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    (a) Time series of annual-mean GMST anomalies from different observational datasets. Anomalies are calculated relative to the period 1880–99, which is indicated by the vertical dashed lines. Linear trends are shown for the period 1880–2000. (b) Time series of annual-mean GMST anomalies from observations and from CMIP5 models; the MME-mean is shown in red, and individual models are shown as thin black lines. Observed GMST anomalies are based on the average of five datasets (or three before 1880). All anomalies are calculated relative to 1880–99. Linear trends for 1880–2000 are shown in K century−1.

  • View in gallery

    GMST changes ending in 2000 from the MME mean (thick red curve) and observations; the horizontal axis identifies the year in which each trend starts. GMST change (here and in subsequent figures) is calculated as the linear trend multiplied by the time period.

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    Changes in GMST from CMIP5 models historical simulations, plotted against (2000 relative to 1850) global-mean aerosol ERF: (a) 1860–2000, (b) 1880–2000, (c) 1910–2000, and (d) 1940–2000. Also shown in each panel are the regression line, the equation for the regression line, the correlation, and the level of significance. The dashed horizontal lines show the observed warming, and the dashed vertical lines show the inferred estimate of aerosol ERF; these values are also given in the legend.

  • View in gallery

    Parameters from the scatterplots in Fig. 3, based on GMST changes ending in 1995 (black), 2000 (blue), and 2005 (red). Each curve is plotted as a function of the year in which GMST trends begin: (a) correlation between (2000 relative to 1850) aerosol ERF and GMST change, (b) inferred estimate of (2000 relative to 1850) aerosol ERF, calculated as in Fig. 3, (c) the slope of the regression line, and (d) the y intercept of the regression line. Note that (b) is the only plot that depends on observations as well as model output.

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    (a) Time dependence of historical global-mean aerosol ERF relative to 1850 for three different assumed trajectories during 1850–2005. The red curve is the forcing time series from IPCC AR5 (IPCC 2013), with peak forcing of −0.74 W m−2 in 2000. The green curve assumes the same peak forcing, but follows the temporal evolution of the WMGHG forcing (with maximum magnitude in 2005). The blue curve assumes that the forcing reaches its maximum magnitude in 1975, and is constant thereafter. (b) Response of GMST to the aerosol forcing shown in (a), based on a global impulse-response function (Boucher and Reddy 2008).

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    1860–2000 changes in GMST from CMIP5 models historicalAA simulations, plotted against (2000 relative to 1850) global-mean aerosol ERF. The slope uncertainty range is a 5%–95% confidence interval, based on a t test.

  • View in gallery

    Time series of annual-mean aerosol ERF, calculated from the historicalAA simulations using Eq. (8). Aerosol ERF values are plotted as anomalies relative to the period 1850–69, or 1860–69 for GFDL-CM3. An 11-yr running mean is applied before plotting to reduce noise.

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    Inferred aerosol ERF as a function of , using Eq. (9).

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Why Does Aerosol Forcing Control Historical Global-Mean Surface Temperature Change in CMIP5 Models?

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  • 1 Oceans and Atmosphere Flagship, CSIRO, Aspendale, Victoria, Australia
  • | 2 Nicholas School of the Environment, Duke University, Durham, North Carolina
  • | 3 Laboratoire de Météorologie Dynamique, Institut Pierre Simon Laplace, CNRS/UPMC, Paris, France
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Abstract

Linear regression is used to examine the relationship between simulated changes in historical global-mean surface temperature (GMST) and global-mean aerosol effective radiative forcing (ERF) in 14 climate models from CMIP5. The models have global-mean aerosol ERF that ranges from −0.35 to −1.60 W m−2 for 2000 relative to 1850. It is shown that aerosol ERF is the dominant factor that determines intermodel variations in simulated GMST change: correlations between aerosol ERF and simulated changes in GMST exceed 0.9 for linear trends in GMST over all periods that begin between 1860 and 1950 and end between 1995 and 2005. Comparison of modeled and observed GMST trends for these time periods gives an inferred global-mean aerosol ERF of −0.92 W m−2.

On average, transient climate sensitivity is roughly 40% larger with respect to historical forcing from aerosols than well-mixed greenhouse gases. This enhanced sensitivity explains the dominant effect of aerosol forcing on simulated changes in GMST: it is estimated that 85% of the intermodel variance of simulated GMST change is explained by variations in aerosol ERF, but without the enhanced sensitivity less than half would be explained. Physically, the enhanced sensitivity is caused by a combination of 1) the larger concentration of aerosol forcing in the midlatitudes of the Northern Hemisphere, where positive feedbacks are stronger and transient warming is faster than in the Southern Hemisphere, and 2) the time evolution of aerosol forcing, which levels out earlier than forcing from well-mixed greenhouse gases.

Corresponding author address: Leon Rotstayn, Oceans and Atmosphere Flagship, CSIRO, Private Bag 1, Aspendale, VIC, 3195, Australia. E-mail: leon.rotstayn@csiro.au

Abstract

Linear regression is used to examine the relationship between simulated changes in historical global-mean surface temperature (GMST) and global-mean aerosol effective radiative forcing (ERF) in 14 climate models from CMIP5. The models have global-mean aerosol ERF that ranges from −0.35 to −1.60 W m−2 for 2000 relative to 1850. It is shown that aerosol ERF is the dominant factor that determines intermodel variations in simulated GMST change: correlations between aerosol ERF and simulated changes in GMST exceed 0.9 for linear trends in GMST over all periods that begin between 1860 and 1950 and end between 1995 and 2005. Comparison of modeled and observed GMST trends for these time periods gives an inferred global-mean aerosol ERF of −0.92 W m−2.

On average, transient climate sensitivity is roughly 40% larger with respect to historical forcing from aerosols than well-mixed greenhouse gases. This enhanced sensitivity explains the dominant effect of aerosol forcing on simulated changes in GMST: it is estimated that 85% of the intermodel variance of simulated GMST change is explained by variations in aerosol ERF, but without the enhanced sensitivity less than half would be explained. Physically, the enhanced sensitivity is caused by a combination of 1) the larger concentration of aerosol forcing in the midlatitudes of the Northern Hemisphere, where positive feedbacks are stronger and transient warming is faster than in the Southern Hemisphere, and 2) the time evolution of aerosol forcing, which levels out earlier than forcing from well-mixed greenhouse gases.

Corresponding author address: Leon Rotstayn, Oceans and Atmosphere Flagship, CSIRO, Private Bag 1, Aspendale, VIC, 3195, Australia. E-mail: leon.rotstayn@csiro.au

1. Introduction

Aerosol effects on climate are highly uncertain; even in the global mean, effective radiative forcing (ERF) caused by anthropogenic aerosols has a 5%–95% uncertainty range of −0.1 to −1.9 W m−2, according to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC AR5; Boucher et al. 2013). Because aerosol forcing is so uncertain, it is difficult to use observations to constrain other critical properties of the climate system, such as transient climate response (TCR; Schwartz 2012). This uncertainty limits our ability to understand historical climate change and make reliable projections of future climate change. According to Hansen et al. (2011, p. 13 442) “aerosol uncertainty is the principal barrier to quantitative understanding of ongoing climate change.”

Despite this uncertainty, it is generally accepted that anthropogenic aerosols have offset some fraction of the global warming caused by increasing concentrations of well-mixed greenhouse gases (WMGHGs). One manifestation of this is that the increase of global-mean surface temperature (GMST) is generally overestimated in historical simulations in which climate models are forced only by increasing WMGHGs (Bindoff et al. 2013). The effects of aerosol forcing on historical changes in GMST in phase 5 of the Coupled Model Intercomparison Project (CMIP5) were also noted by Wilcox et al. (2013) and Jones et al. (2013). Wilcox et al. (2013) showed that indirect aerosol forcing in CMIP5 models improves the simulation of interdecadal variability in historical GMST, especially the cooling of the 1950s and 1960s, compared to models that only treat direct aerosol effects. Jones et al. (2013) found a wider spread of modeled historical changes in GMST in CMIP5 than in the earlier CMIP3 ensemble, and attributed this to a wider exploration of aerosol uncertainty in CMIP5 (especially indirect effects).

Shindell et al. (2013) and Rotstayn et al. (2013) showed that simulated historical changes in GMST in CMIP5 models are correlated with models’ aerosol effective radiative forcing, so that models with stronger (more negative) aerosol ERF tended to underestimate historical GMST change whereas models with weaker aerosol ERF tended to overestimate historical GMST change. This differs from the behavior seen in previous generations of climate models, in which there was a negative correlation between net radiative forcing and climate sensitivity (Kiehl 2007; Knutti 2008). Since differences in radiative forcing are dominated by aerosol forcing, this suggests that modeling groups may have “tuned” their aerosol forcing to obtain a good match between simulated and observed changes in historical GMST. However, Forster et al. (2013) did not find a similar correlation in models from CMIP5. Shindell et al. (2013, p. 2962) hypothesized that “representations of aerosol–cloud interactions have become so complex that the emergent aerosol ERF cannot be readily predicted or adjusted, and hence models must accept limitations in their historical simulations to maintain their most realistic representation of aerosol–cloud physical processes.” Another difference between CMIP3 and CMIP5 is that standard aerosol emissions and concentrations were provided for CMIP5, but they were not for CMIP3 and each group was free to select its own; this may also have reduced the ability of the groups to tune their aerosol forcing to obtain a realistic simulation of historical climate change.

Here we explore the correlation between simulated historical changes in GMST and aerosol ERF in more detail. Aerosol ERF is available for a substantial number of CMIP5 models for 2000 relative to 1850 (but not for other years) from simulations with prescribed sea surface temperatures (SSTs); for this reason, we shall use aerosol ERF to refer to the forcing for 2000 relative to 1850, unless stated otherwise. We show that 1) aerosol ERF is a strong predictor of the models’ simulated historical change in GMST, with large correlations between aerosol ERF and the change in GMST, and 2) the strong correlation between aerosol ERF and changes in GMST is substantially caused by the larger sensitivity of GMST to aerosol forcing compared to forcing from WMGHGs.

2. Data and models

We use output from 14 CMIP5 models, which are listed in Table 1. These are the models for which aerosol ERF can be calculated from published fixed-SST runs, plus the ACCESS1.0 and ACCESS1.3 models. Aerosol ERF includes direct and indirect radiative effects of aerosols, as well as rapid adjustments of the atmosphere and land surface (Boucher et al. 2013). Aerosol ERF for 2000 relative to 1850 is calculated from the difference in net radiation at the top of the atmosphere between two fixed-SST runs, one with aerosols set to year-2000 levels and one with aerosols set to 1850 levels; these are referred to as sstClim and sstClimAerosol, respectively (Taylor et al. 2012). Both sstClim and sstClimAerosol use climatological SSTs derived from a preindustrial control run of the same model, and each run is integrated for a minimum of 30 years. We also use near-surface air temperature from the transient historical experiments, which generally cover the period 1850 to 2005. For each model, Table 2 gives the global-mean aerosol ERF, and Table 1 lists the indirect aerosol effects treated and the ensemble size of the historical experiments. All analysis of the historical experiments uses ensemble means, where more than one run is available.

Table 1.

Details of models. For indirect effects, 0 denotes no aerosol–cloud interaction, 1 denotes the cloud–albedo effect, 2 denotes 1 plus an effect on warm-rain formation, and 3 denotes 2 plus an effect on ice clouds. Runs refer to the number of ensemble members in the historical experiments. [Expansions of acronyms are available online at http://www.ametsoc.org/PubsAcronymList.]

Table 1.
Table 2.

Aerosol ERF, transient climate response (TCR), transient climate sensitivity (TCS), and drift of GMST in preindustrial control run. Aerosol ERF is calculated from fixed-SST simulations as described in the text. TCR is the change in GMST at the time of CO2 doubling in the 1pctCO2 simulations, and TCS equals TCR divided by a standard radiative forcing of 3.7 W m−2 for doubled CO2. Drift of GMST is calculated from a linear fit to GMST over the entire available length of the preindustrial control run. Model output is from CMIP5, except where otherwise indicated.

Table 2.

TCR for each model is calculated from the increase in GMST, averaged over years 61–80 of a simulation in which CO2 concentration increases at 1% per annum (the “1pctCO2” runs from CMIP5). Values of TCR are obtained from Table 1 of Forster et al. (2013), except for ACCESS1.3, for which we calculated it independently; these values are given in Table 2.

Also shown in Table 2 are values of transient climate sensitivity (TCS) for each model, defined as TCR divided by 3.7 W m−2, a standard estimate of radiative forcing for doubled CO2 (; Myhre et al. 1998). Forster et al. (2013) derived TCS using model-dependent estimates of ERF for doubled CO2, calculated by the regression method of Gregory et al. (2004). However, for some models doubled-CO2 ERF estimates based on the regression method can differ substantially from the fixed-SST method, which we used to derive aerosol ERF (Andrews et al. 2012; Shindell 2014). On the other hand, doubled-CO2 ERF estimates from the fixed-SST method are only available for a subset of the models. For these reasons, it is simpler to use a standard value of to calculate TCS, which we shall compare with TCSaer, an analogous quantity defined with respect to changes in historical aerosol forcing instead of doubled CO2. Although TCS is expected to show some sensitivity to the rate of increase of forcing, in practice a constant TCS is a reasonable approximation for historical and projected twenty-first-century forcing changes, as long as the magnitude of the forcing is increasing “fairly steadily” (Gregory and Forster 2008). The time evolution of aerosol forcing in the late twentieth century is uncertain, and it is possible either that it has been relatively flat since the 1970s (Gregory and Forster 2008; Regayre et al. 2014) or that it continued to increase in magnitude until 2000 (Shindell et al. 2013; Myhre et al. 2013); the possible effects of the time evolution of aerosol forcing on TCSaer are considered in section 4a.

Changes in annual-mean GMST from the historical experiments are calculated from ordinary least squares trends, multiplied by the time period. We calculate GMST changes for periods beginning in 1860, since two models (GFDL CM3 and HadGEM2-ES) begin their historical simulations in that year, rather than in 1850. Because “present-day” aerosol ERF is based on the year 2000, our primary focus will be on GMST changes that end in 2000, but we will also explore the effects of varying the end of the period for GMST changes.

Drift is removed from GMST trends by subtracting the linear GMST trend in each model’s preindustrial control run, calculated from all available years; these trends are given in Table 2. We follow the recommendation of Sen Gupta et al. (2013) to use a drift estimate based on the full control time series in order to minimize contamination of the drift estimate by internal variability; however, it should be noted that the best way to treat drift is uncertain. Drift in GMST is negligible in many models compared to the historical trends that we will consider, but for some models drift is significant relative to the forced trend; this is especially so for GFDL CM3, which has drift of 0.1 K century −1.

A useful summary of available GMST data is provided by the National Center for Atmospheric Research (NCAR 2014). We compare modeled changes in GMST with reconstructed, observed changes in annual-mean GMST from the average of five datasets:

  • HadCRUT4 (Morice et al. 2012) combines land surface temperatures from a range of sources with SST measurements from version 3 of the Hadley Centre sea surface temperature dataset (HadSST3). HadCRUT4 is different from most comparable products in that no spatial interpolation is performed. Uncertainty is characterized via an ensemble of 100 realizations of the dataset.
  • Cowtan and Way (2014) use an optimal interpolation algorithm applied to HadCRUT4. Cowtan and Way argue that GMST in HadCRUT4 is subject to bias due to missing data in unobserved regions, and that the interpolated version provides better results than excluding the unobserved regions. However, as shown below, GMST trends from HadCRUT4 are in broad agreement with those from other datasets.
  • The Goddard Institute for Space Studies Surface Temperature Analysis (GISTEMP; Hansen et al. 2010) combines monthly mean land surface air temperatures primarily from the Global Historical Climatology Network (GHCN) version 3 (Lawrimore et al. 2011) with SSTs from the Extended Reconstructed Sea Surface Temperature (ERSST) version 3b (Smith et al. 2008). Spatial interpolation uses linear inverse distance weighting to fill grid boxes with data from stations up to 1200 km away.
  • NOAA’s Merged Land–Ocean Surface Temperature Analysis (MLOST; Smith et al. 2008) is based on similar underlying measurements to GISTEMP. Like GISTEMP, interpolation of the station records is performed to provide broad spatial coverage, but the methodology is different (NCAR 2014).
  • Berkeley Earth is based on an independent analysis of land surface temperatures (Rohde et al. 2013), which is blended with SSTs from a reinterpolated version of HadSST3. The method used to construct Berkeley Earth allows inclusion of short and discontinuous temperature records, so that nearly all temperature data can be used (some 37 000 land stations in total, compared to several thousand in the other datasets).

The various GMST observations show a broadly similar picture when plotted as time series (Fig. 1a). Prior to 1880, GISTEMP and MLOST have no data, so for 1860 to 1879 the average observed GMST is based only on HadCRUT4, Berkeley Earth, and Cowtan and Way. Differences among the data become apparent when GMST trends are calculated. Linear trends are shown in Fig. 1a for 1880–2000; for this time period, Berkeley Earth gives larger GMST trends than the other datasets.

Fig. 1.
Fig. 1.

(a) Time series of annual-mean GMST anomalies from different observational datasets. Anomalies are calculated relative to the period 1880–99, which is indicated by the vertical dashed lines. Linear trends are shown for the period 1880–2000. (b) Time series of annual-mean GMST anomalies from observations and from CMIP5 models; the MME-mean is shown in red, and individual models are shown as thin black lines. Observed GMST anomalies are based on the average of five datasets (or three before 1880). All anomalies are calculated relative to 1880–99. Linear trends for 1880–2000 are shown in K century−1.

Citation: Journal of Climate 28, 17; 10.1175/JCLI-D-14-00712.1

In Fig. 2 we compare GMST changes based on linear trends that end in 2000 for different starting years. GMST changes are generally similar between MLOST and GISTEMP, reflecting their similar underlying data. For shorter time periods, Berkeley Earth, HadCRUT4, and Cowtan and Way give smaller changes than MLOST and GISTEMP. Berkeley Earth has larger GMST changes for periods that start before about 1890, but for shorter time periods Berkeley Earth is similar to the others.

Fig. 2.
Fig. 2.

GMST changes ending in 2000 from the MME mean (thick red curve) and observations; the horizontal axis identifies the year in which each trend starts. GMST change (here and in subsequent figures) is calculated as the linear trend multiplied by the time period.

Citation: Journal of Climate 28, 17; 10.1175/JCLI-D-14-00712.1

Multimodel ensemble (MME)-mean GMST changes (thick red curve) show considerable similarity to observed changes, although the MME mean underestimates GMST changes for periods starting before about 1925. The MME mean shows the largest GMST changes for periods starting just after the eruption of Krakatoa in 1883, and the smallest GMST changes for periods starting in the late 1930s. Similar features appear in the observed changes, although there are also some clear differences. In principle, the shape of the red curve captures the GMST changes that are forced, since the averaging in the MME mean removes natural variability. However, errors in the forcing or response of the models will also contribute to differences between the modeled and observed curves.

3. Relationship between aerosol forcing and changes in GMST

Figure 3 shows the relationship between simulated historical changes in GMST and aerosol ERF. Four time periods are shown for GMST changes (1860–2000, 1880–2000, 1910–2000, and 1940–2000), whereas aerosol ERF always refers to 2000 relative to 1850. For all time periods, the correlation between GMST change and aerosol ERF exceeds 0.9. This suggests that other differences among the models, such as TCR and other forcings, have relatively minor effects on the simulated change in GMST; we shall return to this point in section 4a. Even if we remove the three models that exclude indirect aerosol effects (those with aerosol ERF in the range of −0.3 to −0.4 W m−2), the correlations between GMST change and aerosol ERF are still strong; for example, using the period 1860–2000, the correlation changes from 0.91 to 0.84. The horizontal dashed lines show observed changes in GMST over the relevant time period and the dashed vertical lines show top-down estimates of aerosol ERF implied by the observed changes in GMST and the models’ response to radiative forcing. These amount to −0.95, −0.94, −0.79 and −1.03 W m−2 for the four time periods, respectively.

Fig. 3.
Fig. 3.

Changes in GMST from CMIP5 models historical simulations, plotted against (2000 relative to 1850) global-mean aerosol ERF: (a) 1860–2000, (b) 1880–2000, (c) 1910–2000, and (d) 1940–2000. Also shown in each panel are the regression line, the equation for the regression line, the correlation, and the level of significance. The dashed horizontal lines show the observed warming, and the dashed vertical lines show the inferred estimate of aerosol ERF; these values are also given in the legend.

Citation: Journal of Climate 28, 17; 10.1175/JCLI-D-14-00712.1

Why does inferred aerosol ERF differ, depending on the time period over which GMST change is calculated? It can be explained in terms of (a) natural variability in GMST, which is present in the observations (Schlesinger and Ramankutty 1994; Tung and Zhou 2013) but is filtered out by the process of ensemble averaging the model output, and (b) possible errors in the time history of the forcing or response of the models. Both of these factors may cause the rate of GMST change in the MME mean to be larger or smaller than the observed rate at different times; these fluctuations are seen in Fig. 1b, which compares time series of anomalies in observed GMST and MME-mean GMST.

During some time periods, there are relatively large differences between modeled and observed GMST anomalies. For example, during the period around 1890 and in the 1940s, the MME mean is mostly cooler than the observations, and between about 1905 and 1930 the MME mean is mostly warmer than the observations. These fluctuations help to explain the different values of aerosol ERF diagnosed for the four time periods in Fig. 3, since the linear trend is sensitive to the GMST values in the first few years of the time period. Thus for example, to match the observed 1910–2000 GMST trend, a model would need to have relatively weaker aerosol ERF (which increases the simulated GMST trend), compared to the periods 1880–2000 and 1940–2000.

It is not practical to replicate Fig. 3 for GMST changes calculated over a large number of different time periods. However, one can plot key parameters from Fig. 3 as a function of the start or end of the time period. In Fig. 4 we show (a) the correlation between aerosol ERF and GMST change, (b) the inferred top-down estimate of aerosol ERF, (c) the slope of the regression line, and (d) the y intercept of the regression line. These parameters are plotted as a function of the start of the time period for GMST change, for three different values of the end of the time period (1995, 2000, and 2005); as in Fig. 3, aerosol ERF again refers to 2000 relative to 1850.

Fig. 4.
Fig. 4.

Parameters from the scatterplots in Fig. 3, based on GMST changes ending in 1995 (black), 2000 (blue), and 2005 (red). Each curve is plotted as a function of the year in which GMST trends begin: (a) correlation between (2000 relative to 1850) aerosol ERF and GMST change, (b) inferred estimate of (2000 relative to 1850) aerosol ERF, calculated as in Fig. 3, (c) the slope of the regression line, and (d) the y intercept of the regression line. Note that (b) is the only plot that depends on observations as well as model output.

Citation: Journal of Climate 28, 17; 10.1175/JCLI-D-14-00712.1

Correlations between aerosol ERF and modeled GMST change (Fig. 4a) are large for all periods that start earlier than 1950, but for GMST trends starting later than about 1950 they fall sharply. This reflects the fact that, after 1950, an increasing fraction of the aerosol ERF (and the associated GMST response) is realized in the models, although the details will differ among the models. The correlations are slightly lower for GMST trends that end in 2005, relative to those that end in 1995 or 2000. A possible reason for this is that the spatial pattern of aerosol ERF is likely to have changed between 2000 and 2005, due to declining sulfur dioxide emissions in Europe and North America and increasing emissions in East Asia (Smith et al. 2011; Takemura 2012); to the extent that the details of the change in aerosol ERF are model dependent, this would tend to weaken the correlation between year-2000 aerosol ERF and GMST change.

Corresponding values of inferred aerosol ERF are shown in Fig. 4b. Aerosol ERF is of slightly larger magnitude when inferred from GMST trends that extend to 2005 (since then the observed GMST trends are smaller). Aerosol ERF shows only moderate sensitivity to the start of the time period for periods that start earlier than 1950. Consistent with the discussion above, relatively weak aerosol ERF is diagnosed from GMST trends starting around 1910, and stronger aerosol ERF is diagnosed from GMST trends starting around 1880 and 1940. For GMST trends starting later than 1950, the estimated aerosol ERF is more sensitive to the start of the trend period. In view of the weaker correlations between aerosol ERF and GMST change for these shorter periods, we consider the inferred aerosol ERF to be less physically meaningful after 1950 than for GMST trends based on longer periods.

The mean value of inferred aerosol ERF for 1850–2000, based on the 91 GMST trends that start between 1860 and 1950 and end in 2000, is −0.92 W m−2. Based on all GMST trends that end between 1995 and 2005 (91 × 11 time periods) the mean value is also −0.92 W m−2, so decadal variability around 2000 has little effect on the estimate. The inferred aerosol ERF is similar to the best estimate of aerosol ERF from IPCC AR5 (−0.9 W m−2). However, the time period for the AR5 estimate is 1750–2010, whereas the AR5 best estimate for 1850–2000 is −0.74 W m−2 (IPCC 2013, see Table AII.1.2 therein), somewhat smaller in magnitude than our estimate.

The uncertainty in our inferred aerosol ERF depends on observational uncertainty as well as the regression between the change in GMST and aerosol ERF. Instead of using linear trends (as in the present study), a simpler framework to estimate observational uncertainty is based on the change in GMST between preindustrial and modern-day periods, since temporal averaging inherently reduces the effects of natural variability and the associated uncertainty. For example, Hartmann et al. (2013) give a 90% uncertainty range of 0.65 to 1.06 K for the change in GMST during 1880–2012 (from a linear trend), but a substantially smaller range of 0.72 to 0.85 K for the difference between the average of the 1850–1900 period and the 2003–12 period. We have used the difference of two time periods (1996–2005 minus 1850–59) in a separate study, using a similar set of models (Shindell et al. 2015). This gave an inferred global-mean aerosol ERF and 90% uncertainty range of W m−2. Further, as noted in section 4d, the uncertainty of aerosol ERF also depends on the average TCR of the models, and this additional uncertainty is difficult to quantify. For these reasons, we have not attempted to provide an uncertainty estimate for the inferred aerosol ERF.

The correlation between aerosol ERF and TCR across the models is not significant (), so the slope of the regression line (Fig. 4c) gives a measure of the transient climate sensitivity with respect to aerosol ERF (TCSaer). The slope is relatively flat until about 1930 and then starts to decline, as the aerosol-induced cooling is gradually realized. It then falls more sharply after the 1940s, and by 1960 only about half of the aerosol-induced cooling remains. Since most of the GMST response occurs within several years of the forcing (Held et al. 2010), this gives a rough guide to the timing of aerosol ERF in the models. Also, TCSaer is smaller for GMST changes ending in 1995 than 2000 or 2005, because in 1995 there is less time for GMST changes to equilibrate to the aerosol ERF.

Since aerosol ERF is only available for the period 1850–2000, the most obvious periods from which to take the change in GMST to diagnose TCSaer are those that end in 2000. (There is expected to be less sensitivity to the start of the period used to calculate the change in GMST, provided that the start of the period has similar aerosol ERF to that in 1850.) Based on the period 1860–2000 (Fig. 3a), TCSaer is estimated to be 0.71 K (W m−2)−1. Using the average of all trends that start between 1860 and 1899 and end in 2000, it is estimated to be 0.73 K (W m−2)−1.

It is instructive to compare these estimates of TCSaer with TCS calculated with respect to increasing CO2 concentration. The average TCS of the models (Table 2) is 0.51 K (W m−2)−1. This is a factor of 1.4 smaller than TCSaer [0.71 or 0.73 K (W m−2)−1, depending on the time period]; thus TCSaer is roughly 40% larger than TCS. We shall return to this important point in section 4b, where we show that the enhancement of TCSaer relative to TCS substantially explains the dominant effect of aerosol forcing on simulated changes in GMST.

There is a caveat regarding the direct comparison of TCSaer with TCS (which is calculated from the 1pctCO2 simulations). The value of TCSaer in 2000 is expected to be sensitive to the assumed time evolution of aerosol ERF in the late twentieth century, which is very uncertain and presumably model dependent. If aerosol forcing is relatively flat since the 1970s, as suggested by some studies (Gregory and Forster 2008; Regayre et al. 2014), the time lag will tend to increase TCSaer relative to TCS. In this case, the time evolution of aerosol ERF may contribute substantially to the enhancement of TCSaer relative to TCS. On the other hand, the forcing time series from IPCC AR5 (Myhre et al. 2013; IPCC 2013) suggests that aerosol ERF continued to increase in magnitude until 2000, in which case the time evolution of aerosol ERF may have a relatively small effect; we explore this issue further in section 4a.

The y intercept of the regression line (Fig. 4d) represents the increase in GMST for zero aerosol ERF (which is primarily caused by increasing WMGHGs). There is a slight increase until just after the eruption of Krakatoa in 1883, followed by a slow decline as the effect of WMGHG forcing is slowly realized. The rate of increase of WMGHG forcing accelerates during the 1950s (e.g., Forster et al. 2013), and this causes a more pronounced fall in the unrealized fraction of GMST increase after about 1960. Since the WMGHG forcing increases rapidly between 1995 and 2005, the unrealized warming is largest for periods ending in 2005 and smallest for periods ending in 1995.

4. Discussion

a. Physical reasons for the enhanced response of GMST to aerosol forcing

The strong effect of aerosol forcing on GMST can be substantially understood in terms of the findings of Shindell (2014). He showed that historical GMST in the CMIP5 models responds more strongly to spatially inhomogeneous aerosol plus ozone forcing than to increasing WMGHGs, by an average factor of 1.45, although there were large differences among the models. He characterized the larger effect of inhomogeneous forcing on GMST by an enhancement factor (E); this is essentially the same as the “efficacy” concept of Hansen et al. (2005) but to avoid confusion with the current usage of “effective radiative forcing” we shall use the term “temperature-equivalent forcing” to refer to forcing multiplied by E.

According to Shindell (2014), the primary physical reason for the enhanced response to inhomogeneous forcing was that a larger fraction of the forcing is located over the land-dominated extratropical Northern Hemisphere. There, the temperature response is enhanced by less availability of moisture over land than over ocean (Joshi et al. 2008), strong positive feedbacks at high latitudes (Pithan and Mauritsen 2014), and faster transient response of the Northern Hemisphere compared to the Southern Hemisphere (Stouffer et al. 1989; Drost et al. 2012). For these reasons, the transient response of the Northern Hemisphere was roughly 60% larger than that of the Southern Hemisphere for increasing WMGHGs. With 77% of the net aerosol plus ozone forcing located in the Northern Hemisphere in the CMIP5 models, this causes a larger response of GMST to aerosol plus ozone forcing compared to increasing WMGHGs. A secondary reason for the enhanced response was the different time evolution of aerosol forcing, which peaks earlier than forcing from increasing WMGHGs. With aerosol forcing assumed to evolve with time as in IPCC AR5 (Myhre et al. 2013), Shindell (2014) used a global impulse–response function derived from the Hadley Centre climate model (Boucher and Reddy 2008) to estimate that the effect of the earlier peak in aerosol forcing was on the order of 10% for the period 2000–10. However, in view of the uncertainty of the time evolution of aerosol forcing, it is useful to revisit this question here.

The forcing time series from IPCC AR5 indicates that aerosol ERF continued to increase in magnitude until 2000 (Fig. 5a, red curve). However, this was based on calculations with only five models (Myhre et al. 2013). Some of these models (especially GISS-E2-R and CSIRO-Mk3.6.0) have substantial negative aerosol ERF from nonsulfate aerosols (Boucher et al. 2013, Table 7.5). In GISS-E2-R this is caused by a large negative forcing from nitrate (Shindell et al. 2013), whereas in CSIRO-Mk3.6.0 this is caused by a substantial negative forcing from carbonaceous aerosol (Rotstayn et al. 2012). According to Table 7.5 of Boucher et al. (2013) some other models used in the present study also have substantial negative forcing from nonsulfate aerosols (especially MRI-CGCM3), whereas some models (CanESM2, IPSL-CM5A-LR, GFDL CM3, and HadGEM2-ES) have total aerosol ERF very similar to sulfate ERF. If total aerosol forcing is dominated by sulfate, then aerosol forcing is likely to be relatively flat between the 1970s and 2000, as argued by Gregory and Forster (2008) and Regayre et al. (2014). In this case, aerosol forcing could be weaker in 2000 than the late 1970s, since global SO2 emissions decreased between 1980 and 2000 (Smith et al. 2011). However, any decrease in global sulfate loading during this time is likely to be smaller than suggested by the decrease in global SO2 emissions, because there was a net shift of SO2 emissions toward Asia, where the availability of oxidant to convert SO2 to sulfate is greater than over Europe or North America (Manktelow et al. 2007). As shown in section 4c, some models (notably CanESM2 and IPSL-CM5A-LR) do have weaker aerosol ERF in 2000 than in the late 1970s.

Fig. 5.
Fig. 5.

(a) Time dependence of historical global-mean aerosol ERF relative to 1850 for three different assumed trajectories during 1850–2005. The red curve is the forcing time series from IPCC AR5 (IPCC 2013), with peak forcing of −0.74 W m−2 in 2000. The green curve assumes the same peak forcing, but follows the temporal evolution of the WMGHG forcing (with maximum magnitude in 2005). The blue curve assumes that the forcing reaches its maximum magnitude in 1975, and is constant thereafter. (b) Response of GMST to the aerosol forcing shown in (a), based on a global impulse-response function (Boucher and Reddy 2008).

Citation: Journal of Climate 28, 17; 10.1175/JCLI-D-14-00712.1

The previous paragraph suggests that there are likely to be substantial intermodel variations in the temporal evolution of aerosol ERF in the late twentieth century; this impression is confirmed in section 4c, where we consider an alternative method of calculating aerosol ERF. In view of the uncertainty, we compare the AR5 aerosol ERF time series with an idealized forcing time series, which has the same peak value (−0.74 W m−2 relative to 1850), but it reaches this value in 1975 and is constant thereafter; this is shown as the blue curve in Fig. 5a. The third forcing time series in Fig. 5a also has the same peak value, but it follows the temporal evolution of the WMGHG forcing, with maximum magnitude in 2005 (green curve); comparison of this time series with the other two enables a rough estimate of the effect of the leveling out of aerosol forcing in the late twentieth century.

The impulse–response function used by Boucher and Reddy (2008) and Shindell (2014) gives the response of GMST after t years to a normalized radiative forcing of 1 W m−2 applied during the first year:
e1
where the first exponential approximates the relatively rapid response of the land and upper ocean and the second exponential approximates the slower response of the deep ocean. Figure 5b shows the change in GMST in response to the three aerosol forcing time series described in the previous paragraph. The blue curve (with constant forcing after 1975) shows the largest response, whereas the green curve (with aerosol forcing following the time evolution of WMGHG forcing) shows the smallest response after 1960. Relative to the case in which aerosol forcing follows the time evolution of increasing WMGHGs, the change of GMST in 2000 is 15% larger for AR5 aerosol forcing and 25% larger for aerosol forcing that peaks in 1975. In other words, this idealized calculation suggests that the effect of the leveling out of aerosol forcing is in the vicinity of 15% to 25%, which is a substantial fraction of the ~40% total enhancement of the GMST response. However, as mentioned above, there are likely to be large variations in the temporal evolution of aerosol forcing among the models; this is discussed further in section 4c. Also, it should be noted that Eq. (1) reflects the climate sensitivity and thermal inertia of one particular model, and we have used a global-mean impulse–response function to explore an issue that is intrinsically nonglobal, so the results are only intended to be qualitative.

b. Why does aerosol forcing control historical GMST changes in the models?

Bearing in mind the enhanced response of GMST to aerosol forcing, one might still expect changes in GMST to also depend on other differences among the models, such as TCR. According to Table 2, the current models show a substantial range of TCR (1.4 to 2.5 K for a doubling of CO2); this spans more than 70% of the “likely” range of TCR from IPCC AR5 (1 to 2.5 K; Bindoff et al. 2013).

To explain the strong effect of aerosol forcing on GMST more quantitatively, we use a modified version of the equation in Shindell (2014), namely
e2
where is the change in GMST and is the forcing for a doubling of CO2 concentration (3.7 W m−2). The subscripted quantities in the square brackets represent the forcing in 2000 relative to 1850 for respectively WMGHGs, natural (solar and volcanic) forcing, stratospheric ozone, anthropogenic aerosols, tropospheric ozone, and land-use change; these forcings are generally included in the models in Table 1, though a few omit land-use change (ACCESS1.0, ACCESS1.3, BCC-CSM1.1, CSIRO-Mk3.6.0, and FGOALS-s2; Collins et al. 2013, Table 12.1). The forcing equates to aerosol ERF, as referred to throughout the text. Stratospheric water vapor and contrails are relatively small forcings that may be included in some models, but there is no information in Collins et al. (2013), so we omit these. The regression relations from Figs. 3 and 4 suggest that is a representative enhancement factor for the current set of models, so we set . Following Shindell (2014), we apply the enhancement factor to and as well as , based on the argument that the enhanced response applies to all forcings that are mainly concentrated in the extratropical Northern Hemisphere. As discussed above, part of the enhanced response to aerosol forcing may be caused by its time evolution rather than its spatial distribution, so the appropriate value of E for tropospheric ozone and land-use change may be less than 1.4; however, varying E between 1 and 1.4 for these forcing agents does not substantially change the outcome of the following analysis. The relationship between and TCR in Eq. (2) is valid when the forcing is increasing in magnitude “fairly steadily” (Gregory and Forster 2008). This assumption is a reasonable approximation for most of the forcings in Eq. (2) but is not valid for ; however, is only on the order of 0.1 W m−2 (Forster et al. 2013), so it has only a small effect on the analysis. Also, note that , as defined in section 2.
The following arguments can be conveniently simplified by using best estimates of the nonaerosol forcings, although in reality these vary among the models; below, we shall briefly consider the role of variations in . For anthropogenic forcings other than aerosols, we apply best estimates for the period 1850–2000 as follows (IPCC 2013, Table AII.1.2): , , , and W m−2. Comparable natural forcing is more difficult to assess, given the sporadic nature of volcanic forcing and the cyclical component of solar forcing, so we use a rough estimate of (Forster et al. 2013). Using these values in Eq. (2) gives
e3
or
e4
Note that if TCR is approximated as a constant, the form of Eq. (4) resembles the regression relations in Fig. 3; we shall return to this useful point below.
If a variable f depends on several variables , with uncertainties characterized by variances and covariances , then the uncertainties propagate according to (Bevington and Robinson 2003, p. 41)
e5
If and are not significantly correlated, then the covariance terms can be neglected, and can be approximately attributed to , , and so on. Each partial derivative is evaluated by allowing to vary, while other variables are held fixed at their average values (Kuhlbrodt and Gregory 2012).
Although differences in nonaerosol forcing terms may contribute to variations in , we simplify the arguments by evaluating the variance of caused by variations in TCR and , as suggested by the form of Eq. (4). TCR and are not significantly correlated (), so the covariance terms can be neglected, and we can write
e6
Note that TCR includes a component caused by variations in the ERF for doubled CO2, as do the values of TCS in Table 2, since we have defined TCS as TCR divided by 3.7 W m−2 (a standard estimate of radiative forcing for doubled CO2). As discussed in section 2, we made this assumption because ERF for doubled CO2 is not available for all models from fixed-SST simulations, and values calculated by the regression method may not be directly comparable to those calculated from fixed-SST simulations. A related issue is the fact that the nonaerosol forcings in Eq. (2) (and especially ) differ among the models, and these may contribute to ; the role of variations of is discussed below.
For the 14 models in Table 1, K2 and (W m−2)2; in the following paragraphs, we shall omit the units from some quantities for the sake of clarity, with the understanding that all quantities are in SI units. From Eq. (4), and , and these partial derivatives are estimated using mean values W m−2 and K. Insertion of these values in Eq. (6) yields
e7
where the numbers on the right-hand side represent the effects of variations in TCR and , respectively. In Fig. 3a (which represents the period 1860–2000), , so 0.094 represents about 85% of . Also, the sum of the two terms in Eq. (7) is 0.108, which is close to ; this suggests that the approximations entailed in the use of Eq. (6) are reasonable.

How would these results differ without the enhanced effect of aerosol forcing? With E = 1, Eq. (4) becomes , and the numbers on the right-hand side of Eq. (7) become 0.022 and 0.047, respectively. In that case variations in cause less than half of , and the contribution of variations in is only about twice that of variations in TCR. Also, the sum of the two terms in Eq. (7) would then be only 0.069, which is substantially less than the actual seen in the models.

Another way to look at this is to note that the numerator in Eq. (3) is the temperature-equivalent net forcing, namely the net forcing () after enhancing the effects of aerosols, tropospheric ozone, and land-use change by a factor of 1.4. The difference in temperature-equivalent net forcing between the high-forcing (, W m−2) and low-forcing (, W m−2) cases is a factor of 5.5. With , is 2.18 or 0.93 W m−2 for the high- and low-forcing cases, respectively, and the difference is a factor of 2.3.

Comparison of Eq. (2) with the regression parameters in Figs. 3a and 4 further justifies the choice . Using K and the values given above for nonaerosol forcings, Eq. (2) with gives , which is similar to the equation for the regression line for 1860 in Fig. 3a (). If the slope and intercept are taken as averages over the period 1860–99 instead of 1860, the regression equation amounts to , which is similar. Increasing E to 1.5 in Eq. (2) gives , which agrees less well with the slope in the regression relations. Similarly, decreasing E to 1.3 also yields an inferior result.

In the above calculations, we made the simplifying assumption that the nonaerosol forcing terms in Eq. (2) are constant. This was convenient, not least because the resulting equation then closely resembled the regression relations from Fig. 3. In reality, the other forcing terms do differ between models, although specific details are difficult to assess for some forcing agents.

By far the largest nonaerosol forcing in Eq. (2) is . When it is quantified as a traditional (stratosphere adjusted) forcing, uncertainty in is on the order of 10% (Forster and Taylor 2006), but the uncertainty is larger when is quantified as an ERF, since rapid adjustments of the atmosphere are then included in the forcing estimate. Differences among models may be exaggerated if is calculated by the Gregory et al. (2004) regression method (as in Forster et al. 2013), possibly due to an initial nonlinear cloud response over the eastern edge of ocean basins in the first few years after the forcing is applied in some models (Andrews et al. 2012). For this reason, Shindell (2014) provided fixed-SST estimates of for some models, for which there appeared to be an unusually large discrepancy between fixed-SST and regression-based estimates of . In all, Shindell (2014) gave estimates of for eight models, all of which are included in the present study. Using his estimates, , and the contribution to from uncertainty in is , which is much smaller than the contribution from uncertainty in (0.094).

This calculation gives only a rough guide to the effects of uncertainty in . Also, information is lacking for some of the smaller forcing terms (especially ). However, we have already shown that uncertainties in account for approximately 85% of the variance in , so it is not essential to accurately quantify all of the remaining contributions to .

c. Comparison with aerosol single-forcing historical runs

Several CMIP5 modeling groups carried out transient historical runs forced only by increasing anthropogenic aerosols (which we call “historicalAA”); anthropogenic aerosols are understood to also include those generated by biomass burning, consistent with the treatment in the historical runs. These runs are available for six of the models used in the preceding analysis (see Table 3). This raises the possibility that useful insights might be gained by examining the response of GMST in these runs.

Table 3.

Details of historical simulations forced only by increasing anthropogenic aerosols (historicalAA). Here is the 1860–2000 change in GMST, calculated from a linear trend, is aerosol ERF for 2000 relative to 1850, calculated from fixed-SST simulations (Table 2), and is defined as . Also, is aerosol ERF for 1996–2005 relative to 1850–69 (or 1860–69 for GFDL-CM3), calculated from historicalAA simulations using Eq. (8), and is defined as . TCS is the transient climate sensitivity with respect to increasing CO2, taken from Table 2.

Table 3.

Figure 6 shows the relationship between aerosol ERF () and the 1860–2000 change in GMST () in the historicalAA experiments for these six models. The regression slope, which provides an estimate of TCSaer, is K (W m−2)−1; although the nominal slope is smaller than that in Fig. 3a [0.71 K (W m−2)−1], the limited sample size precludes a meaningful comparison. Since the models are forced only by increasing anthropogenic aerosols in the historicalAA runs, we can estimate TCSaer for each model as . These values range from 0.27 K (W m−2)−1 in GISS-E2-R to 0.91 K (W m−2)−1 in CanESM2, with a mean and 5%–95% uncertainty of K (W m−2)−1 (see Table 3). For two models (CSIRO-Mk3.6.0 and GISS-E2-R), TCSaer is smaller than TCS with respect to increasing CO2, whereas for the other four models TCSaer is larger than TCS; this is discussed below. Although the mean value of TCSaer is larger than the average TCS with respect to increasing CO2 for the 14 models in Table 2 [0.51 K (W m−2)−1], there are large differences among the models, and the limited sample size again prevents us from drawing a general conclusion about the sensitivity to aerosol forcing in these runs. Another source of uncertainty is the fact that aerosol ERF in the historicalAA runs may be markedly different from that in the standard historical runs, since the forcing can be sensitive to the background climate (Miller et al. 2014). Since the historicalAA runs simulate a cooling climate, which differs from the warming climate in the historical runs, the historicalAA runs may have limitations for interpreting aerosol effects in the historical runs (and in the real climate system).

Fig. 6.
Fig. 6.

1860–2000 changes in GMST from CMIP5 models historicalAA simulations, plotted against (2000 relative to 1850) global-mean aerosol ERF. The slope uncertainty range is a 5%–95% confidence interval, based on a t test.

Citation: Journal of Climate 28, 17; 10.1175/JCLI-D-14-00712.1

Despite these possible limitations, a useful aspect of the historicalAA simulations is that they can be used to generate a time series of aerosol ERF, following the method in Forster et al. (2013). In this two-stage approach, the climate feedback parameter (α) is calculated for each model by application of the Gregory et al. (2004) regression method to abrupt4xCO2 simulations, in which CO2 concentration is instantaneously quadrupled; values of α are given in Table 1 of Forster et al. (2013). Then, assuming that α is time invariant and independent of the forcing agent, aerosol ERF after t years of the historicalAA simulation is estimated as
e8
where N is the change in radiative energy imbalance at the top of the atmosphere, and the prime is used to distinguish the forcing calculated by this method from , which is calculated by the fixed-SST method. Note that the assumption that α is independent of forcing may not be accurate, and is inconsistent with our argument that the climate response is sensitive to the spatial pattern of the forcing (both in a transient and equilibrium sense); this approximation may affect the accuracy of . Although the fixed-SST and regression methods can give substantially different results for some models (Andrews et al. 2012), nonetheless provides an interesting comparison, and it also gives a useful insight into the time evolution of the forcing.

The six models generally show a gradual increase in the magnitude of until about 1945, followed by a more rapid increase during the postwar period (Fig. 7). This differs from the time evolution postulated recently by Stevens (2015), who argued that the magnitude of aerosol forcing increased strongly during the early part of the industrial period, because a unit of emissions in a pristine atmosphere is expected to cause a stronger forcing than a unit of emissions in a polluted atmosphere. A possible reason for the different time evolution is that Stevens used a globally averaged model, whereas the models used here allow aerosols and aerosol precursors to be advected to remote regions, which are relatively pristine even in the present climate.

Fig. 7.
Fig. 7.

Time series of annual-mean aerosol ERF, calculated from the historicalAA simulations using Eq. (8). Aerosol ERF values are plotted as anomalies relative to the period 1850–69, or 1860–69 for GFDL-CM3. An 11-yr running mean is applied before plotting to reduce noise.

Citation: Journal of Climate 28, 17; 10.1175/JCLI-D-14-00712.1

As discussed in section 4a, there are marked intermodel differences in the time variation of the forcing in the late twentieth century. Consistent with the discussion there, CSIRO-Mk3.6.0 and GISS-E2-R have forcing that continues to strengthen after the 1970s, whereas some other models (notably CanESM2 and IPSL-CM5A-LR) have peak forcing around 1980. Based on the discussion in section 4a, the time evolution of aerosol ERF in CSIRO-Mk3.6.0 and GISS-E2-R may contribute substantially to their relatively small values of (Table 3). However, it should also be noted that Shindell (2014) identified both of these models as having weak gradients of aerosol ERF between the Northern and Southern Hemispheres, so the spatial pattern of forcing may also be important.

To compare and , we take the difference of between the periods 1996–2005 and 1850–69 (see Table 3). Note that is weaker than for all models (cf. Tables 2 and 3); this is especially true for GISS-E2-R, for which is only 58% as large as . Andrews et al. (2012) found that the ERF for a quadrupling of CO2 was, on average, 8% larger when using the fixed-SST method compared to the regression method, but the results were not consistent across the seven models they examined; thus it is unclear to what extent the differences between and reflect forcing that is actually weaker in the historicalAA runs, or differences between the two methods. The mean value of for the six models (−0.89 W m−2) is 20% smaller in magnitude than the mean value of for the same models.

Since is weaker than for all six models, it follows that TCS′aer is larger than TCSaer (where the prime in TCS′aer denotes that is used in the denominator); see Table 3. The ratio ranges from 1.06 to 1.54, with a mean value of 1.41. Thus the average enhancement of the GMST response in the historicalAA runs is very similar to the factor of 1.4 calculated from the historical runs, if the forcing is estimated from Eq. (8). In view of the uncertainties discussed above and the limited sample size, this may be coincidental.

An intriguing aspect of these runs is the role of nonlinear effects, which have previously been identified in simulations of increasing aerosols in atmospheric models coupled to slab ocean models (Feichter et al. 2004; Ming and Ramaswamy 2009). Nonlinear effects may partly explain the different forcing values we obtained using two different methods. With a full dynamic ocean, there may be even more scope for nonlinearities to occur than with a slab ocean. For example, we noticed that the surface temperature changes in historicalAA in CSIRO-Mk3.6.0 and GISS-E2-R showed a strong warming in the extratropical North Atlantic region (not shown), suggestive of a substantial aerosol-induced strengthening of the Atlantic meridional overturning circulation (Delworth and Dixon 2006; Cai et al. 2006; Collier et al. 2013; Shindell et al. 2015). The associated increase in the mixing of heat between the surface and the deep ocean may affect the rate of change of GMST (Schleussner et al. 2014). Since GMST enters the calculation of via Eq. (8), the forcing estimate may also be affected. These issues are worthy of further study.

d. Effect of a possible systematic bias in TCR

Uncertainties in forcing and climate sensitivity are tightly coupled (e.g., Schwartz 2012). A useful aspect of Eq. (4) is that it can be used to indicate how our estimate of aerosol ERF would change if the models’ average TCR were substantially different from 1.9 K. Using the observed for 1860–2000 (0.61 K), Eq. (4) gives
e9
where it is understood that TCR refers to , the average value of the models’ TCR. This equation is plotted in Fig. 8 for values of between 1 and 2.5 K, which is the “likely” range from IPCC AR5 (Bindoff et al. 2013). With K, the inferred aerosol ERF is −1.02 W m−2; this value differs slightly from our best estimate of aerosol ERF (−0.92 W m−2), because it is based on Eq. (4) instead of the average value inferred from a large set of regression relations. Aerosol ERF changes from to W m−2 for K, or to W m−2 for K. The sensitivity is more severe for small values than large values of .
Fig. 8.
Fig. 8.

Inferred aerosol ERF as a function of , using Eq. (9).

Citation: Journal of Climate 28, 17; 10.1175/JCLI-D-14-00712.1

Some studies have provided evidence that TCR can be more tightly constrained than the range of 1 to 2.5 K. Shindell (2014) accounted for the larger efficacy of inhomogeneous forcing agents (aerosols, tropospheric ozone, and land-use change) compared to WMGHGs. He concluded that TCR is very unlikely to be less than 1.3 K. The inferred aerosol ERF using TCR = 1.3 K in Eq. (9) is −0.55 W m−2, which highlights the importance of the lower constraint on TCR. Some detection and attribution studies, which incorporate information about each model’s spatial response to radiative forcing, suggest that TCR is less than 2.5 K (Gillett et al. 2012; Bindoff et al. 2013). The hyperbolic form of the curve in Fig. 8 highlights that the inferred aerosol ERF depends more critically on the lower constraint than the upper constraint on TCR.

5. Conclusions

We used output from 14 CMIP5 models, consisting of global-mean aerosol ERF (calculated from fixed-SST simulations) and changes in GMST from transient historical simulations. The models have global-mean aerosol ERF that ranges from −0.35 to −1.60 W m−2 for 2000 relative to 1850 and TCR that ranges from 1.4 to 2.5 K, with a mean value of 1.9 K.

Correlations between aerosol ERF and changes in GMST exceeded 0.9 for linear trends in GMST over all time periods that begin between 1860 and 1950 and end between 1995 and 2005. Thus aerosol ERF largely controls intermodel differences in historical GMST change, and the effects of other variables (such as TCR) are relatively small.

With these strong correlations in mind, we calculated top-down estimates of aerosol ERF that gave the best match between modeled and observed GMST changes for each of the time periods. The overall best estimate of aerosol ERF for 2000 relative to 1850 was −0.92 W m−2. If the average TCR of the models were substantially larger (smaller) than 1.9 K, the inferred aerosol ERF would be larger (smaller) in magnitude, with larger changes for reduced values of TCR. We did not provide an uncertainty estimate for the inferred aerosol ERF because of the complexity of dealing with an estimate based on a large number of linear GMST trends. However, in a separate study we have used a simpler approach based on the difference of two time periods (1996–2005 minus 1850–59), instead of linear trends (Shindell et al. 2015). This gave an inferred global-mean aerosol ERF of W m−2.

We showed that the dominant effect of aerosol ERF on historical changes in GMST is substantially caused by the stronger response of GMST to aerosol forcing compared to forcing from WMGHGs, which we characterized by an enhancement factor E. Physically, the enhanced GMST response is caused by a combination of 1) the larger concentration of aerosol forcing in the midlatitudes of the land-dominated Northern Hemisphere, where positive feedbacks are stronger and transient warming is faster than in the Southern Hemisphere, and 2) the time evolution of aerosol forcing, which levels out earlier than WMGHG forcing (although the extent to which this is true is uncertain). Calculations with a global impulse–response function suggested that the time evolution of the forcing may have an effect on the GMST response that is of comparable magnitude to the effect of the spatial pattern of the forcing.

Comparison of Eq. (2) with the regression relations from Figs. 3 and 4 suggested that a representative value for the enhancement factor for aerosol forcing is , which is remarkably similar to the mean value estimated by Shindell (2014) for aerosols relative to historical increases in WMGHGs (). With , 85% of the intermodel variance of simulated GMST change was explained by variations in aerosol ERF, but with less than half would be explained.

We also examined historical simulations forced only by increasing anthropogenic aerosols (“historicalAA”) in a subset of six models. Changes in GMST for the period 1860–2000 showed a tendency to be smaller than expected from our analysis of the historical runs. Assuming that aerosol ERF calculated from the fixed-SST runs is applicable in the historicalAA runs (which is uncertain), changes in GMST suggested values of E ranging from 0.58 to 1.40, with an average of 1.11 for the six models. We also used the regression method of Forster et al. (2013) to estimate time series of aerosol ERF directly from these runs, and obtained aerosol ERF on average 20% smaller in magnitude than obtained from the fixed-SST runs. With these smaller values of aerosol ERF, the implied value of E ranged from 1.06 to 1.88, with an average of 1.41 (similar to that suggested by our analysis of the historical runs). Because of the small sample size, and possible nonlinear effects, it was difficult to draw firm conclusions about aerosol effects in the historical runs from analysis of the historicalAA runs. However, time series of aerosol ERF derived from the historicalAA runs did highlight the extent to which the time evolution of aerosol forcing in the late twentieth century is model dependent: in some models, aerosol forcing weakens after about 1980, while in others it continues to strengthen until 2000.

In summary, our results provide further evidence of the importance of aerosol-related uncertainty in climate change science. Further work is needed to better constrain the magnitude, pattern, and temporal evolution of aerosol forcing.

Acknowledgments

This research is partly supported by the Australian Government Department of the Environment, the Bureau of Meteorology and CSIRO through the Australian Climate Change Science Programme. We acknowledge the World Climate Research Programme’s Working Group on Coupled Modelling and the U.S. Department of Energy’s Program for Climate Model Diagnosis and Intercomparison, and we thank the climate modeling groups (listed in Table 1 of this paper) for producing and making available their model output. We thank Arnold Sullivan, Peter Vohralik, and Julie Noonan for their work on the ACCESS1.0 and ACCESS1.3 fixed-SST runs, and Matt Woodhouse for his helpful comments on an earlier draft of the paper. Constructive comments from two anonymous reviewers helped us to substantially improve the paper.

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