迫信息。内部的存在

1963年(图2b;这些时期的确定性集合扩散特别大;见扩展数据图4a)。 残差的分布显示出很小的时间依赖性,如所有开始年份的差异所显示的那样(图2c-f)。 扩散的时间依赖性通常很弱,这表明我们可以通过分别对图2b和图2c所示的分布进行时间平均,从边际分布中估计确定性扩散和内部变化的幅度。 回归结果的5-95%范围为每十年0.11 uC,残差为每十年0.26 uC; 因此内部变异主导了确定性传播2.5倍。 15年GMST趋势的集合传播中的内部变率优势表明,从1900 – 2012年的整个时期来看,在试图解释模拟和观测趋势之间的差异时,不需要引用系统模型误差。 特别是,由于反馈a而导致的GMST传播并不系统地大于两者的传播

在我们的框架中,通过在方程(1)中加入一个随机项来包含变异性,这样我们的方程就是

D T〜D F =ða z kÞze                                          ð3Þ

由于方程(3)假定ERF的增加趋势,其有效性在火山爆发后有些不确定(参见,

一个

0.4

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15年的GMST趋势来自回归和观测

20

15

        10

        合奏意味着5

HadCRUT4

充足,参考。 25)。 然而,扩展数据图3显示,总体而言,即使ERF趋势为负,我们也可以看到CMIP5集合中ERF和GMST趋势之间的可靠关系。

通过将每个数量写为,我们连接到多个线性回归

x〜x z x 0

那里的overover标志着整体的平均值和最高的整体变化。 等式(3)的线性展开由此产生

1900年1910年1920年1930年1940年1950年1960年1970年1980年1990年0

从回归预测

b

 

0.2 20

0 15

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T D D D 0〜D F

¯a z k¯

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ž

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F 0 {D F a 0

ða z kÞ2

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0.2

4

{D F k 0 z e

ða z kÞ2

这个等式分别适用于每个开始年,并建议回归模型

T j 0〜b 0z b 1 D F j 0z b 2 a 0 j z b 3 k 0 j z e j                j〜1 ,…, 75

因此,我们对每个开始年份执行D T 9与D F 9, a 9和k 9的多元线性回归。回归残差e被解释为来自内部变率的贡献。 完全基于回归的

0

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1900年1910年1920年1930年1940年1950年1960年1970年1980年1990年0

开始一年

d 1927年至1941年 Ë 1998-2012 F 所有时期
6 6 6
4 4 4
2 2 2

GMST趋势预测是通过将整体平均趋势与跨整体变化的回归相加得到的:

0

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0

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0

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T ^ reg  j  CenterDot; D T zz ^ 0z b ^ 1D F j 0z b ^ 2 a 0 j z b ^ 3 k 0 j       j〜1  :::  75(4)

插入标记回归估计值。 我们注意到,对于具有多个实现的模型,相同的D F 9 j ,9 jk 9 j值被多次计数。 针对计算趋势的每个周期长度分别执行回归。 我们将回归结果D T ^ reg  j , j 5 1,…,75的集合扩散解释为残差的确定性扩展和扩展^ j , j 5 1,…,75作为准 -随机传播。

确定性与准随机传播

对于15年的GMST趋势,确定性的整体变异小于内部变异性,如基于回归的总体扩散与回归残差的比较所示(分别为图2b和图2c)。 回归结果显示,只有受到主要火山喷发影响的15年时间内,集合体传播才有相当大的时间依赖性,特别是阿贡火山喷发

趋势(°C每十年)

图2 | a,自1900年以来基于回归和观察到的15年GMST趋势。a,基于回归的GMST趋势(方程(4))的联合相对频率分布,作为起始年和趋势大小的函数(以0.025 uC /以颜色标度显示),基于可获得强制信息的减少的75个成员的集合。 红色粗线表示整体平均值,粗黑线表示观察到的趋势,胡须表示从f导出的5-95%置信范围。 b,回归结果的联合相对频率分布(方程(4)减去总体平均趋势)作为起始年和趋势尺寸(以每十年0.025 uC的单位)的函数。 根据所有回归系数均为零的无效假设,回归的P值在开始年份的中位数为0.075。 c,回归残差的联合相对频率分布是起始年和趋势大小的函数(以每十年0.025 uC的单位)。 d,1927年开始年的c的垂直横截面。e,1998年开始年的c的垂直横截面。f,通过对c中的联合分布进行时间平均而获得的回归残差的边际分布作为趋势尺寸的函数。 所有的直方图都被标准化了

他们的面积积分是统一的。 在a-c中,每个垂直横截面被标准化,并且纵坐标范围是相同的。

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ERF趋势或海洋热量吸收效率,并且远小于内部变率(扩展数据图4和图2;参见参考文献12)。

一个 62年的GMST从回归和观测趋势

0.15      合奏意味着60

对于任何给定的开始年份,剩余价差与满额非常相似

0.1

0.05

HadCRUT4

40

这意味着我们确实可以使用集合传播来度量内部变率(比较图1b,c和图2d,e)。 此外,确定回归resi-

0       20

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b

具有内部变异性的对偶使我们能够表征由内部变异引起的观测不确定性的组成部分(图2a,f)。 这种不确定性并不涉及从单个台站数据(其具有小得多的不确定性5)构建全球平均值,而是涉及观察到的趋势是否在统计上显着(可检测)的问题,因为内部变率引起的序列相关性18。 我们对观测到的15年GMST趋势的5-95%置信区间的基于模型的估计为每10年0.26 uC,略高于基于AR5序列相关估计的观测GMST趋势上的不确定性时期(每十年0.2uC;参考文献4)。 我们认为这是一个可接受的协议,因为估计是通过完全不同的方法获得的。 我们进一步注意到,CMIP5集合已被评估为与GMST5观测到的历史年代际变率基本一致,尽管平均而言它有点高估了对流层低层45的全球变率。

在大部分历史时期,基于回归的模拟15年GMST趋势的整体集合在观测的模型估计的5-95%置信区间内(图2a)。 在阿贡火山喷发和随后的暖化恢复以及1990年以后的开始日期期间,基于回归的模拟集合部分落在此区间之外,其中包括在皮纳图博火山喷发后的变暖恢复和地表变暖间隙(图2a)。 由于火山驱动的冷却和随后的升温阶段与较大的回归相吻合,

我们推测,由于ERF趋势(扩展数据图4)导致锡永扩散

0.1

0

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C

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d

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0

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Ë

0.1

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F

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-0.1

从回归预测,所有贡献

40

20

回归残差40

20

0

从ERF趋势40

20

0

从α80开始

60

40

20

0

从κ80开始

                       60

40

20

火山强迫的实施需要一些气候模式的改进。

62年GMST趋势的集合传播主要是20世纪早期起始年的内部变率,但从1910年起的起始年,确定性传播在1920年和以后的开始年份增加并占主导地位(图3) 。 回归残差的范围为5-95%,每十年为0.059 uC,相比之下,1900年开始时的每十年决定性范围为0.032 uC,1951年开始时为每10年0.093 uC。确定性范围为5-95%所有62年的趋势是每十年0.081 uC,比内部变化的5-95%范围大三分之一。 尽管如此,即使对于62年来的GMST趋势,我们也看到了内部变率的巨大影响。

当考虑到观测不确定性 – 再次基于准随机模型扩散得到的5-95%置信区间时 – 集合平均模拟62年GMST趋势与所有开始年份的观测趋势一致大约在1915年; 在此之前,模拟温度往往偏少(图3a)。 大约在1945年之后,集合平均模拟的62年趋势位于观察到的趋势之上,尽管它们的差异小于内部变率的范围。 从大约1925年开始,最大和最小的基于回归的模拟趋势都在观测加内部变率定义的范围之外,因此被判断为与观测不一致(图3a)。

这种不一致的原因几乎完全可以归因于ERF趋势对回归的贡献(图3)。相比之下, ak贡献的大小在所有的起始年份中每十年约为0.01 uC或更少(图3e,f)。 因此,在62年的GMST趋势中确定性的集合传播因此在整个20世纪ERF的传播中占主导地位(图3)。

讨论

从1900年以来的整个时期来看,GMST模拟和观测的15年趋势之间的差异主要由内部

1900 1905 1910 1915 1920 1925 1930 1935 1940 1945 1950 0

开始一年

图3 | a。自1900年以来的回归和观测到的62年GMST趋势a。基于回归的GMST趋势的联合相对频率分布(方程(4);以色阶表示),作为起始年和趋势大小的函数,强制信息可用的75个成员的合奏。 浓红线表示整体平均值,粗黑线表示观察到的趋势,胡须表示5-95%的置信度

范围从c的边际分布导出。 b,回归结果的联合相对频率分布(方程(4)减去总体平均趋势)作为起始年和趋势大小的函数。 基于所有回归系数的零假设,回归的所有P值均低于0.001

是零。 c,回归残差的联合相对频率分布是起始年和趋势大小的函数。d,有效辐射强迫趋势回归贡献的联合相对频率分布。 e,来自气候反馈参数a的回归贡献的联合相对频率分布。 f,海洋吸热效率k对回归贡献的联合相对频率分布。 在所有联合相对频率分布中,GMST趋势以0.0125μC/十进制的单位收集,并且每个垂直横截面被归一化,使得其面积积分为1。所有的坐标范围都是相同的。

因此很大程度上是由巧合引起的,而火山强迫的一些小贡献在某些模型中有时过强(图2)。 此外,我们确认并延伸至自1900年以来的所有15年辐射强迫趋势,AR5评估中断期间5 CMIP5模型与AR5最佳估计辐射强迫趋势46相比,几乎没有系统偏差46 – 尽管大量分散在集合平均值(扩展数据图2)。 在模拟15年GMST趋势时,内部变率通常占主导地位,这意味着内部变率也会影响中断期间模拟和观测之间的差异。 与相应的AR5评估相比,这一结论显着提高了内部变异的相对作用,强迫错误和响应错误5。虽然在CMIP5模型中没有明显的强迫偏差贡献(扩展数据图2),但是,

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诊断的辐射强迫是不确定的35。 因此,我们的分析不能排除模型中系统强迫偏差12,15,16,46-48的小贡献。 特别是火山强迫估计在1998 – 2012年期间对模拟和观测之间的差异贡献了高达15%,其幅度存在很大的不确定性。 这是我们的方法无法检测到的贡献。 此外,1998-2012年是唯一一个HadCRUT4 15年GMST趋势完全落在CMIP5集合之外的地区(如果狭隘的话),这表明CMIP5模型可能缺少辐射强迫期间的冷却贡献断层周期12,15,16,46-48,或者海洋热量摄取的异常增强没有被任何模型模拟[19]。

对于自1900年以来的62年GMST趋势,模拟和观测之间的差异主要受模型中辐射强迫趋势的扩散影响,而内部变率的影响较小但实质性较强(图3)。 我们对62年GMST趋势的内部变异性的简单回归估计值对应于六十年来60.11 uC温度变化的17-83%范围,与60.10 uC的值一致1951 – 2010年期间使用更为复杂的正式检测和归因方法18。

关于GMST模拟与观测期间断层期间观测结果之间的差异是否可能是一个均衡模型响应的标志,这种模型对给定的系统性太强的辐射强迫作出反应的问题存在科学的,政治的和公共的争论,或者等同地,模拟气候反馈a系统太小(方程(2))。 相比之下,我们发现模拟气候反馈与断层或任何其他时段的模拟气候反馈和模拟GMST趋势之间没有实质性的物理或统计联系,无论是15年还是62年的趋势(图2和图3和扩展数据图4) 。 模拟气候反馈在解释模拟和观测之间差异的作用因此很小甚至可以忽略不计。 通过暗示,模拟和观测的GMST趋势的比较不允许推论CMIP5集合中模拟气候反馈的哪个幅度从0.6到1.8 W m 22 uC 21 – 更好地符合观测结果。 由于观测到的GMST趋势不允许我们区分模拟气候反馈的变化因子为3,所以气候模型系统地高估了GMST对增加温室气体浓度引起的辐射强迫响应似乎是没有根据的。

在线内容方法以及任何附加的扩展数据显示项目和源数据可在网上版本的文件中找到 ; 这些部分独有的参考文献仅出现在在线文章中。

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  1. Ridley,A。 等人 全球火山平流层气溶胶光学深度及其对全球气候变化的影响。 地球物理。 RES。 快报。 41,7763-7769(2014)。

致谢我们非常感谢J. Fyfe为我们提供他的CMIP5 GMST数据集,并感谢D. Notz,J. Risbey和B. Santer对手稿的评论。 我们承认世界气候研究计划的耦合建模工作组负责CMIP,并且我们感谢气候模拟组织(扩展数据表1中列出的模型名称),用于生成和提供其模型输出。 对于CMIP,美国能源部的气候模型诊断和比较计划提供了协调支持,并与全球组织

地球系统科学门户。 这项工作得到了马克斯普朗克科学促进协会(JM)和皇家学会欧胜优秀奖和EPSRC授予EP / 1014721/1(PMF)的支持。

作者贡献作者共同设计了这项研究。 JM分析了数据并撰写了手稿。 两位作者都讨论了结果和手稿。

作者信息重印和权限信息可从www.nature.com/reprint s获取。 作者声明没有竞争的财务利益。 欢迎读者对该论文在线版本发表评论。

函件和材料的请求应该被给予

JM (jochem.marotzke@mpimet.mpg.de) 。

5 7 0 | NATURE | VOL 5 1 7 | 2 9 1月2日0 1 5

一个

1.2

1

0.8

0.6

0.4

0.2

0

-0.2

-0.4

-0.6

-0.8

GMST,全套,36个型号,114个实现

1900年1920年1940年1960年1980年2000年

b

1.2

1

0.8

0.6

0.4

0.2

0

-0.2

-0.4

-0.6

-0.8

GMST,可用ERF的子集合,18个模型,75个实现

1900年1920年1940年1960年1980年2000年

扩展数据图1 | 从1900年到2012年,观测和模拟每年平均GMST异常的时间序列。所有异常与每个单独时间序列的1961-1990年时间平均值不同。

GMST是全球平均合并地表温度(地面和海洋表面温度为2米)。 该图显示单个

模拟CMIP5模型(细线),多模式集合平均值

(粗红线)和HadCRUT427观察结果(粗黑线)。 所有模型结果都使用HadCRUT4观测数据mask11进行二次采样。 a,来自CMIP5档案的114个实现,使用36种不同的型号获得。 b,具有ERF信息可用的18种不同模型的75个实现子集35(扩展数据表1)。 这两个模型合奏几乎难以区分。

ERF趋势,期限长度15年

2

1.5

1

0.5

0

-0.5

-1

-1.5

-2

1900年1910年1920年1930年1940年1950年1960年1970年1980年

开始一年

b

0.5

0.4

0.3

0.2

0.1

0

-0.1

-0.2

-0.3

-0.4

-0.5

ERF趋势,周期长度62年

1900 1905 1910 1915 1920 1925 1930 1935 1940 1945 1950

开始一年

扩展数据图2 | 作为起始年的函数,ERF的时间序列趋势。 a,15年的趋势;b,62年的趋势。 细彩的线条显示以前诊断的个别模型35; 如果一个模型有多个实现可用,那么给出该模型的单个诊断ERF时间序列的总体平均值,如图所示。 粗红线显示所有型号的整体平均值。 粗黑线表示AR546的最佳估计值,例如包括1984-1998(a)和1951-2011(b)期间5-95%的不确定性范围,取自图5。 参考文献8.19。 46.这些不确定性范围,二者均约为每十年0.2微米22 ,不考虑观察性偏差,例如参考文献中诊断的偏差。 48。

尽管CMIP5集合趋势分散,但集合平均值与几乎所有启动年的AR5最佳估计值都非常吻合。 AR5最佳估计ERF将个别强迫项的强制时间序列相加。AR5 ERF的各个时间序列以不同的方式推导出来。 温室气体浓度(观测或推断),平流层气溶胶光学深度

和总太阳辐照度被用来推导使用简单公式估算辐射强迫。 表面反照率强迫来自估计的人为植被趋势。 臭氧和气溶胶强迫来源于化学传输模式结果,强制方面受到其他建模方法或观测的约束,或两者兼有。 ERF将快速调整与传统的辐射强迫相结合。 AR5中的大多数时间序列基于传统的辐射强迫,只有CO 2和气溶胶强迫包括对快速调整的评估。 在其他情况下,ERF和辐射强迫假定是相同的。 最新的2000 – 2011年AR5 ERF包括火山强迫和太阳能强迫的最新估计,并考虑到2008-2009年太阳能最低和

2000年后的火山活动46。 这两种冷却影响不包括在CMIP5 ERF中; 因此,令人惊讶和无法解释的是,为什么CMIP5集合平均15年ERF趋势低于最新估算的AR5 ERF趋势。

一个

1

0.5

0

-0.5

15年,r = 1.73 W m -2 ( o C) -1 b

 

8

6

4

2

0.4

0.3

0.2

0.1

0

-0.1

-0.2

62年,r = 2.06 W m -2 ( o C) -1

60

40

20

0

-0.5 0 0.5

GMST趋势(每十年O C)

扩展数据图3 | 作为GMST趋势和ERF趋势的函数的联合相对频率分布,对于减少的75个成员集合,其强制信息可用并且所有起始年。 a,15年的趋势; 垃圾箱大小为每十年0.025 uC,GMST为每十年0.05 W m 22

和ERF趋势。 b,62年的趋势; bin大小为0.0125 uC每个

-0.2 -0.1 0 0.1 0.2

GMST趋势(每十年O C)

GMST和ERF趋势分别为10年和0.025 W / 10  / 10年。 ‘气候抵抗’ rra 1 k给出 (参考文献35-37)。 对每个联合分布进行归一化,使其面积积分为1。 注意不同的坐标轴,反映了62年趋势之间更密切的相关性。

一个

0.1

0.05

0

-0.05

-0.1

15年的GMST回归趋势

20

15

10

0

b

0.1 25

0.05 20

0 15

-0.05 10

-0.1 5

C

0.1 25

0.05 20

0 15

-0.05 10

-0.1 5

d

0.1 25

0.05 20

0 15

-0.05 10

-0.1 5

1900年1910年1920年1930年1940年1950年1960年1970年1980年

开始一年

扩展数据图4 | a。自1900年以来基于回归的15年GMST趋势。a,回归结果的联合相对频率分布(方程(4)减去总体平均趋势),作为起始年和趋势大小的函数。 基于所有回归系数为零的零假设,回归的P值在开始年份的中位数为0.075。 b,来自趋势的回归贡献的联合相对频率分布

ERF。 c,来自气候反馈参数a的回归贡献的联合相对频率分布a 。 d,来自海洋吸热效率k的回归贡献的联合相对频率分布。 在所有

联合相对频率分布,GMST趋势被收集在箱内

0.025 uC每十年,并且每个垂直横截面被归一化,使得其面积积分为1。

文章

扩展数据表1 | 本研究中使用的CMIP5模型

记录模型的原始机构和出版物在参考文献表9.A1中全面列出。 5。

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5 7 0 | N A T U R E | V O L 5 1 7 | 2 9 J A N U A R Y 2 0 1 5

 

 

 

a

1.2

1

0.8

0.6

0.4

0.2

0

−0.2

−0.4

−0.6

−0.8

GMST, full ensemble, 36 models, 114 realisations

 

1900                                   1920                                  1940                                   1960                                   1980                                  2000

Year

 

 

 

b

1.2

1

0.8

0.6

0.4

0.2

0

−0.2

−0.4

−0.6

−0.8

GMST, sub−ensemble with ERF available, 18 models, 75 realisations

 

1900                                   1920                                  1940                                   1960                                   1980                                  2000

Year

 

Extended Data Figure 1 | Observed and simulated time  series of the anomalies in annually averaged GMST, from 1900 to 2012. All anomalies are differences from the 1961–1990 temporal mean of each individual time series.

GMST is the globally averaged merged surface temperature (2 m height over land and surface temperature over the ocean). The figure shows single

simulations for the CMIP5 models (thin lines), the multimodel ensemble mean

(thick red line) and the HadCRUT427 observations (thick black line). All model results have been subsampled using the HadCRUT4 observational data mask11. a, 114 realizations from the CMIP5 archive, obtained with 36 different models. b, Subset of 75 realizations with the 18 different models for which information on ERF is available35 (Extended Data Table 1). The two model ensembles are nearly indistinguishable.

 

 

a                                                             ERF trend, period length 15 years

2

 

1.5

 

1

 

0.5

 

0

 

−0.5

 

−1

 

−1.5

 

−2

1900              1910              1920              1930              1940              1950              1960              1970              1980              1990

Start year

 

 

 

b

0.5

 

0.4

 

0.3

 

0.2

 

0.1

 

0

 

−0.1

 

−0.2

 

−0.3

 

−0.4

 

−0.5

ERF trend, period length 62 years

 

1900             1905             1910             1915             1920             1925             1930             1935             1940             1945             1950

Start year

 

Extended Data Figure 2 | Time series of trends in ERF, as a function of start year. a, 15-year trends; b, 62-year trends. Thin coloured lines show individual models as diagnosed previously35; if multiple realizations were available for a model, then the ensemble average of the individual diagnosed ERF time series for that model was given35 and is shown here. The thick red line shows the ensemble average over all models. The thick black line shows the best estimate from AR546, including, for illustration, the 5–95% uncertainty range for the periods 1984–1998 (a) and 1951–2011 (b), taken from fig. 8.19 in ref. 46. These uncertainty ranges, both of which are around 0.2 W m22 per decade, do not take into account observational biases such as those diagnosed in ref. 48.

Despite the scatter of the CMIP5 ensemble trends, the ensemble mean is in good agreement with the AR5 best estimate for almost all start years. The AR5 best-estimate ERF sums time series of forcing across individual forcing terms. Individual time series of AR5 ERF were derived in different ways. Greenhouse gas concentrations (observed or inferred), stratospheric aerosol optical depth

and total solar irradiance were used to derive estimates of radiative forcing using simple formulae. Surface albedo forcing was derived from estimated anthropogenic vegetation trends. Ozone and aerosol forcings were derived from chemical transport model results with aspects of the forcing constrained by other modelling approaches or observations, or both. ERF sums rapid adjustments with traditional radiative forcings. Most time series in AR5 were based on traditional radiative forcings, and only CO2 and aerosol forcings included an assessment of the rapid adjustment. In other cases ERF and radiative forcings were assumed to be the same. The AR5 ERF for the most recent 2000–2011 period included updated estimates of volcanic and solar forcing, taking into account the broader 2008–2009 solar minimum and

post-2000 volcanic activity46. These two cooling influences are not included in the CMIP5 ERF; it is hence surprising and unexplained why the CMIP5 ensemble-mean of 15-year ERF trends lies below the best-estimate AR5 ERF trend for the latest start years in a.

 

 

 

a

1

 

 

0.5

 

 

0

 

 

 

−0.5

15 years, r = 1.73 W m−2 (oC)−1                                      b

 

8

 

6

 

4

 

2

 

 

0.4

0.3

0.2

0.1

0

−0.1

−0.2

62 years, r = 2.06 W m−2 (oC)−1

 

60

 

 

40

 

 

20

 

 

0

 

−0.5                                 0                                  0.5

GMST trend (oC per decade)

Extended Data Figure 3 | Joint relative frequency distribution as a function of GMST trend and ERF trend, for the reduced 75-member ensemble for which forcing information is available and all start years. a, 15-year trends; bin sizes are 0.025 uC per decade and 0.05 W m22 per decade for GMST

and ERF trend, respectively. b, 62-year trends; bin sizes are 0.0125 uC per

−0.2        −0.1           0            0.1          0.2

GMST trend (oC per decade)

decade and 0.025 W m22 per decade for GMST and ERF trend, respectively. The ‘climate resistance’, r, is given by r 5 a 1 k (refs 35–37). Each joint distribution is normalized such that its area integral is unity. Note the different axes, reflecting the much tighter correlation of the 62-year trends.

 

 

 

 

a

0.1

0.05

0

−0.05

−0.1

15−year GMST trend from regression

 

20

15

10

5

0

 

 

b

0.1                                                                                                                                                                                                 25

0.05                                                                                                                                                                                                 20

0                                                                                                                                                                                                 15

−0.05                                                                                                                                                                                                 10

−0.1                                                                                                                                                                                                 5

 

 

c

0.1                                                                                                                                                                                                 25

0.05                                                                                                                                                                                                 20

0                                                                                                                                                                                                 15

−0.05                                                                                                                                                                                                 10

−0.1                                                                                                                                                                                                 5

 

 

d

0.1                                                                                                                                                                                                 25

0.05                                                                                                                                                                                                 20

0                                                                                                                                                                                                 15

−0.05                                                                                                                                                                                                 10

−0.1                                                                                                                                                                                                 5

 

1900          1910          1920          1930          1940          1950          1960          1970          1980          1990

Start year

 

Extended Data Figure 4 | Regression-based 15-year GMST trends since 1900. a, Joint relative frequency distribution of regression result (equation (4) minus the ensemble-mean trend) as a function of start year and trend size. The P values of the regression have a median across start years of 0.075, based on the null hypothesis that all regression coefficients are zero. b, Joint relative frequency distribution of regression contribution from the trend in

ERF. c, Joint relative frequency distribution of regression contribution from the climate feedback parameter a. d, Joint relative frequency distribution of regression contribution from the ocean heat uptake efficiency k. In all

joint relative frequency distributions, GMST trend is collected in bins of

0.025 uC per decade, and each vertical cross section is normalized such that its area integral is unity.

 

 

ARTICLE

Extended Data Table 1 | CMIP5 models used in this study

The originating institutions and publications documenting the models are listed comprehensively in table 9.A1 of ref. 5.

English Homework

After seeing the movie Rise of the Planet of the Apes,I got many thoughts in my mind.These thoughts are so strange that I was shocked when it first come out.In my mind, I always thought human might live at the earth as a leader,and human might be the smartest race in the world for a long time.However,this movie tells me the possibility that sciences might lead.The another depression is that human ‘s morality sometimes went bad and some are originally bad.The Caesar,a ape human intelligence,was treated unfairly by a wicked man and developed a bad expression on human.

In my opinion,all races are equal.We all appeal for human’s equal rights but we never ask for other races right on the earth.It’s time we human reflect on ourselves.